~~~~~~~~~~:,dowl ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~PY~~llL ~dPa-. ~~li s~L~sa ---,, I~~~~~~~~~ I~~~~~~~~~~~~~~~~~~~~~~~~-I: —:~1~-~~ ,1 x~: I-I: C:;:I::. z I\~i c~:i; L) :-:::s-::::: p;~~i: i::B ri:: —i:-;-::;:l;:::_:::_::::: r ~-~~a ' ~-:li r::: I;I;; THE CIVIL-ENGINEER & SURVEYOR'S MANUA L: COIMPRISING Surveying, EnlinPeerinl, Practical Astronom3y, GEODETICAL J URISPRUI)ENCE, ANA'LYSES OF MINERALS, SOILS, GRAINS, VEGETABLES, VAI, UATI(ON OF) LANDS, BUIILDINGS,;PERMIANEINT ST'RUCrTIURES, ETC. B V MICHAEL McDERMOTT. C.E., CERIIFIED LAND SURV'E\(YR 1;'OR (RK:F.T. -lITAN AND IREI.AND; PROVINCIAL LAND SURVEYOR FOR 'IE CANADASI C FAliIERS; CIVILIAN ON ON TE ORDNANCE SURVEY OF IRELANDI), PAROCIIIAt SURVEYVOI IN ENGI.AND, CITX' SURVEYOR OF MILW\AUKEE AND CHIICAGO; IMEMBAER OF TIHE ASSOCIATION FORL TIIE ADVANCEMENT OF SCIENCE, CHI-CAGO COLLEGE OF PHARMACY, AND THE CHICAGO CHEMICAL ASSOCIATION. CHICAGO: FERGUS PRINTING COMPA 244-8 ILLINOIS STREET. 1879. ' INY, 7,,W. T~;' I I II I Entered according to Act of Congiess, in the year 1879, by MICIAEL MICDERMOTT, In the Office of the Librarian of Congress, at Washington. I....... I..... I.: $,,,, * s, I -., I. I I; - - C I. I.:. AUTOBIOGRAPHY. I have been born on the ioth day of Sep., i8io, in the village of Kilmore, near Castlekelly, in the County of Galway, Ireland. My mother, Ellen Nolan, daughter of Doctor Nolan, was of that place, and my father Michael McDermott was from Flaskagh, near Dunmore, in the same County, where I spent my early years at a village school kept by Mr. James Rogers, for whom I have an undying love through life. Of him I learned arithmetic and some bookl-keeping. lie read arithmetic of Cronan and Roach, in the County of Limerickl. They excelled in that branch. John Gregory, Esq., formerly Professor of Engineering and Surveying in Dublin; but now of Milwaukee, read of Cronan, which enabled him to publish his " Philosophy of Arithmetic," a work never equalled by another. By it one can solve quadratic and cubic equations, the diophan' tine problems, and summation of series. After having been long enough under my friend Mr. Rogers, I went to the Clarenbridge school, kept by the brothers of St. Patrick, under the patronage of the good lady Reddington. I lived with a family named Neyland, at the Weir, about two miles from the school, where I had a happy home on the sea-side. There I read algebra, grammar, and bookkeeping. After being nearly a year in that abode of piety and learning, I went to Mathew Collin's Mathematical school, in Limerick. IIe was considered then, and at the time of his death, the best mathematician in Europe. Iis correspondence in the English and Irish diaries on mathematics proves that he stood first. I left him after eight months studying geometry, etc., and went to Castleircan, near Cahirconlish, seven miles from Limerick, where I entered the mathematical school, kept by Mi. Thomas McNamara, familiarly known as Tom Mac, and Father of X, on account of his superior knowledge of algebra, he was generally known by the name of "Father of X." Of him I read algebra and surveying; lived with a gentleman farmer- named William Keys, Esq., at Drimkeen, about one and one-half miles south-east of the school. Mr. Mac had a large school, exclusively mathematical, and was considered the best teacher of surveying. After being with him nearly a year, I left and went to Bansha, four miles east of the town of Tipperary. Here Mr. Simon Cox, an unassuming little man, had the largest mathematical class in Ireland, and probably in the world, having 157 students, gathered from every County in Ireland, and some from England. Like Mr. McNamara, he had special branches in which he excelled; these were the use of the globes, spherical astronomy, analytical geometry, and fluxions. The differential and integral calculus were then slowly -getting into the schools. I 'lived 38O-i 0 OO 4 4 ~~~AUTOBIOGRAPHY. wvith Dairyman Peters, near the bridge of Aughahiall, about three miles east of -Bansha. I remained two years with Ai\r. Cox, and then bade farewell to hospitable anid learned Munster, wthere, with. a fewv exceptions, all the great mathematical and classical schools w~ere kept, until the famine plague Of I848 lbroke them uip. I niext foundl( myself in Athicagucc County, Roscommon110, with Mr. Mathew timnilff, who wvas an exceilcutL constructor of e(lniations, and showed the alpllicatioil to the various arts. I received mv diplomia as certified L and Surveyor onl the sixth of September, I836, after a roz("/h examinatioi 1y 'Mr. Fowler, in the theoretical, and William ILongtield, Es. inl the piractice of surveying. I soon got excellent practice, but IN i'hiu'~ for- a wi~ler field of operation), for further information, I joined the Oriidance Survey of I relandl. Worked onl almost every (.epartmient of it, such as plotting, calculating-, registering, surveying, leve~1lln, e 'aiuin, ain(l tranislating I rish names iiito English. Having got a reimmeraivet empullovuienti fromt S. NV. lar-ks, E~s1., lanld surveyor and civil cinuica- inl 1>0v cli, County of Suiffllk, Eng-land..1 left my native Isle in A~pril, i 8S. Suirveyed with Mr. Parks iii the couinties of Suiffolk, Norfolk, anid E~ssc,. For two years, thenr took the field oin my Own account. I left happy, lhuspitatile, and fri-endly Englland in Akpril, 1842, and sailed for Canada. Lauided iii Q2uebec, where I soon learned that I could not survey until I would serve anl appreniticeship, lie examinled, and receive a diploma. I sailed lip the St. ILawreince aiid Ottawa Rivers ti) Iytowii,-thenl a grrowingy to~wn inl the wvoods, -hut nowv called Ottawa, the seat of the GCoyernnment of l;ritih Amnerica. I eiiwa-ed as teacher inl a school inxline nine miles frum By to%,ni (now Ottawa),. At the enid of uiy termi of three months, I joined John _McNauighton, ELsq., land surveyor, and justice of the peace, until I got niv dliplomia as Proinm-cial Lauiid Suirveyor for Upper Caniada, dated D ecembher 16, 8S43, and mx'y diplomia or commiission for Lowver Canada, mated Septemnber 12, 1844. I spent niy time ahout eq~ually dividled hetween makling- surveys for the Hlome (Blritisli) Govermuenit four years, anid the l'rovimmcial Government, and lprivate citizens,, until I left Pytown inl Septeniher-, 1,849, havin~g thrownv tup an excellent situation on the Ordniance D~epartmnent. I never canl forget the happy days I1 have been employed onl ordniance surveys in Ireland, undler Ilieutenants Iiroug-ton and I anicv. Inl (i'amiamla, uinder the suipervision (if lieutenants- Whlite and King, andl Colonel Thompson, of the Royal Enigineers. Il iimy surveys for the Provincial G;overnment of Canlada, I. always found I Ion. Akndrew Russell and Joseph liouchette, Suirvey-orGenerals, anid Ihonmas D)evine, Elsq., Head of Surveys, iiiy warmecst -friends. 11miev arc nlO\V-Octohi)0` 7, 1878 —l-iving at thie hlead of their respective1 Old I epartmnents, having liveid a Ionl life of umscfulness, which I hope will lie prolong-ed. To Si r WVilliam Logami Pmrovinlcidl (cologist, I ami inidebited for much iniformiatiumi. I live.,d neam sy eight yecars iii Ottawa, Canada, whlere my frienids wvere very mnuerous-. 'I'he dearecst of all to me was Aiphon-so WN ells, Provincial Land Surveyom, \u ho was the best stirveyor I ever miet. lIfe had been so badly frost bitten. on a Governmnent survey that it was the remnote cause of his death. On one of iwy surveys, far North, I and one of my mien Nveie badly frostbitten, Ilie dicd shortly after getting home. I lost all the toes of miy left foot and seven fingers, leaving two thumbs anil the smnall finger on the AUTOBIOGRAPIIY. 5 ngnr hand. After the amputation, I soon healed, which I attribute to my strictly temperate habits, for I never drank spirituous liqu r nor used that narcotic weed-tobacco. In Sept., 1849, I left the Ordnance Survey, near Kingston. Having surveved about 120 miles of the Rideau Canal, in detail, with all the Government lands belonging to it. On this service I was four years employed. I came to the City of Milwaukee, September, 1849; could find no surveying to do. I opened a school, October I. Soon gathered a good class, which rewarded me very well for my time and labor. Ilere I made the acquaintance of many of the learned and noble-hearted citizens of the Cream City-Miilwaukee, amongst whom I have found the popular Doctors Johnson and I lulbeschman; 1. A. LAI'IIAI; Pofessor Buck; Peters, the celebrated clock-maker; I1yron Kilbourne, Esq.; Aldermen Edward McGarry, Moses Neyland, James Rogers, Rosebach, Furlong, Dr. Lake; John Furlong, etc., etc. I found extraordinary friendship from all Americans and Germans, as well as Irishmen. I was appointed or elected by the City Council, in the following April, as City Engineer, for 1850 and p)art of r85I. I was reappointed in April, 1851, and needed but one vote of being again elected in I852. I made every exertion not to have my name brought up for a third term, because, in Milwaaukee tlhe correct rule, "Rotation in office is true democracy," was adhered to. I n accordance with a previous engagement, made witllh W\. Clogher, Esq., many years City Surveyor of Chicago, I left Milwaukee with regret, and joined Mr. Clogher, as partner, in April, 1852, immediately after the Milwaukee election. Worked together for one year, and then pitched my tent here since, where I have been elected City Surveyor, City Supervisor, and had a hand in almost if not all the disputed surveys that took place here since that time. I have attended one course of lectures on chemistry, in Ipswich, England, in 1840. and two courses at Ruslh Medical College, under the late Prof.. V. Z. I. laney, and two under Dr. Mahla, on chemistry and pharmacy. By these means, I believe that I have given as much on the subject of analysis as will enable the surveyor or engineer, after a few days application; to determine the quality and approximate quantity of metal in any ore. To the late Sir Richard Griffith, I am indebted for his "Manual of Instructions," which he had the kindness to send me, May 23, I86i. fIe died Sept. 22, 1878, at the advanced age of 94 years; being the last Irishman who held office under the Irish Government, before the Union with England. Hie was in active service as surveyor, civil engineer, and land valuator almost to the day of his-death. 'The principles of geometry and trigonometry are well selected for useful applications. The sections on railroads, canals, railway curves, and tables for earthwork are numerous. 'The Canada and United States methods of surveying are given in detail, and illustrated with diagranus. Sir Richard Gritflih's system of valuation on the British Ordnance Survey, and the various decisions of the Supreme Courts of tle' United States are very numerous, and have been sometimes used in tle Chicago Courts as authority in surveys. Hydraulics, and the sections on building walls, dams, roofs, etc., are extensive, original, and comprellensive. lThe sections and drawings of many bridges and tunnels are well selected, and their properties examined and defined. The tables of sines and tangents are in a new form, with guide lines at every five min 6 AUTOBIOGRAPHY. minutes. The traverse table is original, and contains 88 pages, giving latitude and departures for every minute of four places, and decimals. and for every number of chains and links. The North and South polar tables are the results of great labor and time. The table of contents i; full and explicit. I believe the surveyors, engineers, valuators, architects, lawyers, miners, navigators, and astronomers will find the work instructive. I commenced my traverse table, the first of my Manual, on the 15th of October, 1833, and completed my work on the 8th of October, 1878. The oldest traverse table I have seen was published by D'Burgh, Surveyor General, in Ireland, in 1723, but only to quarter degrees and one chain distance. The next is that by Benjamin Noble, of Ballinakil, Ireland, entitled "Geodesia Hibernica," printed in I768, were to J4 degrees and 50 chains. The next, by Harding, were to x degrees and Ioo chains. In my early days, these were scarce and expensive; that by Harding, sold at two pounds two shillings Sterling, (about $10.50). Gibson's tables, so well known, are but to,$ degrees and one chain distance. Those by the late lamented Gillespie, were but to J4 degrees, three places of decimals, and for I to 9 chains. Hence appears the value of my new traverse table, which is to every minute, and can be used for any required distances. Noble gave the following on his title-page: "Ye shall do no unrighteousness in meteyard, in weight, or in measure." Leviticus, chap. xix, 35; "Cursed be he that removeth his neighbor's landmark." Deuteronomy, -hap. xxvii, 17. I lost thirty-two pages of the present edition of, ooo copies in the great Chicago fire, Oct. 9th and Ioth, I871, with my type and engravings; this caused some expense and delay. The Manual has 524 pages, strongly bound, leather back and corners. MICII'D McDERMOTT. GENERAL INDEX. Section. Squiare..Ar-ea, diagonal, radius of inscribed circle, radius of the circumscrilbing circle, and other properties.............14 Rtectanigle or iparallelogram, its; area, diameter, radius of circumscribing circle. TPhe greatest rectangle that can be inscribed in a semicircle. TIie greatest area when a == 2 b. hlydraulic mean depth. Stiffest aaid strongest beamis, out of -.............. OF THE 'rRIANGLE. Areas and properties by various methods.............. 2.5 To cut off a given area from a given point.............:3 8 To cut off from P, the least triangle poi:,ihle............41 To bisect the triangle by the shorte-t line possible.........43 The greatest rectangle that can be inscribedi in a triangle......44, 'lrhe centre of the inscribed and circumscrilbed circles......... ' Various properties of.3.....................5 Strongest form of a retaining wvall................. OF' TH-i CIRCLE. Areas of circles, circular rings, segmients, sectors, zones, and lunes, 60 1-ydraulic mean depth......................7 Inscribed and circumscribed figrures.................7 To drawv a tangent to any poinit in the circumifcrencc..........8 To find the height and cliordI of any segment.I.......... 13 To find the diameter of a circle wh~ose area, A, is -ivcn,...... 1.41 Important properties of the circle in railwNay curves and arches, 7 S OF THlE ELL1-1I US. l~owv to construct an ellipse and find itsi area............S, 115 Various practical prolperties of..................8S9 Segment of. Circumference of,.................116 PARABOLA. Construction of, 123. Properties, 124. 'iangent to, 12S. Area, I 29. Length of curve, 130. P~arabolic sewver, 13:3. Example, 1:33. Remarks on its use in preference to other forms,, 134. Eggshaped, 140. Hlydraulic mean depth, 136. Perimieter......139 Artificers' wvorks, measuiremnert of............... 31x9 PLAIN TRGNMEIR- FGISANID DISTANCES. Righbt angled triangles, properties of............ 148 The necessary formulas in surveying, in find)(Iing1 any side and angle,. I-lb P~roperties of lines awl angles- comparedi with one another,... 194 Given two sides and containenl anglie to fined the remiaining parts,.. 203 Given three sides to find the angles................20 Heights and distances, chaining, locating lots, villages, or towns,..211 1-ow to take angles and repeat them for greater accuracy.... 1... I-owv to prove that all the interior anle"Is Of the Survey are coi rect,. 213 To reduce interior angles to quarter compass bearings........204 To reduce circumiferentor or compass hearings to those of the quarter compass-.........................214 H-ow to take a traverse survey by the English Ordnani( Survey~ method...........................2!6 De Burgh's method known in America as the Pennsylvanian.....217 Table to chang~e circumferentor to quarter compass hearings.....218 To find the Northings and Southings, ECastings and Westings, by commencing at any point................... 2)19 8 GENEIRAl INDEX. Section. Inaccessible distances where the line partly or entirely is inaccessible, 221 'Ihis embraces fourteen cases, or all that can possibly be met in practice. lFrom a given point P' to find the distances 1' A, I 13, I(.......... in the triangle A 1B C, whose sides A I1, B1 C, anui C 1) ale given, this emblraces three possible positions of the observer n t I',...... 23 SPHEIIRICAL TRIGON(OM E TR''. P'ropl rtics or s)lierical triangles. Page 7'2W 9),.................... 15 Solution o(f rihllt angled spherical trian les,.......................:-(2 Napier's rules for circular parts, witl a table anl exaniille(,......... '(;i3 ()uadrantal spherical triangles,.................................:64 ()blique angled spherical triangles,............................. 365. FIundamental formula applicable to all spherical triangles,......... 36; I"ormlulas for finding sides and angles in every case,...............:37 SP I IRICAt. A\ST RO.NO'MY.' I)efinitions and general properties of refraction, parallax dip, greatest azimuth, refraction in altitui(c, etc., etc.,................:t7. I'intd wvlien a heavenly body will pass the meridian,................ 376 Find wllen it will be at its greatest azimutl i,...................... 384 Find the altitude at this time,.................................. 384 F'indl the lariation of tle compiass by an azimuth of a star.......... 383 Find latitude by an observation of the sun,....................... 77 Fin l latitude when the celestial object is off the meridian,.......... 37S lindl latitude by a double altitude of the sun,..................... 39 Flindt latitude by a meridian alt. of polaris or any circumpolar star,.. 380 Filid( latitude when the star is above the pole,.................... 381 Find latitude by thle pole star at any lour,........................ 382 IE'rror respecting ipolaris and alioth in Ursamajoris \x}lin on the same ver-tical plane. (Note.)...................................... 389 Lctters to the lP:itish and Aimerican Nautical Fplhemleris offices,.... 38! Application and examples for ()bservatory lHouse, corner of Twentvsixth andl lnalsted streets, Chicago. Lat. 41', 50', 3J'. Iong. 87'. 34', 7", W.................................................. 89 Remarkable proof of a Sup)remie Being. Page 72ii'24,............ 386 lr ue time; how determined; example,........................... 37 Ilrue time Iv equal altitudes; example. 'age 7tIi,........... 3(1) True timle bv a horizontal sundial, showing how to construct one,...!90 Longitile. dlifference of...................................:2 I ongitulde ly tihe electric telegraphi,.............................,9 LJongitudet howr determined for ( uebec and Chicago, by Col. rahllam, U. S. Elngineer.................. 393 Lrongitude by tle heliostat. l'age '2 II30),..................... 393a Longitude by the Drummond lizhlt and moon culminating stars,..... 394 Iongitude by lunar distances; \oung's method and example....; 95 Reduction to the centre, that is reducing the angle taken near the point of a spire or corner of a publlic building, to that if taken firom the centre of these points; by two methods,.................. 244 Inaccessible heights. When the line A B is horizontal,.......... 24 When the ground is sloping or inclined, three methods........... 24 TRAVERSE SURVEYI N(;. Methods of. Sec. 213 to 217 and..............................55 1'o find meridian distances,.................................... 237 Method I. Begin with the sum of all tilc: last deplartulres,........ 258 Method II. First meridian pass through tlie most esterly station,. 239 Method III. First meridian pass through the most Nortlherly station, 260 Offsets and inlets, calculation of............................... 26;1 ()rdnance method of keeping field-books,................... (2.Supplying lost liln. and bearings. (Four cases.).................. 2: l'o find the most \W esterly station,............................. 4 To calculate an extensive survey where tlie first meridian is made a base line, at each end of which a station is made, and calculated by the third method;........................................ 2i4 CANADA SURVEYING. Who are entitled to survey.................................... 301 GENERAL INDEX. 9 Section. Maps of towns, lowN made to be of evidence,......................304 I-low side lines are to be ran. Page 72w, in townships,........... 302 I ow side lines in seignories. Page 72w, in townships,............. 30 VIheire the original posts or stakes are lost, law to estallish,........ 306 C(/ipass. —Variation of examples. 26i4h alln.................... 2~4a lFind( at lwhat time polaris or anll other star will ble at its greatest azimulth or elongation,...................................... 2G4b Fi(nd its greatest azilmuth or elongatio(n,........................ 2 4c:in i iits altitude at the above tinme...............................264d Find whlen l)olaris or any othler star culminato i; te or iilmeridian,.264e Example for altitude and azimnuth in the above.....................26 f low to know when polaris is above, below, la-t or West of tie true pole,................................................... 264g HIow to estabilis1 a meridian line. l'age 71,.....................'264h 'To light or illume tl e cross hairs,............................... 265 VINIT;I'l) STAi'I''S II;'IO '11()I o OF Sit\' E:Y N;. Systesm of rectalnglar surveying,f............................. 2() \ lihat the Unite(i States law requires to be (lone,.................. 21;7 MIeasurementl chaining, and marking,.......................... '(;') B]ase lines, princilpal mIerlilians, correction or standard lines,....... 270 North and solth s.c:tiom lilnes, how to lbe survey(l,................ 272 E'ast and we-.; s>ct i(, lilne, random and true lies,.................. 73 E;ast and west illtersecting navigiable streams,..................... 274 In-.ttp'irable ol:staeles, siitneis points.)75 Insupl)arable o..........: t cs, it ess oi ts................................. 27 I,imits in closing on navig able waters and township lines,.......... 2,(; MIeandlerinlgl of navigable streams............................... 277 'ITee s are marked for line, and bearingl trees,..................... 27S Townlsship section corners, witness mounds, etc.,..................,27 ( ourses and distances to witness points,......................... 2s5 Mletliod of kleeping field notes,.................................. 2FS I ines crossing a navigable river, how determined,................. 292 Mleandt ering notes,.......................................... 29 Loot corners, hso to restore.. 294 } ost cornes, how to estole,................................... 24 Pre'sent sulbdivision of sections,................................ 97 Governmlent plat- or maps,.................................... - 9 Surveys of villa es, towns, and cities.............................:0(0 IEstablishing lo.it corners in the above,........................... 30( TIIGO(NO.MIITRICAI, SU;RVElYIN;. ]Page 7211'35. lBase line and primlary triangles, secondary triangles. HIow triaingles are b)est subdivided for detail and checked. 5Method of keeping field-loolks. When there are wood traverse survevinig. To protract the angles. orldnance method,............................. 39 Method of protraction by a table of tangents, etc................. 401 IPlotting, lcI)ermott's method, using two scales,................ 412 Finislling the plan or map, and coloring for vatious States of cultivation,...................................................... 413 Registered sheets for contents,.................................. 402 Computation by scale,........................................ 403 Contouring, field-work, final examination,....................... 411 DIVISION O1 I.LAND. 403.\. Area cut off by a line drawn from a given point, 405. By a line parallel to one of its sides, 40 1. By a line at a given angle to one of its sides, 40,.................................... 40 From a given point 1P within a given figure to draw a line cutting off a given area,....... 420 a given area,........................................................ 420 From a given triangle to cut off a given area by a line drawn through a given point,..............................................420a T, divide any quadrilateral figure into any number of equal parts, 4(9, continued in 41.a,......................................... 409 LEVELLING. Form of field-book used by the English and Irish Boards of Public W orks,................................................... 414 10 GENERAL INI)EX. Section. By McDermott's method..................................... 415 By barometrical observations,................................. 416 Table for barometrical. 'ables 416 and 417,.................... 417 1Eample by Colonel Frome.................................... 418 By boiling water. Tables A and B,............................ 419 CORRECTIONS. Additional, and corrections, geodetical juisprucdence, laying out curves, canals, corrections of D'Arcy's formula,................. 421 GEODETICAL JURISPRUDENCE. United States laws respecting the surveyint of the public lands,.....306a Supreme court decisions of land cases of the State of Alabama,.... 307 Supreme court decisions of land cases of the States of Kentucky and Illinois,.................................................. 30 Various supreme court decisions of several States on boundary lines, highways, water courses, accretion and alluvion, 309c, highways,:;09d, backwater, Page 72B5, 309d, up to date,.................309a Ponds and lakes,............................................. 3 91 ) New streets (continued 421). Page 72u10,....................... 3v9 SIR RICHARD GRIFFITH'S SYSTEM1 OF VALUATION. Act of Parliament in reference to.............................. 3091 Average prices of farm produce, and price of li\ e weights,........ 309j Lands and buildings for scientific, charitable, or public purposes, how valued....................................................30 'ield-book, nature and qualification of soils. 3092 and 309/,......30'h Calcareous and peaty soils. 309k and 309,...................... 309/ Von Thaer's classification of soils, table of,......................309/ Classification of soils with reference to their value,...............309)z 'ables of produce, and scale for arable land and pasture. 309c, 309p, 309q Fattening, superior finishing land, dairy pasture, store pasture, land in medium situation and local circumstances,................... 309r Manure, market, condition of land in reference to trees and plants, 309z Mines, Tolls, Fisheries, Railway waste,......................... 310 Valuation of buildings, classification of same, measurement of,..... 310a Modifying circumstances,...................................... 310e Valuation in cities and towns,................................. 310/ Comparative value,........................................... 310g Scale of increase,........................................... 310i WATER POWER. Horse'power, modulus of, for overshot wheels,................... 31Q/ Form of field-book for water wheels, head of water, etc.,....310k to 310/ Overshot, undershot, and turbine wheels,........................310/( Valuation of water power, modifying circumstances.......3101m to 310t Horse power determined from the machinery driven,.............. 310o Beetling and flour mills. Mills in Chicago, note on,..............310p Valuator's field-book, form of, used on the Ordnance valuation of Ireland,........................................... 310/ to 310w Valuation of slated houses, thatched houses, country and towns. Tables I to V,.....................................310v to 310A Geological formation of the earth. Table, 72B52................310u Rocks, quarts, silica, sand, alumnia, potash, lime, soda, magnesia, felspar, albite, labradorite, mica, porphyritic, hornblende, augite, gneiss, porphyritic, gneiss, protogine, serpentine, syenite, porphyritic granitoid, talc, steatite or soapstone, limestones, impure carbonate of lime, Fontainbleau do., tafa, malaclite satin spar, carbonate of magnesia or dolomite..............................31 0c Sir Wi/liam Logan's report on six specimens of dolomite..........310(: Magnesian mortars. Page 72B56,..............................310c Limestones, cements used in Paris, artificial cements, plaster of Paris, water lime, water cement, building stones. Page 72B56,.........310c Sands (various), Fuller's earth, clay for brick, potter's, pipe, fire brick, marl, chalk marl, shelly and slaty marl. Page 72u57,............ 310c Table of rocks, composition of 310c, composition of grasses,..... 3101> Tal)Ie of rocks, composition of trees, weeds, and plants,...........310E GENERAL INDEX. 11 Section. Composition of grains, straws, vegetables, and legumes,............ 31OF Analysis and composition of the ashes of miscellaneous articles,......310G Analysis and percentage of water, nitrogen, phosphoric acid in m anures,.................................................. 3'0 I Sewage manure. Opposition to draining into rivers............... 310 DESCRIPTION OF MINERALS, Including antimony, arsenic, bismuth, cobalt, copper, nickel, zinc, manganese, platinum, gold, silver, mercury, lead, and iron, with all the varieties of each metal, where found, its lu-:lre, fracture, specific gravity, etc.......................................... 310K Solid bodies, examination of 310L. By Blow-pipe,.............310 Metallic substances. Qualitative analysis of,..................310N Metallic substances. Quantitative analysis,......................310,: 7able-Of symbols, equivalents, and compoundsl................. 3101 Table-Action of reagents on metallic oxides,....3........... 10(. Table-Analysis of various soils................................ 310k Analysis of soils, how made,............................ 310s Analysis of magnesian limestone,................................310r Analysis of iron pyrites...................................... 310u Analysis of copper pyrites, 310u, zinc, 310w.............. 310 to 310\w To separate gold, silver, copper, lead, antimony,.................310x To separate lead, and bismuth. Page 72B94,....................310x To determine mercury, 310y, tin, 310. Page 7235 5,.............3.0xO HYDRAULICS. Hydraulic mean depth of a rectangular water course of a circle,.... 7' Parabolic sewer, 134. Table showing hydraulic mean depths of parabolic and circular sewers, each having the same sectional areas,.... 13:5 Egg-shaped sewer, its construction and )properties,................ 140 Rectilineal water courses, 144. Best form of conduits, including circular, rectangular, triangular, parabolic, and rectilineal.......... 14 Table of rectilineal channels, where a given sectional area is enclosed by the least perimeter, or surface in contact,................... ] 67 A table of natural slopes and formulas,......................... 147 Estimating the density of water, mineral, saline, sulphurous, chalybeate,..................................................... 3 0. BOUSINGAUI.T'S remarks on potable water. I'age 72>i;'},.... 0.....:0 Supply of towns with water,.................................. 310 Solid matter in some of the principal places. Page 721i97,........310z. Annual rain fall in various places and countries,..................310A* laily supply in various cities,.................................. 310 Conduits, or supply mains.................................... 3101* Discharge throw pipes, and olifices under pressure,...............3 i Oc VENA CONTRACTA and coefficient m/ of contraction. P. 72,100,.310c* Adjutages, experiments by Michellotti Weisbach. P. 7'2nI01,..3.310c" Orifices with cylindrical and conical adjutagess.................. 310i)l Table-Angles of convergence, discharge, and velocity,..........310)'' Table-Blackwill's coefficient for ovxerfall weirs. First and scond Experiments,.............................................310 Experiments by Poncelet and Lebros. DuBuats, Smeaton, Brinley, Rennie, with Poncelet and Lebros' table,............ 3101.* and 3101i; Example from Neville's hydraulics. Page '72,105,............... 310.i'Formula of discharge by Boileau................................310)/ Formula of discharge (, for orifices variously placed,..............310 Formula of time and velocity for the alove,......................310,O Formula by 1)'Arcy incorrect, page 264, but here corrected......... 310r Formula, value of coefft., by Frances of l.owell, Thonlpson of Belfast and Girard, of France,..................................... 310l Spouting fluids,.............................................. 310l Water as a motive power. Available horse-power,................10K Iigh pressure turbines for every ten horse-power. 1'. 72;10,.....310j* Artesian wells, and reservoirs. I'age 72O108,...................... 31 Jetties,.................................................... 310.-i: 12 GENERAI, INDEX. Section. LAND) AN1) CITY I)RAINA(IGE AND IRRIGATION. Hilly districts, tile and pipe drains,..............................310p Draining cities and towns, sewers,.............................. 31 0r Sanitary hints,.......................................... 1.310x10 Jrrigation of lands,........................................... 310() Rawlinson's plan,............................................31 O( Supply of guano will soon ble cxlalste-............................ 101; On the steam engine, horse-lpo-wer. Adiralty 'l lIt, wdll donle by expansion,.................................................310s PRESSlRi.: )l' J.l'I.S ') N RITAINING WAI,I,S. Centre of pressure against a rectangurar wall, cylindrical vessel, dams in masonry, foundations of basins and dams, waste weir, thickness of rectangular walls, cascades, 72n11 I,.........................3101 Retaining walls, Ancient, and IIindoo reservoirslS................. 31( ''o find the thickness of the rectangular wall A B to resist its beiln turned over on tlhe lpoint I). 1'age 721:il12,...................:10 ' REVETMENT WA ILS. \\all having an external batter,......................... 31:, 310U * Table for surcharges, 1by P'o celet..-.............................310ao'2 \W alls in masonry, b\y [orin, 310 'c,', dry walls.....................10,4 The greatest height to wlhich a pier can le Ibuilt,...............:..10 (;(a Piers and abutm en ts,........................................:310x)l Vauban, Rondeiet, English engineers, and Colonel \Wurni! 1). P L7 1,5. Pressure on the key and( foundations, bv Riankine, lI'oi, l.lunllee, 1llyth, Ilawkshlaw,, (;eneral l Morin, Vicat....................310-i!) Outlines of some important walls of (locks and damis, including India docks, London, Iiverpool Seawall, dams at Poona and Toolsee, near BombIa, East Indies, Dublin quay wall, Sunderland docks, Bri-tol do. Revetment wall on the l)ullin and Kinigston Railway, Chicago street revetment walls, dam at Blue Island, near Tunnels.,.......................................... 3107.3 Blasting rock,............................................. 310w 7 Chicago, dam at J one., lFalls, Canada......................31l P)ILE DRIVING, COFIEI'-R-I)AMS, ANI) FOT.UN i).\1' I'l 1. ' 72) 1 1....310v The power of a pile, screw pile, hollow pile,...................310vl1 Examples-French standard, Nasmyth steamhammrer. When men are used as power. 72s l 117,................................310vl MR. McAi.lmNEi'S formula derived from facts,.....................3107' Cast-iron cylinders, when and where first used,.................'107' l:oundations of timber. Pile driving engine,................... 310v2 Coffer-dams of earth, Thames tunnel, \ictoria bridge in 5Montreal, Canada...................................................310v3 WO)OD) AN I) I ( N PRI'ES RVI NG. lWhen trees should be cut, natural seasoning, artificial do., Napier's process, 310v4, Kyan's process, corrosive sublimate, Bnrnett's method, 310v4c, Bethell's method, Payne's (lo., Boucher's do., IIyett's do., Lege and Perenot, Harvey's by exhausted steam,.. 72ill19 MORTAR, CONCRII'TEI, AND CEMENT. At Woolwich, Croton Water Vorks, Forts Warren and Richmond. Page 72B121. VICAT'S MlI IHO1I). (;RIOTING', Ix'Y SMFAATON.-Iron Cement. STONEY'S experiments on cement. Page 723121,................ 310r,; Cement for moist climates. I'ae 72nl'122..................... 310v6 Concrete in I,ondon and United States,.........................310z'7 Beton-Mole at Algiers, Afiica,..............................310v7 PRIESERVA.TION 0 IR(ON,.....................................31... I' VICTORIA ART'FICAll. STi sNI. Plage 72tr123,.................. 3107!) RANSOM'S method to make blocks of artificial stone,............310,/11 Silicates of potash, of soda,................................ 310z'10 WAII.S, S EAMIS, AND) PII,LARS. To test building stone,...................................... 310x4 C him ne s,................................................ 310 9 GEINERAI INDEX. 13 Section. Walls and foundations,.................................... 31011 I Table-Kind of wood, spec. grav., both ends fixed and load(ed in the middle. Breaking weight. Transverse strain,................3 10.12 Formula for beams. Page 72u 125............................ 310v12 'imber pillars, by RON-DELEl,...............................310v]3 HIODGKINSON'S FORIMUA for long square pilr,....310]14 BIREREiTON'S experiments on pine timnler,.......................310-,15 Safe load in structures,...................................... 310r'. Strength of cast-iron beamls,.................................31(,16; Strongest form, Fairbairn's form,..............................310A'1 Calculate the strength of a truss-beam,.........................310v17 To calculate a commonl roo,.................................. 310.v7 A ngles of roo,............................................ 310 Beams, wr-onght-irol, —box. 310(k,1 GORDON'S RI;': for cast-i'-,n 1-illar;,.............................310- 21 Depth of foundations,.................................... 310w4 W alls of building,............................... 3.0;,. FORCE AND MOTION. Parallelogram of forces. Polygon of do.,.......................... 11 Falling bodies;. l licoretical and actual mean velocitics of. Virtual velocities,...................................'...... 2 an 31 Compositionl o oti. age 7. e motionn is rctarde(l,.. 312' Centre of ora\xi in a circle, s(lare, triangle, tral)czoi............. 3:13 In a trapeziumn cone or )yn fru-trn o a, circular,.sector, sem icircle, quadrant, circular ring,............................ 31 Of S/lSids. ---()f triangular l)yramid, a cone, conic rfiustlrul, illn any polyhedron. 'araboloid, fi'ustlrum of a, prisioid, or ungula. Spherical sego ent,......................................... 314 SliECl'iC (l v\\lv, aend, dn'.si/l. Page 72lL. Various mletlsti... b 315 () a liquidl,:1I), body lighlter1 than water, 318, of a po'\letr,o!ul)Ic in w ate,................................................. 3 i Table-Splecilic glravitie. of bodies. Weight one ctiubic foot in pounds,..............................................31 'I'lale-Avera-c 1)tilk in cl)ic fee(t of one ton, 22440 l j.lis, l various material,.............................................. 31! 'T'able-Shrinkagl e or iincrearse per cent. of materials,............. 31!) Mechanical powers, levers, pulleys, wheels, axles, inclined )1laii, screws, witl example...............................31!' tl, 31l!)./ Virtual velocity,............................................. 3: IRICTION. CoUL.OMI;.\ 1) ID ORiLINSN' ex)periments ccf'iicict: t of the angle of repose.............................................31!,/ Table-Friction of plane lurfaces sometime in contact,............319c. ''able- lriction of bodies il motion,........................... 3l Friction of axles iln mtion,...................t.................,/ Table-Motive power. \\,ork done by man and lhor.-e,ovinl horiontall,..........................................................31r Table ---Motive power. \rvt!ldone by man and horse vertically,... 319. Motive poi er. Acti ons on ac ine.......................... 31 ROADS ANDI) STRI:E:'S. Roman roads, Appian way, Roman militarys roads, Cartlhainian, Greek,and I'rench roads,....................................319t;erman, Belgium, Sweden, lEnglishl, Irish, and Scotch roads,......31 9t Presentment for making anl repairing roaldstl;......................319r Making or re iairing M1cA i) z 1;i) 1 51xs.......................3; I'hrinkag.e allowance for. Ilow\ the railroad was built over tle lMenomenee marsh near ailwaukee, W isconsin,................................. 31 -v R ETAININ;G \WA.LLS for roads. Page 72j111,......................319) Parapet walls, drainage, drain holes, materials, sandstone, limestone. 'lable-WA^.r;ltr's EXPERIMENTS' on the durability of paving....319v Stones in london, England, in'A.D. 1830 and 1831. Seventeen months,...................................319v Table of comlpression of materials in road making, etc. Page 72j13,.319v 14 GENERAL INDEX. Sect'on. Table. Uniform draught on roads. Page 72j3,.................319?' Table and formulas of friction on roads. Page 72j14,............. 3197, McNeil's improved dynamometer. Page 72J14,.................. 319;' PONCELET'S VALUE of draught to overcome friction,..............319' Table-Showing the lengths of horizontal lines, equal to ascending and descending planes. Pressure of a load on an inclined plane. Page 72J13. Table-MORIN'S EXPERIMENTS. With examples. Page 72J16. Table c-Laying out curves. Radius 700 feet to 10,560 feet radius, by chords and their versed sines in feet, showing how to use them in laying out curves of less radius than 700. Page 72J17. CANALS AND EXCAVATIONS. Page 72K. (See Sec. 421).................................... 320 To set out a section of a canal on a level surface,................. 321 To set out a section when the surface is inclined,..................321a To find the embankment, and to set off the boundary of,..........32 i1 Area of section of excavation or embankment,.................... 3211 When the slope cuts the bottom of the canal,.................... 332 Mean height of a given section whose area = A, base == B V, ratio of slopes r,.................................................. 323 When the slopes are the same on both sides,..................... 323 When the slopes are unequal................................... 323 How the mean heights are erroneously taken,.................. 326 Erroneous or common method, of calculation,.................... 326 To find the content of an excavation or embankment. Page 72'r,... 327 Prism, prismoid, cylinder, frustrum of a cone, pyramid frustrum of a pyramid, prismoid, 334,................................... 327 BAKER'S method of laying out curves, and calculating, earth works, do. modified. Page 72v,.................................... 339 Tables for calculating earthwork deduced from BAKER, KELLY, and SIR JOHN MCNEIL'S tables. Page 72Y to 72H*. TABLES. Comparative values of circular and parabolic sewers,............... 135 Rectilineal channels and slopes of materials,...................... 167 Sines in plane trigonometry,................................... 171 'To change circumferentor to quarter compass bearings,............ 218 Classification of land by Sir Richard Griffith,.................... 309 Indigenous plants,................................... 309 Classification of soils,.....................309; Scale for arable land,.........................................3090 Table of produce,............................................309p Scale of prices for pasture,.....................................309 One hundred statute acres under a li c )ears' rotation. l'age 721,21. Superior finishing land,........................................309r Increase in valuation for its vicinity to towns,................ 310 Classification of buildings,................................... 310c Modifying circumstances,..................................... 310e Valuation of water-power, 310'm;, 310vw,..................310k Valuation of horse-power..................................... 310o Flour mills. Page 72B40, 72B41, 72B42,...................310p, 310q Form of field-book,...........................................310t Form of town-book,.................................... 310w Annual valuation of houses in the country, slated.................310v Annual valuation of houses in the country, thatched,..............310w Basement, stories, offices thatched,........................310z, 310y Prices of houses.. Page 72B51. Geological formation of the earth,............................... 310 Composition of rocks......................................... 310c Composition of grasses and trees..............................31(0D Analysis of trees and weeds or plants,...........................310r. Analysis of grains and straws, vegetables and legumes,........... 310F Analysis of ashes of miscellaneous articles,......................310G Per centage value of manures for nitrogen and phosphoric acid,....310I GEN ERAL IINDESX. 15 Scct'on. Table of symbols, and equivalents,...............................310I Action of reagents on metallic substances,.......................310Q Analysis of various soil',................................... 310R Supply of towns with water,.................................. 310z Value of the Vena contracta from various ai itr.-ls oul Indi anlics,.... 310c* Angles of convergance. Page 72B102. Coefficients of discharge over weirs............................ 310E* Coefficients of Blackwell's experiments,........................310E* l'oncelet and Lebros' experiments. 72i104,..................... 310F* Value of discharge Q through various orifices,....................310/t Available power of water,..................................... 310/ Retaining walls, by Poncelet,.................................310w2 Specific gravities, breaking weight and traverse.strains of beams supported at both ends, and loaded in the middle,..............3iv12 Specific gravities of bodies,....................................319a Average bulk in cubic feet per ton of 2240 pounds. Page 72 1,....319a Shrinkage or increase per cent. of materials. Page 72jJ,...........319a Friction of plane surfaces..................................... 319o Friction of bodies in motion, one upon another...................319p Work done by man and horse moving horizontally,................319r Work done by man moving vertically............................ 319s Action on machines.......................................... 319t Walker's experiments on paving.stones in a street in l.omnd(l,........319v Compression pounds avoirdupois required to crush a cube of one and one-half inches. Page 72ji3. Table of uniform draulght on given inclinations. Page 72j13. Lengths of horizontal lines equal to ascending planes. Page 72J15. Morin's experiments with vehicles on roads. Page 72j16. Table c-For laying out curves, chord A B = 200 feet, or links or any multiple of either giving radius of the curve. Ialf the angle of deflection the versed sine at one-half, the chord, or the versed sine of the angle, also versed sine of one-half, one-fourth, and oneeighth the angle. Page 72j17. Table a-Calculating earthwork prismoids. Page 72j. Table b-Calculating earthwork prismoids. Page 72'*. Table c-Calculating earthwork prismoids. Page 72E*..Sundial Table for latitudes 41~, 49~, 54f, 36' 12~, 30'. Page 2n1*27,.390* Levelling books, English and Irish Board of Works, method,....... 414 M. McDermott's method..................................... 415 Levelling by barometrical observation. Table A................... 416 Levelling by barometrical observation. Table B,................. 417 Table A and table B,......................................... 419 Natural sines to every minute, five places of (lecimals fruom 1~ to 90~. Page 72i* to 72R*. Natural cosines as above. A guide line is at every five minutes. Natural tangents and cotangents, same as for the sines. 72s* to 72B**. The sines are separate from the cosine and tangents to avoid errors. Both tables occupy twenty pages nicely arranged for use. Traverse table, by McDermott, entirely original, calculated to the nearest four places of decimals, and to every minute of degree in the left hand column numbered from 1 at the top to 60 at the bottom, at the top are 1 to 9 to answer for say 9 chains 90 chains, 90 links or 9 links. The latitudes on the lelt hand page, and departures on the right hand page for 45 degrees, then 45 to 90 are found at the bottom, contains 88 pages. Solids, expansion of,.......................................... 165 To reduce links to feet,........................................ 166 To reduce feet to links,........................................ 168 Lengths of circular arcs to radius one............................ 170 Lengths of circular arcs obtained by having the chord and versed sine, 171 Areas of segments of circles whose diameter is unity,............. 173 To reduce square feet to acres and vice vers,..................... 175 Table Villa. Properties of polygons whose sides are unity,....... 176 Table IX. Properties of the five regular bodies................. 176 16 GENFIRALI1)IS Sec tIr p Table X. To reduce square links to acres....................... 17 Table X. To redude hylpothenuse to base, or lhorizotal Iloe;larem ent,.................................................. 177 Table XII. To reduce sidereal time to mean solar time,.......... 17S Table XIII. To reduce mean solar time to sidereal time,......... 1]7 Table XIV. 'o reduce sidereal time to degrees of longitudl,...... 17 Table XV. To reduce longitude to sidereal time',................. 17! Table XVI. D)ip or( depretssion of the horizon, anll tlle di-tllace at sea in miles colrres! onding to givenl heights,.................... 17 Table XVII. CorIection oft thle apparent altitude for refiacilon,.... IS( Table XV I [. SI,'s parallai in altitude,....................... 1 1 Table X IX. Parallax in altitude of the pllnets, I.................. Tabl)e XN. Rl'eduction of the time of the moon's passage over the meridian of ( i'eenwichl to that over any other meridianli.......... 1S1 Ta lll e X X. I;est time for oltainiln apparent tinile,.............. 182 'Tab)le XX II. Bl est altitude for olbtainilg true tinie,................, 8 Ta ble XX Il. lolar tabc, azimutlis or bear-ings of stars in tlhe Northern and Southlern hemislpheres when at tiltir greatest elongations friom the meridian for every one-half a deIree of latitude, anid from onie dereer to latitude 70', and for polar distances ', 4', 0 4, 0 5)', 0 i"55 (, 1 '), 1~ 10' 1-1 5', 1 '2 ', ' 1- ', " '3) y'.3 7~4,, 7 '. 7.', 8 0, i1:', 11-35', 1 1'40', 11~45', 11 50', H o )ii 5', 1:0', 12.5, 12,40', 12.45, 12~50', 12.55, 1: -0-13 ---5 1i '20', 15~25', 15,1,0', 15:3,a, 1l5 40', 1 45', 1.,0,..................... 1.84 [These will eialle the Sutrvceyor, at uearly any hour of the n ght, to run a mrciidian line in any place until A.I). 2000.] Azimuth of Kochab (Beta Ursaminoris), when at its greatest elongations or azimutlhs for 1875 aild every ten years to 1995,.......... 193 Table XXIV. Azimuths of Polaris wlien on the same vertical plaine with gammiia i ( asi.op: ait its unlcer traunsit in latitudes 2~ to 70' firoin 187 until 1940....................................... 1 -14 Table XXV. A.\imutls- of Plolaris when vertical w ith Alioth in Ursa majoris at its unldet tiran.it, same as for table XXV,............ 195 Table XXX VI. \ean places of gamma (ca.ssiopa), and epsilon (alioth), in ursa imajoris at reeiiwicli from A. 1). 1870 until 1950, 196 Table XXV 11. Azimuth, or bearings of alphia, in the foot of the Southern c ross (ic ucis.), when on the same vertical plane withli eta in Hydri, or in the tail of the scrpett f-on.\. A. 1). 1850 iuntil 2150, and for latitude 12~ to ',...................................... 197 Table XXVIII. Altitudes and greatel-t a/imuths for January 1, 1867. For Chicago latitude 41~, 50', 30" N., longitude 87~, 34', 7" W., and Bitenos Ayres 34~,: 3', 40" S., longitude 58~, 24', 34 " V., for thirteen circumplolar starsi in tilhe Northern hemisphere, and ten circumpolar star-, in tlie Southern hemisphere, giving the magnsitude, polar. dlistance, right acension, upper meridian passage, time to greatest azimuth, time o(,-steatest ' aznimuth, time of greatest WV azimuth, greatest azimuth, altitude at its greatest aziimuith of each, 198 Table XXVIII. A. Table of eijual altitudes.................... -19! Table XX VII I. I. To chaige metres into statute miles,.......... 200 Table XX VI II. C. Length of a degree of latitude and longitude in m iles and m etres......................................... 200 Table XXIX. Reduce reich lires iuti culic feet aind imllpcrial gallons,................................................... 20 1 Table XXX. \Weights and measures. Table XXX [. Discharge of wcater through new pipes compiled from D'Arcy's official French talts for 0).01 to 1.00 metres in diameter, and ten centimetres high in 10 i metres to 200 ceintim etres in 100 m tres high,................................... 201 '.Arcv's formurln a and example,........................ '264 THE SURVEYOR AND CIVIL ENGINEER'S MANUAL. STRAIGHT - LINED AN~D CURVILINEAL FIGURES. OF THE SQUARE. 1. Let A BOCD (Fig. 1) be asquare. Let A Bza, and A D d, or diagonal. 2. Then a X a, = a-2 -- the area of the square. 8. And V/2a2- a 1/2 — a X 1,4142136 = diagonal. 4. Radius of the inscribed circle 0 E a 6. Radius of the circumscribing circle - 0 D a X 1,4142136 2 aX 6,707168. 6. Perimeter ofthe square = A B +BD +D 0+C Azza.4 7. Side of the inscribed octagon F G a,-a aXl,4142136-a -a X 0,414214, i. e., the side of the inscribed octagon is equal. to the difference between the diagonal A D and the side A B of a square. 8. Area of the inscribed circle = a-2 X 0,7854. 9. Area of the circumscribed circle 0,7854 X 2 a2. 10. Area of a square circumscribing a circle is double the -square in-, scribed in that circle. RHOMBUS. 11. (Fig. 3.) In a rhombus the four sides are equal to one anothe?;,., but the angles not right-angled. 12. The area the product of the side X perpendicular br~padth A B X C E. 13.' Or, area a2 X natural sine of the acute angle. C A B; iL A B X A C >( nat. sine of tire angle C A B =the area. Or THE RECTANGLE OR PARALLELOGRAM. 14. (Fig. 2.) Let A. B =a B D b, and AD =d. 15. A D d =Va +b d1. radius of the circumscribing circle. ~ A-. Aea a b or the length )( by the breadth.i~. Wh~u a 2 b, the rectangle is the, greatetin, it, ksnt-iz'e1 " - e area. a 6 AREAS AND PROPERTIES OF 20. Hydraulic mean depth of a rectangular water-course is found by dividing the area by the wetted perimeter; i. e., - area divided by the sum of 2 A C + C B. 21. When the breadth is to the depth as 1: 1/2 i. e., as 1: 1,4152, the rectangular beam will be the strongest in a circular tree. 22. When the breadth is to the depth as 1: /3, i. e., as 1: 1,732, the beam will be the stiffest that can be cut out of a round tree. 23. Rhomboid. (Fig 4.) In a rhomboid the four sides are parallel. Area = longest side X by the perpendicular height = A B X C E- A B X A C X nat. sine < C A B. 24. Trapezoid. In a trapezoid only two of its sides are parallel to one another. Let A D E B (fig. 4) be a trapezoid. Area = ~ (C D + A B) X by the perpendicular width C E. OF THE TRIANGLE. 25. Let A B C (Fig. 5) be a triangle. AB 26. If one of its angles, as B, is right-angled, the area -= X B C B C = X A B =j (A B X B C.) 27. Or, area -= A B X tangent of the angle B A C. 28. When the triangle is not right-angled, measure any side; A C as a base, and take the perpendicular to the opposite angle, B; then the area =- (A 0 X E B.) In measuring the line A C, note the distance from A to E and from E to C, E being where the perpendicular was erected. 29.' Or, area 2 X nat. sine of the angle C A B. When the perpendicular E B would much exceed 100 links, and that the surveyor has not an instrument by which he could take the perpendicular E B, or angle C A B, his best plan would be to measure the three sides, A B = a, B C - b, and A C = c. Then the area will be found as follows: 30. Add the three sides together, take half their sum; from that half sum take each side separately; multiply the half sum by the three differences. The square root of the last product will be the area. 31. Area = (a+b+ ).a+b+c a+b-c b)(a+b+_ _c 1 2 )'( 2 -a)*( 2 -b)'- 2 82. Let s equal half the sum of the three sides then Area = /. (s-a). (s-b). (8-c) 88. Or,area= log s + log (s-a) + log (s-b) + log (s-c). to the logarithm of half the sum add the logs of the three differences, divide the sum by 2, and the quotient will be the log of the required area. STRAIGHT-LINED AND CURVILINEAL FIGURES. 7 34. Or, to the log of A C add the log of A B and the log sine of the contained angle C A B. The number corresponding to the sum of these three logs will be double the area, i. e., Log a + log c + log sine angle C A B = double the area. 35. Or, by adding the arithmetical compliment of 2, which is 1,698970, we have a very concise formula, Area = log a 4 log c + log sine angle C A B + 1,698970. Example. Let A B = a =18,74, and A C = c = 1695 and the contained angle C A B 29~ 43/ Log 18,47 chains, - --- 1,2664669 Log 16,95 chains, - - 1,2291697 Log sine 29~ 43/ - --- 9,6952288 Constant log, - - - 1,6989700 11,8898354 Reject the index 10, - - - - - 10 1,8898354 The natural number corresponding to this log will be the required area - 77,5953 square chains, which, divided by 10, will give the area - 7,75953 acres. 35a. In Fig. 5, let the sides A C and B C be inaccessible. Measure a2 sine A X sine B, A B- a; take the angles A and B, then the area a2 ine X se B 2 sine C which, in words, is as follows: Multiply together the square of the side, the natural sines of the angles A and B; divide the contained product by twice the sine of the angle C. The quotient will be the required area. Or thus: Add together twice the log of a, the log sine A, and the log sine B; from the sum subtract log 2 + log sine C. The difference will be the log of the area. Example. Let the < A 50~, angle B = 60~, and by Euclid I. 32, the < at C = 70~; and let A B = a = 20 chains to find the area of the triangle: Log 20, - 1,3010200 2 2,6020400 Angle A - 50~, log sine, - - - 9,8842640 Angle B = 60~, log sine, - - - - - - 9,9376206 (A) 22,4238146 Constant log of 2 - 0,3010300 Angle C - 70~, log sine, - -- 9,9729868 -(B) = 10,2740168 2,1498288 From the sum A subtract the sum B, the difference, having rejected 10 from the index will be the log of the natural number corresponding to the area 141,198 square chains, which divided by 10 gives the area ma: 14~- acres. 8 AREAS AND PROPERTIES OF Or thus: By using the table of natural sines. Having used Hutton's logs, we will also use his nat. sines. See the formula (34) a2 - 20 X 20, - - - 400 Nat. sine 500 = nat. sin. < A - - - -,7660444 Product, - - -- 306,4177600 Let us take this - - - - 306,418 Nat. sine 60~ 0 nat. sin. < B -,86603+ Product, - - - 265,367007334 Nat. sine of 70~ =,939693 2 Divisor, 1,879386 ) 265.367007334 Quotient, - 141,198 square chains, which, divided by 1198 10, gives 14iooo acres. Q. E. F. 35b. If on the line A B the triangles A C B, A D B, A E B, etc., be described such that the difference of the sides A C and C B, of A D and D B, and of A E and E B is each equal to a given quantity, the curve passing through the points C, D and E is a hyperbola. 36. If the sum of each of the above sides A C +- C B, A D + D B, A'E + E B is equal to a given quantity, the curve is an ellipses. 37, In the n A C B, (Fig. 5,) if the base C E is. of the line A C, the A C E B will be - of the L' A C B, and if the base A C be n times the base C E, the A A C B will be n times the area of the A C E B. 38. From the point P in the A A C B, (Fig. 11,) it is required to draw a line P E, so that the A A P E will be 1 the area of the A A C B. Divide the line A B into 4 equal parts, let A D = one of these parts, join D and C and P and C, draw D E parallel to P C, then the A A E P will be = of the A A C B; for by Euclid I. 37, we find that the A E O C - A O D P... the A E P = A C D = A the A A C B, Q.E.F. 39. From the A A C B, required to cut off a L A D E = to 6 of the A A C B by a line D E parallel to B C. By Euclid VI. 20, A A D E: A ACB:: A D2: A B2; therefore, in this case, divide A B into two such parts, so that A D2 = the square of A B. Let D be the required point, from which draw the line D E parallel to B C, and the work is done. 40. In the last case we have A A D E: A C B:: AD2: A B2; i.e., 1: 5:: A D2: AB2. Generally, 1: n:: A D2: A B2; and by A B Euclid VI. 16, n X A D2 _ A B2; therefore, A D -, which is a general formula. 60 Example. Let A B =60 and n =; then A D 2 26,7. 2,236: 41. If D be a point in the \ A C B, (Fig 13,) through which the line. P E is drawn parallel to C B, make C E E F, join F D, and produce it to meet C B in G, then the line F D G will cut off the least possible:1 triangle. i: 42. By Euclid VI. 2, F D = D, because F E = E C. STRAIGHT-LINED AND CURVILINEAL FIGURES. 9 43. To bisect the A A C B (Fig. 16,) by the shortest line P D. Let A C = b, BC = a, C P —x, and C D = y, C P D = A C B, conditions which will be fulfilled when x = C P = — and y C D= 2 2 Hence it follows that C P = C D. (See Tate's Differential Calculus, p. 66.) 44. The greatest rectangle that can be inscribed in any A A C B, is that whose height n m, is = — the height n C of the given triangle (see Fig 14,) A B C. Hence the construction is evident. Bisect A C in K. draw K L parallel to A B, let fall the perpendiculars K D and L I, and and the figure K L I D will be the required rectangle. 45. The centre of the circumscribing circle A C B, (Fig. 7,) is found by bisecting the sides A B, A C, and C B, and erecting perpendiculars from the points of bisection; the point of their bisection will be the required centre. (See Euclid IV. 5') 46. The centre of the inscribed circle (Fig. 6,) is found by bisecting the angles A, B and C, the intersection of these lines will be the required centre, 0, from which let fall the perpendicular 0 E or 0 D, each equal to the perpendicular 0 F = to the required radius. 47. Let R = radius of circumscribing circle and r = radius of the inscribed circle, and the sides A B = a, B C b, and A C = c of the A A B C; then R= ab 2 r (a+b+c) abc and r = — 2 R (a+b+c) 48. To find r, the radius of the inscribed circle in (Fig. 6,) r (a+b+c) = area of the A A B C = A, 2A A. r = = area divided by half of the sum of a+b+c i (a+b+ c) the sides of the A, ab c ab c 4A ___ —. c — e., 2 r. (a + b + c) bc) +b+c) (a- (+b+c) R_ a b c ~ (a+b+ c)_ b c. 4 A ~ (a+b+ -c) 4A 49. Radius of the circumscribing circle is equal to the product of the three sides divided by 4 times the area of the triangle, and substituting the formula in 8 31 for the area of the triangle, we have a b c a b c R =t -_ == -------- i. e., 4 A 2 r (a —b —+c) _ abe R. (s- ).(s —b). (s — )i } where s is 3 the sum of the sides, 4{s (s-a) (s-b)-(s-c) but (a+b+c) -r- = A; therefore, 2A A- < 60. r= a-b+c; 1 X i l - 10 AREAS AND PROPERTIES OP 51. The area of any A C K L (Fig. 14,) will be subtended by the least line K L, when C K = C L. Let x = C K C L, and A = the 2A required area, then x ---- nat. sine < C 52. Of all the triangles on the same base and in the same segment of a circle, the isoceles A contains the greatest area. 53. The greatest isoceles A in a circle will be also equi-lateral and will have each side =r 1/3 where r = radius of the given circle. 54. In a right-angled A, when the hypothenuse is given, the area will be a maximum when the A is isoceles; that is, by putting h for the h h hypothenuse the base and perpendicular will be each = -- - 1 414313 55. The greatest rectangle in an isoceles right-angled A will be a square. 56. In every triangle whose base and perpendicular are equal to one another, the perimeter will be a maximum when the triangle is isoceles. 57. Of all triangles having the same perimeter, the equi-lateral / contains the greatest area. 58. In all retaining walls (walls built to support any pressure acting laterally) whose base equals its perpendicular, or whose hypothenuse makes an angle of 45~ with the horizon, will be the strongest possible. OF THE CIRCLE. Let log of 3,1416 = 0,4971509, of 0,7854 = 1,8950909, and of 0,07958 =2,9008039. 59. Let a = area, d = diameter and c = circumference. n = 3,1416 and m = 0,7854. Const. log 3,1416 = 0,4971509. d X 3,1416 = circumference, or log d + log 0,4971509 = log circumference. 60. d2 X 0,7854 = area = twice log d + constant log of 0,7854 = d c dc (1,8950909), and c2 X 0,07959 = area - X -= 22 4 log of area = 2 log c + constant log 2,9008039. 61. Example. Let d = 46, then 46 X 3,1416 = 144,5136 = circumference; or, by logarithms, 46, log = 1,6627578 3,1416 constant log 0,4971509 2,1599087 = 144,5136 8979 circumference. 108 90 18 62. d = or c = 144,5136 Log = 2,1599087.,;d~. -3,1416 f:?- 3,1416 Log 0,4971509 Difference, 1,6627578 d = 46,....;...flf-: An,... STRAIGHT-LINED AND CURVILINEAL FIGURBS. 1 11 63. Area =d2 X 0O7854=~ = d* d - 0,07958. Log area = twice log d + log 1,8950909, the nat. number of which will give the required area. {1,662757 8 Example. Let d = 45, its log= 1,6627578 Constant log of 0,7854, 1,909 Area = 1661,909 =3,2206065 64. = 2x 0,079,58 = twice log c + log of 0,07958 =log area. Example. Let c = 154. Log c = 2,1875207 2 Log c2 = 4,3750414 Constant log of 0,07-958 = 2,9008039 Log area = 3,2758453 Area =1887,3191 _ a1 65. d=( — ) and c= (0,7854 0,0795'8 66. Area of a Circular Ring = (D2 - d-2) X 0,7854. Here D= diameter of greater circumference, and d, that of the lesser circumference. 67. Area of a Sector of a Circle. (See Fig. 8.) Arc E G F is the arc r E GF of the given sectorO0 E G F, area - arc E G F or area = r - 2 2 but arc E G F = 8 times the arc E 0, less the chord E F, the difference divided by three ==arc E G F (i. e.,) 8 EG - EF r 8 EG -E F Ar E'G F=,.area of sector =X 3 2 3 r 68. i. e., Area= - (8 E G- EF). E G, the chord of jthe are, 6 may be found by Euclid I. 47. For we have 0 E = to the hypothenuse, given, alsojIthe cbord E F = EH,.-. g'(0E2 - EH2) ==OH, and 0E - o H = H G, then V/(E H2 + H G2) = E G. 69. Area degrees of the < E 0 F X diameter X by the constant number, or factor 0,008727, i. e., area = d a X 0,008727 where a< E 0 F in degrees and decimals of a degree. 70. Segment of a Ring. N K M F 0 E, the area of this segment may be found by adding the arcs N KM and E GF of the sector N K M and multiplying j their sum by E N, the height of the segment of the ring, i. e., area arcN MG acK.O 2 X K 71. Segment of a Circle. Let E 0 F be the given segment whose area is required. By 67 find the area of the sector 0 E F, from which take the area of the A GE F, the difference will be the required area. 12 AREAS AND PROPERTIES OF 3 72. 2EFXG H X GH 72. Or, trea ' +2; '. e., to 3 of the product of 3 2'E the chord by the height, add the cube of the height divided by twice the chord of the segment, the sum will be the required area. 73. Or, divide the height G H by the diameter G L of the circle to three places of decimals. Find the quotient in the column Tabular Heights of Table VII., take out the corresponding area segment; which, when multiplied by the square of the diameter, will give the required area. 74. When G H, divided by the diameter G L, is greater than,5, take the quotient from 0,7854, and multiply the difference by the square of the diameter as above, when G H divided by G L does not terminate in three places of decimals, take out the quotient to five places of decimals, take out the areas less and greater than the required, multiply their difference by the last two decimals of the quotient, reject two places of decimals, add the remainder of the product to the lesser area, the sum will be the required tabular area. Example. Let G H = 4, and i the chord = E 1I = 9 E F. By 81 Euclid III. 35, H G X H L = E H H F = E 2 = 81;.-. =20,25 4 H L; consequently, by addition, 20,25 - 4 = 24,25 = G L = diameter. And 4 divided by 24,25 = 0,16494 = tabular number. Area corresponding to 0,164 =,084059 "' "' " 0,165 =,084801,000742 94,000697,48 Lesser area for,164,084059 Correction to be added for 00094 = 697 Corrected tabular area,,084756; which, multiplied by the square of the diameters will give the required area. OF A CIRCULAR ZONE. 75. Let E F V S (Fig. 8,) be a circular zone, in which E F is parallel to S V, and the perpendicular distance E t is given; consequently E S t v may be found by Euclid I. 47, s t = (S v -E F)= d, and S v - d t v, and by Euclid III. 35, t tv t W,.. E t-t tU = E U is Et given. And by Euclid I. 47, the diameter U F is =- /(E U2 +- E F2) And by Euclid III. 3, by bisecting the line, O Z is at right angles to F V; and by Euclid III. 31, the < U V F is a right angle; and by Euclid VI. 2 and 4, UV = 2 o x. And E t: E S:: v t: V U, by substitution we have E t: E:: vt: 2o x. By Euclid VI. 16, o x = (E S X v t) -- E t = *?-'\-:..:.......E t STRAIGHT-LINED AND CURVILINEAL FIGURES. 1 13 Now having o x and o y = radius, we can find the height of the segment x y;.. having the height of the segment x y, and diameter W F of the segment F Y V, we can find its area as follows: The area of the trapezium E FV S ~ (E F~+V8) X Et, to which add twice the segment F Y V, the sum will be the required area of the zone E F V S. In fig. 8, let E F-~a,SV~b, E t ~p,St = d j(v-E F), and T v=e, E W = p +ed ~,and by Euclid I. 47. P p WF= ( p + ed) ~ a~i e., WF (p + 2 p2 ed +e2d2~+p2a2) E S =(p2 + d2)l Because E t: E S: V t: V W E t: E S:: V t: 2 o x E S -V t And by substituting the values of E 8, V t and 2 E t, we have e (p2, -F d2')* 2 p X WF - X. 2 W F = 2 x y + 20 X. Exampte. Let E F:a 20, and s, T=b1=:0, Et~p=25, S t =d, and t vT e, to find the diameter W F and height x y. Here d = 6 and t v =e =25. E S = 6V ~25,494. 25V625+2 25/60 25 X25,495 5x 0 40 50 o X= 12,747, W - 1 908,05 p, 390625 + 156250 + 15625 + 390E6262 + 'fPf W V - o10 PI I v uwzvn I W F 3 6,07= diameter; and haaving the diameter W F and height x y, the area of the segment, subtended by the chords F v and E 8, can be found by Table VII., and the trapesium. E F v t by section 24. OF A CIRCULAR LUNE. 78. Let A C B D, fig. 10, represent a lune. Find the difference between the isegment A C B and A D B, which will be the required area. 3~~~~~~~~~~~~~~~ 14 AREAS AND PROPERTIES OF 77. Hydraulic mean depth of a segment of a circle is found by dividthe area of the segment by the length of the arc of that segment. Of all segments of a circle, the semi-circular sewer or drain, when filled, has the greatest hydraulic mean depth. 78. The greatest isoceles A that can circumscribe a circle will be that whose height or perpendicular C F is equal to 3 times the radius 0 E. 79. Areas of circles are to one another as the squares of their diameters; i. e., in fig. 8, circle A K B I is to the area of the circle C G V L as the square of A B is to the square of C D. 80. In any circle (fig. 9), if two lines intersect one another, the rectangle contained by the segments of one is = to the rectangle contained by the segments of the other; i. e., O M X M C = F M X M H, or O AX A C = F A X A. 81. In fig. 8, a T X b T = I T X K T = square of the tangent T M. 82. In a circle (fig 9), the angle at the centre is double the angle at the circumference; i. e., < C A B - 2 < C 0 B. Euclid III. 20. 83. By Euclid III. 21, equal angles stand upon equal circumferences; i. e., <C 0 B = < C L B. 84. By EuclidIII. 26, the <B C L < B L C < C O B. 86. By Euclid III. 32, the angle contained by a tangent to a circle, and a chord drawn from the point of contact, is equal to the angle in the alternate segment of the circle; i. e., in fig. 9, the < T B C = < B 0 C =- < C A B. This theorem is much used in railway engineering. 86. The angle T B C is termed by railroad engineers the tangential angle, or angle of half deflection. 87. To draw a tangent to a circle from the point T without the circle. (See fig. 9.) Join the centre A and the point T, on the line A T describe a semi-circle, where A cuts the circle, in B. Join T and B, the line T B will be the required tangent or the square root of any line Q T H = T B; i. e., V/ (Q T H) = T M. Then from the point T with the distance T B, describe a circle, cutting the circle in the point B, the line T B is the required tangent. In Section 81, we have T a * T B T M2,.-. /(T a * T B) = T M, and a circle describe with T as centre and T M as radius will determine the point M. OF THE ELLIPSE. 88. An ellipse is the section of a cone, made by a plane cutting the cone obliquely from one side to the other. Let fig. 39 represent an ellipse, where A B = the transverse axis, and D E = the conjugate axis. F and G the foci, and C the centre. Construction.-An ellipse may be described as follows: Bisect the transverse axis in C, erect the perpendicular C D equal to the semi-conjugate, from the point D, as centre with A C as distance describe arcs cutting the transverse axis in the foci F andG. Take a fine cord, so that when knotted and doubled, will be equal to the distance A G or F B. At STRAIGHT-LINED AND CURVILINEAL FIGURES. 15 the points or foci F and G put small nails or pins, over which put the line, and with a fine-pointed pencil describe the curve by keeping the line tight on the nails and pencil at every point in the curve. 89. Ordinates are lines at right angles to the axis, as 01 is an ordinate to the transverse axis A B. 90. Double ordinates are those which meet the curve on both sides of the axis, as H V is a double ordinate to the transverse axis. 91. Abscissa is that part of the axis between the ordinate and vertex, as A 0 and 0 B are the abscissas to the ordinate O I; and A G and G B are abscissas to the ordinate G H. 92. Parameter or Latus rectum is that ordinate passing through the focus, and meeting the curve at both sides, as H. V. 93. Diameter is any line passing through the centre and terminated by the curve, as Q X or R I. 94. Ordinate to a diameter is a line parallel to the tangent at the vertex of that diameter, as Z T is the ordinate being parallel to the tangent X Y drawn to the vertex X of the diameter X Q. 95. Conjugate to a diameter is that line drawn through the centre, terminated by the curve, and parallel to the tangent at the vertex of that diameter, as C b is the semi-conjugate to the diameter Q X. 96. Tangent to any point H/ in the curve, join H F and G H, bisect the angle L H G by the line H K, then H K will be the required tangent. 97. Tangent from apoint without, let P be the given point, (see fig. 40) join P F; on P F and A B describe circles cutting one another in X, join P X and produce it to meet the ellipse in T, then P T will be the required tangent, and H K/ ' tangent to the point h. 98. Focal tangents, are the tangents drawn through the points where the latus rectum meets the curve, K H is the focal tangent to the point H. 99. Normal is that line drawn from the point of contact of the tangent with the curve, and at right angles to the tangent, H N is normal to K H. 100. Subnormal is the intercepted, distance between the point where the normal meets the axis, and that point where an ordinate from the point of tangents contact with the curve meets the axis, as N Ot is the subnormal to the point H. 101. Eccentricity is the distance from the focus to the centre, as C G. 102. All diameters bisect one another in the centre C; that is, C X C Q and C I = C R. 103. To find the centre of an ellipse. Draw any two cords parallel to one another, bisect themf join the points of bisection and produce the line both ways to the curve, bisect this last line drawn, and the point of bisection will be the centre of the ellipse. 104. AB-FD+GB=FI+GI=FH+GtH, etc.; thatis, the sum of any two lines drawn from the foci to any point in the curve, is equal to the transverse axis. '..:::::;'5i?.i I 1 16 18 ~~~~ARRAS AND PROPXiTI-28 OFP 105. The square of half the transverse, is to the square of half the conjugate, as the rectangle of any two abscissas is to the square of the ordinate to these abscissas; i. e., A C2: C DM2:: A 0. 0 B; 0 P2; therefore, AO *OB*CD2 CD) O I =V-( )=.V(A 0-0 B) A C' AC Let us assume - Dequal to n, then A C G H'=V(A G. G B).n. 106. Rectangles of the abscissas are to one another as the squares of their ordinates; i. e., A 0.- 0 B: A G. G B:: 01I2:G 11/2 107. The square of any diameter is to the square of its conjugate, as the rectangle of the abscissas to that, diameter, is to the square of the ordinate to these abscissas; i. e., QX2: H,' b2: Q T. T X: T Z-2; i.e. C X2: C b2: QT T X: T Z-2. 108. To find where the tangent to the point H will meet the transverse axis produced: C 01: AC:-:A C: C K'. Substituting x for C 0', and a for A C a2 X:a:: a: CK';.*.C K'I= therefore, 0K _(a+x (a x 2_. Now, by having the ordin ate 01I =y, we have flK,~Ys+a2-x2)2 =1y2~a2 a2 x-2+x4 __(x2 y2 + a4 - 2 a2 X2 + X') 109. Tangent H K'-=V, here x= CO. X. 110. Equation to the ellipse e+ =1; b~ a2 or, y = ar2i (a2- X2)~ here y =any ordinate O H. Having the semi-transverse axis =a, the semi-conjugate = b o = 0 H = any ordinate, x, = C 0 =co-ordinate of y. Let A 0 S- - greater abscissa, and 0 B s- lesser abscissa. We will from the above deduce formulas for finding either a, b, 5, s, 0 or x. 112. A C l *S{b + V(b2 -0) semi-transverse. 02 STRAIGHT-LINED AND CURVILINVAL FIGURES. 1 17 a2 02 11 113. C D =b=V( ~) = a & o -= semi-conjugate. S * Ss 114. A 0= S= a +! (b2-o02)1 - greater absoessa. b 1 15. Area of an ellipse =A BX DE X,7854 -= 4 a b.7854-~3,1416 X a b. 116. Area of an elliptical segment.-Let h = height of the segment. Divide the height h, by the diameter of which it is a part; find the tabular area corresponding to the quotient taken from tab. VII; this area multiplied by the two axes will give the required area, i. e., h Tab. area ~-.4 a b, when the base is parallel to the conjugate axis; h or, tab. area = 4 a b, when the base is parallel to the transverse axis. 117. Circumference of an ellipse 4/ )- 4.b 3-1416; i.e, 2 Circumference = lV(2 a2 + 2 b2). 3-1416. 118. Application.-Let the transverse == 35, and conjugate 25. Area 35 X 25 X,7854 875 X,7854 =687,225. Circumference = 35! + 25-2) 3-1416 22109 X 3-1416 =69,3979. 2 Let A 0 28 =greater abscissa, then 7 the lesser abscissa, to find the ordinate 0 H. OH=( 28 X7 X_252k -/0 0 352 25 or, O H =5-r Vt28 X 7 10. (See section I111.) Abscissa A 0 = 17,5 + 17,_5 V/625 - 100 ==17,6 + 1,4 X 7,5 =28. 12,5 or' TME rARAnOLA. 122. A parabola is the section of a cone made by a plane cutting it parallel to one of its sides (see fig. 41). 123. To de8cribe a parabola.-] bisect A F in V; then V = verte] directrix C D; attach a fine line ox the end Iland focus F; ruler laid on the derectri: close to the side of the sq slide one K; keep t uare, and ~et D C - directrix and F = focus; r; apply one side of a square to the cord to the side H I; make it fast to side of the square. along the edge of a he line by a fine pencil or blunt needle trace the curve on one side of the axis. 18 AREAS AND PROPERTIE8 OF Otherwise, Assume in the axis the points F B B' B// B/// B"// etc., at equal distances from F; from these points erect perpendicular ordinates to the axis, as F Q, B P, B/ 0, B// N, B//' M; from the fcus F, with the distances A F, A B, A B, A B/, describe arcs cutting the above ordinates in the points Q, P, 0, N, M, etc., which points will be in the curve of the required parabola; by marking the distances F B = B B' = B/ B/, etc., each distance equal about two inches, the curve can be drawn near enough; but where strict accuracy is required, that method given in sec. 122 is the best. 124. Definitions.-C D is the directrix, F = focus, V = vertex, A B - axis. The lines at right angles to the axis are called ordinates. The double ordinate Q R through the focus is equal to four times F V, and is called parameter, or latus rectum. Diameter to a parabola is a line drawn from any point in the curve parallel to the axis, as S Y. Ordinate to a diameter is the line terminated by the curve and bisected by the diameter. Abscissa is the distance from the vertex of any diameter to the intersection of an ordinate to that diameter, as V B is the abscissa to the ordinate P. B. 124a. Every ordinate to the axis is amean proportional between its abscissa and the latus rectum; that is 4 V F X B/ V =- B/ N2, consequently having the abscissa and ordinate given, we find the latus rectum B// N2 - 4 V F =B V; also the distance of the focus F from the vertex B// V B"// N2 -FV —B 4 BW/ N 126. Squares of the ordinates are to one another as their abscissas; i. e., B P2: B' 02:: V B: V Bt. 126. FQ=2FV.. QR=-4FV. 127. The ordinate B S2 = V B * 4 V F; hence, the equation to the curve is y2 = p x, where y = ordinate = B S, and x = abscissa V B, and p = parameter or latus'rectum. 128. To draw a tangent to any point S in the curve, join S F; draw Y 8 L parallel to the axis A B; bisect the angle F S L by the line X S, which will be the required tangent. Otherwise, Draw the line from the focus to the derectrix, as F L; bisect F L in m; draw m X at right angles to F L; then m X S will be the tangent required, because S L = S F. Otherwise, Let S be the point from which it is required to draw a tangent to the curve; draw the ordinate S B, produce B// V to G, making V G == V B; then the line G S will be the required tangent. 129. Area of a parabola is found by multiplying the height by the base, and taking two-thirds of the product for the area; i. e., the area of the parabola N V U = (B// V N W).!.(.;.. Afr,?:::~ STRAIGHT-LINED AND CURVILINEAL FIGURES. 19 130. To find the length of the curve N V B of a parabola: Rule.-To the square of the ordinate N B// add four thirds of the square of the abscissa V B//; the square root of the product multiplied by 2 will be the required length. Or, by putting a = abscissa = V B/, and d - a -2 - 4a2 ordinate N B//; length of the curve N V U =-/( d ~ ) * 2, i.., Length of the curve N V U = -/(3 d2 + 4 a2) X 1,155. Rule 1L.-The following is more accurate than the above rule, but is more difficult. 2d Let q - = to the quotient obtained by dividing the double ordi4VF nate by the parameter. ~q2 q4 3 q6 Length of the curve = 2 d. (1 + - + ) etc. 2.3 2.4.5 2.4.6.7 131. By sec. 57, of all triangles the equilateral contains the greatest area enclosed by the same perimeter; therefore, in sewerage, the sewer having its double ordinate, at the spring of the arch, equal to d; then its depth or abscissa will be,866 d; i. e., multiply the width of the sewer at the spring of the arch by the decimal,866. The product will be the depth of that sewer, approximately for parabolic sewer. 132. The great object in sewerage is to obtain the form of a sewer, such that it will have the greatest hydraulic mean depth with the least possible surface in contact. OF TIHE PARABOLIC SEWER. 133. Given the area of the parabolic sewer, N V U = a to find its abscissa V B// and ordinate B// N such that the hydraulic mean depth of the sewer will be the greatest possible. Let x - abscissa = V B// and y = ordinate N B"; then N U = 2 y. By section 129, x = a; i. e., 4 y x = 3 a 3 3 a a,75 a Y - -,756. 4x x x To find the length of the curve N V U. l + T- = perimeter. 2 ( 1,687 aa 4 2/1,687 aim +4 eer 8;. ) - X,7 ifV X82i ^:.A I: 1 8 '*.'.*M 20 AREAS AND PROPERTIES OF 1,1561/1,6875 a2 + 4 x4 t. e., 11/687 + 4 perimeter, which, divided into the given 1,732 x area, (a) will give a x = hydraulic mean depth. 1,1551/1,6875 + 4 xA a x *. e., = maximum. 1,1551/1,6875 + 4 x4 And by differentiating this expression, we have 1,155. *8 xd x Differential u = a d x * (1,155/1,6875 a2 + 4 x4 - a x (6875 4 x V 1,6875 a3 -+ 4 x4 1,1551/1,6875 a0 + 4 x4 rejecting the denominator and bringing to the same common denominator. du d =_ a- 1,155 (1,6875 a2 + 4 x4) - a x (9,24 x-= 0. dx i. e., 1,949 a2 + 4,62 a x4- 9,24 a x4 = 0. 1,949 a2 = 4,62 a x4 X4 =,4218 a2 2 =,6494 a x =,8061/a= /,649 a = required abscissa. 3 a 0,75 a y _ 3 a = 7 — = required ordinate. 4x x Example.-Let the area = 4 feet = a; then,8061/a =,806 ~ 2 = 1.612 - abscissa = x; 3 an 12 and y = ordinate = - - = 1,863. 4 x 6,448 Now we have the abscissa x = 1,612, and ordinate - 1,863. By Sec. 130, we find the length of the curve N V U = 5,26; and by dividing the perimeter, 5,26, into the area of the sewer, we will have the hydraulic mean depth = - - 0,76 feet. 5,16 134. The circular sewer, when running half full, has a greater hydraulic mean depth than any other segment; but as the water falls in the sewer, the difference between the circular and parabolic hydraulic mean depths, decreases until in the lower segments, where the debris is more concentrated in the parabolic, than in the circular, the parabolic sewer with the same sectional area will give the greatest hydraulic mean depth. This will appear from the following calculations; Where the segment of a circle is assumed equal to a segment of a parabola, which parabola is equal to one-half of the given circle. The method of finding the length of the curve, area and hydraulic mean depth, will also appear. STRAIGHT-LINED AND CURVILINEAL FIGURES. 2 21 That the parabolic sewer, whose abscissa=0,806lp/a- and ordinate= V aV 1,075 (w~here a given area), is better than either the circular or egg-shaped sewer, will appear from the following table and calculations. 135. TABLE, SHOWING THlE HYDRAULIC MEAN DEPTH IN SEGMENTS OF PARABOLIC AND CIRCULAR SEWERS, EACH. HAYING THE SAME *SECTIONAL AREA. THE DIMENSIONS OF THiE PRIMITIVE PARABOLA AND CILRCULAR ARE Ar TILE TOP. PARABOLA, Latus Rectum 2,7. SEMICIRCLE, Diameter 4 feet. 2 _ 2.0 w)4. 0. 1 1( 1.98.1-1 6.9 6.4 0.9 1.9 '2'Ni 5. 78)8 6.8'070 90 1.8) 1.99515.738 6.002 0.965c 1.8 -,)990599 )K2,) 06.0( (Y)87 1. 7 51.9 84 5. _292 5. 781 0.912 11. 2.1461~ 4.8-5.5.81.11 0.839 1.64 1196714.85-5 -5.566 0.873 1.6) 2.079 4.435 5.56910.79 1.53;i.94414.430,5 5~-.334 0.8311 L.) 2.013 4.02) 5.31110.758 1.43 l.17 4.026 5.121 0.78 1.4 1.944 3.6")9;5.0561071t) L 3') 1881 3.629 4.900 0.741 1.3 1.874 3.248 4 802fl0676 1.22 1.842 3.248 4.680 0.694 1. 2 1.80)0 2.88)) 4543 0.6.34 L12121.796 2.880 4.462 0(145,.1 1.723 2.5,-)'7 4 '281A-() 9 1.0211.744 2.527 41.2-24 0.598 1)) 1.643Ki 2.91 4_01()6I(. 4,5 0W9211.68312.191 4.00)1 0.547 09 1559 1.871 '370. 49 0 W8311.62211.871 3-'.784 0.4 94 1 0.8 1.470 1.5)38 23.472 0.451 0. 73. 5441 1. 5)8 3.53)) 0. 444 0.7 1. f37 5 1.283 3 19)) 0.402 0)3641.466 1.283 3).2(91 0.889 0)3 1. 2 73 1.)1.8 2.898iO.351 0.54 l.1.367 1.018 3.010 ).)388 ). 5 1.1.62io.775 21.950.99 0.45~1.264 0.775 2.737 0.283' 0.4 1.089j0.5,59 2 '2740.0246) Because the hydrostatic or scouring force in a sewer is found by multiplying the sectional area by the depth and 621 pounds, and that the depths of the segnients of a parabola nre greater than in the segments of the semicircle, each being equal to the same given area; therefore, from inspecting the above table, it will appear tha~t the parabolic sewers have greater hydrostatic depths nand pressure than the circular segments. It also appears that in the lower half depth of the semicircle, and in all other depths lower than half the radius, the hydraulic mean depth is greater than in circular segments of the same areas. Calculation of the foregoing Table. Example. Required, the ordinate at abscissa 1,2 of the given parabola, whose abscissa ==2,019, and ordinate 2,335, and latus rectum 2,7. Rule,: Multiply the latus rectum by the abscissa of the parabolic segment. The square root of product 'will be the required ordinate. Or by logarithms, let log of 2, 7 -0,41364 log of the given abscissa -0,041 393 log of the product of abscissa and latus rectum 0,472757 which divide by 2 will give the log of the square root of the product 0,2363078 the natural number corresponding to which gives the ordinate 1,800 IC 22 AREAS AND PROPERTIES OF To Find the Area. The given ordinate - 1,800. The chord or double ordinate - 3,600. abscissa 1,2 4,32 This product multiplied by 2 and divided by 3, gives the area - 2,88. That is, two-thirds of the product of the abscissa and double the ordinate is equal to the required area. To Find the Perimeter of the given Segment. 136. Rule. To one and one-third times the square of the abscissa, add the square of the given ordinate. The square root of the sum, if multiplied by 2, will give the perimeter. In the example, abscissa - 1,2, and ordinate - 1,80. Abscissa squared = (1,2)2 = 1,44 one-third of (1,2)2 = 48 square of the ordinate = (1,8)2 = 3,24 5,16 the square root of 5,16 - 2,2715 2 Required perimeter 4,5430 To Find the Ilydraulic Mean Depth. Rule. Divide the area of the segment by the wetted perimeter. The quotient will be the hydraulic mean depth. 2,880 That is, 458 = hydraulic mean depth - 0,634. 4,548 To Find the Height and Chord of a Circular Segment. 137. To find the chord corresponding to a circular segment whose area = that of the parabolic segment (see segment No. 10 in table), where area a a = 1,880,- = tabular segment area, opposite tab. ver. sine. This d2 multiplied by the diameter will be the height of the segment. Here we have a = 2,880. a d2 - 4 X 4 - 16, and the quotient - = 0,18000. d2 Tab. area segment =,18000. Corresponding ver. sine =,280 (by TAB. VII). 4 therefore, 1,120 = depth or abscessa. To Find the Chord or Ordinate to this depth. 138. Diameter of the circle, 4 feet, given height or depth of wet segment = a = 1,12 remaining or dry segment = b - 2,88 1,12 product = a b 3,2256 the square root of this product will (Euclid III, prop. 35) give the ordinate or half chord = 1,796, and the chord of the segment.: — c - 3,592. STRAIGHT-LINED AND CURVILINEAL FIGURES. 23 To Find the Perimeter. 139. We have the height of the segment = a = 1,12, the chord or double ordinate, c = 3,592. Then by TAB. VI, find the tabular length corresponding to the quotient in column tabular length. The tabular number thus found, multiplied by the chord, will be the required length. 3,592) 1,12 quotient,,3118, whose tabular length 1,2419, which multiplied by the chord c = 3,592, will give the product = the required perimeter = 4,461, and the perimeter divided into the given area will give the hydraulic mean depth, 0,645. EGG-SHAPED SEWER. 140. The egg-shaped sewer, in appearance, resembles a parabola, and is that now generally adopted in the new sewerage of London and Paris since 1857. Let A B (fig 41) =width of sewer at the top. Bisect A B in 0, erect the perpendicular O C = A B. On A B describe the circle E A D B, and on D C describe the circle D I C K. Produce A B both ways. Making A G = B H =- the total height C E, join G F and H F. Produce them to the points I and K. From G as centre describe the arc A I, and from H as centre describe the arc B K. Let A B = 4 feet, then D C = 2, and C E = 6, and O C = 4, and OF = 3. Also H B = A G I = H K =6, and H A= B G 2.'. H G = 8. Because G Q A G.. GQ2 -G 02 - OQ2. In this example, Q G2 - 62 - 36, O G2 42 16. The square root of 20 _ 4,472 =- 0 Q. To Find the < 0 G Q by Trigonometry. 4,472 divided by radius 6 = 0,745333, which is the natural cosine of 41~ 49/ 2", and O F divided by G O = 0,75 = nat. tangent of < A G F = 36~ 52'. (By sec. 69) d2 X n X,00218175 - 122 X 36~, 86667 X,00218175 = area G A I = 11,5825. Here d2 - diameter = 12, and n = 36~ 52z' - 36,86967. Area of the A G O F - 2 X 3 6 Sector G A I - G 0 F = 5,5825. To Find the Sector I F C. Because the angle G 0 F 90~, and the angle 0 G F 36~ 52', their sum 126~ 52' taken from 180~ will give < G F 0 = 53~ 8'; but Euclid I, prop. 15, the angle G F 0 < I F C = 53~ 8', and F C = radius = 1, consequently d2 = 4; And by section 69, d2 X n X,00218175 - 0,4636, etc.; Or by TAB. V, length of the,arc corresponding to the angle I F C 53~ 8/ = 53~, 13333 = 0,92'7351. This multiplied by i = the radius, will give the area I C F = 0,4636, etc. 24 AREAS AND PROPERTIES OF And from above we have the area A I G = 11,5825. The sum of these two areas = area of the figure G 0 A I C F G = 12,0461 From this area deduct the A G 0 F found above, = 6 There remains the area of half the sewer below the spring of the arch, 6,0461 This multiplied by 2 gives the area of sewer to the spring of the arch; that is, area of A 0 B K C I = 12,0922 Length of the curve A I may be found by TAB. V. < 0 G F = 36~ 52/ = 360, 86, length of arc to radius 1 =,653444 radius G Q = 6 arc A I = 3,920664 arc I C from above = 0,927351 length of arc A I C = 4,848 2 do. A I C K B = perimeter = 9,696 This perimeter, 9,696, if divided into the area, 12,0922, will give the hydraulic mean depth of the sewer below the spring of the arch = 1,247 feet. 141. To Find the Diameter of a Cirdle whose Semicircular Area = 12,0922. 12,0922 2 Area of required circle = 24,1844 This divided by 0,7854, will give the square of the required diameter = 30,792462, square root = diameter = 5,550. Half of the diameter multiplied by 3,1416 = perimeter of semicircle = 8,718. This perimeter divided into the area 12,0922 = hydraulic mean depth 1,387. Let us Find a Parabolic Sewer equal in area to 12,0922. 142. Abscissa = 0,806 /a = 0,806 V/12,0'92 =2,803. By sec. 133. V/a 3,4774 Ordinate = — _ = 3,2344. 1,075 1,075 Double ordinate, 6,4688. Area corresponding to double ordinate 6,4688, and abscissa 2,803 = 12,088. To Find Perimeter of this Parabolic Sewer. 143. Abscissa squared = (2,803)2 = 7,856809 one-third of do. = 2,618936 Ordinate squared = (3,2344)2 = 10,461343 20,937098 The square root of the sum = 4,575 2 Perimeter of wetted parabola = 9,15 This perimeter divided into 12,088, gives H. M. D. = 1,321. Now we have the following summary: ! i STRAIGHT-LINED AND CURVILINEAL FIGURES. 25 Circular Parabolic Egg-shaped Sewer. Sewer. sewer. Area filled in sewer, 12,0922 12,088 12,0922 Depth of water in sewer, 2,775 2,803 4,000 Hydraulic mean depth of part filled, 1,387 1,321 1,247 Hydrostatic pressure on bottom of sewer depth of water X by 621- lbs. X sectional area, 2097 lbs. 2271 lbs. 3241 lbs. hence it appears that the scouring force, or hydrostatic pressure, is greater in a parabola than in the semicircle, and greater in the egg-shaped sewer than in the parabolic sewer. And that the hydraulic mean depth, and consequently the discharge, is greater in the parabolic than in the egg-shaped, and greater in the circular than in the parabolic. The great depths required by the egg-shaped, renders them impracticable excepting where sufficient inclinations can be obtained. The parabolic segments will give greater hydraulic mean depths than circular or egg-shaped segments, and are as easily constructed as the eggshaped sewers; therefore, ought to be preferred. Having so far discussed curvilineal water courses or sewers, we will now proceed to the discussion of RECTILINEAL WATER COURSES. 144. Let the nature of the soil require that the best slope to be given to the sides be that which makes the < D C A = Q. Let the required area of the section A B D C he a, and h the given depth, to find the width A B = x. Let x = A B = E F, and having the < D C A, we have its compliment < C A E. By Trigonometry, h X cotangent Q = C E = F D, and h X cot. Q X h = h2 X cot. Q = area of the triangles C E A + A B F D, and h X x = area of the figure A E F B; therefore, h x + h2 cot. Q =a, x +- h cot.Q= h, a x -= -- h cot. Q. A general formula. (1.) h a Or, x = -- h tan. comp. Q. (2.) h When the < C A E = 0 then A C, coincides with A E, and - h cot. Q vanishes; then a x = - = value for rectangular figures, where h the depth is limited, as h in the case of canals; but if it were required to enclose the area a in a rectangular figure, open at top, so that the surface will be a minimum. 26 AREAS AND PROPERTIES OF a Here we have A B= x, and A C = B D = -... perimeter C A B D x 2a x2 -+ 2a x + -= --; x x x2 + 2 a that is, y =, and by differentiating this expression, x 2x2dx-x2dx-2 a d x x2 d x - 2adx dy= - - x2 X2 dy x2-2 a __= l = O, d x X2 X 2 a = 0, x = 1/2 a = A B, and = A C = =. Multiply this by 1/2; V2/. 1/2 2 2 then = -. 1/ = / _ =- /2 a — A C. But /2 a = A B. Consequently, A B = twice A C, as stated in sec. 19. Having determined the natural slope from observing that of the adjacent hills-and if no such hills are near, it is to be determined from the nature of the soil,Let A C = required slope, making angle n degrees with the perpendicular A E; then C E = tangent of angle n to radius A E. Let s = secant of the angle C A E; then A C = secant to radius A E and angle n degrees. See fig. 42. Let x == height of the required section, and a == area of the required section C A B D, to find the height x and base A B, n x2 = area of the two triangles A C E + B F D, because C E = n x, and A E x,.. n x2 double area of triangle A C E. Now, we have a - n x2 = area of the rectangle A B E F.. a - n x2 = A B. But s x= A C,and 2 s x = C A +BD; a - n x2 therefore, -- 2 s x = perimeter C A B D = a minimum; a- n x2 +2sx 2 s x2 - n x2 + a x2. (2 s -n) + a t. e., - = __ '' x x x and by differentiating the last expression, 4 s x2d- 2 nx2 d x - nx2 dx a d x we have d y -- dy and = 2 s x2-nx2- a = o, x and x2 = — 2 s -~n a 8 and x = (- ) = A E = height, or required depth. (3.) 2s - n When there is no slope, A C coincides with A E, and S = 1, and n = o; then for rectangular conduits x = ( ) (4.) (2 STRAIGIIT-LINED AND CURVILINEAL FIGURES. 27 Example. What dimensions must be given to the transverse profile (or section) of a canal, whose banks are to have 40~ slope, and which is to conduct a quantity of water Q, of 75 cubic feet, with a mean velocity of 3 feet per minute?- Weisbach's Mechanics, vol. 1, p. 444. Here we have the < D C A = 40~, consequently < C A E = 50~, and the sectional area of figure C A B ) = a = 25 feet. a By formula 3, x = (- ) where s = secant of 50~ = 1,555724, s -n and n = tangent of 50~, 1,191754. 2 s = 3.111448 n 1,191754 1.919694 divided into 25, gives 13,022868, the square root of which = x = depth A E = 3,6087 = 3,609 nearly, and tangent = 1,191754 if multiplied by 3,609 X 3,609 = area of the triangles A C E + B F D = 15,522309, which taken from 25, will leave the rectangle A E F B = 9,477691 This divided by the height, 3,609, gives A B = 2,626 But 3,609 X 1,191754 = C E = 4,301 and F D, 4,301 Upper breadth C D = 11,228 Bottom A B 2,6260 1,555724 X 3,609 = A C = 5,6146 and B D= 5,6146 p = perimeter = A C + A B + B D = 13,8552 which is the least surface with the given slopes, and containing the given area = 25 feet. The results here found are the same as those found by Weisbach's formula, which appears to me to be too abstruse. 145. From the above, the following equations are deduced: a ~ A E = B F = — ) '2s - n a a s2 a A C = B F =( -- ) s... —).:2s-n 2s n a -- n x' V/a r/(2 s - n) A B — X -7... — = (a- n x2) 1 /V2 s n Va 146. Hence it appears that the best form of Conduits are as follows: Circular, when it is always filled. Rectangular, that whose depth is half its breadth. Triangular, when the triangle is equilateral. Parabolic, when the depth of water is variable and conduit covered, and in accordance with section 133. Rectilincal, when opened, and in accordance with section 144. For the velocity and discharge through conduits, also for the laying out of canals, and calculating the necessary excavation and embankment, see Sequel. 28 28 ~~~~AREAS AND PROPERTIES OF 147. TABLE, SHOWING THE VALUE OF THlE HEIGHT A E =x in the equation x = -—,where a =area of the given section, hav2 s -it ing given slopes, and such that the area a is inclosed by tihe least surface or perimeter in contact. s8= secant andna =- tarygent of the an~gle D B F, or complement of the angle of repose (see fig. 42). Ratio of base B G Angle of repose1 AngleC Q Yalue of X __ to perpendicular B F. 'or angle Di B G., oi- < B B3 F orAI Perpendicular 0 to 1 1 to 1 1,5 to 1 21 to 1 2, 5 to 1 3 to 1 3,5 to 1 4 tol1 5 tolI Perfectly dry soil, Moist soil, Very dry sand, I Rtye seed, Fine shot, Finest shot, 900 00'1 450 00,' 9~ 20 Al' 260 '34k 210 48' 1 80 26'G 150 56'1 140 0_2' 110 19' 380 49/1 420 43/ 300 58' 3t)0 00' 2950 00' 220 30' 000 00'1 4,50 00' 660 49/ 60 36 680 1 2', 810 34'1 740 04' 750 58' 480 41' 5010 II/ 470 171' 600 00' 650 00' 670 30' 1,828427 -2 7 4 528 7 a X x(6, 8 9-228 8 a 1,891684 a 1,947647 - a 2, 220497 a X _ - 2,267049 a 2,,587897 2,8120)38 Slopes for the sides of canals, in very compact soils, have II base to 1 perpendicular; but generally they arc 2 base to I perpendicular, as in the Illinois and Michigan Canal. Sea banks, along sea shores, have slopes whose base is 5 to 1 perpendicular for the height of ordinary tides; base 4 to 1 perpendicular for that part between ordinary and spring tides; and slopes 3 to 1 for the upper part. By this means tile surface next the sea is made hollow, so as to offer the least resistance to the waves of the sea. Tile lower part is faced with gravel. Tile centre, or that part between ordinary land spring tides, is faced with stone. The upper part, called tile swash bank, is faced witil clay, having to sustain but that part of the waves which dashes over the spring tide line. (See Ens nbanknienis.) PLANE TRIGONOMETRY. RIGHT ANGLED TRIANGLES. 148. Let the given angle be C A B/ (fig. 9). Let A B = c, C B = a, and A C = c, be the given parts in the right angled triangle A C B. 149. Radius =- A B/ A C. 150. Sine < CA B'= C B = cosine of the complement = cos. <A C D. 151. Cos. <CA B=AB= sine of the comp. of < C A B sine <A C B. 152. Tangent < C A B' = B T = cot. of its complement = cot. < HAC. 153. Cotangent C A B' = H K = tan. of its complement = tan. < H A C. 154. Secant < C A B' = A T = cosec. of its complement = cosec. < HA C. 155. Cosecant < C A B= A K = sec. of its comp. = sec < C A H. 156. Versed sine < C A B = B B'. 157. Coversed sine < C A B/ = H I = versed sine of its complement. 158. Chord < C A B C B' = twice the sine of j the < C A B. 158a. Complement of an angle is what it wants of being 90~. 158b. Supplement of an angle is what it wants of being 180~. 158c. Arithmetical complement is the log. sine of an angle taken from 10, or begin at left hand and subtract from 9 each figure but the last, which take from 10. 159. Let A C B (fig. 9) represent a right angled triangle, in which A B c, B C = a, and A C = b, and A, B, C, the given angles. a 160. Sine <A =b 161. Cos. < A= 162. Tan.< A - 163. Sine C = b b a 164. Cos. C =- - b 165. Tan. C-= 166. Sec. A -- a And the sides can be found as follows: 167. a c tan. A. 168. a b sine A. d w; ~~-:~Si I: 80 PLANE TRIGONOMETRY. 169. a= b cos. C. c a a 170. b - c sec. A= a sec. < C= — cos. A cos. C sine A b 171. c - b cos. A - b sine C = a tan. C -- sec. A Examples. Let A C = the hypothenuse = 480, and the angle at A 63~ 8', to find the base A B and perpendicular A C. By sec. 168, natural sine of < A,8000 = departure of 53~ 8' AC =480 B C =a= 384 = product. Or by logarithms: Log. sine of < A (53~ 8') = 8,9031084 Log. of b = log. of 480 2,6812412 B C = 384 = 2,5843496 And by having the < A = 63~ 8.. the < C = 36~ 52/. Nat. sine of 36~ 52' =,6000 Otherwise, A C - 480 360 52/ Log. sine- 9,7781186 A B = 280 = product. Log. of 480 = 2,6812412 288 nearly 2,4593698 or 287,978 = A B. 171a. Let the side B C = a = 384, and the angle C = 36~ 52' be given to find c, b, and the angle A. 900 - 36~ 52/ =< A = 53~ 8/, and a tan. C = c, that is 384 X 0,7499 = A B = 288 nearly. 171b. Let the sides be given to find the angles A and C. a 884 Sine A = - (per sec. 160) - = 0,8000 - 63~ 8' nearly. b 480 b 480 Sec. A - - (per sec. 166) =- = 1,6666 = 63~ 8' nearly. o 288 c 288 Cos. A = - (per sec. 161) - 0,6000 = 568 8' nearly. b 480 a 384 Tan. A =- (per sec. 162) =-8 1,3888 = 63~ 8' nearly. In like manner the angle C may be found. These examples are sufficient to enable the surveyor to find the sides and angles. The calculations may be performed by logarithms as follows: Log. a =, etc. Log. b = -, etc. Sine of angle A Log. sine of < A. PLANE TRIGONOXETRY. S1 OBLIQUE ANGLED TRIANGLES. 171c. The following are the algebraic values for the four quadrants: From 0to 90. From 90 to 180. From 180 to 270. From 270 to8860 Sine, + + Cosine, + — + Tangent, + -+ Cotangent, + -+Secant, + — + Cosecant, + + — Versed sine, + ~ + + 0" 900 180" 2700 Sine, 0 1 0 - 1 Cosine, 1 0 -1I 0 NoeHretesml Tangent, 0 in! 0 inf NoeHretesml Cotangent, inf 0 inf 0 inf signifies a quantity which Secant, 1 inf - 1 inf is infinitely great. Cosecant, inf I in! - 1 Versed sine, 0 1 2 1 172. a2 =b2 +ces- 2b c. fos. A. 173. b2=a2 + c2 - 2 a ccos. B. 174. c2=a2 + b2- 2 ab -cos. C. Now, from 172, 173, and 174, we find the cosines of the angles A, B, and C.C b2 ~ C2 - a,2 175. Cos.A= 2b b a 176. Cos. B 0 = -b 2 ac A o B b2 + a2 - c2 177. Cos. C= 2 ba - And by substituting a j the sum of the three sides = (a + b + c), we find-' 2 178. SineA=-Vs.s(s-a).(s-b).(s-c) be 179. SnB-V.sa.sb.s-o 180. SineC=-vb's.(as-a) (s -b) (s -c) 181. Cos.___ 2' ba 18. B ssb) 18.Colu.-== 2 so 183. Cos.0 s.s )Also, we find in terms of the tangent-. 2 a 82 32 ~~~~PLANK TRIGONOMIThY. A (s - (s-c 184. 2Tan. -) a 2 ~ ~ *(s-ca) 18. 2 (sb) 186. Tan. — ~ a.( )We can find in terms of sine2 ' s (s- c) 187. Sinei —K b)(sc 2 ~ bc 188. Sine (\K- a)-(5 -b) 2 abC 190. Radius of the inscribed circle in a triangle- r i/s(s,'.(s -b) -(- )which is the same as. given in sec. 48. 191. Radius of the circumscribing circle =R= 4{s(s-a.(-b).(192. By assuming D = the distance between the centres of the inscribed and circumscribed circles, we have D2 B 2 - 2 R r, and D= (R2 - 2 RriI 193. Area of a quadrilateral figure inscribed in a circle is equal to (s - a). (s -b). (s -c) (s - d) } -'where s is equal to the sum of the sides. Sides are to one another as the Sines of their Opposite Angles. 194. a: c: sine A: sine C. 195. a b::sine A sine B. 196. b: c: sine B: sine C. And by alternanclo197. a: sine A: c: sine C. 198. a sine A::bsine B. 199. b: sine B: c: sine C. And by invertendo-. 200. Sine A a: sine C c. 201. Sine A a: sine B: b. 202. Sine B b:sine C c. Having two Sides and their contained Angle given to Find the other Side and A4 gles. 203. Rule. The sum of the two sides is to their difference, as the tangent of half the sum of the opposite angles is; to the tangent of half their difference; i. e., a-fb: a -b: tan. ~(A+B): tan. j(A - B1). PLANX TRIGONOMETRY. 88 Here a is assumed greater than b.. the < A is greater than B.-E. I., 19. (See fig. 12.) Now, having half the difference and half the sum, we can find the greater and lesser angles of those required for half the sum, added to haltf the difference =: greater <, and half the difference taken from the half sum =lesser <. When the Three Side.s of the Triangle are given to Find the Angles.. 205. Rule. As twice the base or longest side A C = b is to the other two sides, so is the difference of these two sides to the distance of a perpendicular from the middle of the base; that is, 2 b: a + c:: a - c: D E. Here B D is the perpendicular, and B E the line bisecting the base; because B C a is greater than A B =- c, C D is greater than A D; because < A is greater than < C, the < A B D is less than K C B D; therefore, the area of the A, C D B is greater than A A D B; consequently, the base C D is greater than A D. Let D E = d; new the A A B C is divided into two right angled triangles A B D and C B D, having two sides and an angle in each given to find the other angles. b b -2 dC In the A A B D is given A D = — d = ___ 2 2 b b +2 d E And A B = c, and B C = a, and C D =- + d = -___ 2 2 D b-2 d By sec. 161, cos. A =And in like manner, 2 c A 0 Cos. C =- b~2d And by Euclid I. 32, angle B is found. Cosine A may be found by sec. 176-, and cosine C by sec. 1717. 2906. Example. Let the < A = 400 (fig. 5), < B - 500, and the side B C equal to 64 chains, to find the side A C. By sec. 194, sine 400' 64 chains sine 500:A C. Or thus: Nat. sine 50' 0,7694 Log. sine 60'= 9,8842-54 Nat. number 64 Log. 64 = 1,806180 Product =49,02656 Sum 11,690434 Nat. sine 400 0,64279 Log. sine 40' =9.882356 Quotient, 76,272 = A C. Dif. 1,882866 Nat. No. = 76,272 chains A C. In like manner, by the same section, A B may be found, because angles A and Btogether =900. < C = 900o 207. Ia the A A BC (fig. 12), let the angle A 400, angie B = 60o1 consequently, < C = 80. Let B C = 64, to find the side A C. Nat. sine 600 = 0.866'2 Or thus: Or thus: Nat. number 64 Log. sine = 9,937581 Log. sine =9,987531 Product,= 65458 Log. = 1.806180 Log. 1,80618D Nat. sine 40' 0,64279 Sum = 11,743711 Arcm 0118 Quotent 6,27 =.sdeAC Log. sine = 9,808068 Sum =1 983648 Quotiet 86,7Di l'. =eA — =86,W2 Diff. = ~1.935648 C Nat. No. =86,227=A C A B may be found by isec. 200. 84 PLANI TRIGONOMITRY. Note. Here ar. comp. signifies arithmetical complement. It is log. sine 400 taken from 10 (seevec. 158 c), or it is the cosecant of 400. Given Two Sides and the Contained Angle to Find the Other Parts. 208. Example. Let A C = 120, B C = 80, and < A C B = 400, to find the other side, A B, and angles A and B. By sec. 203, 120 + 80: 120 - 80:: tan. 700: tangent of the half difference between the angles B and A. i, e., 200: 40:: tan. 700: tan. j dif. B - A. i. e., 6: 1:: 2,747477: 0,549495 = 280 47g..-. 700 + 280 47'-=98047= < B. And 700 - 280 470 = 410 18' = < A. By sec. 194, sine 410 13'1: 80:: sine 40: A B. Nat. sine 400 0,64279 Or thus: Or thus: Nat. number 80 = 80 Log, sine 9,808068 Log. sine 400 9,808068 Product 61,42320 Log. 1,903090 Log. 80 1,903090 Nat. sine 410 17' 0,66891 Sum 11,711168 Ar. comp. 400131= 0,181176 Quotient, 78,043 = A B. Log. sine 9,818825 1,892333 Dif. 1,892333 78,043 = A B. = 78,048 = AB. Given the Three Sides to Find the Angles. 209. Example. A B = b = 142,02, A C = c = 70, and B C = a 104, to find the angles at A, B and C. (See fig. 5.) By sec. 205, 284,04: 174:: 84: D B = 20,828 But A D=DB B=71,010 Therefore, A E = 91,838 = cos. < A X A C. And BE= 0,182 =cos. < B X B C. Consequently 60,182 -. 70 = 0,716885 = cos. < A = 440 12' and 91,888 —. 104 = 0,88306 = cos. < C = 270 69/ Having the angles A and C, the third angle at B is given. Or thus bysec.175: C 2= (142,02)2 = 20169,6804 As = (104)2 10816, D sum, 80986,6804 B a2 -- (70)2 4900, A,2 b a = 29540) 26085,6804 quotient = 0,88806 (Divisor.) (Dividend.) Whlch is the cosine of the < C - 270 591 210. Or thus by sec. 183: HEIGHTS AND DISTANCES. 86 b =142,02, b =104, and a =70. a = 104, c- 70, 2)316,02 = sum. s = 158,01 = half sum, log. = 2,1986846 s - c = 88,01, log. = 1,9445320 a = 104, log. = 2,0170333, ar. comp. 7,9829667 b = 142,02, log. 2,1523495, ar. comp. 7,8476505 2)19,9738338 Cos. < C = 13~ 59' 36" = log. sine 9,986169.the angle A = 27~ 59' 12/. In like manner, cos. i < B may be found by sec. 176. The same results could be obtained by using the formulas in sections 184 and 188. HEIGHTS AND DISTANCES. 211. In chaining, the surveyor is supposed to have his chain daily corrected, or compared with his standard. He uses ten pointed arrows or pins of iron or steel, one of which has a ring two inches in diameter, on which the other nine are carried; the other nine have rings one inch in diameter. The rings ought to be soldered, and have red cloth sewed on them. He carries a small axe, and plumb bob and line, the bob having a long steel point, to be either stationary in the bob or screwed into it, thus enabling the surveyor to carry the point without danger of cutting his pocket. A plumb bob and line is indispensable in erecting poles and pickets; and in chaining over irregular surfaces, etc., he is to have steel shod poles, painted white and red, marked in feet from the top; flags in the shape of a right angled triangle, the longest side under; some flags red, and some white. For long distances, one of each to be put on the pole. For ranging lines, fine pickets or white washed laths are to be used set.up so that the tops of them will be in a line. Where a pole has to be used as an observing station, and to which other lines are to be referred, it would be advisable to have it white-washed, and a white board nailed near the top of it. His field books will be numbered and paged, and have a copious index in each. In his office he will keep a general index to his surveys, and also an index to the various maps recorded in the records of the county in which he from time to time may practice. In his field book he keeps a movable blotting sheet, made by doubling a thin sheet of drawing paper, on which he pastes a sheet of blotting paper, by having a piece of tape, a little more than twice the length of the field book. The sheet may be moved from folio to folio. One end of the tape is made fast at the top edge and back, brought round on the outside, to be thence placed over the blotting sheet to where it is brought twice over the tape on the outside, leaving about one inch projecting over the book. He has offset poles,one of ten links, decimally divided, and another of ten or six feet, similarly divided, mounted with copper or brass on the ends. One handle of the ,, _,.: I, - -.,, - -, - - 1 T,. " 86 HEIGHTS AND DISTANOE8. chain to have a large iroA link, with a nut and screw, so as to adjust the chain when the correction is less than a ring. By this contrivance the chain can be kept of the exact length. Some surveyors keep their chains to the exact standard, but most of them allow the thickness of an arrow, to counteract any deflections-that is allowing one-tenth of an inch to every chain. In surveying in towns and cities, where the greatest accuracy is required, the best plan is to have the chain of the exact length, and the fore chain bearer to draw a line at the end of the chain, and mark the place of the point at the middle of the handle. Turn the arrow so as to make a small hole, if in a plank or stone; if in the earth, hold the handle vertically, so as to make the mark on the handle come to the side of the arrow next the hind chainman. Where permanent buildings are to be located, surveyors use a fifteen feet pole, made of Norway pine, and decimally marked. This, with the plumb line, will insure the greatest accuracy. In locating buildings, the surveyor gives lines five feet from the water table, so as to enable cellars or foundations to be dug. When the water table is laid, the surveyor ought to go on the ground and measure the distance from the water table and face of the walls from the true side or sides of the street or streets and sides of the lot. In making out his plan and report of the survey, he ought to state the date, chiiinmen, the builder and owner of the lot and building, at what point he began to measure, and his data for making the survey. A copy of this he files in his office, in a folio volume of records, and another is given to him for whom the survey has been made, on the receipt of his fees. If any of his base lines used in measuring said land pass near any permanent object, he makes a note of it in his report. In chaining in an open country, he leaves a mark, dug at every ten chains, made in the form of an isoceles triangle, the vertex indicating the end of the ten chains, or 1)00 feet or links. Out of the base cut a small piece about two by four inches, to show that it is a ten chain mark, and to distinguish it from other marks made near crossings of ditches, drains, fences, or stone walls. Some of the best surveyors I have met in the counties of Norfolk, Suffolk and Essex, in England, amongst whom may rank Messrs. Parks, Molton and Eacies, had small pieces of wood about six inches long, split on the top, into which a folded piece of paper, containing the line and distance, was inserted. This was put at the pickets. or triangular marks made in the ground, and served to show the surveyor where other lines closed. In woodland, drive a numbered stake at every ten chains. In open cofntry, note buildings, springs, water courses, and every remarkable object, and take minute measurements to such as may come within one hundred feet of any boundary lines, forfuture reference. In laying out towns and villages, stones 4 feet long and 6 inches square, at least, ought to be put at every two blocks, either in the centre of the streets, or at convenient distances from the corners, such as five feet; * the latter would be best, as paving, sewerage, gasworks or public travel would not interfere with the surveyor's future operations. All the angles from stone to stone ought to be given, and these angles referred, if possible, to some permanent object, such as the corner of a church tower, steeple, or brick building; or, as in Canada, refer them to the true meridian. HEIGH1TS AND DISTANCES. u This latter, although troublesome, is the most infallible method of perpetuating these angles. When the hole is dug for the stone, the position of its centre is determined by means of a plumb line; a small hole is then made, into which broken delf or slags of iron or charcoal is put, and the same noted in the surveyor's report or proces verbal. These precautions will forever prevent 99-100th parts of the litigations that now take place in our courts of justice. The office of a surveyor being as responsible as it is honorable, he ought to spare no pains or expense in acquiring a theoretical and practical knowledge of his profession, and to be supplied with good instruments. Where a difference exists between them, it ought to be their duty to make a joint survey, and thus prevent a lawsuit This appears indispensable when we consider the difficulty of finding a jury who is capable of forming a correct judgment in disputed surveys. When in woodland, we mark trees near the line, blazing front, rear, and the side next the line, and cutting in the side next the line, a-notch for every foot that the line is distant from the tree, which notches ought to be lower than where the trees will be cut, so as to leave the mark for a longer time, to be found in the stumps. State the kind of tree marked, its diameter, and distance on the line. Where a post is set in woodland, take three or four bearing trees, which mark with a large blaze, facing the post. Describe the kind of each tree, its diameter, bearing, and distance from the post. For further, see United States surveying. In order to make an accurate survey, the surveyor ought to have a good transit ifstrument or theodolite, as the compass cannot be relied on, owing to the constant changing of the position of the needle. By a good theodolite, the surveyor is enabled to find the true time, latitude, longitude, and variation of any line from the true meridian. If packed in a box, covered with leather or oiled canvas, it can be carried with as little inconvenience as a soldier carries his knapsack,-only taking care to have the box so marked as to know which side to be uppermost. The box ought to have a space large enough to hold two small bull's eye lamps and a square tin oil can; this space is about 9 inches by 3. Also, a place for an oil cap covering for the instrument in time of rain or dust; two tin tubes, half an inch in diameter and five inches long; with some white lead to clean the tubes occasionally. These tubes are used when taking the bearing of a line at night, from the true meridian. One of the tubes is put on the top of a small picket, or part of a small tree: this we call the tell-tale. The other is made fast to the end of a pole or picket, and set in direction of the required line, or line in direction of the pole star when on the meridian, or at its greatest eastern or western elongation. Some spider's web on a thick wire, bent in the shape of a horse shoe, about six inches long and two and a half inches wide, having the tops bent about a third of an inch, and a lump of lead or coil of wire on the middle of the circular part. This put in a small box, with a slide a fourth of an inch over the wire, so as to keep the web clean. Have a small phial full of shellac varnish, to put in cross hairs when required. In order to have the instrument in good adjustment, have about two pounds of quicksilver, which put in a trough or on a plate, if you have no artificial horizon. In order to have the telescope move in a vertical position, place the instrument, leveled, sb that you can see some remarkable point above the horizon, and reflected in e *~~~~~~~~~~~~~.**-*. l - ^. i.; x > as HEIGHTS AND DISTANCES. the mirror or quicksilver. Adjust the telescope so as to move vertically through these points. Mark on the lid of the box the index error, if any, with the sign —, if the error is to be added, and -, if it is to be subtracted. On the last page of each field book pencil the following questions, which read before leaving home: Have I the true time,-necessary extracts from the Nautical Almanac,-latitude and longitude of where the survey is to be made,-expenses, axes, flags, poles, instrument, tripod, keys, necessary clothing, etc.,-field notes, sketches, and whatsoever I generally carry with me, according to the nature of the survey. It ought to be the duty of one of the chainmen every morning, on sitting to breakfast, to say, "Wind your chronometer, sir." These precautions will prevent many mistakes. The surveyor ought to carry a pocket case filled with the necessary medicines for diarrhoea, dysentery, ague and bilious fever, and some salves and lint for cuts or wounds on the feet; some needles and strong thread, and all things necessary for the toilet; a copy of Simms or Heather on Mathematical Instruments, and McDermott's Manual, and the surveyor is prepared to set out on his expedition. If it so happens that he is to be a few days from home, he ought to have drawing instruments and cartridge paper, on which to make rough outlined maps every night, after which he inks his field notes. He makes no erasures in his report or field notes. When he commits an error, he draws the pen twice over it, and writes the initials of his name under it. This will cause his field book to be deserving of more credit than if it had erasures. The surveyor ought to leave no cause for suspecting him to have acted partially. 212. Let it be required at station A (fig. 12) to C find the < B A C, where the points B and C are at long distances from A. Let the telescope be directed to C, and the limb read 0. Move the telescope to B; let the limb now be supposed to read 20~ +. Direct the whole body with the index at 20 + on C, clamp the under plate and loosen the upper. Bring the A Fig. 12. B telescope again on B, reading 40~ —. Repeat the same operation, bringing the telescope a third time on B, and reading 60~ 23/, which being three 'times the required angle,.-. the < B A C = 20~ 7/ 20//. By this means, with a five inch theodolite, angles can be taken to within twenty or thirty seconds, which is equal to six inches in a mile, if read to twenty seconds. In setting out a range of pickets, one of the cross hairs ought to be made vertical, by bringing it to bear on the corner of a building, on a plumb line suspended from a tree or window. The plumb-bob ought to be in water to prevent vibration. Two corresponding marks may be cut,-one on the Ys and the other on the telescope. These two marks, when together, indicate that the vertical hair is adjusted. Where the surveyor has an artificial horizon or quicksilver, he can, by the reflection of the point of a rod or stake, or any other well defined point, adjust the vertical hair, and then mark the Y and telescope for future operations. 218. All the interior angles of any polygon, together with four right angles, are equal to twice as many right angles as the figure has sides. HEIGHTS AND DISTANCES. 89 Example. Interior angles A, B, C, D, E, F = n~ 4 right angles, 360 Sum - n + 360~ Number of sides = 6. 6 X 2 right angles = 1080~ By subtraction no = 720~ Having the Interior Angles, to Reduce them to Circumferentor Bearings, and thence to Quarter Compass Bearings. 214. Assume any line whose circumferentor bearing is given. Always keep the land on the right as you proceed to determine the bearings. Rule 1. If the angle of the field is greater than 180 degrees, take 180 from it, and add the remainder to the bearing at the foregoing station. The sum, if less than 360 degrees, will be the circumferentor bearing at the present station-that is, the bearing of the next line (forward). But if the sum be more than 360~, take 360 from it, and the remainder will be the present bearing. Rule 2. If the angle of the field be less than 180, take it from 180, and from the bearing at the foregoing station take the remainder, and you will have the bearing at the present station. But if the bearing at the foregoing station be less than the first remainder te this foregoing bearing, add 360, and from the sum subtract the first remainder, and this last remainder will be the present bearing. To Reduce Circumferentor Bearings to Quarter Compass Bearings. Rule 3. If the circumferentor bearings are less than 90, they are that number in the N. W. Quadrant. Rule 4. If the circumferentor bearings are between 90 and 180, take them from 180. The remainder is the degrees in the S. W. Quadrant. Rule 6. If the degrees are between 180 and 270, take 180 therefrom, and the remainder is the degrees in the S. E. Quadrant. Rule 6. If the circumferentor bearing is between 270 and 360, take them from 360, and the remainder is the degrees in the N. E. Quadrant. Rule 7. 360, or 0, is N., 180 is S., 90 is W., and 270 is E. These rules are from Gibson's Surveying, one of the earliest and best works on practical surveying. Why so many editions of his Surveying have been published omitting these rules, plainly shows, that too many of our works on Surveying have been published by persons having but little knowledge of what the practical surveyor actually requires. We will give the same example as that given by Mr. Gibson in the un. abridged Dublin edition, page 269: The following example shows the angles of the field, and method of reduction. The bearing of the first line is given = 262 degrees. 27 40 HEIGHTS AND DISTANCES. Stat'n. Field. Cir. B. Q. C. B. 1 A 159 2 B 200 200 -180 = 20, 262 + 20 282 = N. E. 78 3 C 270270-18090, 282+90=372, 372-360= 12= N.W.12 4 D 80180-80-100,12+360=372,372-100 =272-N.E.88 6 E 98 180 - 98 = 82, 272 - 82 190 S. E. 10 6 F 100 180 - 100 = 80, 190-80 =110 =S.W.70 7 G 230230-180 50, 110 + 0 =160 = S.W. 20 8 H 90 180-90 = 90, 160-90 = 70- N.W.70 9 I 82 180-82 98, (70+ 360-98) =430-98 332 N.E. 28 10 K 191191 -180=11, 332 + 11 =343= N.E. 17 11 L 120 180 -120 60, 343 - 60 = 283 = N.E. 77 Sum, 1620 Add, 360 180 -159 -21, 283 - 21 = 262 = S. E. 82 90 X 11 X 2 = 1980, which proves that the angles of the field have been correctly taken. Also finding 262 to be the same as the bearing first taken by the needle, is another proof of the correctness of the work. 215. Having selected one of the sides as meridian, for example, a line that is the most easterly. This may be called a north and south line; the north, or 360, or zero, being the back station, and 180 the forward station. Let the angles, as you proceed round the land, keeping it on the right, be A, B, C, D, E, and let the line A B be assumed N and S. A = north and B = south. Then the circumferentor bearing of the line A B from station A, is = 180~. If the surveyor begins on the east side of the land, and sets his telescope at zero on the forward station, and then clamps the body, he then turns it on the back station. The reading on the limb will be the interior angle. But if the telescope be first directed to the back station, and then to the forward station, the difference of the readings will be the exterior angle of the field, which taken from 360 will be the interior angle. The circumferentor is numbered like the theodolite, from north to east, thence south-west, etc., to the place of beginning. But the bearings found by the circumferentor are not the same as those found by the ordnance survey method, where any line is assumed as meridian, as A B. ORDNANCE METHOD. 216. The following method is that which has been used on the ordnance survey of Ireland: Assume any line as meridian or base, so as to keep the land to be surveyed on the left as you proceed around the tract to be surveyed. Let the above be the required tract, whose angles are at A, B, C, D, E, F, G, H, I, K and L. In taking the interior angles for to determine the circumferentor bearings, the land is kept on the right; but by this method the land is kept on the left. To determine by this method all the interior angles, we proceed from A to L, L to K, K to I, I to H, H to G, G to F, F to E, E to D, D to C, C to B, and B to A. Let B to A be the first line, and B the first station. Let the magnetic or true bearing of A to B = S. 820 E. HEIGHTS AND DISTANCES. 41 Angle. Let the theodolite at A read on B = 0 0 on L read = 159 A - 159~ Theodolite at L read on A - 159 on forward K, read - 279 L = 120 Theodolite at K, read on L back = 279 read forward on I = 110 K - 191 Theodolite at I, read back on K = 110 read forward on H = 192 I - 82 Theodolite at H, read back on I - 192 read forward on G = 282 H - 90 Theodolite at G, read back on H - 282 read forward on F - 152 G - 230 Theodolite at F, read back on G - 152 read forward on E - 252 F = 100 Theodolite at E, read back on F = 252 read forward on D - 350 E = 98 Theodolite at D, read back on E = 350 read forward on C - 70 D = 80 Theodolite at C, read back on D = 70 read forward on B = 340 C - 270 Theodolite at B, read back on C = 340 read forward on A -= 180 B - 200 When at B, 360 was on station A, and 180 on station B. Now when at A, 180 is on B,-a proof that the traverse has been correctly taken. 217. In traversing by the ordnance method where the survey is extensive, it is necessary to run a check-line, or lines running through the survey, beginning at one station and closing on some opposite one. This will serve in measuring detail, such as fields, houses, etc., and will divide the field into two or more polygons, and enable the surveyor to detect in which part of the survey any error has been committed, and whether in chaining or taking the angles. I consider it unsafe for a surveyor to equate his northings and southings, eastings and westings, where the difference would be one acre in a thousand. When the error is but small, equate or balance in those latitudes and departures which increase the least in one degree. DeBurgh's method-known in America as the Pennsylvania methodis as follows: As the sum of the sides of the polygon is to one of its sides, so is the difference between the northing and southing to the correction to be made in that line. Halt the difference to be applied to each side; as, for example, Let sum of the sides = 24000 feet, and one of them = 000 feet, whose bearing is N. 40~ E. And that the northings = 56,20 equated 56,30 And sum of the southings = 26,40 equated 66,80 dif. 20 and half dif. - 10 As 24000: 600:: 0,10: cor. = 0,0025, correction to be added, because the northings is less than the southings. j - 218. TABLE. To Change Degrees taken by the Circumferentor to those of the Quartered Compass, and the Contrary. Degrees. Degrees. Degrees. Degrees. Degrees. Degrees. Ci Q. ir Q ir. Q. C. C ir. Q. C. C. Cir Q. C. Cir. Q. C. 36C 1 2 8 4 6 6 7 8 9 10 11 12 13 14 16 16 17 18 19 20 21 22 28 24 26 26 27 28 29 38 81 32 83 84 39 36 86 87 38 89 4( 41 42 43 44 46 46 47 48 49 6( 61 62 6E 64 56 6( 56 65 6S 6( North. N. W. 1 2 3 4 6 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 N.W. 30 81 32 38 84 85 86 37 88 39 40 41 42 43 44 45 46 47 48 49 50 61 52 58 64 56 66 67 65 69 N.W.6C 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 96 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 N.W.60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 West. S. W. 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 66 64 63 62 61 S. W. 60 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 178 174 176 176 177 178 179 18C S. W. 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 S.W.30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 South. 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 South. S. E. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 S.E. 30 31 32 33 34 35 36 87 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 67 58 59 S. E. 60 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 S.E. 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 East. N.E. 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 N.E.60 300 301 002 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 N.E. 60 69 58 57 66 55 54 53 62 52 61 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 N.E.30 29 28 27 42C 26 25 24 23 22 21 20 19 18 17 16 16 14 13 12 11 1C 8 7 6 6 4 2 1 North. *: HEIGHTS AND DISTANCES. 48 218a. Traverse surveying is to bepreferred to triangulation. In triangulation, the various lines necessary will have to pass over many obstacles, such as trees, buildings, gardens, ponds, and other obstructions; whereas in a traverse survey, we can make choice of good lines, free from obstructions, and which can be accurately measured, and the angles correctly taken, without doing much damage to any property on the land. In every Survey which is truly taken, the sum of the Northings or North Latitudes is equal to the sum of the Southings or South Latitudes, and the sum of the Eastings or East Departure is equal to the sum of the Westings or West Departure. 219. Let A, B, C, D, E, F, G, H, I, K, be the respective stations of the survey, (see fig. 17b), and N S the meridian, N = north and S = south. Consequently, all lines passing through the stations parallel to this meridian will be meridians; and all lines at right angles to these meridians, and passing through the stations, will be east and west lines, or departures. Let fig. 176 represent a survey, where the first meridian is assumed on the west side of the polygon. Here we have the northings A B c + C d + d o +R A =RQ, and the southings = n F - F G + m I + i L P L. But R Q = P L.. the sum of the northings = sum of the southings, and the eastings C c + o E - E n +- Gm. But C c - D d + D h. Therefore the eastings D d + D h + Q n + G m- Q P + D h, and westings = D h + L R; but L R Q P, and D h = D h. Consequently the sum of the eastings is equal to the sum of the westings. Example 2. Let fig. 17c, being that given by Gibson at page 228, and on plate IX, fig. 1, represent the polygon a b c d e f g. Let a be the first station, b the second, c the third, etc. Let N S be a meridian line; then will all lines parallel thereto which pass through the several stations be also meridians, as a o, b s, c d, etc., and the lines b o, c s, d c, etc., perpendicular to those, will be east or west lines or departures. The northings are e i + g o + h q = a o + b s + c d + f r, the southings. Let the figure be completed,-then it is plain that g o + h q + r k = ao + bs+ c d, and e i -r k = fr. If we add e i - r k to the first, and f r to the latter, we have g o + h q + r k + e i - r k = a o - b s - c d + fr.. e.,g o + h q ei ao+ b +cd+ fr. Hence the sum of the northings - sum of the southings. The eastings c s + q a = o b + d e + i f - r g + o h, the westings. For a q + y o a q + a z = d e + if + r g - o h, and b o = c a -y o; therefore a q + y o + c s-y o = d e - i f + r g + o h + b o..e., a q + cs b o + d e + i f + r g + oh; that is, the sum of the eartings = the sum of the westings. 44 HEIGHTS AND DISTANCES. 220. Method of Finding the Northings and Southings, and Eastings and Westings. (Fig. 17b.) Bearing. Distance. Northing. Southing. Easting. Westing. A B North 29,18 29,1800 B C N.40~ E. 8,00 6,1283 6,1423 C D N. 10~ W. 9,00 8,8633 1,5629 D E N. 50~ E. 12,00 7,7135 8,6603 9,1925 E F S. 30~ E. 10,00 17,0000 5,0000 F G South 17,00 G H East 11,00 11,0000 H I S. 20~ E. 20,00 18,7938 6,8404 I K S. 60~ W. 21,00 10,5000 18,1866 KA N. 80~ W. 17,69 3,0726 17,4257 54,9577 54,9541 37,1752 37,1552 If the above balance or trial sheet showed a difference in closing, we proceed to a resurvey, if the error would cause a difference of area equal to one acre in a thousand. But if the error is less than that, we equate the lines, as shown in sec. 217. By Assuming any Station as the Point of Beginning, and Keeping the Polygon on the Right, to Find the most Easterly or Westerly Station. 221. Let us take the example in section 220, and assume the station F as the place of beginning (see fig. 17b). Total Total Easting. Easting. Westing. Westing. F G South 11,00 G H 11,00 H I 6,84 17,84 I = most easterly station. I K 18,19 18,19 KA 17,43 35,62 A B North A and B the most westerly B C 5,14 stations. C D 1,56 D E 9,19 E F 8,66 Here we see that the point I has a departure east = 17,84 after which follow west departure to A = 35,62 Therefore the point A is west of F = 17,78 Then follows E. dep. 5,14, and W. dep. = 1,56, which leaves points A and B west of C, D, E and F. Consequently point I is the most easterly, and points A and B, or line A B, the most westerly. In calculating by the traverse method, the first meridian ought to pas) through the most easterly or westerly station. This will leave no chanc| of error, and will be less difficult than in allowing it to pass through th0 polygon or survey. However, each method will be given; but we ough to adopt the,simplest method, although it may involve a few more figures in calculating the content. For the first method, see next page. HEIGHTS AND DISTANCES. 45 INACCESSIBLE DISTANCES. Let A B (Fig. 17a) be a Chain Line, C D, a part of which passes through a house, to find C D. 221a. Find where the line meets the house at C; cause a pole to be held perpendicularly at D, on the line A B; make D e = C f; then Euclid I, 34, f e C D. 221b. When the pole cannot be seen over the house, measure any line, A R, and mark the sides of the building; if produced, meet the line A K, in the points i and K. Then byE. VI, 4, A i: C i:: A K; KD. K D is now determined. Let C i be produced until C m = D K. Measure m K, which will be the length required. Distance C D. 221c. Or, at any points, A and G on the line A B, erect the perpendiculars A 0 and G H equal to one another, and produce the line 0 H far enough to allow perpendiculars to be erected at the points L'and M, making L B = M N A 0 == H G.-. the line B N will be in the continuation of the line A B; and by measuring D N and A C, and taking their sum from 0 W, the difference will be equal to C D. 222. When the obstruction is a river. In fig. 18, take the interior angles at C and D; measure C D; then sine < E: C D:: sine < D: C E. When the line is clear of obstructions to the view, make the < D equal to half the complement of the < C. Then the line C E - C D. As, for example, when the < at C is 40~, the half of the complement is 70~ = angle at D = < C E D; consequently (E. I, 5), C E = C D. In this case the flagman is supposed to move slowly along the line A B, until the surveyor gives him the signal to halt in direction of the line D E, the surveyor having the telescope making < C D E = 70~. 223. Or, take (fig. 19) C D perpendicular to A B. If possible, let C D be greater than C E. Take the < at D; then, by sec. 167, C D X tan. < D = C E. Or by the chain only (fig. 20), erect C D and K L perpendicularly to A B; make C F = F D and K L =C D; produce E F to meet D L in G; then G D - C E, the required distance. See Euclid I, prop. 15 and 26. 224. Let A C (fig. 20a) be the required distance. Measure A B any convenient distance, and produce A B, making B E - A B; make E G parallel to A C; produce C B to intersect the line E G in F. Then it is evident, by Euclid VI, 4, that E F -A C and B F = B C. 225. Let fig. 21 represent the obstruction (being a river). Measure any line A B = c, and take the angles H A C, C A B, and A B C, C being a station on the opposite shore. Again, at C take the < A C G and A C B, E being the object. Now, by having the length to be measured from C towards G = C E, E will be a point on the line A F. By sec. 194 we find A C, and having the angles E A C and A C E, we find (E. I, 32) the < A E C = < at E. Then sine < E: A C:: sine < ACE: A E, and sine < E: A C:: sine < C A E: C E; but in the A C D E we have the < at D, a right angle, and the < E given,.. the < E C D may be found. Now, C D being given = to the cosine of the < E C D = sine of < E - C D, we have found A E, C E, and the perpendicular C D; consequently, the line A D E may be found, and continued towards H, and the distances a H, H b, and b D, may be found. D E = cos. E C E. f....,.- K...s;S - ---c --- ` — -' ----~ --- —-r 46 HEIGHTS AND DISTANCES. 226. Let the line A F (fig. 22) be obstructed from a to b. Assume any point D, visible from A and C; measure the lines A D and D C; take the angles A C D, C A D, A D C, and C D Y, Y being a station beyond the required line, if possible. In the triangle B C D we have one side C D, and two angles, C B D and C D B, to find the sides C B and D B, which may be found by sec. 194. 227. Or, measure any line A D (fig. 22); take the angle C A D, and make the angle A D G = 180~ - < C A D; i.e., make the line D H parallel to A C; take two points in the line A H, such as E and G, so that the lines E B and G F shall be parallel and equal to A D, and such that the line E B will not cut the obstruction a b, and that the lines G F parallel to E B will be far enough asunder from it to allow the line B F to be accurately produced. As a check on the line thus produced, take the angle F B E, which should be equal to the angle B E D = C A D. 228. Let the obstruction on the line A W (fig. 23) be from a to b, and the line running on a pier or any strip of land. At the point C measure the line C D = 800, or any convenient distance, as long as possible; make the < A C D = any <, as 140~, and the interior < C D E = any angle, as 130~; measure D E = 400; make the < D E Y - 70~, Y being some object in view beyond the line, if possible. To find the line E B, and the perpendicular E H. In the figure C B E D, we have the interior angles B C D = 40~ C D E -130 D EY- D E B=- 70 240~ Let the interior angle C B E = x~ Sum, 240~ + x~ To which add four right angles, 360 6000~ x~ Should be, by E. I, 32, 720 That is, 600~ + x~ - 720~.. x - 120~ = < A B E; therefore, the angle H B E = 60~. By E. I, 16, the A B E II B E + H E B, but the angle H B E 60~.'. < H E B - 30~; consequently, the interior < D E H = 100~ 70~ + 30~. Now, we have the interior angles H C D - 40~, bearing N. 40~ E. C D E 130 DEB= 70 A B E = 120 D E II = 100 C It E 90 The bearings of these lines are found by sec. 218. We assume the meridian A H, making A the south, or 180~, and II the north, or 00, and keeping the land invariably on the-right hand, as we proceed, to find the bearings. 180 360 120 60 60 300 = N. 60~ E. = bearing of B E, per quarter compass table. (See this table, sec. 218.) HEIGHTS AND DISTANCES. 47 180 360 70 110 110 190 = S. 100 E. - bearing of E D. 180 190 130 50 50 140 = S. 400 W. = bearing of D C. 180 140 40 140 140 000 = north -- bearing of C B or C H. Now we have, by reversing these bearings, and finding the northings and southings by traverse tableSine. Chains Bearing. Northilg. Southing. Easting. Westing. CD -8,00 N. 40( E. 6,1283 C d 5,1423 DE 4,00 N. 10 W. 3,9392 = d 0,6946 EB S. 600 W. x= - B II y B EI B C South. 10,0675 - x 10,0675 10, -x 5,1423 0,6946 + y But as the eastings, per sec. 218a, is equal to the westings, y = 5,1423 - 0,6946 = 4,4477 == E H. Also, from the above, the < II E B = 30, and the < B I E = 90~.'. we have, in the triangle B II E, given the angles, and side E II, to find E B and B I. For the angle B E 11, its latitude or cosine -- 0,866, and its sine or departure = 0,500; therefore E H - 4,4477, divided by 0,866, gives 5,136 = E B, and 5,136 X 0,500 -2,5680 = B H; and by taking B H from C H, i.e., 10,0675 - 2,5680 - C B - 7,4995; and by calling the distances links, we have C B - 749,95 links, and E B =- 513,6. Note. If, instead of having to traverse but three lines, we had to traverse any number of lines, the line E H, perpendicular to the base A W, will always be the difference of departure, or of the eastings and westings, and B H = difference of latitudes, or of the northings and southings. 229. Chain A C (fig. 25), and at the distance A B, chain B D parallel to A C, meeting the line C E in D; then, by E. VI, 4, and V, prop. D, convertendo, A E: B E:: A C - B D:B D.. (E. VI, 16) AB XBD B E B, which is a convenient method. A C -B D C Example. Let B E be requir- D ed. Let A C = 5, B D = 4, and A B = 2, to find B E. By 4 E the last formula, BE 2X= 4 =8 chains. A 230. In fig. 26, the line 0 L is supposed to pass over islands surrounded by rapids, indicated by an arrow. The lines O A, 0 B, and E F, are measured. From the point B erect the perpendicular B G, and take a point H, from which flag-poles can be seen at 0, A, B, C, D, E, and F. Take the angles 0 H A, A H B, B H C, D H B, E H B, F H B. The tangents of these angles multiplied by B H, will give the lines B A, OB BC BD, BE, BF, and BL. 48 HEIGHTS AND DISTANCES. H B is made perpendicular to O L, and the < 0 H B is given.-. the angle B 0 H is given, whose tangent, multiplied by O B, will give the distance B H; consequently, B H multiplied by the tangents of the angles B H C, B H D, B H1 E, etc., will give the sides B C, B D, B E, etc. 231. If one of the stations, as L, be invisible at II, from L run any straight line, intersecting the line B G in K; take the angle B K L and measure H K; then we have the side B K, and the angle B K L, to find B L in the right angled triangle B K L.... B L — B K X tan. < B K L. 232. But if the line B G cannot be made perpendicular, make the < O B G any angle; then having the < 0 B G, we have the < L B K, and having observed the < B K L, and measured the base B K, we find the distance B L by sec. 131. In this case we have assumed-that B K could be measured; but if it cannot be measured, take the < B 0 H and 0 H B; measure 0 B; then we have all the angles, and the side 0 B given in the A 0 I B to find B H, which can be found by sec. 131. Having B H, measure the remaining part H K. 233. Let the inaccessible distance A B (fig. 27) be on the opposite side of a river. Measure the base C D, and take angles to A and B from the stations C and D, also to D from C, and to C from D. Let s C D, a - < AC B, b <B C D, c = <A D C, d= <A D B, e < CAD, and f = < C B D. Sine e s:: sine c: A C. Sine f: s:: sine b: B D. Sine f: s:: sine (c + d): B C. Now having A C and B C, and the included angle, we find (sec. 140) the required line A B. 234. If it be impracticable to measure a line from B (fig. 26), making any angle with the base 0 L, in order to find the inaccessible distance B C, assume any point HI, from which the stations A, B and C are visible. Let A B = g, B C = x. <CAH=a=-BAH. <AHB -c. <ACH =b. <CHB d. Therefore, < A B H = 180 - a - c. g. sine a By sec. 131, sine c: g:: sine a: H B - ie sine c H B sine d sine b: H B:: sine d: x = - sine b Substituting the value of H B in the last equation, we have g * sine a. sine d x= =B C. sine c * sine b This formula can be used, by either using the natural or logarithmic sines. zEample. Let A B = 400 links = g, the angle A H B = c = 60~ B A H = a =- 80~ l..f.'. E. I, 32, AB H =40~:i:n fC H B = d 10~.. < A H C = 70~. s; HRIGHTS AND DISTANCES. 49 180-2(B AH+CHB+BH A) =180 (80~10+60) ==00 =A C H = b. Log. g = log. 400 = 2,6020600 Log. sine a =log, sine 800 = 9,9933515 Log. sine d log, sine 100 = 9,2396702 Sum, 21,8350817 Log. sine c log, sine 600 =9,9375306 Log. sine b =log, sine 300 =9,6989700 19,6365000 2 1985811 -157,98 =B x. And, as in sec. 163, we have A B == 400, and B C =x = 157,98, and the included angle A H C, the lines A H and B LI may be found. 235. Let the land between C D and the river be wood land (see fig. 28). Assume any two random lines, traced from the stations A and B through the wood; let these lines meet at the point C; trace the lines C E and E D in any convenient direction, so that the point A be visible from E, and the point B visible from the point D; take the angles A E C, A C E, A CB, BC D, and C DB,.~.by E. I,32, the angles EA C and C BD caa be found; and by sec. 131, the sides A C and C B are found; and having the contained angle A C B, we find, by sec. 140, the side A B. Note. This case is applicable to hilly countries. 236. The line A B may be found as follows: In direction of the point B (fig. 29) run the random line P B, and from A run the lines A D and A C to meet the line P B; measure the distance D C, and take the angles ADC==a,ACB=c, ACD=b; 1etthe<CAD=d, and<CAB = e, and the < A B D = f. Now, as the angles d, e and f have not been taken, we find them as follows: The angles a and c are given. -. by E. I, 16, < c =< a+ < d... < d =< c-< a, and by E.I, 16, we have < b = < e ~ < f, and 1800 - the sum of the angles a, d, e= < f. Now, bysec. 131, sine< d:D C = ssine< a:A C. s5- sine < a i. e., sine < d:s::sine <a: A C. sine< d s -sine <a s -sine < a sine<ca Also sine < f.: sine <c: — =A B. sine <d sine <d. sine< f 237. By the Chain only. Let it be required to measure the distance A B, on the line 0 R (fig. 30). Measure A G = G E any convenient distances, 50 or 100 links; describe the equilateral triangles G E D and A G C equal to one another; produce G D and B C to meet one another at F; measure D F. Now, because G F and A C are parallel to one another, the A F D C is similar or equiangular to the A, B A C (E. V1, 4). F D: D C:: A C: A B, but A C = C D, because D C =A C. 'F D: DC:: DC: A B and by E. VI, 16. F D X A B = D C2. D C2 AG-2 A B =-i- which is a convenient formula. F D F D~~~~~~~~~~~~~~~~~~~~~~~~1 - -1-"-I- ---- - ------------— -T - ---r-I- -1.-1 — _lrX~ITICJISp9-p~-~ --- 50 HEIGHTS AND DISTANCES. Example. Let A C - 100, and D F - 120; 1000 then A B = = 83J links. 120 This is a practical method, and is the same as that given by Baker in his Surveying, London, 1850. 238. The following problem, given by Galbraith in his Mathematical and Astronomical Tables, pp. 47 and 48, will be often found of great use in trigonometrical surveying (see fig. 31): From a convenient station P there could be seen three objects, A, B and C, whose distances from each other were A B = 8 miles, A C = 6 miles, B C = 4 miles. I took the horizontal angles A P C 330 45', B P C = 22~ 30~. It is hence required to determine the respective distances of my station P from each object. Because equal angles stand upon equal or on the same circumferences, the < B P C = < D A B, and < A P C =< A B D. In this case the point D is supposed to fall in the original A A B C. From this the construction is manifest. Make the < B A D =< A B D as above; join C and D, and produce it indefinitely, say to Q; about the A A D B describe a circle, cutting the line C Q in P; join A and P, and B and P; then, by E. III, 21, the < CPB-=<D AB, and <APD==<ABD. In this case, the < C P B is assumed less than the < C A B, and the < A P B less than A B C. Now having the three sides of the A A B C by sec. 142, we find the angles A, C and B of the A A B C; consequently the < C A D is found; also the < C B D, because, by observation, the < B P C = B A D, and < A T C ABC. In the A D B are given the side A B and the angles D A B and D B A, to find the sides A D and B D and < A D B, all of which can be found by sec. 131. Now having the sides A D and A C, and the contained angle B A D, we find (sec. 140) the < A C B and the side D C; and having the angles A C P and A T C given, we find the < CAP; but above we have found the < C A B.. the < C A P < C A B = < B A P. In like manner we find the < A B P; and by sec. 130, and E. I, 32, we find the distances A P and B P. In like manner we proceed to find C P. COMPUTATION. A C = 6 miles = b, and A P - = 330 45. C B = 4 = a, and C P B = 22~ 30'. B A 8 miles = c. (s - b). (s - c) j By sec. 125, sine A < A = (( — b ) b c Here s = 9 miles. b =6. - b 3. s-c =9 —8=-1. (s —b). (s - c) = 3 X 1 =3. And b c = 6 X 8 48; consequently the value of half the angle A ( 8) - —, but i =,25 =sine 14~ 28/ 39/; therefore B A C-28~571 8. i < B A C == 280 67/18,-. HEIGHTS AND DISTANCES. 61 By see. 126, we find < A B C = 46~ 84' 03" and by sec. 127, < A C B = 104~ 28/ 39" Now we have the < C A B = 28~ 57/ 18/ and by observation, the < D A B = 22~ 30/ 00// — < C P B..'. the < C A D = 6~ 27/ 18// By observation, we have the < D A B = 22~ 30' 00" The < D B A = 33~ 45/00// Their sum = 56~ 15 00"... 180 - 56~ 15' =< A D B = 123 45/ 00// And as the < C A D = 6~ 27' 18"/. this taken from 180, leaves the < A D C < A C D = 273~ 32/ 42// and half the sum of these = 86~ 46' 21" By sec. 131. As sine A D B 123~ 45/ (arith. complement) = 0,0801536 is,to the side A B 8 miles, log. 0,9030900 so is the sine of the < A B D = 33~ 45/ log. sine 9,7447390 to A D = 5,34543. Sum 0,7279826 A C = 6, by hypothesis. As the sum = 11,34543 is to the difference 0,65457, so is tan. i (< A D C + <A C D) = 86046/21// log. 1,0548110 1,8159561 tan. 11,2487967 to the tan. of half the difference of the angles A D C and A C D. 16,0099318 = 45~ 39/ 18".. by sec. 140, the < A C P = 41~ 07' 03/ and the < A D C = 132~ 25/ 39~0 As sine < A P C 33~ 45' is to A C = 6 miles, so is < A C P = 41~ 7' to the distance A P 7,10195. Now we have the < A C B The < A P C Their sum irith. comp. 0,2552610 log. 0,9781513 sine 9,8179654 log. 0,8513777 41~ 07' 03" 33~ 45' 00/ 74~ 52' 03/ 180~ - 74~ 52' 3// = P A C - 105~ 07/ 57/ By sec. 131, sine < A C P = 41~ 7/ 3/ is to P A = 7,10195, so is sine < P A C = 105~ 7/ 56/ arith. comp. 0,1820346 log. 0,8513777 sine 9,9846734 to the side P C = 10,42523 log. 1,0180857 We have found the < A B C = 46~ 34/ 03/. < B A C = 28~ 57/ 18" Their sum 75~ 31/ 21//, which taken from 180, gives the < A C B = 104~ 28/ 39//. But the < A C B has been found = 41~ 07' 03//.. the < B C P = 630 21/ 36// and by hypothesis < C P B = 22~ 30/ 00" the sum of the two last angles = 94~ 09' 24"... the sine of < C P B = (22~ 30//) arith. comp. = 0,4171603 is to B C, 4 miles, log. = 0,6020600 so is sine < B C P (63~ 21 36// sine 9,9512605 to P B, 9,342879 miles. log. 0,9704808 Galbraith finds 9,342850 miles by a different method of calculation. I. M. i:. I I.;..,-... s. mq"!! I i -- 1,..-. I - - 77-, - - I '. -1. 62 HEIGHTS AND DISTANCES. 239. Second Case. Let us assume the three stations, A, B, W, to be on the same straight, and the angles A P W and W P B to be given (see fig. 31), as in the last example. We find the sides A D and D B. And having the sides A D and A W, and the contained angle, we find the < A D P = < A D W, and the < A P D is given by hypothesis.. by E. I, 32, we find the < D A P, and all the angles, and the side A D being given, in the A A D I? we can find, by sec. 131, the sides A P and P W. In like manner we find the side P B. 240. Third Case. Let us assume the station P to be within the A A B C, fig. 32. The < A B D is made equal to the supplement of the < A P C, and the < B A D = the supplement of the < B P C.-. as above, we find the sides A D and B D, and having the sides A B, B C, and A C, we find the angles B A C and A B C; consequently, we have the < D A C. And by sec. 140, we find the angles A D C and A C D, and the < A P C being given by hypothesis,.'. the < C A P is found; and by sec. 130, we find the sides P A and P C. In like manner we find the side PB. Note. When the sum of the two angles at P is 180~, the point P is on the same straight line connecting the stations A, B and C. And when the sum is less than 180~, the point P is without the A A B C. When the sum is greater than 180~, the point P is within the A A B C. * 241. In fig. 33, the sum of the angle B P C is supposed = to the sum of the angles C A B -- C B A, making the < C A B = C P B, and the < C B A - A P C; consequently, the point P is in the circumference of the circumscribing circle about A A B C.. the point P can be assumed at any point of the circumference of the segment A P B, and consequently, the problem is indeterminate. 242. The following equation, given by Lacroix in his Trigonometry, and generally quoted by subsequent writers on trigonometry, enables us to find the angles P A C and P B C, and, consequently, the sides A P, CP, and B P. Let P=< A P C. Let a = A C. P = < B P C. b -BC. R=360~ - P - P c. x < P A C. y < P B C. c < AC B. a * sine P' x =5 cot. R ( + 1) b * sine P. cos. R 243. x -s - (sine P/ * cosec. P * sec. R * cot. R - cot. R) b In the problem now discussed, we have a=6, andP = 33~ 45 00/ b -4, and P/ - 22~ 30' 00/ by sec. 238, 104~ 28 39/ = < A C B. Sum, 160~ 43/ 39/ 360~ R - 199~ 16' 21" a 6 3 By sec. 242, b 4 2 I HEIGHTS AND DISTANCES. 63 a * sine P/ From the equation cot. x = cot. R (- sin + 1) (see sec. b * sine P * cos. R 242), we have8 log, = 0,4771212 2 ar. comp. = 9,6989700 P/ - 22~ 30/ sine - 9,5828397 P = 33~ 45/ ar. comp. sine = 0,2552610 R = 199~ 16/ 21/ neg. ar, comp, cos. = 0,0250452 - 1,09458 log. 0,0392371 +1, 0,09458 log. = 2,9757993 Cot. R = + 199~ 16 21// 10,4563594 Cot, x, (- 105~ 8 10//) = 9,4321587 By sec. 131, as sine 33~ 45/ ar. comp.= 0,2552610 is to sine < P A C, (105~ 8/ 10/) log. sine = 9,9846660 so is 6 log.= 0,7781513 to P C = 10,4251 log. 1,0180783 By sec. 241, R - x = y = 199~ 16' 21/ - 105~ 8/ 10"/ = 94~ 8/ 11/. By sec. 131, we can find the lines A P and P C. Note. - 0,09458 X by + 199~ 16 21', gives a negative product;.'. the cot. is negative, and the arc is to be taken from 180, by sec. 108a. REDUCTION TO THE CENTRE. 244. It frequently happens in extensive surveys that we take angles to spires of churches, corners of permanent buildings, etc. From such points, angles cannot be taken to those stations from which angles were observed. Let C (fig. 34) be the spire of a church. Take any station D, as near as possible to observed station C, from which take the < C D B = D. Let log. sine 1// = 4,6855749; let < C D a, A D B = b, and the distance C D = g, and < A C B = x; g sine (b + a) g sine a then x - b + B C sine 1/ AC sine 1/ Great care is required in taking out the sine of the sine of the angles g * sine (b - a) (a - b), and sine of a. The first term, -, will be positive B C * sine 1// when (a + b) is less than 180~, and the sine of a will be negative. 245. Let A be a station in a ravine, from which it is required to determine the horizontal; distance A H the height of the points D and C above the horizontal line A H (fig. 35). Trace a line up the hill in the plane of A D H, making A B - g feet - 600; take the angles C A H 3~ 10/, < D A H 5~ 20/. Therefore <C A D - 2~ 10' <GAB==<EBA- 20 7/ and <CBE== 1~ 7/ <A H C =90~ 0/ < A C H = 86~ 60' < A D C - 840 40/ In the triangle A B C are given A B 600. The < A B C E< E B A C B 3 14 The < B A C =180~ - C A H- B A G = 1740 43 Consequently, < A C B - 2 3/ g ..- - 54 HEIGHTS AND DISTANCES. By sec. 131, the sides A C and B C may be found. And A C.cos. C A H =A H. And A C * sine C A H = H C. And H A * tan. C A H = H D. And by taking the < C B D, and multiplying its tangent by the line B C, we find the line D C, which added to H C, will give the line H D. Otherwise, We have the angles D A C, C A II, and angle at H a right angle. 180 - 90 - < C A H = < A C H = 86~ 50 = < A D C - < C A D. But < C A D being 2~10/,.. < A D C =84~ 40', and < C A D 2~ 10/, and the side A C may be found; and by sec. 131, C D can be found. As sine 2~ 3 (< B C A) arith. comp. = 1,4464614 is to A B (600), log. = 2,7781513 so is sine 3~ 14' (< A B C) log. sine = 8,7512973 to A C = 946,04, log. Sine 30 10 (< C A H) C H 52,26 log. Also log. A C Cosine (< C A H = 3~ 10') A H = 944,597 log. Tangent (< H A D = 5~ 20/) H D = 88,182 log. C H = 52,26..C. C D = 35,922. Or, C D may be found as follows: As sine (A D C = 84~ 40') arith. comp. is to the log. A C from above, so is sine (< D A C = 2~ 10/) sine to C D = 35,922 log. = 2,9759100 - 8,7422686 = 1,7181686 = 2,9759100 = 9,9993364 = 2,9952464 -= 8,9701350 = 1,9453814 0,0018842 2,9759100 8,5775660 1,5553602 INACCESSIBLE HEIGHTS. 246. When the line A B is in the same horizontal plane (fig. 37), required the height B C. A B * tan. <C A B =B C. 247. Let the point B be inaccessible (see fig. 37a). Measure A D m in the direction of B; take the < C A B = f, and C D B = g; then, by E. I, 16, A C D = g - f h; and, by E. I, 32, < B C D = 90~ - g =k. m * sine f By sec. 131, C D - sine h m * sine f sine g BC= — sine h m ~ sine f. cos. g D B sine — sine h HEIGHTS AND DISTANCES. 65 248. Let the inaccessible object C E be on the top of a hill, whose height above the horizontal plane is required (fig. 38). As in sec. 246, let < C A B = f =44~ 00/ < CD B=g =67~ 50/ and E. I, 16, <A C D = g - f= h - 230 50' <E D B = k = 51~ 00/ <B C D = p = 22~ 10/ And the horizontal distance A D = m = 134 yards. m ~ sine f By sec. 246, C D = ----- sine h m. sine f. sine g B C -- sine h m sine f * cos. g B D= ==-BC. tan. < B C D. sine h And by substituting the value of B C, we havem sine f * sine g * tan. p B D= - - sine h m. sine f * cos. g * tan. k B Esine h m. sine f sine g * tan. p * tan. k ~*or, B E == ---— sine. Now having B C and B E sine h given, their difference, C E, may be found. m = 134 yards, log. 2,1271048 f = 44" 00' log. sine 9,8417713 g - 670 50t log. sine 9,9666533 h = 230 50t cosec. (ar. comp. 0,3935353 B C = 213,36 yards log. 2,3290649 < B C D = p = 22~ 10' tan. 9,6100359 < B DE = k = 51~ 00' tan. 10,0916308 B E = 107,33 yards log. 2,0307314 B C = 213,36... C E = 106,03 = height required over the top of the hill. Note. I have used the formula or value of B E, marked *, which is very convenient. The data of this problem is from Keith's Trigonometry, chap. iii, example 37. 249. Let B C be the height required, situated on sloping ground A B (see fig. 39). At A and D take the vertical angles C A F = a, equal the angle above the horizontal line A F. < C A B = f. < C D B = k. < A C D=h = <BDC - CAB. <AC B =i =90~ - <CAF. < F A B =b. < A D = m, and D B = n,.. A B = m + n. B F = (m + n) sine b. A F = (m + n) cos. b. C F -= (m + n) cos. b * tan. a. 56 HEIGHTS AND DISTANCES. Second Method. 250. Measure on the slope A B the distance A D = m; take the < C A B = f, and the vertical angles E D B p and < C D E = q. m. sine f C D -- sine h m. sine f. cos. q CE sine h m. sine f. cos. q D E = sine h m sine f * cos. q * tan. p B E — sine h Consequently C E - B E = C B. In this case the distance B D is assumed inaccessible, Third Method. m * sine f 251. Having found C D =, we measure on the continuation sine h of the slope D B = n, making the < E D B = as above = p, and the < E D C =q. We find B E = n sineb. m ~ sine f. sine q CEsine h m * sine f * sine q.'. C- n. sine b. sine h 252. Let the land, from A towards B, be too uneven and impracticable to produce the line B A (see fig. 39). Measure any line, as A G =- m; take the horizontal < C G A a. < C A G = b. Then 180~ - a- b = x = < A C G =c. Let the vertical angle C A F = o. <CAB = f. < BA F = 1. m. sine a By sec. 181, A C = ---- sine c m ~ sine a * sine o CF= sine c m * sine a * cos. o * tan. b BF - sine c Consequently, C F - B F = B C = the required height. Example. Let < a- 64~ 30' < o = 58~ < b 72 10 < 1 = 33~ <c = 43~ 20/ m= 52 yards, to find C B. m * sine a. sine o To find C F. We have from this article C F = sine c m 52 yards, log. 1,71600 a - 64~ 30/ log. sine 9,95549 o - 58~ 00 sine 9,92842 c = 43~ 20/ ar. comp. 0,16352 C F = 68,1 log. 1,76343 To find the height B F. We find the value of B F by the last equation of this article. TRAVERSE SURVEYIN. 67 m = 1,71600 < a sine 9,95549 < o cosine 9,72421 <c ar. comp. 0,16352 < 1 tan. = 9,81252 B F - 23,536, log. = 1,36174.'. 58 - 23,536 - 34,464 yards - B C. 253. At sea, at the distance of 20 miles from a lighthouse, the top of which appeared above the horizon; height of the observer's eye above the sea, 16 feet. Required, the height of the lighthouse above the level of the sea. Here 16 feet == 0,003 miles. Assuming the circumference of the earth 25020 miles, and its semidiameter 2982 miles. As 417: 120:: 20 miles: 0~ 17' 16// nearly = < B C D. And because the angle at D is right angled, 90 - 0~ 17/ 16" -_ 89~ 42' 44 =- < C B D... by sec. 131, as sine <B: C D:: rad.: B C. = 3982,003 = C D, log.= 3,6001013 rad. 10 13,6001013 890 42/ 44/ log. sine = 9,9999945 3,6001068 B C = 3982,05 AC- 3982 A B,05 miles. 5280 A B = 264 feet, 26400 By sec. 107, < C D * sec. < B C D = B C. But as the secant in small angles change with little differences, it would be unsafe to use it. In this example, < B C D = 0~ 17/ 16/, the secants 17/ and 18' show no difference for 1/. 254. When the altitude is 45~, the error will be the least possible; in, which case 1 would make an error of 9 part of the altitude; and generally the error in altitude is to the error committed in taking the altitude, as double the height is to double the observed angle.-Keith's Trigonometry, chap. iii., example xxix. TRAVERSE SURVEYING. 255. Let the figure A, B, C, D, E, F and G (see fig. 17d) be the polygon. This is the same figure given by Gibson on plate 9, fig. 3. Let S N be a meridian assumed west of the polygon; let A W = meridian distance of the point A from the assumed meridian; then M B = mer. dist. of the point B, N C - mer. dist. of point C, D Z = mer. dist. of point D, T E = mer. dist. of E, Q F = mer. dist. of the point F, and G S1 = mer. dist. of G. Let Y I = mer. dist. to middle of A B, 0 K = mer. dist. to the middle of B C, L L1 = mer. dist to middle.of C D, X M = mer. dist. to middle of D E, R R2 = mer. dist. to middle of E F, P a = mer. dist. to middle of F G. 58 TRAVERSE SURVEYING. It also appears that W M = northing of A B, M N - the northing of B C, N Z = southing of C D, Z T = southing of D E, Q F = southing of E F, and Q SI = the northing of F G. By the method of finding the areas of the trapeziums (sec. 24), we have as follows: North Area. South Area. W M. Y I = area of A B M W W M Y I M N O K areaof BCNM M N O K N Z LL1 =areaof C D Z N N Z L L Z T M X =areaof DE T Z = ZT.MX TQ.RR1 - area of EFQT = T Q * R R QS1.P a areaof FG S Q = QS P a Hence appears the following rule, which is substantially the same as Gibson's Theorem III, section v: 256. Rule. Multiply the meridian distance taken in the middle of every stationary or chain line by the particular northing or southing of that line. Put the product of southings in the column of south areas, and the product of northings in the column of north areas. The difference of the area columns will be the required area of the polygon; to which add the offsets, and from the sum take the inlets. The remainder will be the area of the tract which has been surveyed. To Find the Numbers for Column B, entitled Meridian Distance. 257. Let A W (fig. 17d) represent the first number-viz., 61,54 chains, and N Q the first meridian line; and since the map is on the east side of this meridian, all those lines that have east departure will lie farther from the first meridian than those that have west departure; therefore, knowing the length of the line A W, the length of the other lines, I Y, B M, etc., may be found by adding the eastings and subtracting the westings. The first meridian is supposed to be the length of the whole departure, or the entire easting or westing from the first station; for should the first station be at the eastermost point of the land, the first meridian will then pass through the most westerly point, and the map will entirely be on the east of the first meridian. But if the meridian distance be assumed less than the whole easting or westing from the most easterly point of the land, then it is plain that the first meridian will pass through the polygon or map, and that part of the land will be east and part west of that meridian. In this case, in that part which would be east of the meridian, we would add the eastings and subtract the westings; but in that part west of the meridian, we would add the westings and subtract the eastings. In method 1, the sum of all the east departures is assumed as the first meridian distance. In method 2, the first meridian is made to pass through the most westerly station. In method 3, the first meridian is made to pass through the most northerly station of the polygon, as station E (see fig. 17b). i TRAVERSE SURVEYING. 69 258. METHOD I.-Commencing Column B with the Sum of all the East Departures (see fig. 17b). Bearing. Dist. N.lat. S. lat ep.. dep. AWde or at. ' or N. Area. S. Area. and I dep. mer.dis. North. N. 40~ E. N. 10~ W. N. 50~ E. S. 30~ E. South. East. S. 20~ E. S. 60~ W. N. 80~ W. Ch'ns. 29,18 8,00 9,00 12,00 10,00 17,00 11,00 20,00 21,00 17,694 I 29,178 6,128 8,863 7,714 0,000( 5,142; 9,192i 5,000( 11,000 6,840 3 I 8,661 17.001 East. 18,794 10,500 3,073 1,5629 0 4 18,1866 17,4257 N. 29,178 0,000 N. 6,128 E. 2,57115 N. 8,863 W. 0,78145 N. 7,714 E. 4,59625 S. 8,661 E. 2,5000 S. 17.001 37,1752 37,1752 E. 37,1752 E. 39,74635 E. 42,3175 E. 41,53605 E. 40,7546 E. 45,35085 E. 49,9471 E. 52,4471 E. 54,9471 E. '4.9471 E. 1084,6979 243,5659 368,1336 349,8376 I I 454,2445 9.4.1afi In column A, the top line of each 0 0 49471 E pair is the north or south latitude, and the under number is half the 0,0000 60,4471 E. corresponding departure. E. 5,5000 65,9471 E. In column B, the sum of all the S. 18,794 69,3673 E. 1303,6890 east departures is assumed as the E. 3,4202 72,7875 E. first meridian distance, thus making S. 10,500 63,6942 E. 668,7891 the first meridian to be west of the most westerly station. W. 9,0933 54,6009 E. The meridian distance is found by N. 3,073 45,888 E. 141,0138 adding half the eastings twice, and W. 8,71285 37,1752 E. subtracting half the westings twice. 2187,2488 3360.8780 These give the meridian distances at 2187,2488 half the lines. 173,6292 Example. The first line is N. lat. Area 117 acres. 29,178, and departure = 0,.'. 0 added to 37,152 gives the meridian distance - 37,152, and 37,152 + 0 37,152 = lower number of the first pair in column B. The next half departure is = 5,57115 east,.-. 2,57115 + 37,152 = meridian distance - 39,7463; add 2,57118 to 39,7463; it will give the under line of second pair = 42,3175. From 42,3175 take half the next departure, 0,78146, and it gives meridian distance = 41,53605, etc., always adding the eastings and subtracting the westings. The product of the upper numbers in columns A and B will give the areas. If the upper number in column A is north latitude, the product is put under the heading, north area; but if the upper number in column A be south latitude, then the product is put under the heading, south area. Having found the last number in column B to agree with the first meridian distance at top, is a proof that the calculation is correct. The difference between the north area and south area columns determine the area of the given polygon in square chains. The area could be found in like manner by assuming the principal meridian east of the polygon, and adding the westings, or west departures, and subtracting the eastings, or east departures. I 60 TRAVERSE SURVEYING. 259. METHOD II.-The First Meridian passes through the Most Westerly Station (see fig. 17b). Bearing. ------------ North. N. 400 E. N. 10~W. N. 60~E. S. 30~E. South. East. S. 200 E. S. 60~ W. N. 80~ W. Dist. N. lat 29,178 29,17E 8,00 6,128 9,00 8,863 12,00 7,714 10,00 17,00 11,00 20,00 21,00 17,694 3,0730. S. lat. E. dep. W. dep. 0,000( 5,1423 9,1925 5,0000 0,0000 11,0000 6,8404 8,661 17,001 East. 18,794 10,500 - 1,562l 18,1860 17,4257 A or lat., B or and dep. mer. dist. 0,0000 N. 29,178 0,0000 0,000 0,0000 N. 6,128 2,57115 E. E. 2,57115 5,14230 E. N. 8,863 4,36085 E. W. 0,78145 3,57940 E. N. 7,714 8,17565 E. E. 4,5962512,77190 E. S. 8,661 15,27190 E. E. 2,5000 17,77190 E. S. 17,001 17,77190 E. 0,0000 17,77190 E. 0,0000 22,27190 E. E. 5,5000 28,77190 E. S. 18,794 32,19210 E. E. 3,4202 35,61230 E. S. 10,500 26,51900 E. W. 9,0933 17,42570 E. N. 3,0730 18,71285 E. W. -8,71285 10,0000 15,7563 38,6507 63,0673 26,7747 N. Area. S. Area. In this example we take the corrected distances and correct balance sheet; that is, the numbers are such as to give the northings equal to the southings, and the eastings equal to the westings (see sec. 220). By sec. 221, the point or station A is found to be the most westerly station on the survey. By making the first meridian pass through the most easterly station, we find the area by adding the westings and subtracting the eastings. By This is satisfactory proof. 132,2699 302,1401 605,0183 278,4495 I 144,2490 1317,8768 North area = 144,2490 Area of the polygon = 117,36288 acres. By first method = 117,36292 acres. second method = 117,36288 acres. Note. The surveyor ought to adopt some uniform system, as by this means he will be in less danger of committing errors. I have invariably made the principal meridian pass through the most westerly station of the polygon according to this method, and checked it by the third method, thereby making one method check the other. Making the first meridian pass through the polygon requires less figures, but more care in passing from east to west, and vice versa; also in entering the areas in their proper columns, as sometimes the north area is to be put in the south area columns, and the contrary. But in the first and second methods, the north area is always put in north area column, and the south area in south area column. it TRAVERSE SURVEYING. 61 260. METHOD III.-The First Meridian passes through the Most Northern Station of the Polygon, as through Station E (see fig. 17b). Bearing. S. 30~ E. South. East. S. 203 E. S. 600 W. N. 80~ W. North. N. 40~ E. N. 10~ W. N. 50~ E. Dist. N. lat. 10,00 17,00 1 11,00 20,00 1 21,00 1 17,694 3,0730 29,178 29,178 8,00 6,128 9,00 8,863 12,00 7,714 5. lat. E. dep.W.dep 8,661 7,001 0,000.8,794.0,500 5,0000 0,0000 11,0000 6,8404 5,1423 9,1925 18,1866 17,4257 1,5629 A or lat., B or and M dep. mer. dist. 0,0000 S. 8,661 2,5000 E. E. 2,5000 5,0000 E. S. 17,001 5,0000 E. 0,0000 5,0000 E. 0,0000 10,5000 E. E. 5,5000 116,0000 E S. 18,794 19,4202 E. E. 3,4202 22,8404 E. S. 10,500 13,7471 E. W. 9,0933 4,6538 E. N. 3,0730 4,0591 W. W. 8,7129 12,7720 W. N. 29,178 12,7720 W. 0,000 12,7720 W. N. 6,128 10,2009 W. E. 2,5711 7,6298 W. N. 8,863 8.4112 W. W. 0,7814 9,1927 W. N. 7,714 4,5965 W. E. 4,5962 0,0003 21,525 85,0050 364,9832 144,3446 12,4736 372,6614 N. Area. S. Ares. In this method, everything is the same as in methods 1 and 2, except finding the areas. Rule. The north or south multiplied by their respective east meridian distances, are put in their respective columns of areas, as in methods 1 and 2; but north and south latitudes multiplied by their respective west meridian distances, are put in contrary area columns. That is, S. lat. X E. mer. dist. is put in south area column; N. lat. X "E. mer. dist. is put in north area 62,5111 74,5485 35,4574 Area in acres = 117,3637 Second method = 117,3629 First method = 117,3629 column; S. lat. X W. mer. dist. is put in north area column; N. lat. X W. mer. dist. is put in south area column. The proof of the above rule will appear from the following (see fig. 17b). Draw the meridian E W through the point or station E; let p F, g H, r D, s K, R s, C w, and D x, be the departures respectively. North South Area Area Column. Column. n F X F p = south X by east = a a FG X (FP + G q)= south X by east = a/ a m I X i (H q + I r) = south X by east = a/ a/ I L X ' (I r + K L) south X by east = a/// at/ This includes figure I r v K + A V K S, S K being the b east meridian distance of K; then S K - i (K A) = mer. b' dist. of the middle of the line A K, which is - or east, if. b S K is more than K A K; but if S K is more than i A K, b/// then the meridian distance will be - or east, and if the mer. diet. S K is equal to ~ A K, then the mer. dist. of line K A - o. h l i -.; c:;.,.. ' ' ':. -,,. ' **.,. ' 62 TRAVERSE SURVEYING. We now suppose that S K is less than K A; therefore mer. distance to middle of K A = S K - A g = west or negative, and (S K -- A G). g K = figure g Ks y - A g K =- figure gKvy + K v s - AAg K; but the meridian distance being negative,.. the product must be negative; that is, the above product A A gK -g K v y K v S, which is equal to the A A y v, because we have to deduct g K v y + K v s, which have been including the figure K I r s; consequently north by west is to be added or put in south area column. Let this area be equal to b, and entered in the south area column. The mer. dist. of A is the same as that of B, and is found by adding j A g to the last mer. dist. to the middle of A K. That mer. dist. X by A B, gives an area to be added - figure g A B b - b, which is put in south area column. Also the mer. dist. in middle of B C is west, which multiplied by B C, will give the area B C w b = b//, which put in south area column. In like manner we find the area C D x w = b///, which put in south area column; and the area of D E x is west of the meridian b"", and is to be put in south area column. Hence it appears that those areas derived from east meridian distances are put under their respective heads, S. and N.; but those having west meridian distances, are put in their contrary columns. 261. Calculating the Offsets and Inlets. (See fig. 17e.) Sum Double Double The letters a, b, etc., show between Line 1. Base. of area. area. offs'ts add. Subt'ct what points on the line the areas are On a to b 40( 14 l9ti -- calculated. 107 78 8346 -- - When the area, and not the double 103 84 8652 -- 116 14 1604 _- area, of the polygon is given, then we On b to F take half the double area of the differ98 16 1568 ence of the offset and inlet columns, 190 46 --— 8740 and add of subtract to or from the area 102 60 --- 5100 94 30 2820 of the polygon, as may be the case., ( _um of ad _ -dition 205662 18228 In making out the bases, we subtract Sum of addition, 20562 18228 Sum of a tion, 2 12 150 from 190; put the difference, 40, Sum of subtraction, 18228 Sm on, in base column, and opposite which, Difference, 2334, to be in offset column, put 14; then 40 X 14 added to the area of the polygon. will give double the area of the A between 150 and 190. Again, take 190 from 297; the difference, 10?, is put in base column, opposite to which, in offset column, is put 78 = 14 + 64; then 107 X 78 = double the area of the trapezium between 190 and 297. This method of keeping field notes facilitates the computation of offsets and plotting detail. We begin at the bottom of the page or line, and enter the field notes as we proceed toward the top or end of the line. The chain line may be a space between two parallel lines, or a single line, as in fig. 17e. If the field book is narrow, only one line ought to be on the width of every page, and that up the middle (see sec. 211). I i II TRAVERSE SURVEYING. 63 ORtDNANCE METHOD. 262. Field Book, No. 16, Page 64. On the first day of May, 1838, I commenced the survey of part of Flaskagh, in the parish of Dunmore, and county of Galway, Ireland, surveyed for John Connolly, Esq. MICH'L MCDERMOTT, C. L. S. THOMAS LYNSKEY, Chain bearers THOMAS KING, J The angles have been taken by a theodolite, the bearing of one line determined, from which the following bearings have been deduced (see fig. 17e). Land kept on the right. We begin at the most northerly station, as by this means we will always add the south latitudes and subtract the north latitudes. Explanation. On line 1, at distance 210, took an offset to the left, to where a boundary fence or ditch, etc., jutted. The dotted line along said fence shows that the face next the dots is the boundary. At 297, offset of 64 links to Mr. JAWES RoaER's schoolhouse. At 340, offset of 70 links to south corner of do. The Width = 30, set down on the end of do. At 400, offset to the left of 14 links to a jutting fence. From 150 to 400, the boundary is on the inside or right, as shown by the characters made by dots and small circles joined. See characters in plates. From this point, 400, the boundary continues to the end of the line, to be on the left side of fence. At 804, met creek 30 links wide, 6 deep, clear water, running in a southern direction. At 820, met further bank of do. At 830, dug a triangular sod out of the ground, making the vertex the point of reference. Here I left a stick 6 inches long, split on top, into which split a folded paper having line 1-830 in pencil marks. This will enable us to know where to begin or close a line for taking the detail. At 960, offset to the right 20 links. At 1000, met station F, where I dug 3 triangular sods, whose vertexes meet in the point of reference. This we call leveling mark. The distance, 1000 links, is written lengthwise along the line near the station mark. The station mark is made in the form of a triangle, with a heavy dot in the centre. Distances from which lines started or on which lines closed, are marked with a crow's foot or broad arrow, made by 3 short lines meeting in a point. Along the line write the number of the line and its bearing. Line 2 may be drawn in the field book as in this figure, or it may be continued in the same line with line 1, observing to make an angle mark on that side of the line to which line 2 turns. This may be seen in lines 4 and 5, where the angle mark is on the right, showing that line 5 turns to the right of line 4. Line 2, total distance to station G = 1700 links. The distance from the station to the fence, on the continuation of line 2, is 10 links, which is set correctly on the line. 64 TRAVERSE SURVEYING. Key offset. See where line 2 starts from end of line 1. At the end of line 1, offset to corner of fence = 10. At 10 links on line 2, offset to corner = 2. This is termed the key offset, and is always required at each station for the computation of offsets and inlets. Running from one line to another. We mention the distance of the points of beginning and closing as follows: Line 5. This shows that the line started from 830, on line 1, o S and closed on 600, line 5. It also shows, from the - ~ ~ manner in which distances 804, 820 and 830 are written, that the line turns to the right of line 1. When we use a distance, as 830, etc., we make 2 broad arrows opposite the distance. This will enable us to mark them off on the plotting lines for future reference. We take detail on this line-it will serve as a check c when the scale is 2, 3, or 4 chains to 1 inch scale. o X We number it and enter it on the diagram, which must always be on the first page of the survey. The diagram will show the number of the line; the distances on which it begins and ends; the reference distances. This will enable the surveyor to lay down his plotting or chain lines, and test the accuracy of the survey. Having completed the plotting plan, we then fill in the detail, and take a copy or tracing of it to the field, and then compare it with the locality of the detail. This comparison is made by seeing where a line from a corner of a building, and through another corner of a fence or building, intersects a fence; then from the intersection we measure to the nearest permanent object. We draw the line in pencil on the tracing, and compare the distance found by scale with the measured distance. Some surveyors can pace distances near enough to detect an error. On the British Ordnance Survey, the sketchers or examiners seldom used a chain, unless in filling in omitted detail. On Supplying Lost Lines or Bearings. 263. It would be unsafe to depend on this method, unless where the line or lines would be so obstructed as to prevent the bearings and distances to be taken. The surveyor seeing these difficulties, will take all the available bearings and measure the distances with the greatest accuracy, leaving no possible doubt of their being correctly taken. Then, and not till then, can he proceed to supply the omissions. Case 1. In fig. 17b, we will suppose that all the lines and bearings have been correctly taken, but the distance I K has been obliterated, and that its bearing is given to find the distance I K. Let the bearing of I K be S. 60 W. From sec. 259, method 2, we have calculated the departure of K from the line A B = 17,4257 departure of I from do. - 35,6123 consequently the departure of line I K is = K L - 18,1866 We have the angle K I L = 60~, therefore the < I K L - 30~, and its departure,5000 The product of the last two numbers will give (by sec. 167) I L = 9,0933 By E. I, 47, from having I K and K L we find 10,50 = I K or I L = 9,1933, divided by the lat. or cos. of 60~ or,86603 = 10,50 = I K F: TRAVERSE SURVEYING. 65 Case 2. The bearing and distance of the line I K is lost. Here we have to find the lines I L and L K. From the above sec., method 2, we haveLat. K A 3,0726 N. Lat. E F = 8,6610 S. Lat. A B -_ 29,1780 N. Lat. F G = 17,0010 S. Lat. B C 6,1280 N. Lat. H I 18,7940 S. Lat. C D 8,8630 N. 44,456 S. Lat. D E 7,7140 N. 54,9556 N. 44.4560 S. Lat. I L = 10,4996, and from above K L - 18,1866. Therefore, by E. 1, 47, K L2 + L I2 -- K I2; consequently K I is found. But I K * cos. < K I L I L. IL Therefore -- = cosine < K I L, which take from table of lat. and dep., I K and it gives < K I L = 60~. Consequently the bearing is S. 60~ W., K L 9,0933 or -- 8 —,8662 = cos. <IKL;.. the < I K L -30~, and I K 10,50 the bearing of the line K I = N. 60~ E. from station K. Case 3. Let there be two lines wanted whose bearings are known to be S. 60~ TW. and N. 80~ IW. Here the station K may be obstructed by being in a pond, in a building, or that buildings are erected on part of the lines I K and A K (see fig. 17b). We find from case 2 that A is south of F = 51,8830 I is south of F = 44,4560 A is south of I == t g = A a 7,4270 We have above, a I = dep. of I - d = 35,6123 Now we have A a and a I,.'. we find the line A I. And A a divided by a I gives the tangent of < A I a -,2085. And the < A Ia = 110 47... I a divided by the cosine 10~ = A I = 35,6123 -,9789 - 36,38. Now we have the < A I a = 11~ 47/ and the < A a I =90;.-. the < a A 1 78~ 13 consequently the < g A I = 11~ 47/ but the < gA K = 10~ 00,.-. < K A I = 21~ 47/. Again the < K I a = 30~ 00 and the < A a = 11~ 47T,.'. AIK 18~13t. And by Euclid I, 32, we have the < A K I = 140~ 30/. By sec. 194, we have sine < K A K IA I:: sine < A I K: A K. sine < A K I A I:: sine < K A I: K I. Case 4. Let all the sides be given, and all the bearings, except the bearings of I K and A K, to find these bearings. By the above methods we can find the departure a i of the point, east of the meridian A B. We also have the difference of lat. of the points A and I = t g = A a..'. (A a)2 - (I a)2 = the square of A I;.-. A I may be found. Or, A a.- I a = tangent of the < A I a;.'. <A I a may be found. And I a - cos. < A I a, will give the side A I. Now having the sides A 1, A K and K I, by sec. 205, we can find thee angles K A I and K I A. And the < A I a and < A I K are given;. their sum < A I K is given;.. the bearing of the line I K is given. I i. t I I I I '- , - 11 — -,;..Z.. ., 1 11 i,:, i7, - - I, 7 14. i 1 , I. I I f I I;,;.! , : ", il I 66 TRAVERSE SURVEYING. 264. Calculation of an Extensive Survey (fig. 17c), where the First has been made. Calculated ist. Equated Equated Line. Bearingr. in N. lat. S. let. E. dep. W. dep. Equted iI ___ _______ chains B C N. 400 E. 8,00 6,1283 5,1423 6,128 C D N. 100 W. 9,00 8,8633 1,5629 8,863 D E N. 50 E. 12,00 7,7135 9,1925 7,714 E F S. 30~ E. 10,00 8,6603 5,0000 8,660 F G South. 17,00 17,0000 17,000 G H East. 11,00 11,0000 H I S. 200 E. 20,00 18,7938 6,8404 18,794 I K S. 60~ W. 21,00 10,5000 18,1866 10,500 KA N. 80~ W. 17,69 3,0727 17,4260 3,073 A L North. 7,00 7, 7,0000 700 L M West. 8,00 8,0000 M N N. 550 W. 9,00 5,1622 7,3724 5,162 N 0 N. 75~ W. 7,00 1,8117 6,7615 1,812 0 P N. 27~ W. 6,00 5,3461 2,7239 5,346 P Q N. 33~ E. 10,00 8,3867 5,4464 8,387 QR N. 77~ W. 9,00 8,9330 1,0968 8,933 R S N. 37~ W. 9,00 7,1878 5,4163 7,188 S T N. 43~ E. 11,00 8,0449 7,5020 8,045 T U S. 520 E. 13,00 8,0036 10,2441 8,003 U B IS. 29~ E. 16,80 14,6936 8,1448 ___14,694 77,6502 77,6512 68,5125 68,54667751 7751 7,651 Here we find that line K A, which theoretically should close on A, wants but 1,3 links.. i To find the Most Westerly Station. By looking to fig. 17d, it will appear that either the point S or P is the most westerly. L M 8,000 west. MN — 7,370 W. NO= 6,766W. OP- 2,722W. Point P = 24,858 west of the assumed point L. PQ - 5,448E. 19,410. QR = 1,095 W. RS 5,414W. i Point S = 25,919 west of the assumed point L. Therefore the point S is the most westerly station, through which, if the first meridian be made to pass the area, can be found by the second i method. To Find the Meridian Distances. When the first mer. passes through the most westerly station, we add the eastings and subtract the westings. When the first mer. is through the most easterly station, we add the w estings and subtract the eastings. When the first mer. passes through the polygon, we add the eastings in that part east of the first mer., and subtract them in that part west of that mer. We also subtract the westings in that part east of that mer., and add them west of it. I i1 TRAVERSE SURVEYING. Meridian is made the Base Line A B, at each of which a Station by the Third Method. 67 Equated Equated A or latitude, B, or North area. South area. E. dep. WV dep. alfd Meridian dist. balf departuire. 6,145 9,195 5,002 11,002 1,561 N. 6,128 E. 2,572j N. 8,863 W. 0,7801 N. 7,714 E. 4,597kl 2,572j E. 5,145 4,364k E. 3,584 8,181 k E. 12,779 6,842 18,184 17,423 8,000 7,370 6,760 2,722 5,448 1,095 5,414 7,503 10,246 8,146 68,529 68,529 S. 8,660 15.280 E. E. 2,501 17,781 S. 17,000 17,781 E. 0,000 17,781 0,000 23, 282 E. E. 5,501 28,783 S. 18,794 32,204 E. E. 3,421 35,625 S. 10,500 26,533 E. W. 9,092 17,441 N. 3,073 8,7294 E. W. 8,711k 0,018 N. 7,000 0,018 E. 0,000 0,018 0,000 3,982 W. W. 4,000 7, q82 N. 5,162 11,667 WV. W. 3,685 15,352 N. 1,812 18,732 W. W. 3,380 22,112 N. 5,346 23,473 W. W. 1,361 24,834 N. 8,387 22,110 W. E. 2,724 19,386 N. 8,93S3 19,933 W. W. 0,547k 20,481 N. 7,188 23,188 W. W. 2,707 25,895 N. 8,045 22,143 W. E. 3,751j 18,392 15,7643 38,6826 63,1121 26,8258 0,1260 106,1915 59,8487 132,3248 302,2770 605,2420 2 78,5965 60,2261 33,9424 125,4867 185,4366 178,0660 166,6763 178,1445 S. 8,003 E. 5,123 S. 14,694 B. 4,0 73 13,269 W. 8,146 4,073 W. 0,000 1 310,5513 t 2246,4179 310,5613 Required area = 1935, e chains, or 193,5867 acres. I; % " w.,p a 68 VARIATION OF THE COMPASS. VARIATION OF THE COMPASS. 264a. In surveying an estate such as that shown in fig. 17c, we run a base line through it, such as A M. We find the magnetic bearing, and its variation from the true meridian. We measure it over carefully, then take a fly-sheet and remeasure the same, then compare, and survey a third time if the two surveys differ. With good care in chaining, it is possible to make two surveys of a mile in length to agree within one foot. With a fifteen feet pole they agree very closely. We refer the base line A M to permanent objects as follows: Theodolite at station A, read on station M, 0~ 00 On the S.W. corner of St. Paul's tower, 15~ 11I On the S.E. corner of the Court Iouse (main building), 27~ 10/ On the S.W. corner of John Cancannon's Mill, 44~ 16' On the N.E. corner of John Doe's stone house, 2760 15' On the N.W. corner of Charles Roe's house, 311~ 02' Any two or three of these, if remaining at a future date, would enable us A determine the base A M, to which all the other lines may be referred. The variation of the compass is to be taken on the line at a station where there is no local attraction, the station ought to be at same distance from buildings. We find the magnetic bearing of A M = N. 64~ 10' E., as observed at the hour of 8 A. M., 8th December, 1860, at a point 671 links north of station A, on the base line A M. Thermometer = 40~, and Barometer 29 inches. Let the latitude of station - 530 45/ 00"O Polar distance of Pole Star (Polaris) - 1~ 25/ 30/ (Declination of Polaris being - 88~ 34/ 30//,.. its polar distance is found by taking the declination from 90.) To Find at what time Polaris will be at its Greatest Azimuth or Elongation. 264b. Rule. To the tan. of the polar dist. add the tan. of the lat.; from the sum take 10. The remainder will be the cosine of the hour angle in space, which change into time. The time here means sidereal. To Find the Greatest Azimuth or Bearing of Polaris. 264c. Rule. To radius 10 add sine of the polar distance; from the: sum take the cosine of the latitude. The remainder will be the sine of the greatest azimuth. To Find the Altitude of Polaris when at its Greatest Azimuth. 264d. Rule. To the sine of the latitude add 10; from the sum take the cosine of the polar distance. The difference will be the log. sine of the altitude. In the above example we have lat. = 53~ 45t, and its tan. = 10,1357596 Polar distance = 1~ 25' 30/, and its tangent = 8,3957818 88~ 3/ 056 = hour angle in space, whose cosine = 8,5315414 This changed into time gives 5 h., 52 m., 12,3 s. This gives the time from the upper meridian passage to the greatest elongation. i i, ' VARIATION OF THE COMPASS. 69 To Find when Polaris will Culminate or Pass the Meridian of the Station on Line A M, being on the Meridian of Greenwich on the 8th Dec., 1860. 264e. From Naut. Almanac, star's right ascension = lh. 08m. 43,5s. Sun's right ascension of mean sun (sidereal time) = 17 09 59,9 Sidereal time, from noon to upper transit = 7 68 52,6 Sidereal time, from upper transit to greatest azimuth = 5 00 01 Sidereal time from noon to greatest eastern azimuth = 2 58 52 Now, as this is in day time, we cannot take the star at its greatest eastern elongation, but by adding 5h. 52m. 12,3s. to 7h. 58m. 52,6s., we find the time of its greatest western azimuth - 13h. 51m. 4,9s. from the noon of the 8th December, and by reducing this into mean time, by table xii, we have the time by watch or chronometer. To Find the Altitude and Azimuth in the above. 264f. Lat. 530 45 N., sine + 10 + 19,906575 cos.- 9,771815 N. polar dist. 1~ 25/ 30/, cos. = 9,999866 sine + 10 + 18,395648 sine = 9,906709 sine = 8,623833 True altitude = 53~ 46' 27". Greatest azimuth = 2~ 24' 37/". Alpha and Beta are term- *. o~ ed the pointers, or guards, * * because they point out the,d <. a Pole star, which is of the S * same (second) magnitude, i * and nearly on the same line. The distance from Alpha URSAMAJO, or DIP, or DI or THE PLOUGH, Ursamajor to the Pole star at its under transit. is about five times the distance between the two pointers. When Alioth and Polaris are on the same vertical line, the Pole star is supposed to be on the meridian. Although this is not correct, it would not differ were we to run all the lines by assuming it on the meridian; but as we sometimes take Polaris at its greatest azimuth, both methods would give contradictory results. 264g. Alioth and Polaris are always on opposite sides of the true pole. This simple fact enables us to know which way to make the correction for the greatest azimuth. (For more on this subject, see Sequel Canada Surveying, where the construction and use of our polar tables will be fully explained.) Variation of the Compass. 264h. Variation of the compass is the deviation shown by the north end of the needle when pointing on the north end of the mariner's compass and the true north point of the heavens; or, it is the angle which is made by the true and magnetic meridians. N M When the magnetic meridian is west of the C true meridian, the variation is westerly. Let S N = true meridian, S = south, and N = north../ B Let M 0 = magnetic meridian through station 0. Let the true bearing of B = N. 60~ 40 E. 0 Let the magnetic do. N. 50 50/ E. Variation east 9~ 50/ In this case, the true bearing is to the right of the magnetic. S i a 70 VARIATION OF THE COMPASS. Let M = magnetic and N = true North Pole. M N Let the true bearing of B = N. 60~ 50' E. Let the magnetic do. - N. 70~ 40/ E. Variation west = 9~ 50/ Here the true bearing is to the left of the B magnetic. In the first example we protract the < N 0 C = < M 0 B, which show that B is to the right of C. In the second example we make the < N 0 D 0 =M 0 B, which shows that B is to the left of D. Hence appears the following rule: S Rule 1. Count the compass and true bearings from the same point north or south towards the right. Take the difference of the given bearings when measured towards the east or towards the west; but their sum when one bearing is east and the other west. When the true bearing is to the right of the magnetic, the variation is east. When the true bearing is to the left of the magnetic, the variation is west. Example 3. Let the true bearing = N. 60~ W. = 300~, and the magnetic bearing- N. 70~ W. = 290~. Variation east - 10~. Here we have the true bearing at 300~, counting from N. to right, and the magnetic bearing at 2900, counting from N. to right. 10~ variation east, because the true bearing is to the east of the magnetic. Example 4. Let true bearing = N. 60~ W. = 300~, from N. to right. and magnetic bearing = N. 70~ W. = 290~, from N. to right. Variation 10~ west, because the true bearing is to the right of the magnetic. Example 5. Let true bearing = N. 5~ E. = 5 from N. to right, and the magnetic bearing = N. 5~ W. = 365 from N. to right. Variation 10~ east, because the true bearing is to the right of the magnetic. Rule 2. From the true bearing subtract the magnetic bearing. If the remainder is +-, the variation is east; but if the remainder or difference is -, the variation is west. Example 6. True bearing N. 60~ 40' E. Magnetic bearing = N. 500 50 E. + 9~ 0/ = variation east. Example 7. True bearing = N. 5~ E. = +, Magnetic bearing = N. 5~ W. - -. - 10~ east. Hery we call the east +, and the west negative -; and by the method of subtracting algebraic quantities, we change the sign of the lower line, and add them. Example 8. Let true bearing = N. 16~ W. -, and magnetic bearing = N. 6~ W. -. - 10~ = variation 10~ west. i [ I VARIATION OF THE COMPASS. 71 Let us now find the true bearing of the line A M in fig. 17c. By sec. 264a, we have the magnetic bearing of A M = N. 64~ 10/ E., < from Polaris, at its greatest western elongation, to the base line A M, as determined = 80~ 40'. The work will appear as follows: On the evening of the 8th December, 1860, we proceeded to the station mentioned in sec. 264a. Set up the theodolite on the line A M. At a distance of 10 chains, I set a picket fast in the ground, whose top was pointed to receive a polished tin tube, half an inch in diameter. Not wishing to calculate the necessary correction of Polaris from the meridian, I preferred to await until it came to its.reatest western azimuth, being that time when the star makes the least change in azimuth in 6 minutes, and the greatest change in altitude, this being the time best adapted for finding the greatest azimuth and true time of any celestial object.' The station is assumed on the meridian of Greenwich. If on a different meridian, we correct the sun's right ascension. (See our Sequel Spherical Astronomy, and Canada Surveying.) On the morning of 9th December, 1860, at lh. 51m. 5s., found the base line A M to bear from Polaris = N. 80~ 40 00// E. Magnetic bearing of line A M = N. 64~ 10' 00 E. Polaris at its greatest azimuth = N. 80~ 40/ 00/ E. Greatest azimuth from sec. 264f - 20 24/ 37" Bearing of the line A M from true meridian = N. 78~ 15' 23/ E. Magnetic bearing of line A Mh = N. 64~ 10' 00" E. By rule 2, the variation = N. 14~ 05' 23" E. From sec. 264f, we have the star's altitude when at its greatest azimuth. True altitude = 53~ 46G 27// Correction from table 14 for refraction = 42" Apparent altitude = 53~ 47' 09/ We had the telescope elevated to the given apparent altitude until the star appeared on the centre, then clamped the lower limb, and caused a man to hold a lamp behind the tin tube on the line A M. Found the < 80~ 40/, as above. Here the vernier read on Polaris at its greatest western azimuth 279~ 20' 00" Read on the tin tube and picket on the line A M 00~ 00' 00" On the true meridian - 281~ 44' 37/ The last bearing taken from 360~ will give the true bearing of A M N. 78~ 15/ 23/ E. After having taken the greatest azimuth, we bring the telescope to bear on A M; if the vernier read zero, or whatever reading we at first assume, the work is correct. If it does not read the same, note the reading on the lower limb, and, without delay, take the bearing of the Pole star, which is yet sufficiently near to be taken as correct, and thus find the angle between it and the base line. The surveyor, having two telescopes, will be in no danger of committing errors by the shifting of the under plate, can have one of the telescopes used as a tell-tale fixed on some permanent object, on which he will throw the light shortly before taking the azimuth of Polaris, to ascertain if the lower limb remained as first adjusted. 264i. A second telescope can be attached to any transit or theodolite, so as to be taken off when not required for tell-tale purposes, as follows: To the under plate is riveted a piece of brass one inch long, three-fourths IN:..:.. * 72 UNITED STATES SURVEYING. inch wide, and two-tenths thick. On this there is laid a collar or washer, about one-eighth inch thick. To these is screwed a right angled piece in the form of L, turned downwards, and projecting one inch outside of the edge of the parallel plates. Into the outer edge of the L piece is fixed a piece having a circular piece three-fourths inch deep, having a screw corresponding to a thread on the telescope of the same depth. This screw piece is fastened on the inside of the L piece by a screw, and has a vertical motion. When we use this as a tell-tale, we bring it to bear on some well defined object, and then clamp the lower plate. We then bring the theodolite telescope to bear on the above named object or tin tube, and note the reading of the limb. After every reading we look through the tell-tale telescope to see if the lower plate or limb is still stationary. If so, our reading is correct; if not, vice versa. The expense of a second telescope so attached will be about twelve dollars, or three pounds sterling. The instrument will be lighter tan those now made with two telescopes, such as six or eight inch instruments. This adjustment attached to one of Troughton and Simm's five inch theodolite has answered our purposes very well during the last twenty-two years. We prefer it to a six inch, as we invariably, for long distances, repeat the angles. (See sec. 212.) 265. To Light the Cross Hairs. Sir Wm. Logan, Provincial Geologist of Canada, has invented the following appendage: On the end of the telescope next the object is a brass ring, half an inch wide, to which a second piece is adjusted, at an angle of 450. This second piece is elliptical, two inches by two and three-eights, in the centre of which is an elliptical hole, one inch by three-eighths. This is put on the telescope. The surface of the second piece may be silvered or polished. Our assistant holds the lamp so as to illuminate the elliptical surface, which then illuminates the cross hairs. Hle can vary the light as required. This simple appendage will cost one and a half dollars, and will answer better than if a small lamp had been attached to the axis of the telescope, as in large instruments. Those surveyors who have used a hole in a board, and other contrivances, will find this far more preferable. We have a reflector on each of our telescopes. The tell-tale being smaller is put into the other, and both kept clean in a small chamois leather bag, in a part of the instrument box. (See sec. 211.) UNITED STATES SURVEYING. The following sections are from the Manual of Instructions published by the United States Government in 1858, which are called New Instructions, to distinguish them from those issued between 1796 and 1855, which are called the Old Instructions. The notes are by M. McDermott. SYSTEM OF RECTANGULAR SURVEYING. 266. The public lands of the United States are laid off into rectangular tracts, bounded by lines conforming to the cardind point..-.:. X UNITED STATES SURVEYING. 72m These tracts are laid off into townships, containing 23040 acres. These townships are supposed to be square. They contain 86 tracts, called sections, each of which is intended to be 640 acres, or as near that as possible. The sections are one mile square. A continuous number of townships between two base lines constitutes a range. 267. The law requires that the lines of the public surveys shall be governed by the true meridian, and that the township shall be six miles squaretwo things involving a mathematical impossibility, by reason of the convergency of the meridians. The township assumes a trapezoidal form, which unequally develops itself more and more as the latitude is higher. * In view of these circumstances, the act of 18th May, 1796, sec. 2, enacts that the sections of a mile square shall contain 640 acres, as nearly as may be. * The act 10th May, 1800, sec. 3, enacts "That in all cases where the exterior lines of the townships thus to be subdivided into 'sections, or half sections, shall exceed, or shall not extend six miles, the excess or deficiency shall be specially noted, and added to or deducted from the western and northern ranges of sections or half sections in such township, according as the error may be, in running the lines from east to west or from south to north. 268. The sections and half sections bounded on the northern and western lines of such townships, shall be sold as containing only the quantity expressed in the returns and plats respectively, and all others as containing the complete legal quantity." The accompanying diagram, marked A (see sec. 271), will illustrate the method of running out the exterior lines of townships, as well on the north as on the south side of the base line. OF MEASUREMENTS, CHAINING AND MARKING. 269. "Where uniformity in the variation of the needle is not found, the public surveys must be made with an instrument operating independently of the magnetic needle. Burt's Solar Compass, or other instrument of equal utility, must be used of necessity in such cases; and it is deemed best that such instruments should be used under all circumstances. Where the needle can be relied on, however, the ordinary compass may be used in subdividing and meandering."-Note Traversing. BASE LINES, PRINCIPAL MERIDIANS, AND CORRECTION OR STANDARD LINES. 270. Base Lines are lines run due east and west, from some point assumed by the Surveyor General. North and south of this base line, townships are laid off, by lines running east and west. Standard or Correction Lines are lines run east and west, generally at 24 miles north of the base line, and 30 miles south of it. These lines, like the townships, are numbered from the base line north or south, as the case may be. Principal Meridians are lines due north and south from certain given points, and are numbered first, second, third, etc. Between these principal meridians the tiers of townships are called ranges, and are numbered 1, 2, 8, 4, etc., east or west of a given principal meridian. 72b UNITED STATES SURVEYING. All these lines are supposed to be run astronomically; that is, they are run in reference to the true north pole, without reference to the magnetic pole. In proof of this, it is well to state that the Old Instructions has shown, in the specimen field notes, that the true variation has been found. See pages 13 and 18, and in the New Instructions, pages 28 to 35, both inclusive. Here the method of finding the greatest azimuth is not given, although there is a table of greatest azimuths for the first day of July for the years 1851 to 1861, and for lat. 32~ to 44~. At page 30 is given the mean time of greatest elongation for every 6th day of each month, and shows whether it is east or west of the true meridian. At page 27 are given places near which there is no variation. At page 29 are given places with their latitudes, longitudes, and variation of the compass, with their annual motion. The method of finding these for other places and dates is not given in either manual. For these, see sequel Canadian method of surveying side lines. For formulas and example, see sections 264a and 264b of this manual. Principal Meridians. The 1st principal meridian is in the State of Ohio. The 2nd principal meridian is a line running due north from the mouth of the Little Blue River, in the State of Indiana. The 3d principal meridian runs due north from the mouth of the Ohio River to the State line between Illinois and Wisconsin. The 4tl principal meridian commences in the middle of the channel, and at the mouth of the Illinois River; passes through the town of Galena; continues through Illinois and Wisconsin, until it meets Lake Superior, about 10 chains west of the mouth of the Montreal River. For further information, see Old Instructions, page 49. Ranges are tiers of townships numbered east or west from the established principal meridian, and these lines run north or south from the base line. They serve for the east and west boundary lines of townships. On these lines, section and quarter section corners are established. These corners are for the sections on the west side of the line, but not for those on the east side. (See Old Instructions, page 50, sec. 9.) Note. This is not always the case. There are many surveys where the same post or corners on the west line of the township have been made common to both sides. This is admitted in the Old Instructions, page 54, sec. 21. Townships are intended to be six miles square, and to contain 36 sections, each 640 acres. They are numbered north and south, with reference to the base line. Thus, Chicago is in township 39 north of the base line, and in range 14 east of the third principal meridian. Township lines converge on account of the range lines being run toward the north pole, or due north. This convergency is not allowed to be corrected, but at the end of 4 townships north, and 5 south of the base line, this causes the north line of every township to be 76,15 links less than the south line, or 304,6 links in 4 townships. The deficiency is thrown into the west half of the west tier of sections in each township, and is corrected at each standard line, where there is a jog or offset made, so as to make the township line on the standard line six miles long. In surveying in the east 5 tiers of sections, each section UNITED STATES SURVEYING. 72. is made 80 chains on the township lines. In the east tier of quarter sections of the west tier, each quarter section is 40 chains on the east and west township and section lines. Example. Let 1, 2, 3 and 4 represent 4 townships north of the base line. Township number 1 will be 6 miles on the base line, and the North boundary of section 6, in township 1 - 7923,8 links. North boundary of section 6, in township 2 - 7847,7 links. North boundary of section 6, in township 3 7771,5 links. North boundary of section 6, in township 4 7695,4 links. Here we make the south line of sec. 30, in township 5 = 8000 links. 271. Townships are subdivided into 36 sections, numbered from east tc west and west to east, according to the annexed diagram. Lot 1 invariably begins at the N.E. corner, and lot 6 at the N.W.; lot 30 at S.W., and lot 36 at the S.E. corner. * Surplus or deficiency is to be thrown into the north tier of quarter sections on the north boundary, and in the west tier of quarter sections on the west boundary of the township. 78,477 5 78,477 4 3 2 1 7 8 9 10 11 12 18 17 16 15 14 13 T. 2 N. 19 24 30 25 31 36 80 80 80 80 79,238 T. 1 N. 80 R. IE. R. IIE. Base Line. North and South Section Lines How to be Surveyed. 272. Each north and south section line must be made 1 mile, except those which close to the north boundary line of the township, so that the excess or deficiency will be thrown in the north range of quarter sections; viz., in running north between sections 1 and 2, at 40,00 chains, establish the quarter section corner, and note the distance at which you intersect the north boundary of the township, and also the distance you a~. 0. f 0 v f Of *t0@~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 72d UNITED STATES SURVEYING. fall east or west of the corresponding section corner for the township to the north; and at said intersection establish a corner for the sections between which you are surveying.-Old Instructions, p. 9, sec. 28. East and West Section Lines. Random or Trial Lines. * 273. All east and west lines, except those closing on the west boundary of the township, or those crossing navigable water courses, will be run from the proper section corners east on random lines (without blazing), for the corresponding section corners. At 40 chains set temporary post, and note the distance at which you intersect the range or section line, and your falling north or south of the corner run for. From which corner you will correct the line west by means of offsets from stakes, or some other marks set up, or made on the random line at convenient distances, and remove the temporary post, and place it at average distance on the true line, where establish the quarter section corner. The random line is not marked but as little as possible. The brushwood on it may be cut. The true line will be blazed as directed hereafter. The east and west lines in the west tier are by some run from corner to corner, and by others at right angles to the north and south adjacent lines. East and West Lines Intersecting Navigable Streams. 274. Whenever an east and west section line other than those in the west range of sections crosses a navigable river, or other water course, you will not run a random line and correct it, as in ordinary cases, where there is no obstruction of the kind, but you will run east and west on a true line (at right angles to the adjacent north and south line) from the proper section corners to the said river or navigable water, and make an accurate connection between the corners established on the opposite banks thereof; and if the error, neither in the length of the line nor in the falling north or south of each other of the fractional corners on the opposite banks, exceeds the limits below specified in these instructions for the closing of a whole section, you will proceed with your operations. If, however, the error exceeds those limits, you will state the amount thereof in. your field notes, and proceed forthwith to ascertain which line or lines may have occasioned the excess of error, and reduce it within proper bounds by resurveying or correcting the line or lines so ascertained to be erroneous, and note in your field book the whole of your operations in determining what line was erroneous, and the correction thereof. (See Old Instructions, p. 10, sec. 32.) Limits in closing = 150 links. Note. From sec. 272 we find that the north and south lines are intended to be on the true meridian from the south line of the township to its north boundary. This is the intention of the act Feb., 1805. From sec. 273 we find that in the east 5 tiers of sections of every township, a true line is that which is run from post to post, or from " a corner to the corresponding corner opposite." But in the west tier of sections, a true line is that which is run at right angles to the adjacent north and south line; that is, the north and south line must be run before the east and west line can be established. This agrees with the above act, which requires that certain lines are to be run due east or west, as the ease may be.-Old Instructions, p. 10. UNITED STATES SURVEYING. 72s Note 2. In many of the old surveys, the field notes show that the surveyor ran from corner to corner on the west and north tiers of sections. This appears to be the case in town. 39 N., range 14 E., of the third principal meridian, surveyed by Mr. John Walt in 1821. This will also appear from the Old Instructions, p. 54, sec. 21, where it is stated as follows: "Previous to 1828, some of the deputies considered, in making the calculations of the area of the north and west tiers of quarter sections in a township, that the quarter section corners on the township and range lines were common to the sections on both sides of the line, whilst others adopted the method now in use, and particularly explained in diagram numbers 4 and 6." At one time, some of the deputy surveyors, in subdividing a township through which a navigable stream passed, ran a random line east between the proper sections, and corrected it west, making the corner to the fractional sections on both banks of the river, and on the true line. Others pursued the method as now required. Note 3. From this appears the necessity of having a copy of the original Field Notes, so as to know which method to pursue in order to reestablish any line or corner, and to know if the surveyor deposited charcoal at the corner or corners. Insuperable Obstacles. Witness Points. 275. Whenever your course may be obstructed by insuperable obstacles, such as ponds, swamps, marshes, lakes, rivers, creeks, etc., you will prolong the line across such obstacles, by taking the necessary right angle offsets, or, if this is inconvenient, by a traverse or trigonometrical operation, until you regain the line on the opposite side. And in case a north and south, or a true east and west line is regained in advance of any obstacle, you will prolong and mark the line back to the obstacle so passed, and state all the particulars in relation thereto in your field notes; and at the intersection of lines with both margins of impassable obstacles, you will establish a witness point (for the purpose of perpetuating the intersections therewith), by setting a post, and giving in your field notes the course and distance therefrom to two trees on opposite sides of the line, each of which trees you will mark with a blaze, and notch facing the post, except on the margins of navigable water courses or navigable lakes. In these cases you will mark the trees with the proper number of fractional section, township and range.-O. I., p. 7, sec. 22. This sec. is the same as that in the N. I., p. 3. Note. In fractional townships it appears that the north and south lines are first established, and afterward the east and west lines are run due east ad west, or at right angles to the north and south lines. (See the U. S. act 11 Feb., 1805, and sections 272 and 273.) Note 2. It appears from the manuals that where a north and south line meets a navigable stream, it runs directly across it, and that some surveyors run directly across navigable waters on east and west lines, and others close on it, showing the jog or difference in closing, which must not be more than 150 links from a straight line. Hence it appears that where the official field notes do not show a jog, none exists. Limits in Closing. 276. Any excess or deficiency in the length of any township boundary %::~~~~~~~~~i.~i%:' ': lIP~_;. 72f UNITED STATES SURVEYING. line, or excess of error in the falling off from the corner to which any closing township line shall be run, that may exceed five chains, or any excess or deficiency exceeding one chain in the length of any section line, or excess of error in falling off from the corner to which any section line shall be run, that shall exceed one chain in closing the lines of a whole section; and at the same rate for the section lines, and at the same rate of one chain and fifty links per mile. of the meanders (traverse survey), in closing the meanders of a navigable river, or other water course, with the line or lines of a fractional section, must be corrected by you, and reduced within those limits, before leaving the ground, by resurveying the line or lines which may have occasioned the excess or deficiency in the length of such township or section line, or excess of error in closing the lines of a township, or of a whole or fractional section.-O. I., p. 8, sec. 25. Meandering of Navigable Streams. 277. Standing with the face looking down the stream, the bank on the left is termed the "left bank," and that on the right, the "right bank." Both these banks are to be meandered (traversed) by taking the bearings and distances of their sinuosities, and the same entered in the field book. Where township or section lines cross navigable waters, the line is marked by posts, and bearing trees, and mounds, as the case may require at the time of running those lines. In meandering, you are to commence at one of those corners and meander to the next meander corner, carefully noting your intersections with all meander corners, The opposite bank is to be meandered in like manner. The crossing distance between the meander corners, on the same line, is to be ascertained by triangulation, in order that the river may be protracted with entire accuracy. The particulars to be given in the field book. All lakes and deep ponds of the area of 25 acres and upwards, also all bayous, shallow ponds readily to be drained, are not to be meandered. Notice all streams of water falling into the river, lake or bayou you are surveying, stating the width at their mouth; also all springs, noting their size, depth, and kind of water; also the head and mouth of all bayous, and all islands, rapids and bars are to be noticed, with intersections to their upper and lower points to establish their exact situation. Note the elevation of the banks of rivers and streams, the heights and falls of cascades, and the length of rapids. Trees are Marked for Line and Bearing Trees. 278. All trees left standing on a line are marked with 3 marks or blazes on front and rear; the distance on the line, the kind of timber, and diameter, is marked in the field book. Trees are also marked on both sides of the line, making one blaze on the front, another on the rear, and one on the side next the line. By these means the situation of the line may be determined approximately at a future time. (See sec. 211.) Note. It is hard to expect a true line from corner to corner where trees are allowed to stand on the line. The Canadian plan of cutting everything off the line is preferable. 279. Township corners are marked by a post, whose 4 sides are marked UNITED STATES SURVEYING. 72g by 6 notches, directed to the 4 cardinal points. Posts to be 3 feet above the ground, not pointed but set in the ground. There are to be, when possible, 4 bearing trees marked, 1 in each township, each having a large blaze facing the post, having marked thereon with a marking iron the range, township and section. 280. Section corners have 4 bearing trees, one in each section. Quarter section corners have but two bearing trees. The bearings, distances, wood, and diameter of these are entered in the field book. The section corner post will be notched on two sides. Example. The post corner sections 9, 10, 15, 16, will have 2 marks or notches on the north side and 4 on the south side, to signify that this is 2 miles from the north boundary and 4 miles from the south boundary. Bearing trees have the sections cut on them. Note. It would be well in this example to have 3 marks on the east side, to show that it is three miles from the east boundary of the township. These notches would at any future time enable us to know which corner we are at in the absence of bearing trees. 281. Township corners in a prairie, or other situation where bearing or witness trees are not at hand, will be perpetuated by depositing in the ground, and at least 3 inches beneath the natural surface thereof, a portion of charcoal (the quantity to be specified in your field notes), not less than two quarts at the place of such corner, over which you will erect a mound of earth 3 feet high, 5 feet square at the base, and 2 feet square at the top, the sides whereof must be revetted or faced with sods laid horizontally and in successive layers on each other, each of said layers having an offset inwards, corresponding to the general slope of the face of the mound; in this there is to be a post which must rise 1 foot above the top of the mound. Or you will deposit at the place of the corner 3 stones, not less than 5 inches square by 3 inches thick, all of which you will describe in the field notes. The top of the uppermost stone to be 3 inches below the natural surface of the ground, and the other 2 successively and beneath the first; and over said stone erect a mound, as if it were made over charcoal or stone. You may perpetuate the corner by inserting endways into the ground, a stone of the dimensions marked, and set in the manner mentioned, over which no mound need be erected. 282. If a township corner, where bearing or witness trees are not to be found within a reasonable distance therefrom, shall fall within a ravine, or any other situation unfavorable to the erection of a mound, you will select in the vicinity thereof a suitable plot of ground as a site for a bearing or witness mound, and erect thereon a mound of earth, as if it were at the township corner, with charcoal or stone deposited beneath, as before directed for township corner, and measure, and state in your field notes the distance and course from the position of the true corner, of the bearing or witness mound so placed and erected. Witness Mounds to Section Corners. 283. Section corners, where bearing or witness trees cannot be had, will be made as if for a township corner, except that where mounds are made they need be only 2 feet 6 inches high, by 4 feet square at the base, and 2 feet at the top. -c~~: *'7- BB ^1'' 72h UNITED STATES SURVEYING. Witness mounds to quarter section corners are 3 feet 6 inches at base, 1 foot 6 inches square at top. Under the post no charcoal or stone is put. -Old Instructions, sec. 18, 19, 20 and 21. In the above we do not find the manner of digging the pits for the mounds, but the following from the New Instructions shows the manner now adopted: "At the point or corner dig out a spadeful or two, and in the cavity put a stone or charcoal, which note in the field book. A charred stake is driven 12 inches in the ground, and in the centre of the cavity. Either of these will be a witness for the future. The spot from which the earth for the mound is taken is called a pit. The pits are made at uniform distances from the centre on each side of every mound, so as to indicate hereafter the place of the mound, when it may become obliterated by time or accident. Mounds are to present a conical shape. There is dug around the base a quadrangular trench, 1 spadeful deep of earth. At about 18 inches from this trench, dig pits at the 4 cardinal points; the length of the north and south pits to be east and west, and those of the east and west pits to be north and south. 284. For corner mounds common to 2 townships, or 2 sections, the quadrangular trenches at north and south are at right angles to the north and south line; but where the mound is common to 4 townships, or 4 sections, the north and south line cuts the quadrangle diagonally." (See New Instructions, diagram C.) Courses and Distances to Witness Trees. 285. You will ascertain and state in your field notes the course and distance from the several section and township corner posts, trees or stones, to a tree in each section for which they stand as a corner. Each of said trees you will mark with a notch and blaze, facing the post, tree or stone; the notch to be at the lower end of the blaze, and on it, which must be neatly made. M'ark with a marking iron, in a plain, permanent manner, the letter S, with the number of the section, and over it the letter T, with the number of the township, and above this the letter R, with the number of the range. Where there is no tree within reasonable distance of the corner, note that in the field notes.-O. I., p. 5, sec. 17. 286. From this we infer that at township corners 4 trees are marked, and also at section corners; but at quarter section corners only 2 are marked. Note. This does not point out the necessity of describing the kind of tree marked, and its diameter, although we find that all the Government field notes give the kind of tree, and its diameter. In the specimen field book, the bearing trees are described with reference to their diameter and wood. Quarter section corners have simply a blaze, and i S marked on it, and two bearing trees marked. Note 2. Surveyors, in getting out of wood into open land or prairie, are always accustomed to mark line trees, and to describe the kind of wood and their diameters, and, if possible, they mark another tree or trees on the opposite side of the mound, on the same line. By these means the place of the mound can be determined, if these trees are to be found. UNITED STATES SURVEYING. 72i 287. Corner Stones. These stones not to be less than a stone 14 inches long by 12 inches wit and 3 inches thick; are set with the edge facing north and south, for north and south lines, and east and west, for east and west lines; they are to be 7 or 8 inches in the ground. Where stones are placed as range and township lines, as many notches will be distinctly cut with a chisel or pick on the two sides, in direction of the line, as the corner is sections from the nearest section corners. At township corners, 6 notches will be cut on each edge or side toward the cardinal points. At section corners in the interior of a township, as many notches will be cut on the south edge and east side as the corner is sections distant from the south and east boundaries of the township. At the corners of subdivisional intersections with the north boundaries of the townships, 6 notches on the south edge, and at the intersections with the west boundary 6 notches on the east edge, and as many notches on the north or south sides, as the case may require, as the corner is sections distant from the township corner. Quarter section corner stones will have 1 S on the west side, on north and south lines; and on the north side, on east and west lines.-Old Instructions, p. 5, sec. 16 and 17. 288, Note. These two sections from the Old Instructions are the same in substance as those given in the New Instructions. 7 or 8 inches without a mound will not be deep enough; better have it at least 1 foot in the ground, and then build a heap of stones around it, and afterwards a mound. Under every stone there ought to be some charcoal, broken delf, glass or slags of iron, or a stone, into which a hole 1 inch deep is cut, to perpetuate the centre or true corner. The manuals do not mention which part of the stone is to be taken, but the usual custom is to take the middle, unless something to the contrary is mentioned. The New Manual of Instructions gives a specimen field book of township 25 N., range 2 W., Williamette meridian. In these it appears that the corners on the north and west boundaries of the township have been made common to the adjacent townships. That in every case the north and south lines crossed rivers and lakes on the same line, excepting on the line between 4 and 5, where the river came within 4,00 links of the north boundary. Here he ran south as follows: From the corner to sections 4, 5, 32 and 33, on the north boundary of the township, I runSouth on a true line, between sections 4 and 5. Chains. Variation 18~ east. 2,10. A white oak, 15 inches diameter. 4,00. Set a post on the right bank of Chickeeles River, for corner to fractional sections 4 and 5, from which a bur oak, 16 inches diameter, bears N. 25~ E., 34 links distance; a black oak, 20 inches diameter, bears N. 33~ W., 21 links. From these field notes we find that the north and south lines have crossed a navigable stream and lakes on 8 lines, and on straight lines, with the above exception. That on the east and west lines, 4 lines crossed a navigable river, 2 of which are on a straight line, one makes a jog of 12 links, and the other a jog of 16 linksa 72j UNITED STATES SURVEYING. Manual of Old Instructions gives specimen field notes, showing that the variation has been taken, and that comptd with the east boundary of the township. That the north and south section lines are run staight across navigable water. That jogs are made on the north and west boundary lines. That the amount of each jog or offset is invariably given. That on east and west lines crossing navigable rivers, jogs are made, and the amount shown, how determined, and the distance between the corresponding corners on the river. Both Instructions show that in meandering, the surveyor begins at some fractional corner, and traverses along the stream to the next corner, and. so on from section line to section line. Note 2. Hence it appears that a traverse survey is not to be used in determining where a section line crossed or met a river. (See Re-establishing Lost Corner.) SUMMARY OF OBJECTS AND DATA REQUIRED TO BE NOTED. 289. Lengths of all lines, with the offsets thereon. The kind and diameter of all bearing trees, with the courses and distances of the same from their respective corners. The material of which mounds are constructed; the bearing of the pits from which the earth was dug from the centre; the material put under the post-if charcoal, etc.; how much. Trees on the line; their names, diameters and distance on the line. Intersections by the line of land objects, and the distance to each settler's claim, and also at leaving it. Distances to and at leaving woods, prairies, rivers, creeks, lakes, ravines, top and bottom of hills, bottom or swamp lands, underbrush or brushwood. Describe the surface of the land-whether level, rolling, or hilly. The soil-whether first, second, or third rate quality. The several sorts of timber and undergrowth, in the order in which they predominate. Bottom lands-whether wet, dry, or subject to inundation. If subject to be inundated, show to what depth. Note. It would be well, as in Europe, to show the high and low water nark. Springs of water-if fresh, saline, or mineral; with the course of the stream flowing from them. Note. This supposes that the surveyor has a knowledge of chemistry. To those who have not such knowledge, we refer them to the Sequel for our sections on analysis of soils, water, and ashes of plants. Lakes and ponds-describe their banks; give their height, depth of 'water, and whether the water is pure or stagnant. Note. State if there is any inlet or outlet, and the course of these coming to or leaving the lakes or ponds. Improvements, towns and villages, Indian towns and wigwams, houses, cabins, fields, sugar tree groves, sugar camps, mill seats, forges and factories. Coal banks or beds, peat or turf grounds, minerals and ores; with a description of their quality and extent, and all diggings therefor; also salt springs and lakes. UNITED STATES SURVEYING. 72k Roads and trails (or pathways), with their directions-whence they come and whither they go. Rapids, cataracts, cascades, or falls of water, with the height of their falls in feet. Precipices, caves, sink holes, ravines, stone quarries, ledges of rocks, with the kind of stone they afford. Natural curiosities, interesting fossils, petrifications, organic remains, etc.; also all ancient work of art, such as mounds, fortifications, embankments, ditches, or objects of like nature. The variation of the needle must be noted at all points or places on the lines where there is found any material change of variation, and the positions of such points must be perfectly identified in the field notes. Besides the ordinary notes taken on the line (and which must always be written down on the spot, leaving nothing to be supplied by memory), the deputy will subjoin, at the conclusion of his book, such further description or information touching any matter or thing conneeted with the township (or other survey), which he may be able to afford, and may deem useful or necessary to be known, with a general description of the township in the aggregate, as respects the face of the country, its soil and geological features, timber, minerals, water, etc.-New Instructions, pp. 17, 18. Note. Surveyors keep a loose or random field book, where they keep the notes in running lines from corner to corner, and crossing rivers, lakes, etc.; and when they have performed the work, copy the result into the proper field book. That this has been the custom with surveyors will appear by referring to their field books, where the crossing distances on rivers, etc., are given without the necessary notes. 290. Field Notes of the Subdivision Lines and Meanders of Chickeeles River, in Township 25 N., Range 2 W., Williamette Meridian. Chains. To determine the proper adjustment of my compass for subdividing this township, I commence at the corner to townships 24 and 25 N., range 1 and 2 W., and run north on a blank line along the east boundary of section 86, Variation 17~ 51' E. 40,05 To a point 5 links west of the quarter section corner, 80,09 To a point 12 links west of the corner to sections 25 and 36. To retrace this line, or run parallel thereto, my compass must be adjusted to a variation of 17~ 46' E. Note. 12 divided by 8009 gives,00149, which is the natural sine of 5 minutes; ard because the blank line was run west-of the true line, the correction is to be taken from 17~ 51', which will give the true magnetic variation of the east side of section 36. The variation here is not that from the true meridian, but is that from the section line assumed as base or meridian. Subdivision Commenced February 1, 1851. 291. From the corner to sections 1, 2, 3, 5 and 36, on the south boundary of the township, I ran 721 UNITED STATES SURVEYING. -- Ulalns. 9,19 A beech, 30 inches diameter (marked 3 blazes on front and rear). 29,97 A beech, 30 inches diameter (on line marked as above). 40,00 Set a post for quarter section corner, from whichA beech, 8 inches diameter, bears N. 23~ W., 45 links dist. A beech, 15 inches diameter, bears S. 48~ E., 12 links dist. 51,00 A beech, 18 in. diam. (this is a line tree, and marked as above). 71,00 A sugar tree (maple), 30 inches diameter. 80,00 Set a post for corner to sec. 25, 26, 35 and 36, from whichA beech, 28 inches diameter, bears N. 60~ E., 45 links dist. A beech, 24 inches diameter, bears N. 62~ W., 17 links dist. A poplar, 20 inches diameter, bears S. 700 W., 50 links dist. A poplar, 36 inches diameter, bears S. 66~ E., 34 links dist. Land level; second-rate quality. Timber-poplar, beech, sugar tree, and some oak, undergrowth and hazel. Chains. East on a random line, between sections 25 and 36, Variation 17~ 46/ E. 9,00 A brook, 20 links wide, runs north, 15,00 To foot of hill; bears north and south. 40,00 Set a post for temporary quarter section corner, 55,00 To opposite foot of hill; bears north and south. 72,00 A brook, 15 links wide, runs north. 80,00 Intersected the east boundary at the corner post to sections 25 and 36, from which corner I ranWest, on a true line, between sections 25 and 36. Variation 17~ 46/ E. 40,00 Set a post on top of hill; bears north and south; from whichA hickory, 14 inches diameter, bears N. 60~ E., 27 links dist. A beech, 15 inches diameter, bears S. 74~ W., 9 links dist. 80,00 The corner to sections 25, 26, 35 and 36. Land-east and west parts level; first-rate. Middle part broken, and third-rate. Timber-beech, oak and ash; undergrowth; same and spice in the branch bottoms. Chains. We proceed as above, N. bet. 25 and 26, then E. bet. 25 and 36. Again, N. between 23 and 24, then E. between 24 and 25. Again, N. between 14 and 13, then E. between 13 and 24. Again, N. between 11 and 12, then E. between 12 and 13. Again, N. between 1 and 2, as follows: North, on a random line. Variation 17~ 46' E. 40,00 Set a temporary post for quarter section corner. 80,11 Intersected the north boundary of the township 32 links east of corner to sections 1 and 2, from which corner I ranSouth, on a true line, between sections 1 and 2. Variation 18~ E. 40,11 Set a post for quarter section corner, from whichA white oak, 20 inches diameter, bears N. 81~ W., 65 links dist. UNITED STATES SURVEYING. 72m Chains. A sugar tree, 14 inches diameter, bears S, 49.~ E., 82 links dist. 80,11 The corner to sections 1, 2, 11 and 12. Land level; good; rich soil. Timber-walnut, sugar tree, beech, and various kinds of oak; open woods. February 2, 1851. Note. Here we find that the line between sections 1 and 2 is run from post to post, making no jog or offset on the north boundary of the township; and that the south quarter sections in the north tier of sections are 40 chains, from south to north, leaving the surplus of 11 links in the north tier of quarter sections. Field Notes of a Line Crossing a Navigable Stream on an jast and West Line. 292. West, on strue line, between sections 30 and 31, knowing that it will strike the Chickeeles River in less than 80,00 chains. Variation 17'- 40V E. 3,41 A white oak, 15 inches diameter. 6,00 Leave upland, and enter creek bottom, bearing N.E. and S.W. 8,00 Elk creek, 200 links wide; gentle current; muddy bottom and banks; runs S.W. Ascertained the distance across the creek on the line as follows:: Cause the flag to be set on the right bank of the creek, and in the line between sections 30 and 31. From the station on the left bank of creek, at 8,00 chains, I run south 245 links, to a point from which the flag on the right bank bears N. 45~ W., which gives for the distance across the creek, on the line between sections 30 and 31, 245 links. 25,17 A bur oak, 24 inches diameter. 40,00 Set a post for quarter section corner, from whichA buck-eye, 24 inches diameter, bears N. 15Q W., 8 links dist, A white oak, 30 inches diameter, bears S. 65~ E., 12 links dist. 41,90 Set a post on the left bank of Chickeeles River, a navigable stream, for corner to fractional sections 30 and 31, from whichA buck-eye, 16 inches diameter, bears N. 50~ E., 16 links dist. A hackberry, 15 inches diameter, bears S. 799 E., 14 links dist. Land and timber described as above. Note. We find this part of the line between sections 30 and 31 in the Manual of New Instructions, page 35, and the other part in page 42, as follows: From the corner to sections 30 and 31, on the west boundary of the township, I ranEast on a true line, between sections 30 and 31. Variation 18~ E. 15,10 A white oak, 16 inches diameter. 23,50 Intersected the right bank of Chickeeles River, where I set a post for corner to fractional sections 30 and 31, from whichA black oak, 16 inches diameter, bears N. 60~ W., 25 links dist. A white oak, 20 inches diameter, bears S. 35~ W., 32 links diet. k, J{*^ 72n UNITED STATES SURVEYING. Chains. From this corner I run south 12 links, to a point west of the corner to fractional sections 30 and 31, on the left bank of the river. Thence continue south 314 links, to a point from which the corner to fractional sections 30 and 31, on the left bank of the river, bears N. ~2~ E., which gives for the distance across the river 9,65 chains. The length of the line between sections 30 and 31, is as follows:: Part east of the river, 41,90 chains. Part across the river, 9,65 " Part west of the river, 23,50 " Total, 75,05 chains. Note. Here the method of finding the distance across the river, and of showing the amount of the jog or deviation from a straight line, is shown. MEANDERING NOTES. (Nezw Manual, p. 42.) 293. Begin at the corner to fractional sections 25 and 30, on the range line. I chain south of the quarter section corner on said line, and run thence down stream, with the meanders of the left bank of Chickeeles River in fractional section 30, as follows: Chains. S. 41~ E. 20,00 At 10 chains discovered a fine mineral spring. S. 49~ E. 15,00 Here appeared the remains of an Indian village. S. 42~ E. 12,00 S.120~E. 6,30 Tb the fractional sections 30 and 31. Thence in section 31, S. 12~ W. 13,50 To mouth of Elk River, 200 links wide; comes from the east. S. 41~ W. 9,00 At 200 links (on this line) across the creek. S.680 W. 11,00 S. 35 W. 11,00 S. 20~ W. 20,00 At 15 chains, mouth of stream, 25 links wide, comes from S.E. S.231~W. 8,80 To the corner, to fractional sections 31 and 36, on the range line, and 8,56 chains north of the corner to sections 1, 6, 31 and 36, or S.W. corner to this township. Land level, and rich soil; subject to inundation. Timber-oak, hickory, beech, elm, etc. RE-ESTABLISHING LOST CORNERS. (New Instruction', p. 27.) 294. Let the annexed diagram represent an east and west line between Sec. 81. Sec. 82. Sec. 33. Sec. 84. Sec. 85. Sec. 86. _.__ 5.d a....... Sec.. Sec.. 4. Sec. 3. Sec. 2. Sec. 1.b Sec. 6. Sec. 5. Sec. 4. Sec. 3 Sec. 2. Sec. 1. UNITED STATES SURVEYING. 720 two townships, and that all traces of the corner to sections 4, 5, 32 and 33 are lost or have disappeared. I restored and re-established said corner in the following manner: Begin at the quarter section corner marked a on diagram, on the line between sections 4 and;33. One of the witness trees to this corner has fallen, and the post is gone. The black oak (witness tree), 18 inches diameter, bearing N. 25~ E., 32 links distance, is standing, and sound. I find also the black oak station or line tree (marked b on diagram), 24 inches diameter, called for at 37,51 chains, and 2,49 chains wesf of the quarter section corner. Set a new post at the point a for quarter section corner, and mark for witness tree. A white oak, 20 inches diameter, bears N. 34~ W., 37 links dist. West with the old marked line. Variation 18~ 257 E. At 40,00 chains, set a post for temporary corner to sections 4, 5, 32 and 33. At 80,06 chains, to a point 7 links south of the quarter section corner (marked c on diagram), on line between sections 5 and 32. This corner agrees with its description in the field notes, and from which I run east, on a true line, between sections 5 and 32. Variation 18~ 22'. At 40,03 chains, set a lime stone, 18 inches long, 12 inches wide, and 3 inches thick, for the re-established corner to sections 4, 5, 32 and 33, from whichA white oak, 12 inches diameterW bears N. 21~ E., 41 links dist. A white oak, 16 inches diameter, bears N. 21~ W., 21 links dist. A black oak, 18 inches diameter, bears S. 17~ W., 32 links dist. A bur oak, 20 inches diameter, bears S. 21~ E., 37 links dist. Note 1. The diagram, and letters a, b, c, and that part in parentheses, are not in the Instructions. Note 2. Hence it appears that the surveyor has run between the nearest undisputed corners, and divided the distance pro rata, or in proportion to the original subdivision. Although in this case the line has been found blazed, and one line or station tree found standing, the required section corner is not found by producing the line from a, through b, to d. Although I have met a few surveyors who have endeavored to re-establish corners in this manner, I do not know by what law, theory or practice they could have acted. It is in direct violation of the fundamental act of Congress, 11 Feb., 1805, which says that lines are to be run "from one corner to the corresponding corner opposite. (See sequel Geodcetical Jurisprudence.) Re-establishing Lost Corners. (From Old Instructions, p. 63.) 295. Where old section or township corners have been completely destroyed, the places where they are to be re-established may be found, in timber, where the old blazes are tolerably plain, by the intersections of the east and west lines with the north and south lines. If in prairie, in the following manner: c.- '.......,;. i, ^ I AP UNITED STATES SURVEYING. Let the anteted diagram represent part of the township. This example is often given. Suppose that the corner to sections 25, 26, 35 and 36 to be missing, and that the quarter section corner on the line between sections 35 and 36 to be found. Begin at the said quarter section corner, and run north on a random line to the first corner which can be identified, which we will suppose to be that of sections 2:3, 24, 2-5 and 26. At the end of the first 40 chains, set a temporary post corner to sections 25, 26, 35 and 36. At 80 chains, set a temporary quarter section corner ~5 ~..1.4..... 13......1 22...... 283 24......4 27......2 6 5......25 34...... 3 5.... 36.... post, and suppose als* that 121,20 chains would be at a point due east or west of said corner 23, 24, 26 and 26. Note the falling or distance from the corner run for, and the distance run. Thence from said corner run south on a true line, dividing tie surplus, 1,20 chains, equally between the three half miles, viz.: At 40,40 chains, establish a quarter section corner. At 80,80 chains, establish the corner to sections 25, 26, 35 and 36. Thence to the quarter section corner, on the line between sections 35 and 36, would be 40,40 chains. The last mentioned section corner being established, east or west random or true lines can now be ran therefrom, as the case may require. This method will in most cases enable the surveyor to renew missing corners; by re-establishing them in the right place. But it may happen that after having established the north and south line, as in the above case, the corner to sections 26, 27, 34 and 35 can be found; also the quarter section corner on the line between 26 and 35. In this case it might be better to extend the line from the corner 26, 27, 34 and 35, to said quarter section corner, straight to its intersection with the north and south line already estcablished, and there establish the corner to sections 25, 26, 35 and.36. If this point should differ much from the point where you would place the corner by the first method laid down, it might be well to examine the line between sections 25 and 36. Note 1. Hence it appears that the north and south lines are first established, in order that the east and west lines may be run therefrom; and that when the east and west lines can be correctly traced to the north and south line, that the point of intersection would be the required corner. It is also to be inferred that where the lines on both sides can be traced to the north and south line, a point equidistant between the points of intersection would be the required corner. \ ote 2. It will not do to run from a section or quarter section corner on the west side of a north and south line, to a section corner, or quarter section, on the east side of the line, and make its intersection with the north and south line, the required corner, unless that these two lines were originally run on the same variation, which is seldom the case. Note 3. Having found approximately the missing corner, we ought to UNITED STATES SURVEYINg. 72q search diligently for the remains of the old post, mound, bearing trees, or the hole where it stood. Bearing trees are sometimes so healed as to be difficult to know them. By standing about 2 feet from them, we can see part of the bark cut with an even face. We cut obliquely into the supposed blaze on the tree to the old wound. We count the layers of growth, each of which answers to one year. By these means we find the years since the survey has been made, which, on comparing with the field notes, we will always find not to differ more than one year. Remains of a post, or where it once stood, may be determined as follows. Take the earth off the suspected place in layers with a sharp spade. By going down to 10 or 12 inches, we will find part of the post, or a circular surface, having the soil black anzd loose, being principally composed of vegetable matter. By putting an iron pin or arrow into it, we find it partially hollow. We dig 6 feet or more around the suspected place. Where such remains are found, we make a note of it, and of those present. Put charcoal, glass, delf, or slags of iron) in the hole, and re-establish the corner, noting the circumstances in the field book. Ditches or lockspitting are sometimes made on the line to perpetuate it. This will be an infallible guide, and we only require to know if the edge or centre of the ditch was the line or boundary, or was it the face or top of the embankment. These answers can be had from the record, or from the persons who have made the ditch, or for whom it has been made; Should this ditch be afterwards ploughed and cultivated, we can see in June a difference in the appearance of the plants that grow thereon, being of a richer green than those adjoining the ditch. Or, we dig a trench across the suspected place. The section will plainly show where the old ditch was, for we will find the black or vegetable mould in the bottom of the old ditch. We may have the line pointed out by the oldest settlers, who are acquainted with the locality. Surveyors ought to spare no pains to have all things so correctly done as to prevent litigation, and to bear in mind that "where the original line was, there it is, and shall be." ESTABLISHING CORNERS. (Old Instructions, p. 62.) 296. In surveying the public lands, the United States Deputy Surveys ors are required to mark only the true lines, and establish on the ground the corners to townships, and sections, and quarter sections, on the range) township and sectional lines. There are, no doubt, many cases where the corners are not in the right place, more particularly on east and west sectional lines, which, doubtless, is owing to the fact that some deputy surveyors did not always run the random lines the whole distance and close to the section corner, correct the line back, and establish the quarter section corner on the true line, and at average distance between the proper section corner; but only ran east or west (from the proper section corner) 40,00 chains, and there established the quarter section corner. In all cases.where the land has been sold, and the corners can be found and properly identified, according to the original approved field notes of the survey, this ofice haa no authority to remove them. ~.;;^.l..' '.,. a ': ',... ^... *.:*. '..,, 72r UNITED STAtES SURVEYING. RE-ESTABLISHING CORNERS IN FRACTIONAL SECTIONS, AND ALSO TIE INTERIOR CORNER SECTIONS. (Old Instructions, p. 65.) Present Subdivision of Sections. 297. None of the acts of Congress, in relation to the public lands, 'make any special provision in respect to the manner in which the sub'divisions of sections should be made by deputy surveyors. The following plan may, however, be safely adopted in respect to all sections, excepting those adjoining the north and west boundaries of a township, where the same is to be surveyed: Let the annexeddiagram rep- A B 0 C resent an interior section, as 79,80 sec. 10. B, D, H and F are quarter section corners. Run a true line from F to D; estab- N lish the corner E, making D E =E F; then make straight Sec. 10. lines from E to B and from E D E F to H, and you have the section,divided into quarters. If it is required to subdivide: s e X ~ the N. E. quarter into 40 acre o C tracts, make E L - L F, and B 0 = OC, and G P P H, 80, 20 and DK- KE; also EM- G P Q M B, and F N = N C. Run from M to N on a true line, and make M I =-4 N. Here the N. E. quarter section is divided into 4 parts, and the S.W. quarter section into two halves. Note. As the east and west sides of every regular section is 80 chains,,and that the quarter section corners on the north and south sides are at average distances, it is evident that the line B H will bisect D F, or any line parallel to G Q. Consequently the method in the section is the same in effect as that in the next. But if, by a re-survey, we find that A B is not equal to B C, or that G H is not equal to H Q, then we measure the line from D to F, and establish the point E at average distance. 298. Let the annexed dia- o V gram represent a subdivision of section 3, adjoining the north boundary of a township, being a fractional section. K In this case, we have on the original map A F = 38,67, B E 89,78, D E = 39,75, F D = A 89,95, I C = 39,75, and C H - 89,75. The S.E. and S.W. quarter sections each equal to 160 acres. Lot No. 1 each equal to 80 acres. In the N.W. quarter section the west half of lot 2 - 87,41 acres, and the east half.... 'O No. 2. No. 2.? N M 0 No. 1. No. 1. E Sec. 3. i- G G Cl 8 ~^ 160 ac. 160 ac. 39,75 _ 89,75 I: --- C -- H L.4 UNITED STATES SURVEYING. M2r of lot 2 - 37,96 acres. These areas are taken from the original survey. In the N.E. quarter section, the west half of lot 2 = 38,23 acres, and the east half of lot 2 = 38,78. In this example, there can be but one rule for the subdivision, to make it agree with the manner in which the several areas are calculated. You will observe that the line I H is 79,50 chains, and that the one half of it, = 39,75, is assumed as the distance from E to D, which last distance, 39,75, is deducted from 79,50, the length of the line E F leaving 39,95 chains between the points F and D. Consequently the line C D must be exactly parallel to the line H E, without paying any respect to the quarter section corner near D, which belongs entirely to section 34 of the township on the north. Run the line A B in the same manner as that of D F on diagram sec. 297, except that the corner G is to be established at the point where the' line A B intersects the line C D. After surveying thus far, if the S.E and S.W. quarters are to be subdivided, it can be done as in diagram sec. 297. In this casetto subdivide the N.E. and N.W. quarters, the line K L must be parallel to A B. The two lines ought to be 20 chains apart. The corner, M, is made where K L is intersected by C D. But as two surveyors seldom agree exactly as to distances, there might be found an excess or deficiency in the contents of the N.E. and N.W. quarters. If so, the line K L should be so far from A B as to apportion the, excess or deficiency between lots 1 and 2, not equally, but in proportion. to the quantities sold in each. If the lots numbered 2 are divided on the township plat by north and south lines, then that of the N.W. quarter must have its south end equidistant between K and M, and its north end equidistant between F and D. The N.E. quarter will be subdivided by a line parallel to M D and L E, exactly half way between them. Note. Here we have the quarter section corners A, B, C and D given, and where the line A B intersects C D,, gives the interior quarter section corner. We find also that A K = B L = 20 chains generally, and that K N NM, and F Q =QD. Also MO = OL, andD P = P E. Let us suppose that the original map or plat in this example gave the N.E. quarter 157 acres-that is, lot 1 = 80 and lot 2 = 77 acres, and that in surveying this quarter section we find.the area =159 acres, then we say, as 157: 159: 80 to the surplus for lot 1, or, as 157: 159:: 77 to surplus in lot 2; and having the corrected area of lot 1, and the lengths of B G and L M, we can easily find the width B L. Note 2. The above method of establishing the interior corner, M, is according to the statutes of the State of Wisconsin, and appears to be the best, as the original survey contemplates that the lines I F, H E, F E, I H, A B and C D are straight lines. Government Plats or Afaps. 299. The plats are drawn on a scale of 40 chains to one inch. The section lines are drawn with faint lines; the quarter section lines are in dotted lines; the township lines are in heavy lines. The number of the section is above the centre of each section, and its area in acres under it. On the north side of each section is the length thereof, excepting the south section lines of sections 32, 33, 34, 35 and 36. The section corners on the township lines are marked by the letters A, B, C, D, etc., A being at???!:i~ i!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 72t VNITED STATES SURVEYING. the N.E. corner, G at the N.W., N at the S.W., and T at the S.E. The quarter section corners are marked by a, b, c, d, etc., a being between A and B, f between G and F, n between N and 0, and s between S and T. (See New Instructions, diagram B.) Note. On the maps or plats which we have seen, A begins at N.W. corner and continues to the right, making F at the S.W. corner of the township. The quarter section corner on the north side of every section is numbered 1, 2, 3, 4, 5 and 6, beginning on the east side, and running to the west line. Number 1 is at the quarter section corner on the north side of each section, 12, 13, 24, 25 and 36. Number 6 is at the quarter section corners on the north side of each, of sections 7, 18, 19, 30 and 31. There is a large hook of field notes, showing only where mounds and trees are made landmarks. The kind of trees marked as witness trees; their diameter, bearing and distances, are given for A, a, B, b, C, c, to X, x, Y, y. For interior section corners, begin *t S.E. corner, showing the notes to sections 25, 26, 35, 36; 23, 24, 25, 26; and two after two to sections 6, 6,- 7, 8, at N.W. corner of the township. For interior quarter section corners, begin at M, the N.E. corner of section 36, and run to U, N.W. corner of section 31, thus: M to U, at 1, post in mound. 2, bur oak, 18 inches diameter, bears N. 3~ E. 80 links. bur oak, 12 inches diameter, bears S. 89~ W. 250 links. 6, post in mound. Next run L to V, K to W, I to X, and H to Y, giving the witness trees, if any, at quarter section corners numbered 1, 2, etc., as above. Then begin to note from south to north, by beginning at O and noting to F, then P to E, Q to D, R to C, and S to B. The plats show by whom the outlines and subdivisions have been surveyed; date of contract; total area in acres; total of claims or land exempt from sale; the variation of the township and subdivision lines; and the detail required by section. SURVEYS OF VILLAGES, TOWNS AND CITIES. 800. A. lays out a village, which may be called after him, as Cleaverville, Kilbourntown, Evanston; or it may be named after some river, Indian chief, etc., as Hudson, Chicago. This village is laid out into blocks, streets and alleys. The blocks are numbered 1, 2, 3, etc., generally beginning at the N.E. corner of the village. The lots are laid off fronting on streets, and generally running back to an alley. The lots are numbered 1, 2, 3, etc., and generally lot 1 begins at the N.E. corner of each block. The streets are 80, 66, 50 and 40 feet-generally 66 feet. In places where there is a prospect of the street to be of importance as a place for business, the streets are 80 feet. Although many streets are found 40 feet wide, they are objectionable, as in large cities they are subsequently widened to 60 or 66 feet. This necessarily incurs expenses, and causes litigations. Sidewalks. The streets are from the side of one building to that ol another on the opposite side of the street; that is, the street includes the carriage way and two sidewalks. Where the street is 80 feet wide, eact l~e5.-. UNITED STATES SURVEYING. 72u sidewalk is usually 16 feet. When the street is 66 feet, the width of the sidewalk is usually 14 feet. Where the street is 40 feet, the width of the sidewalk is usually 9 feet. Corner stones. The statutes of each State generally require corner stones to be put down so as to perpetuate the lines of each village, town, or addition to any town or city. Maps orplats of such village, town or addition, is certified as correct by, the county or city surveyor, as the State law may require. The map or plat is next acknowledged by the owner, before a Justice of the Peace or Notary Public, to be his act and deed. Plat recorded. The plat is then recorded in a book of maps kept in the Recorder's or Registrar's office, in the county town or seat. Dimensions on t/imap. Show the width of streets, alleys and lots; the depths of lots; the angles made by one street with another; the distances from corner or centre stones to some permanent objects, if any. These distances are supposed to be mathematically correct, and according to which the lots are sold. Lots are sold by their number and block, as, for example: "All that parcel or piece of land known as lot number 6, in block 42, in Matthew Collins' subdivision of the N.E. quarter section 25, in township 6 north, and range 2 east, of the third principal meridian, being in the county of --, and State of -." All plats are not certified by county or city surveyors. In some States, surveyors are appointed by the courts, whose acts or valid surveys are to' be taken as prima facie evidence. In other States, any competent surveyor can make the subdivision, and swear to- its being correct before a Justice of the Peace. Lots are also sold and described by metes and bounds, thus giving to the first purchasers the exact quantity of land called for in their deeds, leaving the surplus or deficiency in the lot last conveyed. Metes and bounds signify that the land begins at an established point, or at a given distance from an established point, and thence describes the several boundaries, with their lengths and courses. Establishing lost corners. When some posts are lost, the surveyor finds the two nearest undisputed corners, one on each side of the required corners. He measures between these two corners, and divides the distance pro rata; that is, he gives each lot a quantity in proportion to the original or recorded distance. Where there is a surplus found, the owners are generally satisfied; but where there is a deficiency, they are frequently dissatisfied, and cause an inquiry to be made whether this deficiency is to be found on either side of the required lots, or in one side of them. As mankind is not entirely composed of honest men, it has frequently happened that posts, and even boundary stones, have been moved out of their true places by interested parties or unskilful surveyors. In subdividing a tract into rectangular blocks, we measure the outlines twice, establish the corners of the blocks on the four sides of the tract, and, by means of intersections, establish the corners of the interior blocks. Let us suppose a tract to be divided into 86 blocks, and that block 1 begins at the N.E. corner, and continues to be numbered similar to township surveys. We erect poles at the N.W. corners of blocks 1, 2, 3, 4 and 6, and at the N.E. corners of blocks 12, 13, 24, 25 and 36. We set the in1 72v CANADA SURVETING, strument on the south line at S.W. corner of block 36; direct the telescope to the pole at the N.W. corner of block 1. Let the assistant stand at the instrument. We stand at the N.W. angle of 31, and make John move in direction of the'pole at the N.W. angle of 36, until the assistant gives the signal that he is on his line. This will give the N.W. angle of 36., where John drives a post, on the top of which he holds his pole again on line, and drives a nail in the true point. We then move to the N.W. angle of 30, and cause John to move until he is en our assistant's line, thereby establishing the N.W. corner of 25, and so on for the N.W. corners,of 24, 13 and 12. We move the instrument to the S.W. corner 35, and set the telescope on the pole at N.W. corner of 2, and proceed as before. 'This method is strictly correct, and will serve to detect any future fraud,.and enable us to re-establish any required corner. Where the blocks are large, the lots may be surveyed as above. Where the ground is uneven, or woodland, this method is not practicable. However, proving lines ought to be run at every three blocks. CANADA SURVEYING. 301. No person is allowed to practice land surveying until he has -obtained license, under a penalty of ~10, one-half of which goes to the prosecutor. Each Province has a Board of Examiners, who meet at the Crown Land Office, on the first Monday of January, April, July and October. The candidate gives one week's notice to the Secretary of the Board. He must have served as an apprentice during three years. He must have first-rate instruments, (a theodolite, or transit with vertical arch, for finding latitude and the true meridian.) He must know Geometry, (six books of Euclid,) Trigonometry, and the method of measuring superficies, with Astronomy sufficient to enable him to find latitude, longitude, true time, run all necessary boundary lines by infallible methods, and be versed in Geology and Mineralogy, to enable him to state in his reports the rocks and minerals he may have met in his surveys. He must have standard measures, one five links long, and another three feet. He gives bonds to the amount of 1)00 dollars. His fees, when attending court, is four dollars per day. He keeps an exact record of all his surveys, which, after his death, is to be filed with the clerk of the court of the county in which he lived. Said clerk is to give copies of these surveys to any person demanding them on paying certain fees, one-half of which is to be paid to the heirs of the surveyor. The Government have surveyed their townships rectangularly, as in the United States, except where they could make lots front on Government roads, rivers and lakes. This has been a very wise plan, as several persons can settle on a stream; whereas, in the United States, one man's lot may occupy four times as much river front as a man having a similar lot in Canada. 302. Lines are run by the compass in the original survey, but all subsequent side lines are run astronomically. In the United States, lines are run from post to post, which requires to have two undisputed points, CANADA SURVEYING. 72w and that a line should be invariably first run and then corrected back for the departure from the rear post. In the Canada system, we find the post in front of the lot, and then run a line truly parallel to the governing line, and drive a post where the line meets the concession in rear. The annexed Fig. represents a part of the town. of Cox; b c, a d, etc., are concession lines. Heavy lines are con- cession roads, 66 feet wide, always between every two con- cessions. There is an allowance of road generally at every fifth lot. The front of each concession is that from which the concessions are numbered; that is, the front of concession II is on the line a d. Where posts wereplanted, or set on the river, the front of concession B is the river, and that of concession A is on the concession line n f, etc, 303. Side lines are to be run parallel to the township line from which the lots are numbered. The line between lots 7 and 8, in concession II, is to be run on the same true bearing as the township line a b; but if the line m, n, o, p, s, etc;B be run in the original survey as a proving line, then the line between 7 and 8 is to be run parallel to the line p s, and all lines from the line p a to the end are to be run parallel to p s, and lines from a to p are to be run parallel to a b. When there is no proving or township line where the lots are numbered from, as in con. A, we must run parallel to the line v w; but if there is a'proving line as m n, all lines in that concession shall be run parallel to it. When there is no town line at either end of the concession, as in con. B, the side lines are ran parallel to the proving line, if any. When there is neither proving line or township line at either end, as in concession B, we open the concession line k w, and with this as base, lay off the original angle. Example. The original bearing of k w is N. 160 W., and that of the side lines N. 660 E.. To run the line between lots 14 and 15, in con. B, we lay off from the base k w an angle of 820, and run to the river. The B original posts are marked on the four sides thus. This shows that the allowance for road is in rear of con. C; that is, the concession line between conVI i-. II cessions B and C is on the west line of allowance *. i * i *!. of road. The original field nots are kept as in the United States, showing the quality df timber, soil, etc. If the concessions were numbered from a river or lake, and that no Posts were set on the water's edge, then the lines shall be run from the rear to the water. 72x CANADA SURVEYING. When concession lines are marked with two rows of posts, and that the land isadescribed in half lots, then the lines shall be drawn from both ends parallel to the governing line, and to the centre of the concession if the lots were intended to be equal, or proportional to the original depths. When the line in front of the concession was not run in the original survey, then run from the rear to a proportionate depth between said rear line and the adjacent concession. (See Act, 1849, Sec. XXXVI.) Example. The line a d has not been run, but the lines b c and t v have been ran. Let the depth of each concession = 8000 links. Road, on the line a d, 100 links. Run the line between 7 and 8, by beginning at the point h, and running the line h q parallel to a b, and equal to half the width of concession I and II. Measure h q, and find it 8200 links. Suppose that the allowance for road is in the rear of each concession; that is, the west side of each concession road allowance is the concession line; then 8200 links include 100 links for one road, leaving the mean depth of concession II = to be 8100 links = h q. In like manner we find the depth of the line between 8 and 9, and the straight line joining these points is the true concession line. (See Act, May, 1849, Sec. XXXVI.) 304. Maps of towns or villages are to be certified as correct bya land surveyor and the owner or his agent, and shall contain the courses and distances of each line, and must be put on record, as in the United States, within one year, and before any lot is sold. These maps, or certified copies of them, can be produced as evidence in court, provided such copy be certified as a true copy by the County Registrar. When A got P. L. surveyor S, to run the line between 6 and 7 in concession II, and finds that the line has taken part of his lot 6, on wtich he has improved; that is, he finds part of B's lot 7 included inside his old boundary fence. The value of his improvements is 400 dollars, belonging to A, and the value of the land to be recovered by B is 100 dollars. Then, if B becomes plaintiff to recover part of his lot 7, worth 100 dollars, he has to pay A the amount of his damages for improvement, viz. 400 dollars, or sell the disputed piece to A for the assessed value. (See Act of 1849, Sec. L.) 305. In the Seigniories, fronting on the St. Lawrence, the true bearing of each side line is N. 45~ W., with a few exceptions about the vicinity of St. Ignace, below Quebec. In the Ottawa Seigniories, the true or astronomical bearing is N. 11~ 15' E. This makes it easier than in the townships, as there is -no occasion to go to the township line for each concession. 306. Where the original posts or monuments are lost. "In all cases when any land surveyor shall be employed in Upper Canada to run any side line or limits between lots, and the original post or monument from which such line should commence cannot be found, he shall in every such case, obtain the best evidence that the nature of the case will admit of, respecting such side line, post or limit; but if the...'c., t i-,o:: t i-f..tiriiv autcertained, theni the surveyor shall measure the true distanee between the nearest undisputed posts, limits or monumients, an(d d(ivide such distance into such number of lots as the same contained in the original survey, assigning to each a breadth proportionate to that intended in such original survey, as shown on the plan and fieldnotes thereof, of record in the office of the Commissioner of Crown Lands of this Province; and if any portion of the line in front of the concession in which such lots are situate, or boundary of the township in which such GEODEDICAL JURISPRUDENCE. 72y concession is situate, shall be obliterated or lost, then the surveyor shall run a line between the two nearest points or places where such line can be clearly and satisfactorily ascertained, in the manner provided in this Act, and in the Act first cited in the preamble to this Act, and shall plant all such intermediate posts or monuments as he may be required to plant, in the line so ascertained, having due respect to any allowance for a road or roads, common or commons, set out in such original survey; and the limits pf each lot so found shall be taken to be, and are hereby declared to be the true limits thereof; any law or usage to the contrary thereof in any wise notwithstanding." [This is the same as Sec. XX of the Act of May, 1849, respecting Lower Canada, and of the Act of 1855, Sec. X.] GEODEDICAL JURISPRUDENCE. The general method of establishing lines in the United States, may be taken frot the United States' Statutes at Large, vol. II, p. 313, passed Feb. 11, 1805. C CHAP. XIV., Feb. 11, 1805.-An Act concerning the mode of Surveying the Public Lands of the United States. [See the Act of May 18, 1796, chap. XXIX, vol. I, p. 465.] Be it enacted by the Senate and House of Representatives of the United States of America, in Congress assembled, That the Surveyor General shall caie all those lands north of the river Ohio which, by virtue of the Act intituled "An Act providing for the sale of the lands of the United States in the territory N.W. of the river Ohio, and above the mouth of the Kentucky River," were subdivided by running through the townships parallel lines each way, at the end of every two miles, and by marking a corner on each of the said lines at the end of every mile, to be subdivided into sections, by running straight lines from those marked to the opposite corresponding corners, and by marking on each of the. said lines intermediate corners, as nearly as possible equidistant from the corners of the sections on the same. And the said Surveyor General shall also cause the boundaries of all the half sections which had been purchased previous to the 1st July last, and on which the surveying fees had been paid, according to law, by the purchaser, to be surveyed and marked, by running straight lines, from the half mile corners heretofore marked, to the opposite corresponding corners; and intermediate corners shall, at the same time, be marked on each of the said dividing lines, as nearly as possible equidistant from the corners of the half section on the same line. Provided, That the whole expense of surveying and marking the lines shall not exceed three dollars for every mile which has not yet been surveyed, and which will be actually run, surveyed and marked by virtue of this section, shall be defrayed out of the moneys appropriated, or which may be hereafter appropriated for completing the surveys of the public lands of the United States. SEC. 2. And be it further enacted, That the boundaries and contents of the several sections, half sections and quarter sections of the public lands of the United States shall be ascertained in conformity with the following principles, any Act or Acts to the contrary notwithstanding: 1st. All the corners marked in the surveys returned, by the Surveyor General, or by the surveyor of the land south of the State of Tennessee respectively, shall be established as the proper corners of sections or subdivisions of sections which they were intended to designate; and the corners of half and quarter sections, not marked on the said surveys, shall be placed as nearly as possible equidistant from those two corners which stand on the same line. 2nd. The boundary lines, actually run and marked in the surveys re-. . 72z GEODEDICAL JUR:ITSPRIUDENCE. turned by the Surveyor General, or by the surveyor of the land south of the State of Tennessee, respectively, shall be established as the proper boundary lines of the sections or subdivisions for which they were intended, and the length of such lines as returned by either of the surveyors aforesaid shall be held and considered as the true length thereof. And the boundary lines which shall not have been actually run and marked as aforesaid, shall be ascertained by running straight lines from the established corners to the opposite corresponding corners; but in those portions of the fractional townships where no such corresponding corners have been or can be fixed, the said boundary lines shall be ascertained by running from the established corners due north and south, or east and west lines, as the case may be, to the water course, Indian boundary line, or other external boundary of such fractional township. An Act passed 24th May, 1824, authorizes the President, if he chooses to cause the survey of lands fronting on rivers, lakes, bayous, or water courses, to be laid out 2 acres front and 40 acres deep. (See United States' Statutes at Large, vol. IV, p. 34.) An Act passed 29th May, 1830, makes it a misdemeanor to prevent or obstruct a surveyor in the discharge of his duties. Penalties for so doing, from $50 to $3000, and imprisonment from 1 to 3 years. SEC. 2 of this Act authorizes the surveyor to call on the proper author rities for a sufficient force to protect him. (Ibid, vol. IV, p. 417.) The Act for adjusting claims in Louisiana passed 15th Feb., 1811, gave the Surveyor General some discretionary power to lay out lots, fronting on the river, 58 poles front and 65 poles deep. (Ibid, vol. II, p. 618.) FROM THE ALABAMA REPORTS. 307. Decision of the Supreme Court of Alabama in the case of Lewin v. Smith. 1. The land system of the United States was designed to provide in advance with mathematical precision the ascertainment of boundaries; and the second section of the Act of Congress of 1805 furnished the rules of construction, by which all the disputes that may arise about boundaries, or the contents of any section or subdivision of a section of land, shall be ascertained. 2. When a survey has been made and returned by the Surveyors, it shall be held to be mathematically true, as to the lines run and marked, and the corners established, and the contents returned. 3. Each section, or separate subdivision of a section, is independent of any other section in the township, and must be governed by its marked and established boundaries. 4. And should they be obliterated or lost, recourse must be had to the best evidence that can be obtained, showing their former situation and place. 5. The purchaser of land from the United States takes by metes and bounds, whether the actual quantity exceeds or falls short of the amount estimated by the surveyor. 6. Where a navigable stream intervenes in running the lines of a section, the surveyor stops at that point, and does not continue across the river; the fraction thus made is complete, and its contents can be ascertained. Therefore, where there is a discrepancy between the corners of a section, as established by the United States' Surveyor, and the lines as run and marked-the latter does not yield to the former. 7. Whether this would be the case where a navigable stream does not cross the lines.-Query. This is the case of Lewin v. Smith: Error to the Circuit Court of Tuskaloosa. Plaintiff-an action of trespass on pfrtion of fractional sec. 26, town. 21, range 11 W., lying north and west of the Black Warrior,River. GEOI)EDICAL JUIRSPRUDENCE. Line a b claimed' / by Lewin. Line b c claimed by Smith. Field Notes. Beginning at N.W. corner, south 730 50k, to a post on N. bank of the river, from which north 800 W. 0.17, box elder-S. 660 E., 0.18, do. Thence with the meander of the river K AC K a S. 740 E., 7.50. N. 320 E., 10. N. 90 W., 20. N. 100 E., 22. N. 40 V., 24.50, to a poplar on the south boundary of sec. 23; thence west 13.7 q to S.W. corner, containing 100650 acres. NoTE.-Here the line claimed by Smith was established, by finding the original corners, b and c. Lewin claimed that, although there was no monument to be found at a, that such would be legally established by the intersection of a line from b to d, d being a fractional corner at the stockade fence supposed to be correct. The Court decided that the linq b to c was the true line, as the line and bearing trees corresponded with the field notes, and therefore decided in favor of Smith. The disputed gore or triangle, a b c, contained 9 acres, and the jog, a c = 207 links. —Ml D. FROM TIHE KENTUCKY REPORTS. 308. From the Kentucky Reports, by Thomas B. Monroe, vol. VII, p. 333. Baxter v. Evett. Government survey made in 1803. Patent deed issued in 1812. Ejectment instituted in 1825. Decision in 1830. The rule is, that visible or actual boundaries, natural or artificial, called for in a certificate of survey, are to be taken as the abuttals, so long as they can be found or proved. The legal presumption is, that the surveyor performed the duty of marking and bounding the survey by artificial or natural abuttals, either made or adopted at the execution of the survey. And if this presumption could be destroyed by undoubted testimony, yet, as this was the fault of the officer of the Goveinment, and not of the owner of the survey, his right ought not to be injured, when the omission can be supplied by any rational means, and descriptions furnished by the certificate of survey. In locating a patent, the inquiry first is for the demarkation of boundary natural or artificial, alluded to by the surveyor. If these can be founr extant, or if not now existing, can be proved to have existed, and their locality can be ascertained, these are to govern. The courses and distances specified in a plat and certificate of survey, are designed to describe the boundaries as actually run and made by the surveyor, and to assist in preserving the evidence of their local position, to aid in tracing them whilst visible, and in establishing their former position in case of destruction, by time, accidentor fraud. As guides for these purposes, the courses and distances named in a plat and certificate of survey are useful; but a line or corner.established by a surveyor in making a survey, upon which a grant has issued, cannot be alte~red because the line is longer or shorter than the distance specified, or because the relative bearings between the abuttals vary from 'the course named in the plat and certificate of survey: so, if the line run by the surveyor be not a right line, as supposed from his description, but be found, by tracing it, to be a curved line, yet the actual line must 72B GEODEDICAL JURISPRUDENCE. govern, the visible actual boundary the thing described, and not the ideal boundary and imperfect description, is to be the guide and rule of property. These principles are recognized in Beckley v. Bryan, prim. dec. 107, and Litt. sel. Cas. 91; Morrisson v. Coghill, prin. dec. 382; Lyon v. Ross, 1 Bibb. p. 467; Cowan v.tFauntelroy, 2 Bibb. p. 261: Shaw v. Clement, 1 Call, p. 438, 3d point; Herbert v. Wise, 3 Call, p. 239; Baker v. Glasscocke, 1 Hen. & Munf., p. 177; Helm v. Smallhard, p. 369. From the same State Reports. 5 Dana, p. 543-4. Johnson v. Gresham. Here Gresham found the section to contain 696 acres; had it surveyed into four equal parts, thus embracing 1 to 3 acres of Johnson's land, which extended over the line run, with other improvements. Greshanr had purchased that which Johnson had pre-empted. Opinion of the Court by Judge Ewing, Oct. 19, 1837. 1. Though the Act of 1820, providing for surveying the public lands west of the Tennessee River, directs that it shall be laid off into townships oft miles square, and divided into sections of 640 acres each, yet it is well known, through the unevenness of the ground, the inaccuracy of the instruments, and carelessness of surveyors, that many sections embrace less, and many more, than the quantity directed by the Act. The question therefore occurs, how the excess or deficiency shall be disposed of among the quarters. The statute further directs that in running the lines of townships, and the lines parallel thereto, or the lines of sections, "that trees, posts, or stones, half a mile from the corners of sections, shall be marked as corners of quarter sections." So far, therefore, as the corners or lines of the quarters can be ascertained, they should be the guides and constituted boundaries and abuttals of each quarter. In the absence of such guides, and of all other indicea directing to the place where they were made, the sections should be divided, as near as may be, between the four quarters, observing, as near as practicable, the courses and distances directed by the Act. When laid down according * to these rules, the quarter in contest embraces 174 acres, and covers a part of the field of the complainant, as well as his washhouse. FROM THE ILLINOIS REPORTS. 309. From the Illinois Reports, vol. XI. Rogers v. McClintock. Th'l:oorners of sections on township lines were made when the township 0'as'laid out. They became fixed points, and if their position can now be shown by testimony, these must be retained, although not on a straight line-from A to B. The township line was not*run on a straight line from A and B. It was run mile by mile, and these mile points are as sacred as the points A to B. (Land Laws, vol. I, pages 50, 71, 119 and 120.) Therefore, if the actual survey, as ascertained by the monuments, show a deflected line, it is to be regarded as the true one.-Baker v. Talbott, 6 Monroe, 182; Baxter v. Evett, 7 Monroe, 333. Township corners are of no greater authority in fixing the boundary of the survey than the section corners.-Wishart v. Crosby, 1 A. R. Marsh, 383. Where sections are bounded on one side by a township line, and the line cannot be ascertained by the calls of the plat, it seems quite clear that if the corners,f the adjacent section corners be found, this is better evidence to locate the township line than a resort to course merely.1 Greenleaf Evidence, p. 369, sec. 301, note 2; 1 Richardson, p. 497. Chief Justice Caton's Opinion. All agree that courses, distances and quantities must always yield to the monuments and marks erected or adopted by the original surveyor, as indicating the lines run by him. Those monuments are facts. The fiela notes and plats, indicating courses, distances and quantities, are but descriptions which serve to assist in ascertaining those facts. Established GEODEDICAL JURISPRUDENCE. 7ZBa monuments and marked trees not only serve to show the lines of their own tracts, but they are also to be resorted to in connection with the field notes and other evidence, to fix the original location of a monument or line, which has been lost or obliterated by time, accident or design. The original monuments at each extreme of this line, that is, the one five miles east, and the other one mile west of the corner, sought to be established, are identified, but unfortunately, none of the original monuments and marks, showing the actual line which was run between townships 5 and 6, can be found; and hence we must recur to these two, as well as other original monuments which are established, in connection with the field notes and plats, to ascertain where those monuments were; for where they were, there the lines are. Much of the following is from Putnam's U. S. Digest: 309A. A survey which starts from certain points and lines not recognized as boundaries by the parties themselves, and not shown by the evidence to be truepoints of departure, cannot be made the basis of a judgment establishing a boundary. 12 La. An. 689 (18.) See also U. S. Digest, vol. 18, sec. 23, Martin vs. Breaux. a. A party is entitled to the lands actually apportioned, and where the line marked out upon actual survey differs from that laid in the plat, the former controls the latter. 1 Head (Tenn.) 60, Mayse vs. Lafferty. b. When a deed refers to a plat on record, the dimensions on the plat must govern; and if the dimension on the plat do not come together, then the surplus is to be divided in proportion to the dimensions on the plat. Marsh vs. Stephenson, 7 Ohio, N. S. 264. c. Courses and distances on a plat referred to, are to be considered as if they were recited in the deed. Blaney vs. Rice, 20 Pick. 62. d. Where, on the line of the same survey between remote corners, the length varies from the length recorded or called for, in re-establishing intermediate monuments, marking divisional tracts, it is to be presumed that the error was distributed over the whole, and not in any particular division, and the variance must be distributed proportionally among the various subdivisions of the whole line according to their respective lengths. 2 Iowa (Clarke) p. 139, Moreland vs. Page. Bailey vs. Chamblin, 20 Ind. 33. e. Where the same grantor conveys to two persons, to each one a lot of land, limiting each to a certain number of rods from opposite known bounds, running in direction to meet if extended far enough, and by admeasurement the lots do not adjoin, when it appears from the same deeds that it was the intention they should, a rule should be which will divide the surplus over the admeasurement named in the deeds ascertained to exist by actual measurement on the earth, between the grantees in proportion to the length of their respective lines as stated in their deeds. 28 Maine 279, Lincoln vs. Edgecomb. Brown vs. Gay, 3 Greenl. 118. Wolf vs. Scarborough, 2 Ohio St. Rep. 363. Deficiency to be divided pro rata. Wyatt vs. Savage, 11 Maine 431. f. Angel on Water Courses, sec. 57, says of dividing the surplus: "By this process justice will be done, and all interference of lines and titles prevented." 11 I 72Bb GEODEDICAL JURISPRUDENCE. No person can, under different temperatures, measure the same line into divisions a, b, c and d, and make them exactly agree; but if the difference is divided, the points of division will be the same. When we compare the distance on a' map, and find that the paper expanded or contracted, we have to allow a proportionate distance for such variance. (See Table II, p. 165.) 309B. The system of dividing pro rata is embodied in the Canada Surveyors' Act, and quoted at sec. 306 of this work. It is also the French system. By the French Civil Code, Article 646, all proprietors are obliged to have their lines established. In case it may be subsequently found that the survey was incorrect, and that one had too much, if the excess of one would equal the deficit of the other, then no difficulty would occur in dividing the difference. If the excess in one man's part is greater than the deficit in the other, it ought to be divided pro rata to their respective quantities, each participating in the gain as well as the loss, in proportion to their areas. This is the opinion of the most celebrated lawyers. The following is the French text: "Le terrain excidant au celui qui manque devra etre partage entre les parties, au pro rata de leur quantite' respective, en participant au gain comme a la perte, chacun proportionnellement a leur contenance; c'est 1' avis de plus celebres jourisconsultes." Adverse possession or prescriptive right, does not interfere when the encroachment was made clandestinely or by gradual anticipation made in cultivating or in mowing it. For prescriptive right, see the French Civil Code, Article 2262:,"~'Cependant la prescription ne sera jamais invoque daus le cas on' la possession sera clandestine. C'est-a-dire lorsqu' elle est le resultat d'une anticipation faite graduellement en labourant ou en fauchant." Cours Complet. D'Arpentage. Paris, 1854. Par. D. Puille, p. 250. a. No one has a right to establish a boundary without his contiguous owner being present, or satisfied with the surveyor employed. The expense of survey is paid by the adjacent owners. The loser in a contested survey has to pay all expenses. In a disputed survey, each appoints a surveyor, and these two appoint a third. If they cannot agree on the third man, the case is taken before a Justice of the Peace, who is to appoint a third surveyor. The surveyors then read their appointments to one another, and to the parties for whom the survey is made. They examine the respective titles, original or old boundaries, if any exist, all land marks, and then proceed to make the necessary survey, and plant new boundaries. On their plan and report, or process verbal, they show all the detail above recited, mark the old boundary stones in black, and the new ones in red. A stone is put at every angle of the field, and on every line at points which are visible one from another. The stones are in some places set so as to appear four to six inches over ground; but where they would be liable to be damaged, they are set under the ground. GEODEDICAL JURISPRUDENCE. 72B c b. Boundary Witnesses. Under each stone is made a hole, filled with delf, slags of iron, lime or broken stones, and on or near this, is a piece of slate on which the surveyor writes with a piece of brass some words called a mute witness. Witness. He then sets the stone and places four other stones around it corresponding to the cardinal points. The mute witness or expression can be found after an elapse of one hundred years, provided it has been kept from the atmosphere. Ibid. p. 252 and 253. The United States take pains in establishing a corner where no witness tree can be made. Under the stake or post is placed charcoal. The mound and pits about it are made in a particular manner. (See sec. 281.) In Canada, if in wood land, the side lines from each corner is marked or blazed on both sides of the line to a distance of four or. five chains, to serve as future witnesses. 309c. When the number of a lot on a plan referred to in the deed, is the only description of the land conveyed, the courses, distances, and other particulars in that plan, are to have the same effect as if recited in the deed. Thomas vs. Patten, 1 Shep. 329. In ascertaining a lost survey or corner, help is to be had by considering the system of survey, and the position of those already ascertained. See Moreland vs. Page, 2 Clarke (Iowa) 139. a. Fixed monuments, control courses and distances. 3 Clarke (Iowa) 143, Sargent vs. Herod. b. Metes and bounds control acres; that is, where a deed is given by metes and bounds, which would give an area different from that in the deed, the metes and bounds will control. Dalton vs. Rust, 22 Texas 133. c. Metes and bounds must govern. 1 J. J. Marsh, Wallace vs. Maxwell. d. Marked lines and corners control the courses and distances laid down in a plat. 4 McLean 279. e. If there are no monuments, courses and distances must govern. U.S. Dig., vol. 1, sec. 47. f. So frail a witness as a stake is scarcely worthy to be called a monument, or to control the construction of a deed. Cox vs. Freedley, 33 Penn. State R. 124. g. Stakes are not considered monuments in N. Carolina, but regarded as imaginary ones. 3 Dev. 65, Reed vs. Schenck. h. Lines actually marked must be adhered to, though they vary from the course. 2 Overt. 304, and 7 Wheat. 7, McNairy vs. Hightour. i. It is a well settled rule, that where an actual survey is made, and monuments marked or erected, and a plan afterwards made, intended to delineate such survey, and there is a variance between the plan and survey, the survey must govern. 1 Shep. 329, Thomas vs. Patten. i. The actual survey designated by lines marked on the ground, is 72Bd GEODEDICAL JURISPRUDENCE. the true survey, and will not be affected by subsequent surveys. 7 Watts 91, Norris vs. Hamilton. 309D. In locating land, the following rules are resorted to, and generally in the order stated: 1. Natural boundaries, as rivers. 2. Artificial marks, as trees, buildings. 3. Adjacent boundaries. 4. Courses and distances. Neither rule however occupies an inflexible position, for when it is plain that there is a mistake, an inferior means of location may control a higher. 1 Richardson 491, Fulwood vs. Graham. a. Description in a boundary is to be taken strongly against the grantor. 8 Connecticut 369, Marshall vs. Niles. b. Between, excludes the termini. 1 Mass. 91, Reese vs. Leonard. b. Where the boundaries mentioned in a deed are inconsistent with one another, those are to be retained which best subserve the prevailing intention manifested on the face of the deed. Ver. 511, Gates vs. Lewis. 309E. The most material and most certain calls shall control those that are less certain and less material. 7 Wheat. 7, Newsom vs. Pryor. Thomas vs. Godfrey, 3 Gill & Johnson 142. a. What is most material and certain controls what is less material. 36 N. H. 569, Hale vs. Davis. b. The least certainty in the description of lands in deeds, must yield to the greater certainty, unless the apparently conflicting description can be reconciled. 11 Conn. 335, Benedict vs. Gaylord. 309F. Where the boundaries of land are fixed, known and unquestionable monuments, although neither course nor distance, nor the computed contents correspond, the monuments must govern. 6 Mass. 131. 2 Mass. 380. Pernan vs. Wead. Howe vs. Bass. a. A mistake in one course does not raise a presumption of a mistake in another course. 6 Litt. 93, Bryan vs. Beekley. b. When there are no monuments and the courses and distances cannot be reconciled, there is no universal rule that requires one of them to yield to the other; but either may be preferred as best comports with the manifest intent of parties, and with the circumstances of the case. U. S. Dig., vol. 1, sec. 13. c. The lines of an elder survey prevail over that of a junior. Ib. 77. d. Boundaries may be proved on hearsay evidence. Ibid. 167. e. The great principle which runs through all the rules of location is, that where you cannot give effect to every part of the description, that which is more fixed and certain, shall prevail over that which is less. 1 Shobhart 143, Johnson vs. McMillan. 309a. A line is to be extended to reach a boundary in the direction called for, disregarding the distance. U. S. Dig. vol. 7, 16. GEODEDICAL JURISPRUDENCE. 72Bse a. Distances may be increased and sometimes courses departed from, in order to preserve the boundary, but the rule authorizes no other departure from the former. Ibid. 13. b. If no principle of location be violated by closing from either of two points, that may be closed from which will be more against the grantor, and enclose the greater quantity of land. Ibid. sec. 14. 309H. What are boundaries described in a deed, is a question of law, the place of boundaries is a matter of fact. 4 Hawks 64, Doe vs. Paine. a. What are the boundaries of a tract of land, is a mere question of construction, and for the court; but where a line is, and what are facts, must be found by a jury. 13 Ind. 379, Burnett vs. Thompson. b. It is not necessary to prove a boundary by a plat of survey or field notes, but they may be proved by a witness who is acquainted with the corners and old lines, run and established by the surveyor, though he never saw the land surveyed. 17 Miss. 459, Weaver vs. Robinett. c. A fence fronting on a highway for more than twenty years, is not to be the true boundary thereof under Rev. St. C. 2, if the original boundary can be made certain by ancient monuments, although the same arc not now in existence. 11 Cush (Mass.) 487, Wood vs. Quincy. d. The marked trees, according to which neighbors hold their distinct land when proved, ought not to be departed from though not exactly agreeing with the description. 3 Call. 239. 7 Monroe, 333. Herbert vs. Wise. Baxter vs. Evett. Rockwell vs. Adams. e. Where a division line between two adjoining tracts exists at its two extremities, and for the principal part of the distance between the two tracts, and as such is recognized by the parties, it will be considered a continuous line, although on a portion of the distance there is no improvement or division fence. 6 Wendell 467. f. If the lines were never marked, or were effaced, and their actual position cannot be found, the patent courses so far must govern. 2 Dana 2. 1 Bibb. 466. Dimmet vs. Lashbrook. Lyon vs. Ross. g. Or, if the corners are given, a straight line from corner to corner must be pursued. Dig. vol. 1, sec. 33. h. Abuttals are not to be disregarded. Ibid. vol. 12, sec. 4. 809i. Where there is no testimony on variation, the court ought not to instruct on that subject. Wilson vs. Inloes, 6 Gill 121. a. The beginning corner has no more, or the certificate of survey has no greater, dignity than any other corner. 4 Dan. 332, Pearson vs. Baker. b. Sec. 34. Where no corner was ever made, and no lines appear running from the other corners towards the one desired, the place where the courses and distances will intersect, is the corner. 1 Marsh 382. 4 Monroe 382. Wishart vs. Crosby. Thornberry vs. Churchill. 72Bf GEODEDICAL JURISPRUDENCE. c. The land must be bounded by courses and distances in the deed where there are no monuments, or where they are not distinguishable from other monuments. Dig., vol. 1, sec. 47, 48, 49. d. Seventy acres in the S. W. corner of a section, means that it must be a square. 2 Ham. 327, Walsh vs. Ruger. 309J. The plat is proper evidence. Dig., vol. 1, sec. 61, and Sup. 4, sec. 51. a. Mistake in the patent may be corrected by the plat on record. The survey is equal dignity with the patent. Dig., vol. 1, sec. 60. b. A survey returned more than twenty years, is presumed to be correct. 7 Watts 91, Norris vs. Hamilton. 309K. Declaration by a surveyor, chain carrier, or other persons present at a survey, of the acts done by or under the authority of the surveyor, in making the survey, if not made after the case has been entered, and the person is dead, is admissible. U. S. Dig., vol. 12, Boundary, sec. 10. See also English Law Reports, vol. 33, p. 140. a. An old map, thirty years amongst the records, but no date, and the clerk, owing to his old age, could give no account of it, map admissible. Gibson vs. Poor, 1 Foster (N. H.) 240. 309L. The order of the lines in a deed may be reversed. 4 Dana 322, Pearson vs. Baxter. a. Trace the boundary in a direct line from one monument to another, whether the distance be greater or less. 41 Maine 601, Melche vs. Merryman. NOTE. This is the same as the U. S. Act of 11th February, 1805. b. Northward means due north. Haines 293. Dig., vol. 1, sec. 4. Northerly means north when there is nothing to indicate the inclination to the east or west. 1 John 156, Brandt vs. Ogden. c. It is a well settled fact, where a line is described as running towards one of the cardinal points, it must run directly in that course, unless it is controlled by some object. 8 Porter 9, Hogan vs. Campbell. e. A survey made by an owner for his own convenience, is not admissible evidence for him or those claiming under him. 1 Dev. 223, Jones vs. Huggins. 309M. Parties, to establish a conventional boundary, must themselves have good title, or the subsequent owners are not bound by it. 1 Sneeds (Tenn.) 68, Rogers vs. White. a. Parties are not bound by a consent to boundaries which have been fixed under an evident error, unless, perhaps, by the prescription of thirty years. 12 La. An. 730, Gray vs. Cawvillon. b. The admission by a party of a mistaken boundary line for a true one, has no effect upon his title, unless occupied by one or both for fifteen years. 10 Vermont 33, Crowell vs. Bebee. GEODEDICAL JURISPRUDENCE. 72Bg c. A hasty recognition of a line, does not estop the owner. Overton vs. Cannon, 2 Humph. 264. d. In a division of land between two parties, if either was deceived by the innocent or fraudulent misrepresentation of the other, or there was any mistake in regard to their right, the division is not binding on either. 14 Georgia 384, Bailey vs. Jones. e. A division line mistakenly located and agreed on by adjoining proprietors, will not be held binding and conclusive on them, if no injustice would be done by disregarding it. U. S. Digest, vol. 18, sec. 32. See, also, 29 N. Y. 392, Coon vs. Smith. English Reports 42, p. 307. f. A mistaken location of the line between the owners of contiguous lots is not conclusive between the immediate parties to such location, but may be corrected. App. 412, Colby vs. Norton. g. If S surveys for A, A is not estopped from claiming to the true line. 9 Yerg. 455, Gilchrist vs. McGee. h. When owners establish a line and make valuable improvements, they cannot alter it. Laverty vs. Moore, 33 N. Y. 650. 309N. A fence between tenants, in common, if taken down by one of them, the others have no cause of action in trespass. 2 Bailey 380, Gibson vs. Vaughn. 309o. A line recognized by contiguous owners for thirty years, controls the courses and distances in a deed. 32 Penn. State R. 302, Dawson vs. Mills. a. A line agreed on for thirty years, cannot be altered. 10 Watts 321, Chew vs. Morton. b. Adjacent owners fixed stakes to indicate the boundary of water lots. One filled the part he supposed to belong to him; the other, being cognizant of the progress of the work, held that the other and his grantees were estopped to dispute the boundary. 32 Barb. (N. Y.) 347, Laverty vs. Moore. c. To establish a consentable line between owners of adjoining tracts, knowledge of, and assent to the line as marked, must be shown in both parties. 4 Barr. 234, Adamson vs. Potts. d. When two parties own equal parts of a lot of land, in severalty, but not divided by any visible monuments, if both are in possession of their respective parts for fifteen years, acquiescence in an imaginary line of division during that time, that line is thereby established as a divisional line. 9 Vernon 352, Beecher vs. Parmalee. e. Sec. 29. Where parties have, without agreement, and ignorant of their right, occupied up to a division line, they may change it on discovering their mistake. Wright 576, Avery vs. Baum. f. Where A and B and their hired man built a fence without a compass, and acquiesced in the fence for fifteen years, it was held to be the 'true line in Vermont. 18 Verm. 395, Ackley vs. Nuck. 72Bh GEODEDICAL JURISPRUDENCE. g. Quantity generally cannot control a location. Dig. vol. 10, sec. 49. h. Long and notorious possession infer legal possession. Newcom vs. Leary, 3 Iredell 49. i. A hasty, ill-advised recognition is not binding. Norton vs. Cannon, Dig., vol. 4, sec. 73. j. The line of division must be marked on the ground, to bring it within the bounds of a closed survey. Ibid. sec. 106. k. Bounded by a water course, according to English and American decisions, means to the centre of the stream. (See Angel on Water Courses, ch. 1, sec. 12.) 1. East and north of a certain stream includes to the thread thereof. Palmer vs. Mulligan, 3 Caines (N. Y.) 319. m. Bank and water are correlative, therefore, to a monument standing on the bank of a river, and running by or along it, or along the shore, includes to the centre. 20 Wend. (N.Y.) 149. 12 John. (N.Y.) 252. n. Where a map shows the lots bounded by a water course, the lots go to the centre of the river. Newsom vs. Pryor, 7 Wheat. (U. S.) 7. o. To the bank of a stream, includes the stream itself. Hatch vs. Dwight, 17 Mass. 299. p. Up a creek, means to the middle thereof. 12 John. 252. q. Where there are no controlling words in a deed, the bounds go to the centre of the stream. Herring vs. Fisher, 1 Sand. Sup. Co. (N.Y.) 344. r. Land bounded by a river, not navigable, goes to the centre, unless otherwise reserved. Nicholas vs. Siencocks, 34 N. H. 345. 9 Cushing 492. 3 Kernan (N.Y.) 296. 18 Barb. (N. Y.) 14. McCullough vs. Wall, 4 Rich. 68. Norris vs. Hill, 1 Mann. (Mich.) 202. Canal Trustees vs. Havern, 5 Gilman 548. Hammond vs. McLaughlin, 1 Sandford Sup. Ct. R. 323. Orindorf vs. Steel, 2 Barb. Sup. Ct. R. 126 3 Scam. Ill. 610. State vs. Gilmanton, 9 N. Hamp. 461. Luce vs. Cartey, 24 Wend. 641. Thomas vs. Hatch, 3 Sumner 170. a. On, to, by a bank or margin, cannot include the stream. 6 Cow. (N. Y.) 549. t. A water course may sometimes become dry. Gavett's Administrators vs. Chamber, 3 Ohio 495. This contains important reasons for going to the centre of the stream. u. Along the bank, excludes the stream. Child vs. Starr, 4 Hill 369. v. A corner standing on the bank of a creek; thence down the creek, etc. Boundary is the water's edge. McCulloch vs. Allen, 2 Ramp. 309, also Weakley vs. Legrand, 1 Overt. 205. w. To a creek, and down the creek, with the meanders, does not convey the channel. Sanders vs. Kenney, J. J. Marsh 137. (See next page, which has been printed sometime in advance of this.) GEODEDICAL JURISPRUDENCE. 72s1 monuments and marked trees not only serve to show with certainty the lines of their own tracts, but they are also to be resorted to in connection with the field notes and other evidence to fix the original location of a monument or line which has been lost, or obliterated by time, accident, or design. The original monuments at each extreme of this line-that is, the one five miles east, and the other one mile west of the corner-sought to be established, are identified; but, unfortunately, none of the original monuments and marks, showing the actual line which was run between townships 5 and 6, can be found, and hence we must recur to these two, as well as other original monuments, which are established in connection with the field notes and plats, to ascertain where those monuments were, for where they were, there the lines are. WATER COURSES, 309a. Eminent domain is the right retained by the government over the estates of owners, and the power to take any part of them for the public use. First paying the value of the property so taken, or the damages sustained to their respective owners. 3 Paige, N. Y. Chancery Rep. 45. The British Crown has the right of eminent domain over tidal rivers and navigable waters, in her American colonies. Each of the United States have the same. See Pollard v. Hogan, 3 Howe, Rep. 223; Goodtitle v. Kibbe, 9 Howe Rep. 117; Stradar v. Graham, 10 Howe Rep. 95; Doe v. Beebe, 13 Howe Rep. 25. From these appear that the State has jurisdiction over navigable waters, provided it does not conflict with any provision of the general government. The Constitution of the U. States reserves the power to regulate commerce-which jurists admit to include the right to regulate navigation, and foreign and domestic intercourse, on navigable waters. On those waters the general government exercises the power to license vessels, and establish ports of entry, consequently it can prevent the construction of any material obstruction to navigation, and declare what rules and regulations are required of vessels navigating them. Prescriptive right must set forth that the occupier or person claiming any easement, has been in an open, peaceable and uninterrupted possession of that which is claimed, during the time prescribed by the statute of limitation of the country, or state in which the easement is situated. In England, the prescribed time is 20 years. Balston v. Bensted, 1 Campbell Rep., 463; Bealey v. Shaw, 6 East. Rep. 215. In the United States the time is different-in New Hampshire, 20; Vermont and Connecticut, 15; and South Carolina, 5 years. Water Course, is a body of water flowing towards the sea or lake, and is either private or public. It consists of bed, bank and water. Public water course, is a navigable stream formed by nature, or made and dedicated to the. public as such by artificial means. Navigable streams may become sometimes dry. A stream which can be used to transport goods in a boat, or float rafts of timber or saw logs, is deemed a navigable stream, and becomes a public highway. But a stream made navigable by the owners, and not dedicated to the public, is a private water course. See Wadsworth v. Smith, 2 Fairfield, Maine Rep. 278. 12 72B2 GEODEDICAt JURISPRUDENCE. The owners of the adjoining lands have a title to the bed of the river; each proprietor going to the centre, or thread thereof, when the river is made the boundary. Should the river become permanently dry on account of being turned off in some other direction; or other cause, then the adjoining riparian owners claim to the centre of the bed of the stream, the same as if it were a public highway. Bounded by a water course-signifies that the boundary goes to the centre of the river. Morrison v. Keen, 3 Greenleaf, Maine Rep. 474; 1 Randolph, Va., Rep. 420; Waterman v. Johnson, 3 Pickering, Mass. R., 261; Star v. Child, 20 Wendell, N. Y. Rep., 149. To a swamp, means to the middle of the stream or creek, unless described to the edge of the swamp. Tilder v. Bonnet, 2 McMull South Carolina Report, 44. Any unreasonable or material impediment to navigation placed in a navigable stream, is a public nuisance. 12 Peters, U. S. Rep. 91. The legislature cannot grant leave to build an obstruction to navigation. 5 Ohio Rep., 410. A winter way on the ice, dedicated to the public for 20 years, becomes a highway, and cannot be obstructed. 6 Shepley, Maine Rep., 438. The legislature cannot declare a river navigable which is not really so, unless they pay the riparian owners for all damages sustained by them. 16 Ohio Rep. 540. Rivers in which the tide ebbs and flows are public, both their water and bed as far as the water is found to be affected by local influences, but above this, the riparian owners own to the centre of the river, and have the exclusive right of fishing, etc., the public having the right of highway. See 26 Wendell, N..Y. Rep. 404. Banks of a navigable river are not public highways, unless so dedicated, as the banks of the Mississippi, in Illinois and Tennessee, and the rivers of Missouri for a reasonable time. See 4 Missouri Rep. 343; 3 Scammon 610. This last decision had reference to a place in an unbroken forest, where it was admitted that the navigators had a right to land and fasten to the shore. It would be unfair to give a captain and crew of any vessel the right to land on a man's wharf, or in his enclosure without his permission; therefore, it would appear " that the public have the privilege to come upon the river bank so long as it is vacant, although the owner may at any time occupy it, and exclude all mankind." Austin v. Carter, 1 Mass. Rep. 231. Obstructing navigation by building bridges without an act of the legislature, sinking impediments or throwing out filth, which would endanger the health of those navigating the river, is a nuisance. See Russel on Crimes 486. Although an obstruction may be built under an act of the legislature in navigable waters, he who maintains it there, is liable for any damage sustained by any vessel or navigator navigating therein. 4 Watts, Pennsylvania Rep. 437. Bridges can be built over navigable rivers by first obtaining an act of the legislature, Commonwealth v. Breed, 4 Pick, Massachusetts R. 460; Strong v. Dunlap, 10 Humphrey, Tenn. R. 423. See Angel on Highways, sec. 4. GEODEDICAL JURISPRUDENCE. 72B3 The State of Virginia, authorized a company to build a bridge at Wheeling, across the eastern channel of the Ohio river, it was suspended so low as to obstruct materially the navigation thereof. The Superior Court ordered its removal, but gave them a limited time to remove it to the other channel, where the company proposed to have sufficient depth of water and a drawbridge of 200 feet wide. The Court did not consider the additional length of channel nor the necessary time in opening the draw a material impediment. Subsequently an act of Congress declared the first bridge built on the eastern channel not to be a material or unreasonable obstruction, and ordered that captains and crews of vessels navigating on the river should govern themselves accordingly by lowering their chimneys, etc. 13 Howe Rep. 618; 18 Howe Rep. 421. If a bridge is built across a river in a reasonable situation, leaving sufficient space for vessels to pass through, and causing. no unreasonable delay or obstruction, and is built for the public good, it is not deemed a nuisance. Rex v. Russel, 6 Barn. and Cresw. 566; ]5 Wendell, 133. For further, see Judge Caton's decision in the Rock Island Bridge case, delivered in 1862. Canals. If after being built, a new road is made over it, the canal company is not obliged to erect a bridge. Morris Canal v. State, 4 Zabriskie, N. Y. Rep. 62. In America, when two boats meet, each turns to the right. They carry lights at the bow. Freight boats must give away to packet or passenger boats. Farnsworth v. Groot, 6 Cowen, N. Y. Rep. 698. In Pennsylvania, the descending boat has preference to the ascending. Act of Pennsylvania, April 10, 1826. Perries. The owner of a public ferry ought to own the land on both sides of the river. Savill 11 pl. 29. A ferry cannot land at the terminus of a pnblic highway, without the consent of the riparian owners. Chambers v. Ferry, 1 Yeates. A use of twenty years, does not confer the right to land on the opposite side without the consent of the adjacent owners. If A erects a dam or ditch on his own land, provided it does not overflow the land of his neighbor B, or diverts the water from him, he is justified in so doing. Colborne v. Richards, 13 Mass. Rep. 420. But if A injures B, by diverting the water or overflowing his land, B is empowered to enter on A's land and remove the obstructions when finished, but not during the progress of the work, doing no unnecessary damage, or causing no riot. In this case, B cannot recover damages for expense of removal, etc. If B enters suit against A, he recovers damages, and the nuisance is abated. Gleason v. Gary, 4 Connecticut Rep. 418; 3 Blackstone Comm. 9 Mass. Rep., 216; 2 Dana, Kentucky Rep. 168. If B, C and D, as separate owners, cause a nuisance on A's property, A can sue either of the offending party, and the non-joinder of the others cannot be pleaded in abatement. 1 Chitty's Pleadings, 75. The tenant may sue for a nuisance, even though it be of a temporary nature. 'Angel on Water Courses, chap. 10, sec. 398. The reversioners may also have an action where the nuisance is of a permanent one. Ibid. If A and B own land on the same river, one above the other, one of them cannot erect a dam which would prevent the passage of fish to the other. Weld v. Hornby, 7 East. R. 196; 6 Pickering, Mass. Rep. 199. 72B4 GEODEDICAL JURISPRUDENCE. One riparian owner cannot divert any part of the water dividing their estate, without the consent of the other; as each has a right to the use of the whole of the stream. 13 Johnson, N. Y. Rep. 212. It is not lawful for one riparian owner to erect a dam so as to divert the water in another direction, to the injury of any other owner. 3 Scammon, Illinois Rep. 492. Where mills are situate on both banks of a river, each having an equal right; one of them, in dry weather, is not allowed to use more than his share of the water. See Angel on Water Courses, chap. 4. p. 105. One mill cannot detain the water from another lower down the stream, nor lessen the supply in a given time. 13 Connecticut Rep. 303. One riparian owner cannot overflow land above or below him by means of a dam or sluices, etc., or by retaining water for a time, and then letting it escape suddenly. See 7 Pickering, Massachusetts Rep. 76, and 17 Johnson, N. Y. Rep. 306. Hence appears the legality of constructing works to protect an owner's land from being overflowed. Such work may be dams or drains leading to the nearest natural outfall; for it is evident, that if by making a drain, ditch or canal, to carry off any overflow to the nearest outlet, such proceedings would be legal, and the party causing the overflow would have no cause of complaint. Merrill v. Parker Coxe, New Jersey Rep. 460. For the purpose of Irrigation. A man cannot materially diminish the water that would naturally flow in a water course. Hall v. Swift, 6 Scott R. 167. He may use it for motive power, the use of his family, and watering his cattle; also for the purpose of irrigating his land, provided it does not injure his neighbors or deprive a mill of the use of the water. That which is made to pass over his land for irrigation if not absorbed by the soil, is to be returned to its natural bed. Arnold v. Foot, 12 Wendell, N. Y. Rep. 330; Anthony v. Lapham, 5 Pickering, Mass. Rep. 175. A riparian owner has no right to build any work which would in ordinary flood cause his neighbor's land to be overflowed, even if such was to protect his own property from being destroyed. Angel on Water Courses, chap. 9, p. 334. In several countries, the law authorizes A to construct a drain or ditch from the nearest outlet of the overflow on his land, along the lowest level through his neighbor's land, to the nearest outfall. This is the law in Canada. Callis on Sewers, 136. If A raises an obstruction by which B's mill grinds slower than before, A is liable to action. 7 Con. N. Y. Rep. 266, and 1 Rawle, Penn. Rep. 218. Back water. No person without a grant or license is allowed to raise the water higher than where it is in its natural state, or, unless the so doing has been uninterruptedly done for twenty years. Regina v. North Midland Railway Company, Railway Cases, vol. 2, part 1. p. 1. No one can raise the level of the water where it enters his land, nor lower it where it leaves it. Hill v. Ward, 2 Gill. Ill. Rep. 285. GEODEDICAL JURISPRUDENCE. 72B5 Let a s represent the urltace ot a unltorim channel, and w v its bottom. Let w t = datum line, parallel to the horizon; f b, g m, h d and t s the respective heights above datum. Let from a to b belong to A, b to d belong to B, and d to s belong to C. B found that on his land he had 10 feet of a fall from d to n, and the same from n tof. He built a dam = c m, making the surface of the water at x the same height as the point d, and claimed,that he did no injury to the owner C. If C had a peg or reference mark at d, before B raised his dam, he could prove that B caused back water on him. When this is not the case, recourse must be had to the laws of hydraulics. Mr. Neville, County Surveyor of Louth, Ireland, in his Hydraulics, p. 110, shows that (practically) in a uniform channel, when the surface of the water on the top or crest of the dam is on the same level with d, the water will back up to p, making xp ==1.5 to 1.9 times x d. The latter is that given by Du Buat, and generally used. See Encyclopedia Britannica, vol. 19. The former, 1.5, by Funk. See D'Aubuison's Hydraulics by Bennett., sec. 167. When the channel is uniform, the surface x o p is nearly that of a hyperbola, whose assymptote is the natural surface; consequently, the dam would take effect on the whole length of the channel. All agree that the effect will be insensible, when the distance, xp, from the dam is more than 1.9 times the distance x d. Let x be the point behind the dam where the water is apparently still, then m n is half the height of x above m, as the water, in falling from x, assumes the hydraulic curve, which is practically that of a parabola. As we know the quantity of water passing over in a given time, and the length of the dam, we can find the height m n, twice of which added to c m gives the height of x above c. Let this height of x above c = H. Find where the same level through x, will meet the natural surface as at d, then measure dp =nine-tenths of d x, the point p will be the practical limit of back water, or remous. Within this limit we are to confine our inquiries, as to whether B has trespassed on C, and if the dam will cause greater damage in time of high water than when at its ordinary stage. For further, see sections on Hydraulics. Owners of Islands, own to the thread of the river on each side. Hendrick v. Johnson, 6 Porter, Alabama Hep. 472. The main branch or channel is the boundary, if nothing to the contrary is expressed. Doddridge v. Thompson, 9 Wheal, U. S. Report, 470. Above the margin goes to the centre. N. Y. Rep. 6 Cow. 618. 72B6 GEODEDICAL JURISPRUDENCE. Natural and permanent objects are preferred to courses and distances. Hurley v. Morgan, 1 Devereaux and Bat. N. Carolina Report, 425. Boundary may begin at a post or stake on the land, by the river, then run on a given course, a certain distance to a stake standing on the bank of the river, and so along the river.} The law holds that the centre of the river or water course, is the boundary. 5 New Hampshire Rep. 520; see also Lowell vs. Robinson, 4 Maine Rep. 357. A grant of land extending a given distance from a river, must be laid off by lines equidistant from the nearest points on the river. Therefore a survey of the bank of the river is made, and the rear line run parallel to this at the given distance. Williams v. Jackson, N. Y. Rep. 489. PONDS AND LAKES. 309b. Land conveyed on a lake, if it is a natural one, extends only to the margin of the lake. But if the lake or pond is formed by a dam, backing up the water of a stream in a natural valley, then the grant goes to the centre of the stream in its natural state. State v. Gilmanton, 9 N. Hampshire R. 461. The beds of lakes, or inland seas with the islands, belong to the public. The riparian owners may claim to low water mark. Land Commissioners v. People, 5 Wend. N. Y. R. 423. Where a pond has been made by a dam across a stream, evidence must be had by parol, or from maps showing where the centre of the river was; for if the land was higher on one side than on the other, the thread of the original stream would be found nearer to the high ground. Island in the middle of a stream not navigable, is divided between the riparian owners, in proportion to the fronts on the river. 2 Blackstone, 1. But if the island is not in the middle, then the dividing line through it, is by lines drawn in proportion to the respective distances from the adjacent shores. 13 Wendell, N. Y. Rep. 255. If no part of the island is on one side of the middle of the river, then the whole of the island belongs to the riparian owners nearest to the island. See Cooper, Justice, lib. 2, t. 3, and Civil Code of Louisiana, art. 505 to 507. An island between an island and the shore, is divided as if the island was main land, for if it be nearer the main land than the island, it id divided in proportion as above. Fleta, lib. 3, c. II. 8. Where there are channels surrounding one or more islands, one has no right to place dams or other obstructions, by which the water of one channel may be diverted into another. 10 Wendell, N. Y. Rep. 260. If a river or water course divides itself into channels, and cuts through a man's land, forming an island, the owner of the land thus encircled by water can claim his land. 5 Cowen, 216. ACCRETION OR ALLUVION. 309c. Accretion or alluvion is where land is formed by the accumulation of sand or other deposits on the shore of the sea, lake or river. Such accretions being gradual or imperceptibly formed, so that no one exactly can show how much has been added to the adjacent land in a given time, the adjacent owner is entitled to the accretion. 2 Blackstone Cor. 262. See also Cooper Justice, lib. 2, tit. 1. GEODEDICAL JURISPRUDENCE. 72B7 In subdividing an accretion, find the original front of each of the adjacent lots, between the respective side lines of the estates; then measure the new line of river between the extreme side lines, and divide pro rata, then draj lines from point to point, as on the annexed diagram. The meandered lines are taken from corner to corner of each lot, without regard to the sinuosities of the shore as b i. It is sometimes difficult to determine the position of the lines c d and a b. As some may contend that A c produced in a straight line to the water, would determine the point d, also B a produced, would determine b, from the above diagram appears that by producing B a to the water, it would intersect near i, thus cutting off one owner from a part of the accretion, and entirely from the water. The plan adopted in the States of Maine and Massachusetts, in determining b and d, is as follows: From a draw a perpendicular to B a, and find its intersection on the water's edge, and call it Q. From a with a h as base, draw a perpendicular, and find its intersection on the water's edge, and call it P. Bisect the distance P Q in the point r, then the line a r, determines the point b. In like manner we determine the point d. Having b and d, we find i, k, etc., as above. In Maine and Massachusetts the point i, k, I and m are found as we have found b and d, erecting two perpendiculars from each abuttal, on the main land, one from each adjacent line and bisecting their distance apart for a new abuttal. 6 Pickering, Mass. Rep. 158; 9 Greenleaf, Maine Rep. 44. When A c and B a are township lines, as in the Western States, they are run due East and West, or North and South. In this case, d and b would be found by producing A c and B a due East and West, or North and South, as the case may be. Now, let B a c be the original shore, and d, b, n, a and B the present shore, making c, x, n, d the accretion or alluvion. It is evident that it would be incorrect to divide the space a, n, b, d, between the riparian owners, that only b d should be so divided. When A c and B a are township lines run East and West, or North and South, as in the Western States, they are run on their true courses to the water's edge, intersecting at the points d and b. Here it would be plain that the space b d should be divided in proportion to the fronts c e, ef, etc., by the above method. 72B8 GEODEDICAL JURISPRUDENCE. We do not know a case in Wisconsin or Illinois, where a surveyor has adopted this method. They run their lines at right angles to the adjacent section lines, which many of them take for a due East and West, or North and South line, as required by the act of Congress, passed 1805. The accretion b, a, n, in our opinion, would belong to him who owns front a h. There is a similar case to this pending for some time in Chicago, where some claim that the water front a, n, b, d should be divided; others claim that only b to d, as the part a, b, n may be washed away, by the same agent which has made it. " Where land is bounded by water, and allusions are gradually formed, the owner shall still hold to the same boundarry, including the accumulated soil. Every proprietor whose land is thus bounded, is subject to a loss by the same means that may add to his territory, and as he is without remedy for his loss in this way, he cannot be held accountable for his gain." New Orleans v. United States, laid down as a fundamental law by Judge Drummond, Oct. 1858, in his charge to the jury in the Chicago sand bar case. When the river or stream changes its course. If it changes suddenly from being between A and B, to be entirely on B, then the whole river belongs to B. But if the recession of a stream or lake be gradual or imperceptible, then the boundary between A and B will be on the water, as if no recession had taken place. 2 Blackstone, Com. 262; 1 Hawkes, North Carolina R. 56. When a stream suddenly causes A's soil to be joined to B's, A has a right to recover it, by directing the river in its original channel, or by taking back the earth in scows, etc., before the soil sb added becomes firmly incorporated with B's land. 2 Blackstone Com. 262. HIGHWAYS. 309d. IHighway is a public road, which every citizen has a right to use. 3 Kent Comm. 32. It has been discussed in several States, whether streets in towns and cities are highways; but the general opinion is that they are. Hobbs v. Lowell, 19 Pick. Mass. Rep. 405; City of Cincinnati v. White, 8 Peters,. U. S. Rep. 431. A street or highway ending on a river or sea, cannot be " blocked up" so as to prevent public access to the water. Woodyer v. Hadden, 5 Taunton R. 125. When a road leads between the land of A and B, and that the road becomes temporarily or unexpectedly impassable, the public has a right to go on the adjoining land. Absor v. French, 2 Show, 28; Campbell v. Race, 7 Cushing, Mass. Rep. 411. Width of public highways is four rods, if nothing to the contrary is specified, or unless by user for twenty years, the width has been less. Horlan v. Harriston, 6 Cow 189. Twenty years uninterrupted user of a highway is prima facie evidence of a prescriptive right. 1 Saund., 323 a, 10 East 476. Unenclosed lands adjoining a highway, may be travelled on by the public. Cleveland v. Cleveland, 12 Wend. 376. Owners of the land adjoining a public highway, own the fee in the road, unless the contrary is expressed. The public having only an easement in it. When the road is vacated, it reverts to the original owners. Comyn digest Dig. tit. Chemin A 2; Chatham v. Brand, 11 Conn. R. 60; Kennedy v. Jones, 11 Alabama R. 63; Jackson v. Hathaway, 15 Johnson's Rep. 947. GEODEDICAL JURISPRUDENCE. 72 9 A road is dedicated to the public, when the owners put a map on record showing the lots, streets, roads or alleys. Manly et al v. Gibson, 13 Illinois, 308. In Illinois the courts have decided, that in the county the owners of land adjoining a road have the fee to the centre of it, and that they have only granted an easement, or right to pass over it, to the public. Country roads are styled highways. In incorporated towns and cities, roads are denominated streets, the fees of which are in the corporations or city authorities. The original owner lias no further control over that part of his land. Huntley v. Middleton, 13 Illinois, 54. In Chicago, however, the adjacent owners build cellars under the streets, and the corporation rents the ends of unbridged streets on the river, for dock purposes. Where streets are vacated, they revert to the original owners, as in other States. The adjacent owners must grade the streets and build the sidewalks, yet by the above decision they have no claim to the fee therein. It appears strange that Archer road outside the city limits is a highway, and inside the limits, is a street. The road outside and inside is the same. Part of that now inside, was in January, 1863, outside; consequently, what is now a street, was 10 months ago a highway. Then, the fee in the road was in the adjacent owners, now by the above decision, it is in the corporation. It seems difficult to determine the point where a highway becomes a street, and vice versa. Footpaths. Cul-de-sac are thoroughfares leading from one road to another, or from one road to a church or buildings. The latter is termed a cul-de-sac. These, if used as a highway for 20 years, become a highway. Wellbeloved on Highways, page 10. See Angel on Highways, sec. 29. A cannot claim a way over B's land. A cannot claim a way from his land through B's; but may claim a way from one part of his land to another part thereof, through B's, that is when A's land is on both sides of B's. Cruises' English Digest, vol. 3, p. 122. If A sells part of his land to l:, which is surrounded on all sides by A's, or partly by A's and others, a right of way necessarily passes to B. 2 Roll's Abridgment, Co. P. L. 17, 18. If A owned 4 fields, the 3 outer ones enclosing the fourth, if he sells the outer three, he has still a right of way into the fourth. Cruise, vol. 3, p. 124; but he cannot go beyond this enclosure. Ibid, 126. When a right of way has been extinguished by unity of possessions, it may be revived by severance. Ibid, p. 129. Boundaries on highways, when expressed as bounded by a highway, it means that the fee to the centre of the road is conveyed. 3 Kent Comm. 433. Exceptions to this rule are found in Canal Trustees v. Haven, 11 Illinois R. 554, where it is affirmed that the owner cannot claim but the extent of his lot. By, on, or along, includes the middle of the road. 2 Metcalf, Mass. R. 151. By the line of, by the margin of, by the side of, does not include the fee to any part of the road. 16 Johnson, N. Y. R. 447. 13 72B10 GEODEDICAL JURISPRUDENCE. The town that suffers its highways to be out of repair, or the party who obstructs the same, is answerable to the public by indictment, but not to an individual, unless he suffers damage by reason thereof in his person or property. Smith v. Smith, 2 Pick. Mass. Rep. 621; Forman v. Concord, 2 New Hampshire Rep. 292. Individuals and private corporations are likewise liable to pay damages. 6 Johnson, N. Y. Rep. 90. Lord Ellenborough says two things must concur to support this action; an obstruction in the road by the fault of the defendant, and no want of ordinary care to avoid it on the part of the plaintiff. Butterfield v. Forrester, 11 East. Rep. 60. Towns, or corporations, are primarily liable for injuries, caused by an individual placing an obstruction in the highway. The town may be indemnified for the same amount. In Massachusetts the town or corporation is liable to double damages after reasonable notice of the defects had been given, but they can recover of the individual causing it but the single amount. Merrill v. Hampden, 26 Maine Rep. 224; Howard v. Bridgewater, 16 Pick, Mass. Rep. 189; Lowell v. Boston and Lowell Railroad corporation, 23 Pick. Mass. R. 24. By the extension of a straight line, is to be understood, that it is produced or continued in a straight line. Woodyer v. Hadden, 5 Faunl.*Rep. 125. Plankroads, if made on a highway, continue to be highways, the public have the right to pass over them, by paying toll. Angel on Highways, sec. 14. The Court has the jurisdiction to restrain any unauthorized appropriation of the public property to private uses; which may amount to a public nuisance, or may endanger, or injuriously affect the public interest. Where officers, acting under oath, are intrusted with the protection of such property, private persons are not allowed to interfere. 6 Paige, Chancery Rep. 133. Railroads may be a public nuisance, when their rails are allowed to be 2 to 3 inches above the level of the streets, as now in Chicago,-thereby requiring an additional force to overcome the resistance. See Manual, 319e, where it has been shown, that the rail was 3 inches above the level of the street, and required a force of 969 pounds to overcome the resistance. This state of things would evidently be a public injury, and be sufficient reasons to prevent a recurrence of it in any place where it had previously existed. It may be a private injury, when the track is so near a man's sidewalk, as to prevent a team standing there for a reasonable time to load or unload. When a road is dedicated to the public at the time of making a town plat or map, it is held that the street must have the recorded width though the adjoining lots should fall short, because the street has been first conveyed. When a new street is made, the expense is borne by the adjacent owners or parties benefitted. Subsequent improvements are usually made by a general city or town tax; sometimes by the adjacent owners-the city paying for intersections of streets and sidewalks. In February, 1864, Judges Wilson and Van Higgins, of the Cook County (Illinois) Superior Court, decided that a lot cannot be taxed for more than the actual increase in its value, caused by the improvement in front thereof. SIR RICHARD GRIFFITH'S SYSTEM OF VALUATION. NOTE.-All new matter introduced is in italics or enclosed in parenthesis. 309e. The intention of the General Valuation Act was, that a valuation of the lands of Ireland, made at distant times and places, should have a relative value, ascertained on the basis of the prices of agricultural produce, and that though made at distant periods, should be the same. The 11th section of the Act, quoted below, gives the standard prices of agricultural produce, according to which the uniform value of any tenement is to be ascertained, and all valuations made as if these prices were the same, at the time of making the valuation. 309f. Act 15 and 16 Victoria, Cap. 63, Sec. A7l.-Each tenement or rateable hereditament shall be separately valued, taking for basis the net annual value thereof with reference to prices of agricultural produce hereinafter specified; all peculiar local circumstances in each case to be taken into consideration, and all rates, taxes and public charges, if any, (except tithes) being paid by the tenant. NOTE.-(The articles in italics are not in the above section, but inserted so as to extend the system as much as possible to America and other places.) General average prices of 100 lbs. of Wheat, Os. 9d. or $1.62 Mutton, 36s. lid. or $8.86 Oats, 4s. 4d. " 1.04 Pork, 28s. 10d. " 6.91 Barley, 4s. 11d." 1.19 Flax, 44s. d. " 10.58 Maize, Hemp, Rice, Tobacco, Butter, 58s. 10d. or 14.11 Cotton, Beef, 35s. 3d. or 7.65 Sugar, &c. &c. &c. To find the price of live weights.-Deduct one-third for beef and mutton, and one-fifth for pork. Houses and Buildings shall be valued upon the annual estimated rent which may be reasonably expected from year to year, the tenant paying all incidental charges, except tithes. Sections 12 to 16, inclusive, of the act, treat of the kind of properties to be valued. 309g. Lands and Buildings used for scientific, charitable or other public purposes, are valued at half their annual value, all improvements and mines opened during seven years; all commons, rights of fishing, canals, navigations and rights of navigation, railways and tramways; all right of way and easement over land; all mills and buildings built for manufacturing purposes, together with all water power thereof. But the valuation does not extend to the valuation of machinery in such buildings. A tenement is any rateable hereditament held for a term of not less than one year. Every rateable tenement shall be separately valued. The valuator shall have a map showing the correct boundary of each tenement, which shall be marked or numbered for references. The map shall show if half streets, roads or rivers are included. 72B12 GRIFFITH'S SYSTEM OF VALUATION. The Field Book is to contain a full description of every tenement in the townland (or township), the names of the owners and occupiers, together with references to the corresponding numbers on the plan or map. The book to be headed with the name of the county, parish (or township), each townland (or section). Gentlemen of property, learning, or the law, should have "Esquire" attached to their names. Land, is ground used for agricultural purposes. Houses and Offices, are buildings used for residences. Other tenements, such as brickfield, brewery, &c. To determine the value of land, particular attention must be paid to its geological and geographical position, so far as may be necessary to develope the natural and relative power of the soil. NATURE OF SOILS. 309h. Examine the soil and subsoil by digging it up, in order to ascertain its natural 6apabilities; for if guided by the appearance of the crops, the valuator may put too high a price on bad land highly manured. This would be unjust, as it is the intrinsic and not the temporary value which is to be determined. To obtain an average value, where the soil differs considerably in short distances; examine and price each tract separately, and take the mean price. The value of soil depends on its composition and subsoil. Subsoil may be considered the reg/ulator or governor of the powers of the soil, for the nature of its composition considerably retards or promotes vegetation. In porous or sandy soil, the necessary nutriment for plants is washed away, or absorbed below the roots of the plants. In clayey soils, the subsoil is impervious, the active or surface soil is cold and late, and produces aquatic plants. Ience appears the necessity of strict attention to the subsoil. Soils are compounded of organic and inorganic matter: the former derived from the disintegration and decomposition of rocks. The proportion in which they are combined is of the utmost importance. A good soil may contain six to ten per cent. of organic matter; the remainder should have its greater portion silica; the lesser alumina, lime, potash, soda, &c.-(See tables of analysis at the end of these instructions.) Soils vary considerably in relation to the physical aspect; thus in mountain or hilly districts, where the rocks are exposed to atmospherical influence, the soils of the valleys consist of the disintegrated substance of the rocks, whilst that of the plains is composed of drifted materials, foreign to the subjacent rock. In the former case the soil is characterised by the locality; in the latter it is not. By reference to the Geological Map of Ireland, it will be seen that the mountain soil is referable to the granite, schistose rocks and sandstone. The fertility of the soil is to some extent dependent on the proportion or combinations which exist between the component minerals of the rocks from which it may have been formed; thus granite in which feldspar is in excess when disintegrated, usually forms a deep and easily improved soil, whilst that in which it is deficient will be comparatively unproductive. GRIFFITH'S SYSTEM OF VALUATION. 72B13 The detritus of mica slate and the schistose rocks form moderately friable soils fit for tillage and pasture. Sandstone soils derived from sandstone, are generally poor. The most productive lands in Ireland are situate in the carboniferous limestone plain, which, as shown on the Geological Map, occupies nearly two-thirds of that country. When to the naturally fertile calcareous soils of this great district, foreign matters are added, derived from the disintegration of granite and trappean igneous rocks, as well as from mica slate, clay slate, and other sedementary rocks, soils of an unusually fertile character are produced. Thus the proverbially rich soil of the Goldenvale, situate in the limestone district extending between Limerick and Tipperary, is the result of the intermixture of disintegrated trap derived from the numerous igneous protusions which are dispersed through that district, with the calcareous soil of the valley. Lands of superior fertility occur near the contacts of the upper series of the carboniferous limestone and the shales of the millstone grit, or lower coal series; important examples of this kind will be found in the valley of the Barrow and Nore, etc., etc. For geological arrangement the carboniferous limestone of Ireland has been divided into four series. 1st Series beginning from below the yellow sandstone and carboniferous slate. 2d Series, the lower limestone. 3d Series, the calp series. 4th Series, the upper limestone. Soil derived from 1st Series is usually cold and unproductive, except where beds of moderately pure limestone are interstratified with the ordinary strata, consisting of sandstone and slate-shale. The 2d Series, when not converted by drift, consisting chiefly of limestone-gravel intermixed with clay, usually presents a friable loam fit for producing all kinds of cereal and green crops, likewise dairy and feeding pastures for heavy cattle, and superior sheep-walks. The 3d Series consists of alternations of dark grey shale, and dark grey impure argillo-siliceous limestone, producing soil usually cold, sour, and unfit for cereal crops; but in many districts naturally dry, or which has been drained and laid down for pasture. This soil produces superior feeding grasses, particularly the cock's foot grass. These pastures improve annually, and are seldom cultivated, because they are considered the best for fattening heavy cattle. The 4th Series produces admirable sheep pasture, and, in some localities, superior feeding grounds for heavy cattle, and produces every variety of cereal and green crops. 309i. It is of the utmost importance that the valuator should carefully attend to the mineral composition of the soil in each case, and a reference to the Geological Map will frequently assist his judgment in this respect, the relative position of the subjacent rocks having been determined upon sectional and fossiliferous evidence. He should carefully observe the changes in the quality and fertility of the soil near to the boundaries of different rock formations, and should expect and look for sudden transitions from cold, sterile, clayey soils, as in the millstone grit districts, into the rich unctuous loams of the adjoining limestone districts, which 72u14 GRIlFFITH S SYSTEM OF VALUATION. usually commence close to the line of boundary; and similar rapid changes will be observed from barrenness to fertility, along the boundaries of our granite, trap, and schistose districts, an; likewise on the border of schistose and limestone districts, the principle being that every change in the composition of the subjacent rocks tends to an alteration in the quality both of the active and subsoils. As it appears from the foregoing that the detritus of rocks enters largely into the composition of soils and other formations, the most trustworthy analysis is supplied, which, compared with the crops usually cultivated, will show their relative value and deficiencies. NoTE.-(The table of analysis given by Sir Richard Griffith is less than one page. Those given by us in the following pages of these instructions are compiled from the most authentic sources, and will enable the valuator or surveyor to make a correct valuation. The surveyor will be able, in any part of the world, to give valuable instructions to those agriculturists with whom he may come in contact. We also give the method of making an approximate analysis of the rocks, minerals and soils which he may be required to value. Where a more minute analysis is required, he may give a specimen of that required to be analysed to some practical chemist-such as Jackson, of Boston; Hunt, of Montreal; Blaney, Mariner, or Mahla, of Chicago; Kane, or Cameron, of Dublin; Muspratt, or Way, of England, etc. etc. Table in section 310 contains the analysis of rocks and grasses. Section 310a, analysis of trees and grasses. Section 310b, analysis of grains, hemp and flax. Section 310c, analysis of vegetables and fruit. Section 310d, analysis of manures. Section 310e, comparative value of manures; the whole series making several pages of valuable information. In Canada, the law requires that Provincial Land Surveyors should know a sufficient share of mineralogy, so as to enable them to assist in developing the resources of that country. In Europe, all valuations of lands are generally made by surveyors, or those thoroughly versed in that science; but in the United States a political tinsmith may be an assessor or valuator, although not knowing the difference between a solid and a square. This state of things ought not to be so, and points out the necessity of forming a Civil Engineers' and Surveyors' Institute, similar to those in other countries.) From these tables it will appear what materials are in the formation of the soil, and the requirements of the plants cultivated; thus, in corn and grasses, silica predominates. Seeds and grain require phosphoric acid. Beans and leguminous plants require lime and alkalies. Turnips, beets and potatoes require potash and soda. The soils of loamy, low lands, particularly those on the margins of rivers and lakes, usually consist of finely comminuted detrital matter, derived from various rocks; such frequently, in Ireland, contain much calcareous matter, and are very fertile when well drained and tilled. The rich, low-lying lands which border the lower Shannon, etc., are alluvial, and highly productive. It is necessary that the valuator should enter into his book a short, accurate description of the nature of the soil and subsoil of every GRIFFITH'S SYSTEM OF VALUATION. 72B15 tenement which may come under his consideration, and that all valuators may attach the same meaning or descriptive words to them. The following classification will render this description as uniform as possible: Classification of soils, with reference to their composition, may be be comprehended under the following heads, viz: Argillaceous or clayey-clayey, clayey loam, argillaceous, alluvial. Silicious or sandy-sandy, gravelly, slaty or rocky. Calcareous-limey, limestone gravel, marl. Peat soil-moor, peat. The color of soils is derived from different admixtures of oxide or rust of iron. Argillaceous earths, or those in which alumina is abundant, as brick and pipe clays. The soil in which alumina predominates is termed clay. When a soil consists chiefly of blue or yellow tenacious clay upon a retentive subsoil, it is nearly unfit for tillage; but on an open subsoil it may be easily improved. Clayey soils containing a due admixture of sand, lime and vegetable matter, are well adapted to the growth of wheat, and are classed amongst the most productive soils, where the climate is favorable. Soils of this description will, therefore, graduate from cold, stiff clay soils to open clay soils, in proportion as the admixture of sand and vegetable matter is more or less abundant, and the subsoil more or less retentive of moisture. Loams are friable soils of fine earth, which, if plowed in wet weather, will not form clods. A strong clayey loam contains about one-third part of clay, the remainder consisting of sand or gravel, lime, vegetable and animal matters, the sand being the predominating ingredient. A friable clayey loam differs from the latter by containing less clay and more sand. In this case the clay is more perfectly intermixed with the sand, so as to produce a finer tilth, the soil being less retentive of mois ture, and easier cultivated in wet weather. Sandy or gravelly loams is that where sand or gravel predominates, and the soil is open and free, and not sufficiently retentive of moisture. A stiff clay soil may become a rich loam by a judicious admixture of sand, peat, lime and stable manure, but after numerous plowings and exposure to winter frosts in order to pulverize the clay, and to mix with it the lime, peat, sand, etc. Alluvial soils are generally situated in flats, on the banks of rivers, lakes, or the sea shore, and are depositions from water, the depositions being fine argillaceous loam, with layers of clay, shells, sand, etc. The subsoil may be different. On the sea shore and margin of lakes, the the clay subsoils usually contain much calcareous matter in the form of broken shells, and sometimes thick beds of white marl. The value of the soil and subsoil depend on the proportion of lime it may contain. This may be found by an analysis. (See sequel for analysis.) Rich alluvial soils are the most productive when out of the influence of floods. These soils are classed as clayey, loamy, sandy, etc., according to their nature. Flat lands or holms, on banks of rivers, are occasionally open and sandy, but frequently they are composed of most productive loams. 72B16 GRIFFITHI'S SYSTEM OF VALUATION. SILICEOUS SOILS. 809j. Sandy soils vary very much in their grade, color and value, according to the quality of the sand. White shelly sands, which are usually situated near the sea shore, are sometimes very productive, though they contain but a very small portion of earthy matter. Gravelly soils are those in which coarse sand or gravel predominates; these, if sufficiently mixed with loam, produce excellent crops. Slatey soils occur in mountains composed of slate rock, either coarse or fine grained. In plowing or digging the shallow soils on the declevities of such places, a portion of the substratum of slate intermixes with the soil, which thus becomes slatey. Rocky soils. Soil may be denominated rocky where it is composed of a number of fragments of rock intermixed with mould. Such soils are usually shallow, and the substratum consists of loose broken rock, presenting angular fragments. CALCAREOUS SOILS. 309k. Calcareous or limestone soils, are those which contain an unusual quantity of lime, and are on a substratum of limestone. These lands form the best sheepwalks. Limestone gravel soil, is where we find calcareous or limestone gravel forming a predominant ingredient in soils. Mlarly soils are of two kinds, clayey marl, or calcareous matter combined with clay and white marl, which is a deposition from water, and is only found on the margins of lakes, sluggish rivers and small bogs. On the banks of the River Shannon, beds of white marl are found 20 feet deep. When either clayey or white marl enters into the composition of soils, so as to form an important ingredient, such soils may be denominated marly. PEATY SOILS. 3091. Flat, moory soils are such as contain more or less peaty matter, assuming the appearance of a black or dark friable earth. When the peat amounts to one-fourth, and the remainder a clayey loam, the soil is productive, especially when the substratum is clay or clayey gravel. When the peat amounts to one-half, the soil is less valuable. When the peat amounts to three-fourths of the whole, the soil becomes very light, and decreases in value in proportion to the increase of the peat in the soil. Peaty or boggy soils are composed of peat or bog, which, when first brought into cultivation, present a fibrous texture and contain no earthy matter beyond that which is produced by burning the peat. The quantity of ashes left by burning is red or yellow ashes, about oneeighth of the peat, generally one-tenth or one-twelfth in shallow bogs. In deep bogs the ashes are generally white, and weigh about one-eightieth of the peat. Such land is of little value unless covered with a heavy coat of loamy earth or clay. Hence it appears that the value of peaty soil depends on the amount of red ashes it contains. For this reason peaty soils are valued at a low price. NOTE.-(Bousingault, in his "Rural Economy," says: " The quality of an arable land depends essentially on the association of its clay and sand or gravel." GRCIFFITHL' SYSTEM OF VALUATION. 21 72BI 7 Sand, whether it be siliceous, calcareous or felspathbic, always renders a soil friable, permeable and loose; it, facilitates the access of the air and the (irainage of the water, and its influence depends more or les,-s on the myinute dlivision of its particles.) Trhe following table, given by Sir Richard Griffith, is from Von Thaer's Chemistry, as found by jiim and Einhoff: CLASS. ~~~~Saud, or Carbonate IIU sConipa1 -309in. ca~~~~~~ss. 01~~"Y, (uavel, ofLime umu rative per cent. per cent per cent per cent Yalue. I First class strong wheiat land. 74 it) 4.5 11.5 100 2 DO........... 81 6 4 8.7 98 13 ~ I)o............. It) 4 6.5 96 4 Do............40 22 ~ 36(1 4 90 5 Rich light land in natural grass, 1 4 49 10 27 - 6 Rich barley land...........20 67 3 10 78 7 Good wheat land...........58 86 2 4 7 8 Wheat land...............56 3 0 12 2 75 9 Do................ 60O 88 2 70 11 Do........6........ 8 80 K 2 65 12 Good barley land.......... oS 6 0. ~ 2 60 18) Do. second quality.y........33 65 0 29 14 Do. Do.............28 70 0 2 15 Oat lands............... 28 75 F 1.5 I16 Do................184 80 I1.5 1 7Rye land.................14 85 1 18 Do do............... 9 90 1 1 9 Do do.............. 4 9- 5 0 75 20 Do do................... 2 97.5 0.5 Under the head clay, has been included alkalies, chlorides, and supposed to be in fair proportions. The soil in each case supposed to be uniform to tile depth of six inches. in I/hc Field Booke the following explanatory terms may be used as occassion may require: S'f-Where a soil contains a large proportion (say one-hnlf or even more-) of tenacious clay; this cracks in dry weather, forming into lumips. FPioble-Where it is loose and] open, as in sandy, gravelly or nmoory lands. Str-ong.-Where it haks a tendency to form into clods. Deep)-Where the depth is less than 5 inches. Dry.-No springs. Friable soil, and porous subsoil. W1et.-Numerous springs; soil and subsoil tenacious. Sharp.-A moderate share of gravel or small stones. Phin or soft-No gravel: chiefly composed of very fine sand, or soft, ilnligt earth, without gravel. Cold.-Parts on a tenacious clay subsoil, and has a tendency, When inl pasture, to produce rushes and other aquatic plants. Sandy or gravellg.-A large proportion of sand or gravel. Satey.-Where the slatey substratum is much mixed with the soil. Worn.-Where it haes been a long time cultivated without rest or manure. Poor.-When of a bad quality. Jfangry?.-W hen consisting Of a great proportion of gravel or coarse Sand resting on a gravelly subsoil. On such land manure does not produtce, the usual effect. The color of tlie soil and the features of thje land ought to be mentioned, such as, Steep, level, rocky, shrubby, etc., etc. 1 4 72r,18. CRIFFITIL'S SYSTEM OF VALUATION. Indigenous plants should be observed, as they sometimes assist to indicate particular circumstances of soil and subsoil. rzame of I'lant. Indicates Thistle...................................................... Strong, good soil. Dockweed and nettle.................................. Rich, (lairy land. Sheep sorrell.................................... Gravelly soil. Trefoil and vetch...................... Good dry vegetable soil. W ild thyme............................................. Thinness of soil. lRagweed................................................ Deep soil. 1 ouse-ear hawk-weed............................. )Dryness of soil. Iris, rush and lady's smock.......................... Moisture of soil. Purple red nettle and naked horsetail.............. etentive subsoil. Great Ox-eye....................P........ l'overty of soil. CLASSIFICATION OF SOILS WITHI EFl'.REN'CE TO THEIR VAIlrE. 309n. All lands to be valued may be classed under arable and pasture. Arable land may be divided into three classes, viz Prime soils, rich, loamy earth. Medium soils, rather shallow, or mixed. P'oor soils, including cultivated moors. Pasture, as fattening, dairy and stone land pastures. The prices set forth in the Act (see sec. 309f) is the basis on which the relative and uniform valuation of all lands used for agricultural ipurposes must be founded. It is incumbent on the valuator to ascertain thle depth of soil and nature of subsoil, to calculate the annual outlay per acre. IHe should calculate the value per acre of the produce, according to the scale of the Act, and from these data deduce the net annual value of the tenement. 309o. Tables of produce, etc., formulea for calculation, and an acreable scale of prices, supplied in the following sections, are given as auxiliaries with a view to produce uniformity among the valuators employed. Thus, if the valuator finds it necessary to test his scale of prices for a certain quality of land, he may select one or more farms characteristic of tlie average of the neighborhood. Their value should be correctly calculatedl and an average price per acre obtained, from wlich he deduces tlhe standard field price of such description of land. The farms (or fields) tlhus examined will serve as points of comparison for the remainder of the district. SC\ALE 1FOR AIRABLE. Class and Description. Avernlg prili peL v I v' l('. 1l. Very superior, friable clayey loam, deep and rich, From. T,. lying well, neatly fielded, on good, sound clayey subsoil, having all the properties that constitute a suo5 perior subsoil, average produce 9 barrels (or s. d. s. d.: 4 stones -- lbs. - bushels) per acre...................?0 () 26i 0 2. Superior, strong, deep and rich, with inferior spots deducted, lying well on good clay subsoil.............. 27 0 24 0; 3. Superior, not so deep as the foregoing, or good alluvial soils-surface a little uneven....................... 2 0 22 () (4 Good medium loams, or inferior alluvial land of an 5. Good loams, with inferior spots deducted............ 17 C 15 0 | 6. Medium land, even in quality, rather shallow, deep '' and rocky........................................................ 14 0 10 ( (RIFFIT'I'S SYSTE1IM IF VALUATION. 72u 19 7. Cold soil, ralther shallow and mixed, lying steep on jcold clayey, or cold, wet, sandy subsoil................. 0 7 0 8. Poor, dry, worn, clayey or sandy soil, on gravelly o or sandy subsoil.............................................. 0 9. Very poor, cold, worn, clayey, or poor, dry, shall low, sandy soil, or liigh, steep, rocky, had land........ 4 0 1 0 10. (ood, heavy moor, well (drained, on g,)ool, clayey G | Subsoil.................................................................. 1 O 10 0) 11. Medium moory soil, drained, and in good conS - dition.............................................................. G O 12. Poor moory, or boggy arable, wet, and unmixed a [ w ith earth....................................................... v. 1 0 The above prices opposite each clllass is what the valuator's field price lhouldl be in an ordinary situation, sulbject to be increased or decreased for local circumstances, togethler with lleductions for rates and taxes. O0'1)p. Of ArabI, l1(1d.-Thle amount of crop raised depends on the system of tillage, and the crops raised. The system of cultivation should be such as would maintinn an adequate number of stock to manure the farm, and the crops should be suited to the soil; tlius, lands oin which oats or rye could be profitably grown, may not repay the cost of cultivating it for wheat. The following tables show the average maximum cost, produce and value of crops in ordinary cultivation for one statute acre. TABLE OF 1I' OD)UCE..u L ()T i l (.rzl l. ' (I i,.trios a 1:l ilm ' |(Ir;n.e. j__I; }()ranvle. Total Ipr(du(ce in to 1....... 7 2 ' 2, '20 ). 1/ I.., s. (.. /I. s.!.,s. d /. Price per ton................... 40 l( 10 0, 0 U 5: S: s.. C. I s.,.. Total vil. ofprodu( cpr acr.1 3 4 0 l ' ' 08 (; 0 5 0 S 0 Total cost of culture pracr. S 10 li 7 0 3 1 S 5 10 i Wheat. i Iarley. O(ats. lye. Meadow. - _ ----. —:- -! --- I0. ~ t. | 2; I < > i Totnl produce pi.! 1r'l s. Ti s, 1BIls. Tns MI-is. i'ns. lils. Tns C\ t. 'lns.Tns lTns. re.................. 2 10 1 11 l 1 1 ['rice per............... 1S 9 1 1 ', 5 1 17 14 45; 5 30, oti; ~v l.o,. /;. (...!.. s.. 1. T"ltal val ofpr'dluce 0 0 *O i l 1 ' '; t ( 11. ' 4 7 tiL 1 lt I'otalcostofculturel 3 9 0 i:; 0:11 0i 3 t0 )0 | 7 S, 1 9 62 0 NOTn.-'The bar;rel is pounds, and the ton 2-, 210 pounds. From this table it appears that the cost of cultivating turnips, anid other broad-leaved plants, is greater than that for grain crops. 721u20 (GlIFFITIl'S SYSTEM OF VALUATION. SCALE OF P1IC1S, FOIR PASTUIE. Average. Classes and Descriptionl. Stok in i C('attle. Shlee. Sw Price p,'r Acre. a -' I 6~ -1 ~4 ------------------ ----- - - I. Very superior f'attening' ] i ' ' s. S. land. soil composed of ilne- " -l _'.., ly coniminuated loaml, pro- I | - < (licilig tile most succulent > 10 3-; i-; - 35 to 31 (lualities it' grass, x(clls-:, ' ively usc(tl flr linshin |;- -: - _ ~ O heavy cattle 1and slheep,. o ^ * I -*F _, L^ ^OJ I 2. Superior dairy pIrsture or i filtteninfg land, witli verges 3 3 30 to 24 tteI' t t 15!.I ailnd 3 3 30 to 24 of ]prime lleavy moors, all: *calves. having a grassy teildeiie., j 3. (iool dlairy Itst uir on clay or sanlldv soils, or good; 1 Six rocky pastture, each adal)te(d: 20 t1a 3 - 3 23 to 17 to d.l/i,, mlrnmi~.,s tl. orf tl- Cal]CS. Observations. f T'lis soil being used fir '1 finisliilin '' cattle adl(1 slieel), tlle latter replace thle former wheln finishlI ed for market. t. " '.... " j I'" 'I- '' -.. illg;11hll. 01. < 1. '(rlerable' mixed clayey oM i lomitv pl)astures, or tootl. jrocky p]asture, adt(pl)ttl 1to lairil purploses or tllt realr[ ill of younl catt.le or slit'ep. 25' I. ( {5. (Coarse sour' 'ruslly pstuille oil shallow cllayey (r l ()1!'(ory soil, or dry irocky slhrubbylli, )il sture, ada(l ted to lile t'tLrear- ' | iiig of youig cattle or stoirel; shee p.. I 6. tlnferior coarse sour lpstlure I onI cold shallow clayey or1'' slIalllow mlloory soil, or dry rocky - slrul)by pistlure, a- ' 3; _ dlapled cliielly to \ilitergc I 1lo'r Nolilui cattle or stole: ' Svlt'epl... - 7. (iod lnlixel,gl-e( all h11(ai t! lp;stuille ii tile hlli, esteadtl = ot moutilitis or i'1erio,r. dry! rocky slirubby lpastur, 'i- ) (lapted to tile rearingl ot, < lililt dry cattle or sliheel,. i. M r, i ( r,',,m,1.,11~1 Ild I ltl-'!,C;is tiritl: i;,,, o: t, c;:3 c 3( ~I;J ct;,3 r ~lr3rJ~C1:; r..; i j",: '"J 'I: "3"3 i?j ~=;,' =' CC cl r,; c13.3 w cr 3 rV cce V T= =I( iS 3 I;~ to 11 - 10 to 5 f Tlis land iscalJ culated at 3 fiirkills of buttter to eachl cow. Thlis soil is calculated at 2.' lirkins of bttler to eacl cow. f This desertip}tion of soil is calculated at 2" tiiirkiis of butter to eachl cow. f T'I's descriplill (|ot soil is calciilted fi.) r tlIe IIrpIo(e of' rearing yoIung cattle or [ slheep. 'I'le descript imon of' landl that llis bra c e indclu(Ies c astre so l'r lverCr.I'S SOf lrI'ges, infterior dry rocky pl)ast1ures, and lmixed.reell and lheatlhy pal'SI...,...:'..; to 'I 41 I Ii 3 I -,, v j...........6.. s........-..... l.2 f irtes, Cln iilly al nmoutain pastiTr, or inI,.' ll lllallted fi ll d lo!e'iori close rocky or sllrll b - s 1)y pasture, adai tote to tlie, tI< ' a, l t I rearing of young cattle or1j ': vonlg cettle of 'sleel:,..; - '! j 0 51all infierior (e9. Mixed brown heathliy lps-i " ' tllres witli slots of glreelln; sc ip' i o. intermilixed, or- very illfteri-! 5 * cF. I- Is. to 9. or 1ba, e rlocky l):stllles, or! ' I. -,. ^' \." steel) srllrbby banks near, homestead,...._ ' s 10. Ileathly pastures liigl all' l I rentote, or cut away og, - - - Sd to 4d partly pasturable. remote mountaini tops,, F 12. lrecipitous clilts,. - - NOTE.-The price inserted opp)osite eaclh class of lands, according to its respecltive produce, is what the valuator's field price should be in an ordinary situatioll, subject to be increased or reducced for parlicular local circumstances, together with deductions for rates a1end taxes. In the calculations for testilig his scale price, the vall:ltor tsould tabulate, as above, at the prices per ton or l::rrel, tle a.verage produce per acre of tle district under consideration. These values lie will again tabulate according to the system of farming ladopted. The following may serve as a formula: (.II'FFT1'1'S SYSTEM OF VALUATION. 72I 21 ONE IIUNI)DED STATUTE ACRES UNDER FIVE YEARS' ROTATION AS FOLLOWS: Acres. ('ost of Value tat. Tillage. of T illage.! n I 5 ~ s. d. Potatoes,.. 3 25 1) 0 1st e I', 1 Vetches,. ' 6; 0 1st 2ea, M5or 0n) rC:,- tMgel Wurtzel. 8 20 5 0 [Turnips,..1" 14 0 0 (Winter Wheat,.)' n 0 ~ 2d YCear, 5 or 20') Ie, Spring Wheat,. ) Balrley,. 8 2-t 17 0 1 aIl:y,. (;I 8 17 0 hid Year, or 2 acres', Clover,.. 1 0 PaIsture, 1. 1 0 0 o)ito )lots, t) -tth Year, 5 oe 20 aci e s, Pasture,. 20! t;5h YcYear, 1 r 2!) acr, es, 20 70 13 0 1(0 vo 4 I.1 0 Allow for w;ear 'and tear of implements,. 0 0 Five per cent. on ~5()0 capital, '25) DeLduct Expenses,. N cit~t ~Anal. Value of Produce, jINctt Annual Value of Produce,.. ~ s. (. 42 0 () 12 0 0 330 15 0 96 0 0 1t8 0 0 52 0 0 2; 5 0 4 10 0 95 0 0 123 0 0 592 10 0.59 10 0 282 14 0 FATTENING LANDS. 309r. It ]las becii ascertained that the fat in an ox is one-eighth of the lean, 1and is in proportion of the fatty nmatter to the saccharine and protein compounds in the herbage. Tle method of grazing, too, has some influence. Thie best lands will produce about ten tons of grass per acre, in one year. ()Oc beast will cat from seven to nine stones in one d(y. Six sheep will eat as m1uch1 as one ox. One Irish statute acre of prime pasture will finish for the market two sets of oxen frorn April to September. From September until December it is fed by sheep. The general fornmul. may be as follows: S'PEIllOR FINISIIIN( I,.ANI). Mdof'ofNett Ac t. ]3ode of Farmilng and Description of Stock. incease An cwt.qrs.lbs s. 4. s. d. Two sets of cattle to be finished in the senson, the lands preserved during the months of January, Februairy and 1'March. A four-year old heifer, weighing a:bout 5 cwt.,i well wintered, andl coming o0n in good condition, in the first two months of April and May, will increasse,..1 2 0 35 62 13 3 A heifer in the same condition, in the months ofi June, July:l August, will increase,.. 1 O " 2 13 3 Oni tile sa;tme l;,till, 5 sheep to the Irish acre will increase at the rate cf 2 11). per week, for Oc — tober, November and Deceniber,.. 1 ]0 4 0 1 11 3 Gross produce on one Irish acre, or 1,. 29. P)l. statute nme:sure,...... 7 17 9 72u22 GRIFFITIIHS SYSTEM OF VALUATION. Expenses. ~ s. d. Interest on capital for one beast to the Irish acre, at 5 per cent. for ~10,...10 0 Ierd, per Irish acre, (a herd will care 150 Irish acres,) at 2s. per acre,.0.. ( Contingencies,... 10 0 Commission on the sale of 2 beasts and 7 sheep, at 2} per cent.,........ 11 9 0 Extra expenses,.. 8 0 Deduct expenses,....3 19 0 Nctt produce per Irish acre, or IA. 2it. (0., statute measure,. 3 18 9 Cattle in good condition will fatten quicker on this description of land during the early months than under the system of stall-feeding. D.\RY PASTURE..309s. Dairy pasltres are more succulent than fattening lands. The average quantity of butter which a good cow will give in the year maly be taken at 3- firkins -- 218 lbs.; or, allowing nine quarts to the pound of butter, the milk will le 1,900 qluarts. If the stock be good, under similar circumstances its plroduce may be considered to vary with tlle quantity and quality of the herbage. This and the quality and suitability of the stock must be carefully discrimina.ted and considered. The general form ula is casfollocws: In column A, set the cows anid produce; the hogs, and increase in weight; the calves, when reared; tile milk used by the family. In colunil B, set the weight of the produce. Il column C, set the Act price. And in column D, the amount. The sum of column 1) will be the gross receipts, from which deduct the slim of' all the expenses, rent of land under tillage, and tlie difference will be the nett annual produce for that part used as a dairy pasture. STORE PASTURE. 309t. Tile value of store pasture depends on the amount of' stock it can feed. The valuator will estimate the number of acres which would feed a three years beast for the season, from -which the number of stock for tile whole tenement may be ascertained, wlich, calculated at an average rate for their increase or improvement, will give the gross value. This valuation must be checked for all incidental expenses and local circumstances-in general, two-thirds of the gross produce may be considered as a fair value. In mountain districts, it is divided into inside and remote grazing. Tlhe inside is allotted for milch cattle and winter grass The remote or outside pasture is for summer grazing for dry cattle and sheep. The annual value of these pastures is to be obtained from tle herds or persons living on or adjacent to themr, taking for basis the number of sums grazed and the rate per sum. The following will enable the valuator to estimate the number of sums on any tenement: One three years old heifer is called a "su m" or colloy; one sum is - to three yearlings = one two years old and one, one year old -four GRIFFITII'S SYSTE3M OF VALUATION. i 72B23 ewes and four lambs -= five two years old sheep -= six hoggets (one year old sheep) r= to two-thirds of a horse. LAND IN IMEDI)IUM SITUATI'ON. 30(9u. The above classifications, scales of prices, etc., for different kinds of land, have been calculated with reference to the quality of the soil and its productive capabilities, arising from the composition, depth and nature of the subsoil, without taking into consideration the extremes of position in which each particular kind may occasionally be found. The value thus considered may be defined as the value of land in medium or ordinary situation. Land in an ordinary or medium situation. Should not be distant more than five or six miles from a principal market town, having a fair road to it, not particularly sheltered or exposed, not very conveniently or very inconveniently circumstanced as to fuel, lime and manures; not remarkably hilly or level, the greatest elevation of which slall not exceed ()00 feet above the level of the sea. When the valuation of the property is made, lie will enter in the first column the valuations obtained, and in the second column tle valuations corrected for local circumstances. r,LOCA L CIRCUMSTANCES. 309v. The local circumstances may be divided into two classes, viz: natural and artificial. Natural, is that which aids or retards the natural powers of the soil in bringing the crop to maturity. Artificial, is that which afford or deny facilities to maintain or increase the fertility of the soil, and such as involve the consideration of remunerations for labor of cultivation. Local circumstances may, therefore, be classed under-climate, malnure, and market. 309w. Climate includes all the phenomena which affect vegetation, suchl as temperature, quantity of atmospheric moisture, elevation, prevailing winds, and aspect. Various combinations of these, and other external causes, are what cause diversity of climate. The germination of plants, and the amount of atmospheric moisture, are considerably dependent on temperature; hence the advantage of a locality in which its mean is greatest. Its average in Ireland varies from 48~ (Fahrenheit) in the north to 51~ in the south, the corresponding atmosplheic moisture being from 4.27 to 4.83 grains to the cubic foot. These arc considerably modified by elevation, which produces nearly the same cff.ct as latitude, every 350) feet in height being equivalent to one degree of temperature. 3(09x. The average depth of rain which falls in one year in Ireland, varies from 40 inches on the west coast to 33 on the cast. The proportion of thle rain fall is greater for the mountain districts than for the low lands. Tlie general effect of elevation on arable lands in this case are, that tlme soluble and fine parts of the soil are washed out, and ultimately carried down by the stre('tLs Stucl e evated districts are also frequently exposed to high winds, etc. The prevailing winds, and how modified, are to be taken into consideration. 309y. In Ireland, on land exposed to westerly winds, the crops are fre - 72B24 GRIFFITI'S SYSTEM OF VALUATION. quently injured in the months of August and September. A suitable deduction should therefore be made for such lands, although the intrinsic value may be similar to land in a, more sleltered situation. To determine the influence of climate requires considerable care and extensive comparison. Thus, the soil which in an elevated district is worth 10s. per acre, will be worth 15s. if placed in an ordinary situation, about 300 feet above the level of the sea, and not particularly sheltered or exposed. The same description of lands, however, in a more favorable situation, say from 50 to 100 feet above the sea, distant from mountains, and having a south-east aspect, may be worth 20s. per acre. In making deductions from cultivated lands, in mountainous districts, the following table will be found useful, and may be applied in connection with heights given in Ordnance Survey maps: Altitude in feet. Deduct per E~. 800 to 90() feet........................ shillings. 700 800 0"......................4 i 600 " 700 "........................3 500 " I "....................... 400 " 500 "(.......................1 Arahle land in the interior of mountains, may be considered 100 feet of altitude, worse than on the exterior declivities on the same heigllth; so also tlose on the north may be taken 100 worse tlian those having a southern aspect, both having the same height. In mountain districts, take the homestead pasture at 3, the outer at 2, and the remote at 1. Deduct for steepness in proportion to the inconvenience sustained by the farmer in plowing and manuring. Deduct for bad roads, fences, and for difference in the soils of a field where it is of unequal quality. MANURE. 309z. Mianures are that which improve the nature of the soil, or restore the elements which have been annually consumed by the crops. The most important of tlese, in addition to stable manure and that produced from towns, consist of limestone, coal turbary, sea weed, sea sand, etc. In a limestone country, where the soil usually contains a sufficient quantity of calcareous matter, the value of lime as a manure is trifling when compared to its striking effects in a drained clayey or loamy argillaceous soil. It promotes tlhe decomposition of vegetable or animal matter existing in the soil, and renders stiff clay friable when drained, and more susceptible of benefit from the atmosphere, by facilitating the absorption of ammonia, carbonic acil gas, etc.; decomposes salts injurious to vegetation, such as sulphate of iron, (which it converts into sulphlite of lime and oxide of iron, and known here as gypsum or plaster of Paris,) and further it improves the filtering power of soils, and enables them to retain what fertilizing matter may be contained in a fluid state. Lime may therefore be used in due proportion, either on moory arenacious or argillaceous soils; hence the vicinity of limestone quarries is to be considered relatively to the value of lime as a manure to the leandls., GRIFFITH9S SYSTEM OF VALUATION. 72B26 under consideration: say from sixpence to two shillings STERLING per pound to be added according to circumstances. The vicinity of coal mines and turf bogs are likewise an important consideration affecting the value of land, for the expense of hauling fuel, for burning lime and domestic purposes, must be considered. The per' centage should vary from sixpence to two shillings and sixpence per pound' Sea manure includes sea weed and sea sand, containing shells, both of which are highly valuable, especially the former. Where sea weed of good quality is plentiful and easy of access, the land within one mile of the strand is increased in value 4s. in the pound at least. Where the soil is a strong clay or clayey loam, shelly sea sand, when abundant, will increase the value of the land 2s. 6d. in the pound, for the distance of one mile. The valuator will consider whether sea weed is cast on the shore or brought in boats, and the nature of the road. If hilly, reduce them to level by table at p. 72J15. The following will enable the valuator to ascertain the value at any distance from the strand: Supply rather scarce at one mile, 2s. For every one-half mile ' middling " 3s. deduct 6d. " plentiful " 4s. Theproximity to towns, as a source of manure and market farm, garden and dairy produce, is to be considered. MARKET. 310. To this head may be referred the influence of cities, towns and fairs; these possess a topical influence in proportion to their wealth and population. The following is a classification of towns: Villages, from 250 to 500 inhabitants. Small market towns, from 500 to 2000. Large market'towns, from 2000 to 19,000. Cities, from 19,000 to 75,000, and upwards. Small villages, of from 250 to 500 inhabitants, do not influence the value of land in the neighborhood beyond the gardens or fields immediately behind the houses. The increase in such cases above the ordinary value of the lands will rarely exceed 2s. in the pound. Large villages and small towns, having from 500 to 1000 inhabitantsr usually increase the value of land around the town to a distance of three miles. For the first half mile, the increase is 3s. in the pound; for the next half mile, 2s.; next, 16d. etc., deducting one-third for each half mile, making, for three miles distant, 6d. in the pound, or one-fortieth. Mlarket towns, having from 8000 to 75,000 inhabitants, town parks, or land within one mile, is 10s. in the pound higher than in ordinary situations. Beyond this the value decreases proportionately to 6s. at the distance of three miles from the town. Thence, in like manner, to a distance of seven miles, where the influence of such town terminates. Cities and large towns, having apopulation of from 19,000 to 75,000 inhabitants. The annual value of town parks will exceed by about 14s. in the pound the price of similar land in ordinary situations; and this increased value will extend about t wo miles in every direction from the houses of the town, beyond which the adventitious value will gradually decrease for the next mile to 12s. in the pound; at the termination of four miles, to 6s.; at seven miles, to 4s.; and at nine and a half miles, its influence may be considered to end. 15 72B26 72B26 ~GRIFFITH'5 SYSTEM OF VALUATION. Its increase to be made for the vicinity of towns, is tabulated as follows: Distance in Miles. R opulation. --- ----- - - s. d.js. d.1s. d. s. d.1s. d. s.d. s. d. s. d. s.d. s.d,. s.d.sd! 9 From 2050 to 500, - ~2 i1 0:06 8" 500 1,000, - 3Oi 20 1 0 061 7 1,000" 2,000, - 4. 0H02 0 1 006 ~- 6 "2,000 "4,000, - F 0 5 I 5" 4,000 8,000,.... 80I 60(4 0!20 1 00 6..... 4 "8,000 15.000, - 1 060 20 10 006 --- 3 "15,000 19,000, - F12 0110 08 0!6 0 4 02 01 0 06 —.2 "19,000"75,000, - - -14 012 0F100 8 06 04 02 01t0 0 1 75,000 and upwards,- 22 0i20C18 0 H)0 10 06 03 02 t010 In applying the -above table, the population must be used onl~y for a gena eral index, as it is the wealth and commercial influence which principally fixes the class; the valuator must use his judgment, combining the cornparative wealth with the population, and raise it one class in the tables, or even more. If' there 1)0 a large poor class, he should take a class lower. The general influence of markets and towns includes the effects of railways, canals, navigable rivers, and highways; thus, of two districts equally distant from a market, and equal in other respects, that which is intersected by or lies nearer to the best and cheapest mode of communication for sale of produce, is the most valuable. Bleach greens, fair greens, orchards, osieries, etc., should be valued according to the,agricultural value of the land which they occupy. Plantations and woods, are valued according to their agricultural value. (NOTE.-We have made up the following section from Sir Richard Griffith's instructions, and Brown on American Forest Trees. The latter is a very valuable work.) 310a. The condition of trees is worthy of,attention, as indicating the nature of the soil, thus: Acer. Maple. Requires a deep, rich, moist soil, free from stagnant water; some species will thrive in a drier soil. Alnus. Alder. A moist damp soil. Betula. Birch. 1'n every description-from the wettest to the driest, generally rocky, dry, sandy, and at great elevation. Carpinus. Ironwood and Hornbeam. Poor clayey loams, incumbent on sand and chalky gravels. Castanea. Chestnut. Deep loam, not in exposed situationg. A rich, sandy loam and clayey soils, free from stagnant water. Cupressus. Cypress. A sandy loam, also clayey soil. Chamerops. Cabbage Tree. A warm, rich, garden mould. Gleditacida. Locust. A sandy loam. Jugem~s. Hickory. Grows to perfection in rich, loamy soils. Also succeeds in light siliceous, sandy soils, as also in clayey. ones. Larix. Larch. A moist, cool loam, in shaded localities. GRIFFITH S SYSTEM OF VALUATION. 72B27 Lauras. Sassafras. A soil composed of sand, peat and loam. Lyriodendron. Poplar, or Tulip Tree. A sandy loam. Pinus. Pine. Siliceous, sandy soils; rocky, and barren ones. Platanus. Buttonwood, or Sycamore. Moist loam, free from stagnant moisture. Quercus. Oak. A rich loam, with a dry, clayey subsoil. It also thrives on almost every soil excepting boggy or peat. Robinia.s Locust. Will grow in almost any soil; but attains to most perfection in light and sandy ones. Tilia. Lime Tree. Will thrive in almost any soil provided it is moderately damp. (For further, see Brown on Forest Trees, Boston: 18X12.) It would be well, in every instance, to make sublets of plantations. In some instances, plantations may be a direct inconvenience or injury to the occupying tenant. In such cases, the circumstances should be noted, and a corresponding deduction be made for the valuation of the farmi so affected. Boys and turbarsy should be valued as pasture. The vicinity of turf, as well as coal, is one of the local circumstances to b( considered as increasing the'value of the neighboring arable land. Where the turf is sold, the bog is valued as arable, and tle expense of cutting, saving, etc. of turf deducted from the gross proceeds, will give the net value. Bogs, swamps, and morasses, included within the lilits of' a farm, should be made into sublots, if of sufficient extent. Mlines,' qtorries, potteries, etc. The expense of working, proceeds of sales, etc., should be ascertained from three or four yearly returns. Mines, not worked during seven years previous, are not to be rated. Tolls. The rent paid for tolls of roads, fairs, etc., should be ascertained, and also the several circumstances of the tolls. If no rent be paid, the value must be ascertained from the best local information. Fisheries and ferries. From the gross annual receipts deduct the annual expenses for net proceeds. It will be necessary to state if the whole or part of a fishery or ferry is in one township, or in two, etc., and to apportion the proceeds of each. Railways and canals. "T he rateable hereditament," in the case of railways, is the land which is to be valued in its existing state, as part of a railway, and at thle rent it would bring under the conditions stated in the Act. The profits are not strictly rateable themselves, but they enter materially into the question of the amount of the rate upon the lands by affecting the rent which it, would bring, or which a tenant would give for the railway, etc., not simply its land, butt as a railway, etc., with its peculiar adaptation to the production of profit; and that rent must be ascertained by reference to the uses of it (with engines, carriages, etc., the trading stock), in the same way as the rent of a farm would be calculated, by reference to the use of it, with cattle, crops, etc. (likewise trading stock). In neither cases would the rent be calculated on the dry possession of the land, without the power of using it; and in both cases, the profits are derived not only from the stock, but from the land so used and occupied. It will be necessary, therefore, to ascertain the gross receipts for a 72B28 GRIFFITH)S SYSTEM OF VALUATION. year or two, taken at each station along the line; also the amount of receipts arising from the intermediate traffic between the several stations. From the total amount of such receipts, the following deductions are to be made, viz.: intorest on capital: tenants' profits; working expenses; value of stations: depreciation of stock. It. is to be observed, that the valuation of railway station houses, etc., should be returned separately. WASTE. The value of the ground under houses, yards, streets, and small gardens, is included in their respective tenements. So also in the country, roads, stackyards, etc., are included in the tenements. The area of ground occupied by these roads should be entered as a deduction at the foot of the lot, in which they occur. When a farm is intersected 6b more roads than is necessary to its wants, the surplus may be considered rwaste. Also deduct small ponds, barren cliffs, beaches along lakes, and seashores. OF TlE VALUATION OF BUILDINGS. 310b. By a system analogous to that pursued in ascertaining the value of land, the value of buildings may be worked out; the one being based on the scale of agricultural prices, and modified by local circumstances; the other, on an estimate of the intrinsic or absolute value, modified by the circumstances which govern house letting. The absolute value of a buildiag is equivalent to a fair percentage on the amount of money expended in its construction, and it varies directly in proportion to the solidity of structure, combined with age, state of repair, and capacity, as shown in the following classification: Buildings are divided into two classes: those used as houses, and those used as offices. In addition to tile distinction of tenements already noticed in sec. 309gy, it may here be observed that houses and offices, together with land, frequently constituted but one tenement. All outbuildings, barns, stables, warehouses, yards, etc., belonging or contiguous to any house, and occupied therewith by one and the same person or.persons, or by his or their servants, as one entire concern, are to be considered parts of the same tenement, and should be accounted for separately in the house book, such as herd's house, steward's house, farm house, porter's house, gate house, etc. A part of a house given up to a father, mother, or other person, without rent, does not form a separate tenement. Country flour mills, with miller's house and kiln, form one tenement. 81 C. CLASSIFICATION OF BUILDINGS WITH REFERENCE TO THEIR SOLIDITY. Slated, J House or office (1st class), Built with stone lated,. Basements to do. (4th), or brick, and B.uilding. r [ HIouse or office (2nd),. lime mortar.. Stone walls with mud mortar. Thatched, ouse or orffice (8rd),.. Dry tone walls, I pointed. Good mud walls, Offlces (6th),., Dry stone walls, GRIFFITH'S SYSTEM OF VALUATION. 72B29 The above table comprises four classes tf houses and five of offices, of each of which there may be three conditions, viz., new, medium, and old, which may also be classified and subdivided, as follows: CLASSIFICATION OF BUILI)INGS WITH REFERENCE TO AGE AND REPAIR. Quality. Description. F A J~ f Built o o s, or ornamented with cut stoeolid| r X ity and finish. NEW, XA. Very substantial building, and finished without cut stone ornament.. - J Ordinary building and finish, or either of the above, when \ 1 * i built twenty years. B. -- Not newv, but in sound order and good repair. MEDIUMbt B. Slightly decayed, but in good repair. B. - Deteriorated in age, and not in perfect repair. C. - Old, but in repair. OLD, C. Old, out of repair. C. Old, dilapidated, scarcely habitable. The remaining circumstance to be considered is capacity or cubical content, from which, in connexion with the foregoing classifications, tables have been made for computing the value of all buildings used either as houses or offices. (See sequel for tables.) Houses of one story are more valuable, in proportion to their cubical contents, than those of two stories. Those more than two stories diminish in value, as ascertained by their cubical contents, in proportion to their height. Tables are calculated and so arranged on a portion of a house 10 feet square and 10 feet high, = 100 cubic feet, so that a proportionate price given for a measure of 100 cubic feet, as above, is greater than for a similar content 20 feet high, or for 10 square feet and 30 or 40 feet high. For example, in an ordinary new dwelling house, the price given by the table for a measure containing 10 square feet and 10 feet high, is 7T pence; for the same area and 20 feet high, the price is ls. 03d.; for the same area and 30 feet high, is. 4}d.; and for the same area and 40 feet high, the price is Is. 6}d. OF THE IMEASUREMENT OF BUILDINGS. 310d. Ascertain the number of measures (each 100 square feet) contained in each part of the building. Measure the height of each part, and examine the building with care. Enter in the field book the quality letter, which, according to the tables, determines the price at which each measure containing 10 square feet is to be calculated. The houses are to be carefully lettered as to their age and quality. AdMdition or deduction is to be made on account of unusual finish or want of finish, etc. Such addition or deduction is to be made by adding or deducting one or more shillings in the pound to meet the peculiarity, taking care to enter in the field book the cause of such addition or deduction. Enter also the rent it would bring in one year in an ordinary situation. If any doubts remain as to the quality letter, examine 'the interior of the building. In measuring buildings, the external dimensions are taken —length, breadth and height-from the level of the lower foor to the eaves, In 72B30 GRIFFITH'S SYSTEM OF VALUATION. attic stories formed in the roof, half the height between the eaves and ceiling is to be taken as the height. Basement stories or cellars, both as dwellings and offices, are to be measured separately from the rest of the building. Main house is measured first, then its several parts in due form. Extensive or complicated buildings should have a sketch of the ground plan on the margin of the field book, with reference numbers from the plan to the field book. If a town land boundary passes through a building, measure the part in each. IMODIFYING CIRCUMSTANCES. 310e. The chief circumstances which modify the tabular value are deficiences, unsuitableness, locality, or unusual solidity. Deficiences.-In large public buildings, such as for internal improvements, an allowance of 10 to 30 per cent. is made; also in stables and fuel houses. When the walls of farm houses exceed 8 or 12 feet in height, but have no upper flooring, they should not be computed at more than 8 feet, except in the cases of grain houses, factories, barns, foundries, etc. The full height is, however, to be registered in each case. Unsuitableness.-Houses found too large, or superior to the farm and locality-where there are too many offices or too few. All buildings are to be valued at the sum or rent they would reasonably rent for by the year. Buildings erected near bleach greens, or manufactories which are now discontinued, or if they were built in injudicious situations, should be considered an incumbrance rather than a benefit to the land; consequently, only a nominal value should be placed on them. The tabular amount jbr large country houses, occupied by gentlemen, usually exceeds the sum they could be let for, and this difference increases with the age of the building. The following is to correct this defect: Houses amounting Reduction K Ieductio fron to per Pound. per cent. ~10 ~35 None. None. 35 40 ()s. f6d. 0.025 40 50 1 0 0.05 50 60 1 6 0.075 60 70 2 0 0.10 70 80 2 a6 0.125 80 90 23 0 0.150 90 100 3 6 0.175 100 110 4 0 0.200 110 120 4 6 0.225 120 140 5 0 0.250 140 160 5 6 0.275 160 200 6 0 0.300 200 300 7 0 0.350 300 and upwards, 8 0 0.400 Where any improvements have been made to gentlemen's houses, care should be taken to ascertain whether any part of the original house was made useless, or of less value. If so, deduct from the price given by the table as the case may require. Locality includes aspect, elevation, exposure to winds, means of access, abundance or scarcity of water, town influence, etc., each of which is to be carefully considered on the ground. GRIFFITH'S SYSTEM OF VALUATION. 72i81 In determining the value of buildings immediately adjoining large towns, ascertain the percentage which the town valuator has added to the tabular value of these on the limits of the town lot. Those in the town lot are referred to another heading, as will appear from sec. 310f. Solidity.-In large mills, storehouses, factories, etc., well built with stone or brick, and well bonded with timber, a proportional percentage should be added to the tabular value for unusual solidity and finish, which will range from 30 to 50 per cent. The value thus found may be checked by calculating the tabular value of the ground floor, and multiplying this amount by the number of floors, not including the attic.. VALUATION OF HOUSES IN CITIES ANI TOWNS. 810f. In valuing houses in cities and towns, there are'circumstances for consideration in addition to those already enumerated, viz., arrangement of streets, measurement, comparative value, gateways, yards, gardens, etc. To effect this object, each town should be measured according to a regular system; and the following appears to be a convenient arrangement for the purpose: Arrangement of streets.-The valuator should commence at the main street or market square, and work from the centre of the town towards the suburbs, keeping the work next to be done on his right hand side, measuring the first house in the street, and marking it No. 1 on his field map and in his field book. Afterwards proceed to the next house on the same side, marking it No. 2, and so on till he completes the measurement of the'whole of the houses on that side of the street. IIe is then to turn back, proceeding on the other side, keeping the work to be done still at his right hand. The main street being finished, he proceeds to measure the cross streets, lanes or courts that may branch from it, commencing with that which he first met on his right hand in his progress through the main street. This street is measured in the same manner as the main street; and all lanes, courts, etc., branching from it are measured in like manner, observing the same rule of measurement throughout. Having finished the first main street, with all its branches, he is to take the next principal street to his right hand, from the first side of the first main street, and proceed as in the first, measuring all its branches as above. (NOTE.-Let Clark and Lake streets, in the city of Chicago, be the two principal streets, and their intersection one block north of the Court House, the principal or central point of business. Clark street runs north and south; Lake street, east and west. Nearly all the other principal streets run parallel to these. We begin at the west side of Clark and north side of Lake, and run west to the city limits, and return on the south side of the street, keeping the buildings on the right, to Clark street. We continue along the south side of Lake, east to the city limits, and then return on the north side of Lake, keeping the buildings on the right, to the place of beginning. Having finished all the branches leading into this, we take the next street north of Lake, and measure on the north side of it west to the city limits, and so proceed as in the first main street. Having finished all the east and west streets north of the first or Lake street, we proceed to measure those east and west streets south of. the first or Lake street, as above. We now proceed to measure the 72B82 GRIFFITH'S SYSTEM OF VALUATION. north and south streets, taking first the one next west of Clark, and run north to city limits; then return on the west side of the street to Lake, and continue south to the city limits; return on the east side of the street to the place of beginning. Thus continue through the whole city.) In measuring buildings, the front dimensions, and that of returns, is set in the first column of his book, the line from front to rear is placed in the second column, and the height in its own place. In offices, the front is that on which the door into the yard is situated. In houses with garrets, measure the height to the eave, and set in the field book, under which set the addition made on account of the attic, and add both together for the whole height. Every house having but one outside door of entrance, is to be numbered as one tenement. Where there are two doors, one leading to a shop or store, to which there is internal access from the house, the whole is to be considered as one tenement; but if the shop and other part of the house be held by different persons, the value of each part should be returned. Where a number of houses belonging to one person are let from year to year to a number of families, each house is to be returned as one tenement. Buildings in the rear of others in towns are to be valued separately from those in front. COMPARATIVE VALUE. 310g. In towns, a shop for the sale of goods is the most valuable part of a house; and any house having much front, and affords room for two or three shops, is much more valuable than the same bulk of house with only one shop. When a large house and a small one have each a shop equally good, the smaller one is more valuable in proportion to its cubical contents, as ascertained by measurement, and a proportionate percentage should be added to the lesser building to suit the circumstances of the case. Where large houses and small mean ones are situated close to each other, the value of the small ones are advanced, and that of the large ones lessened. In such cases, a proportionate allowance should be made. Stores (warehouses) in large towns do not admit of so great a difference for situation as shops-a store of nearly equal value, in proportion to its bulk, in any part of a town, unless where it is adjoining to a quay, railway depot or market; then a proportionate additional value should be added. Gateways.-In stores or warehouses in a commercial street, where there is a gateway underneath, no deduction is made. In shops or private dwellings, a gateway under the front of the house is a disadvantage, compared to a stable entrance from the rear. In such cases, a proportionate deduction should be made on account of the gateway. In measuring gateways, take the height the same as that of the story of which it is a part. Passages in common are treated similar to gateways. Where any addition or deduction is made on account of gateways, it should be written in full at the end of the other dimensions, so as to be added or subtracted as the case may be. GRIFFITH'S SYSTEM OF VALUATION. 72B33 Where deductions are made on account of want of finish in any house, state the nature of the wants, and where required. Stores do not want the reductions for large amount, which has been directed in the case of gentlemen's country seats. OF TOWN GARDENS AND YARDS. 310h. In large towns, the open yard is equal to half the area covered by the buildings; if more, an additional value is added, but subtracted if less. Allowance is made if the yard is detached or difficult of access. The quantity of land occupied by the streets, houses, offices, warehouses, or other back buildings belonging to the tenements, together with the yards, is to be entered separately at the end of the town lots in which they occur, the value of such land being one of the elements considered in determining the value of the houses, etc. A timber yard, or commercial yard, is to be valued. If large, state the area, and if paved, etc., the kind of wall or enclosure, and if any offices are in it, their value is to be added to that of the yard. Gardens in towns.-In towns, the yards attached to the houses are to be considered as one tenement; but the garden, in each case, is to be surveyed separately, and not included in the value of the tenement. The gardens in towns are to be valued as farming lands under the most favorable circumstances. OF TIE SCALE FOR INCREASING TIIE TABULAR VALUE OF HOUSES FOR TOWN INFLUENCE. 310i. Ascertain the rents paid for some of the houses in different parts of the city. This will enable one to determine the tabular increase or decrease. As it is better to have a house rented by a lease than by the year or half year, therefore a difference is made between a yearly rent and a lease rent: for a new house, two shillings in the pound in favor of the lease rent; for a medium house, about three shillings in the pound; and for an old house, about four shillings in the pound. In all houses whose annual value is under ten pounds, the rent from year to year is higher in proportion to the cubical contents than in larger houses let in the same manner, but the risk of losing by bad tenants is greater for small houses, therefore in reducing such small houses, when let by the year or half year, to lease rents, five shillings in the pound at least should be deducted. In villages and small market towns, an addition of twenty-five per cent. to the prices of the tables will generally be found sufficient. In moderate sized market towns, the prices given in the tables may be trebled for the best situations in the main street, near the market or principal business part of the town; and in the second and third classes, the prices will vary from one hundred to fifty per cent. above the tables; and in large market towns, the prices for houses of the first class, in the best situations, will be about three and one-half times those of the tables. In dividing the streets or houses of any town into classes, the valuator is, in the first instance, to fix on a medium situation or street, and having ascertained the rents of a number of houses in it, he is, by measurement, to determine what percentage, in addition to the country tables, should 16 72s34 6RIFFITH'5 SYSTEM OF VALUATION. be made, so as to produce results similar to the average of the ascertained rents. Having determined the percentage to be added to the price given in the tables for houses in medium situations, the standard for the town about to be valued may be considered as formed; and from this standard, percentages in addition are to be made for better and best situations, or for any number of superior classes of houses, or of situations which the size of the town may render necessary. In towns, the front is the most invaluable, therefore value the front and rear of the building separately, so as to make one gross amount. It is impossible to determine accurately the proportion between the value of the front and rear buildings; but it has been found that in revising the valuations of several towns, that the proportion of five to three was applicable to the greater number of houses in good situations; that is, the country price given by the tables should be multiplied by five for the front, and three for the back buildings, stores and offices. WATER-POWER. 310j. Ascertain the value of the water power, to which add that of the buildings. I horse-power is that which is capable of raising 33,000 pounds one foot high in one minute. The herse-power of a stream is determined by having the mean velocity of the stream, the sectional area, and the fall per mile. The fall, is the height from the centre of the column of water to the level of the wheel's lower periphery. The weight of a cubic foot of water is 62.25 pounds. Total weight discharged per minute -= V * A. 62.25. Here A = sectional area, and V= mean velocity in feet per minute. A body falling through a given space acquires a momentum capable of raising another body of equal weight to a similar height; therefore, the total weight discharged per minute, multiplied by the modulus of the wheel, and this product divided by 33,000 pounds, will give the required horse-power. Modulus for overshot wheel....................................0.75.... breast wheel, No. 1, with buckets..........; "'.... " t No. 2, with float boards.....55.. turbine.............................................65 to 78.' * undershot wheel...................................33 NOTE.-James Francis, Esq., C.E., has found at Lowell, Massachusetts, as high as 90 to 94, from Boyden's turbines. Fourneyron and D'Auibuison give the modulus for turbine of ordinary construction and well run -=0.70. To measure the velocity of a stream. Assume two points, as A and B, 528 feet apart; take a sphere of wax, or tin, partly filled and then sealed, so as to sink about one-tlird in the water; drop the sphere in the centre of the water, and note when it comes on the line A-A, and on the line B-B. A and A may be on opposite sides of the river, or on the river, or on the same side ut light, angles to the thread of the strean. Let the time in passing from the line AA to the line BB be six minutes. Tlhn as six min.: 528 ft.:: 60 min. to 5280 ft.; that is, the measured suifalce velocity is one mile per hour. GRIFFITH'S 8YSTEM OF VALUATION. 72B85 M. Prony gives V = surface, W = bottom, and U = mean velocity, and U = 0.80 V = mean velocity, W = 0.60 V = bottom velocity; therefore, as 6 minutes gives a surface velocity of 88 ft.; this multiplied by 0.80, gives 70.4 ft. per minute as the mean velocity. 310k. The following may serve as an example for entry of data and calculation: Data. Ft. i. A Breast Wheel,i No. 1. Mean velocity of stream per minute, 144 Breadth of streaml in trough, - Depth of do. - jFall of water, 12 In. 36 8 36 8 288 = 2 feet - Sectional area - A. 144 288 - Cubic content per minute. 62-25 - Weight of one foot. 18000 lbs. - Weight discharged. 12 - Fall of water. 216000 - Total available power. ~66 - Modulus. 1425600 This divided by 33000, gives 4-32 effective horse-power. Otherwise: Data. Ft. la. Breast wheel No. 1. Revolutions per minute, 6-6. Diameter of wheel. 14 Breadth of do. 36 Depth of shrouding, 85 Fall of water, 12 - 36 x 8-5 - 2-12 feet - sectional area of bucket. 14 x 12 = 168, and 168 - 8-5 = 159-5 = 13-29 - reduced diameter at centre of buckets. 13-29 x 3-1416 = circumference at centre of buckets — 41-751, 41'751 x 6'6 - 2'12 and 7- 6 -12 292 cub. ft. in buckets half full. 2 292 x 6225 - 18250 12 = fall of water. 219000 66 = modulus. 33000 ) 144540-00 ( = 4-38 effective horse-power. For undershot wheels, the data are as follow: Data. Ft. In. Revolutions per minute. 5-2. Diameter of wheel, 16 Breadth of float board, 4 6 Depth of do., 2 - Velocity of stream per minute, 798 Height of fall due to velocity, 2 9 Depth of do. under wheel, - Ft. In. 4 6 = Breadth of float boards. 10 Depth of do. acted on. 3-75 Area of float boards. 798 Velocity of stream. 2992 62-25 Weight of one cubic foot. 187031-25 2-75 Height of fall due to velocity. 514335-9 ~33 Modulus. 169730 - 14 horse-power. 33000 3101. It is to be observed that the horse-power deduced from measurement of a bucket-wheel may be found in some instances rather greater than that from the velocity and fall of water, as it is necessary that space should be left in the buckets for the escape of air, and also to economize the water. When a bucket-wheel is well constructed, multiply the cubic content of water discharged per minute by.001325, and by the fall; the product will be the effective horse-power approximately. Aur turbines, the effective cubical content of water discharged per minute multiplied by the height of the fall, and divided by 700, will be equal to the effective horse-power. 72B36 GRIFFITH'S SYSTEM OF VALUATION. In practice, twelve cubic feet of water falling one foot per second, is considered equal to a horse-power. When the water is supplied from a reservoir, and discharged through a sluice, measure from the centre of the orifice to the surface of the water, and note the dimensions of the orifice. Head of water.-The velocity due to a head of water is equal to that which a heavy body would acquire in falling through a space equal to the depth of the orifice below the free surface of the fluid; that is, if V=velocity, and M =116, feet, or the space fallen through in one second, and H = the height, the velocity may be represented thus: V - 2 / M H; thus the natural velocity for.09 feet head of water will be V = 2 V (162 X.09) =- 2.4 feet per second. In practice, V = 8 / H. The effective velocity = five times the square root of the height. (See sec. 312.) VALUE OF WATER-POWER. 310m. The water-power is to be valued in proportion'as it is used, and the time the mill works. One horse running twenty-two hours per day during the year, is valued at ~1 15s. This amount multiplied by the number of horses' power, will give the value of the water-power. The annexed table is calculated with reference to class of machinery and time of working. Quality Number of Working Hours. of _ Machinery. s 10 12 14 16 18 20 22 s.d. s.. s. d. s. d. s. d.d. d. s. d. s.d. New,........ 13 3 18 6 23 3 26 9 28 9 30 9 33 0 35 0 Medium,... 12 0 16 9 21 0 24 3 26 0 27 9 29 6 31 6 Old.........10 6 15 0 18 9 21 6 23 3 24 9 26 6 28 0 In this, two hours are allowed for contingencies and change of men. The highest proportionate value is set on 14 hours' work, as during that time sufficient water can be had, and one set of men can be sufficient. Where the supply of water throughout the year is not the same, the valuator is to determine for each period by the annexed table. Description of Mill............................... Class of M achinery............................... A. Working Time. Horses' of Numberof Value of Observations. Power. Number of Number of Water-power. Observations. Months Hours per Year. per Day._ __ ~ a. d. For 8 months the full power 9 8 22 10 10 0 of the wheel is used, but for the ~6 4 1 2 6 6 remaining 4, not more than 16 4.i_ _ 1 two-thirds of the water-power 12 16 6 can be calculated on. I ~ ~~~ 1 2 16 GRIFFITH'S SYSTEM, OF VALUATION. 72A287 Where a mill is worked part of the year by water and another part by steam, care must be taken to determine that part worked by water, and also to value the machinery, as it sometimes happens that the mill may be one quality letter and the machinery another-higher or lower. MODIFYING CIRCUMSTANCES. 310n. The wheel may be unsuitable and ill-contrived; the power may he injudiciously applied; the supply may be scarce, may overflow, or have backwater. In gravity wheels, the water should act by its own weight-the principle upon which its maximum action depends being that the water should enter the wheel without impulse, and should leave it without velocity. The water should, therefore, be allowed to fall through such a space as will give it a velocity equal to that of the periphery of the wheel when in full work, thus: if the wheel move at the rate of five feet per second, the water must fall on it through not less than two-fifths of a foot; for the space through which a falling body must move to acquire a given V2 V2 velocity is expressed thus: - 4 Al e4. 33 For mills situate in inland towns of considerable importance, such as Armagh, Carlow, Navan, Kilkenny, etc., in a good wheat country, where wheat can be bought at the mill, and the flour sold there also, five shillings in the pound may be added on the water-power for the advantage of situation. The vicinity of such towns, say within three to four miles, may be called an ordinary situation. Beyond this distance, where the wheat has to be carried from, and flour to, the market, the water-power gradually decreases in value; and from such a town to ten miles distance from it, the water-power may be rated according to the following table. s. (d. F 10 0 per pound within the town lot. 8 0 when distant from 0 to 1 mile. i 60 " 1 to 3 Add to water-power, -l 4 0 " 3 to 5 " 20 " 5 to 8 " 1 0 " 8 tolO 1 t0 0 ) " " 10 and upwards. Beyond ten miles from a good local market, a flour mill can rarely require percentage for market. But this rule of increase does not apply to small mills, such as flour mills, where only one pair of millstones is used; in this case, only half the above percentage is to be added within three miles of a large town; beyond that distance, no addition is to be made. In the case of bleach mills, they should be as near to their purchasing or export market as flour or corn mills, and the valuator should make deductions for a remote situation, especially where the chief markets for buying linen are distant, or add a percentage to the water-power where the situation has unusual advantages in these respects. 72B388 GRIFFITH'S SYSTEM OF VALUATION. 310o. HORSE-POWER DETERMINED FROM THE MACHINERY DRIVEN. In aflax mill, each stock is equivalent to one horse-power. The bruising machine of three rollers = 1i stocks. The numbering of horse-power in the mill may thus be counted, and the value ascertained from the table for horse-power from sec. 3101. In spinning mills, the horse-power may be determined from the number of spindles driven, and the degree of fineness spun, for in every spinning mill the machinery is constructed to spin within certain range of fineness. Therefore ascertain the range of fineness and number of spindles. Yarn is distinguished by the degree of fineness to which it is spun, and known by the number of leas or cuts which it yields to the pound. One lea or cuf = 300 lineal yards. 12 leas = 1 hank; 200 leas - 16 hanks: anrd 8 lens = 1 bundle 60000 yards. Leas to the pound. No. of Spindles. From 2 to 3, 40 throstles require one horse-power. From 12 to 30, 60 " (( (< From 70 to 120, 120() In cotton mills, the throstle spindle is used for the coarser yarns, and for the finer kinds the mule spindle. Leas to the pound. No. of Spindles. From 10 to 30, 180 throstles equal one horse-power. From 10 to 5,0, 500 mules " " ( In bleaching mills, ascertain the number of beetling engines; measure the length of the wiper beam in each, together with the length of beetles, and their depth, taken across the direction of the beam; also the height the beetles are raised in each stroke. From these data, the horse-power of such engine can be found by inspection of the table calculated for this purpose. Ascertain the number of pairs of washing feet, and if of the ordinary kind; the pairs of rubboards, starching mangle, squeezing machine, calender, or any other machine worked by water, and state the horse-power necessary to work each. The standard for a horse-power in a beetling mill is taken as follows: Beam, furnished with cogs for lifting the beetles, 10 feet long. The wiper beam makes 30 revolutions in a minute; and being furnished with two sets of cogs on its circumference, raises the beetle 60 times per minute, working beetles 4 feet 4 inches in length, and 3 inches in depth, from front to rear, making 30 revolutions per minute, or lifting the beetles 60 times in a minute one foot high, is equal to one horse-power. This includes the power necessary to work the traverse beam and guide slips, which retain the beetle in a perpendicular position. Taking the wiper beam at 10 feet long, and height lifted as 1 foot, making 30 revolutions per minute, the following table will show, by inspection, the proportionate horse-power required to raise beetles of other dimensions 60 feet in one minute, assuming the weight of a cubic foot of dry beach wood = 712 ounces. When the engine goes faster or slower, a proportionate allowance must be made. GRIFFITH'S SYSTEM OF VALUATION. 72B39 Inches LENGTH OF BEETLES. from front Ft. In Ft. IFt. I n. Ft. In. Ft. I n. Ft. I. n.Ft. n.lFt. In. to rear. 4 4 4 6 8 /4 10 5 0 5 2 5 4 5 6 5 8 5 10 6 0 Number of Horse Power. 3 1.00 1.03 1.06 1.10 1.13 i 1.16 1.20 1.24 1.28 1.32 1.36 3 1.07 1.1() 1.14 1.18 1.22 1.26 1.30 1.34 1.38 1.42 1.46 3 1.15 1.19 1.23 1.27 1.32 1.36 1.40 1.45 1.49 1.53 1.58, 3- 1.231.2 1 1.32.37 1.41. 1.45 1 ' 1.48 1.6 5 1. 69 4 1.31 1.36 1.41 1.45 1 1.50 155 1.0 1.65 1.70 1.75 1.80 4} 1.40 1.44 1.4 1.4 1.59 1.64 1.70 1.75 1.80 1.85 1.91 41 1.48 1.53 1.58 1.64 1.69 1.75 11.80 1.85 1191 1.97 2.03 From this table it appears that a ten feet wiper beam, having its beetles four inches in depth, five feet long, and to lift those beetles one foot high sixty times in a minute, would require the power of one and one-half horses. If the wiper beam be more or less than ten feet in length, or if the lift of the beetles be more or less than one foot, a proportionate addition or deduction should be made. The following is given to assist the valuator in determining the value of the other machinery in a bleaching mill: One pair of rub-boards, = 0.5 to 0.7 horse-power. " starching mill, 1 " " drying and squeezing machine, 1 ( ' pair of wash-feet, 1.5 to 2 " calender (various), 3 to 8 4 In beetling mills, the long engine, with a ten feet wiper beam, is considered the most eligible standard for computing the water-power. Such a beam, having beetles four inches long and three inches deep, is equal to one horse-power. On these principles, the value of water-power may be ascertained from the table, sec. 3101. 310p. Inflour mills, the power necessary to drive the machinery night nud day for the year round, has been determined as follows: The grinding portion, or flour millstones, have been considered to require, for each pair, four horses-power. The flour dressing machine of ordinary kind, together with the screens, sifters, etc., or cleansing machinery, require, on an average, four horses-power. Some machines, however, from their size and feed with which they are supplied, will require more or less than four horses-power, and should be noted by the valuator. Every dressing, screening and cleansing machine is equal to one pair of stones. (NOTE.-ln Chicago, ten horses power is estimated for one pair of stones, together with all the elevating and cleansing machinery.-M. M'D.) The following table has been made for one pair of millstones, four feet four inches diameter, for one year: Quality Number of Working Hlours per Day. of _ Machine. 1. 10. | 12. 1 S. 18.. 0 22. -! - I --- —---- I! — - -- ----. -.. - K S. dI ~ ~.s I. dt d.,. l..~ s.. s... New, A. 2 1 0 14 04 13 ' 7 05 15 0 6 3, 06 12 0(); 0 0 Medium, B 2 8 0 7 04 4 04 17 05 4 0 5 11 0 18 016 6 0 Old, C.2 2 0 0 1 04 6 0.4 1 3 04 19 0)'5 6 015 12 0 _ --- —---....._.___ 72B40 GRIFFITH'S SYSTEM OF VALUATION. If more than one pair of millstones be used in the mill, multiply the above by the number of pairs usually worked, and if they are more or less than four feet four inches in diameter, make a proportional increase or decrease. In flour mills, the valuator will state the kind of stones, how many French burrs, their diameter, the number worked at one time, the number of months they are worked, the number of months that there is a good supply, a moderate one, and a scarcity of supply. FORM POR FLOUR MILLS.-NO. 1. Description of Mill,........................Flour Mill. Class of Machinery,................. A. | Working Time. - No of N o.o Value of 0 W Noaof Ioof ter-power. N Observations. (d * I ~' Months ITours S Vi 5z? perYear. per Day.; i. In this mill there are five II pairs of stones, one pair al- 4 6 22 14 ) 0 ways up, being dressed; ma2 3 I 16 2 18 0 1 chine and screens and sifters only used when one or two - 1 3 10 0180 pairs of stones are stopped, 1 Only used when one and not worked in summer, or two pairs of stones _ __ except one or two days in the I are thrown out. i 17 16 O week. Two sets of elevators __~I! -_~ - usel along with the millstones. INo. 2. Description of Mill,..................... Flour Mill. Class of Machinery,........................B. c:; J.. I 1. 1.';. 1) Working Time. - ~.. - Value of No. of No. of Water-powe. Months Iours p'erYear per Day. l ii l Observations. 4 1.) 22 22 '5-, ~c s. d/. 4 40 0 11 0 0 14 0 2 13 0 8 20 In this mill there are three pairs of stones - one pair generally up, two driven for four months along with machines, screens and sifters, and one for one month with them also; during three months the machines and one pair of millstones must be worked alternate days, and during the other four months there is no work done. One set of elevators used along with the millstones. 3 10q. TI oatmeal mills, one pair of grinding stones require three horsespower; one pair of shelling stones, fans and sifters, require two horsespower. Elevator is taken at one-eighth of the power of the stones. The following table, for one pair of millstones for one year, is to be used as the table for flour mills: GRIFFITHI'5 SYSTEM 0? VALUATION.724 72x4l Quality, Number of Working Hours per Day. of Machinery. 8 10 12 14 16 18 20 22 Ls. d.L a. d.L a. d a:. d.L a. d. 1 s. d. I. d.Z s. d. New,A....2 0 0216 0'310 04 0 04 6 041201419 05 5 0 Medium, B. 1 160 02 10 03 3 083 13 0 3 18 0 4 3 014 9 0 4 15 0 Old, C.... 12 02, O216OO3 4O03lOO 3l14O0 31904 4 0 310r. In corn mills, ascertain the number of pairs of grinding and shelling millstones and other machinery, and note the time each is worked. Where there are two pairs-one of which is used for grinding and the other for shelling; if there be fans and sifters, the shelling and sifters is to two horses' power == two-thirds of a pair of grinding stones. Where one pair is used to shell and grind alternately, it is reckoned at three-fourths pair of grinding stones, unless the fans and sifters be used at the same time. In this case they will be counted as seven-eighths pair of stones. Where there are two pairs of grinding, with one pair of shelling with fans and sifters, the water power is equal to two and two-thirds pairs of millstones; but if one pair is idle, then the power = one and two-thirds pairs of grinding millstones, etc. Foax No. 1. Description of Mill..............Corn Mill. Class of Alachitiery.............A. No. of Pairs Worked.! orig ie - Grlndi'gjti.- No. of No 01 Value of Observations.. Grindi'g Shelling and "O-'.G Months Ho~urs Water-power. ______ ~Shefling. A *. perYear. per Day. I s. d. 2 1 - 2j 8 22 9 6 0 In this mill there are three pairs of stones. 1 1 ~~~- ij 4 12 1 19 0 with elevators, fans, and sifters. hlorse11 s 0 power for 8 months Add 1/g equal to 8. or 2~ for Ele- grinding stonesr; and vators,. 1 8 0 for 4 months 5 horse — power, or 1Y3 grind. 12 13 0 ingstoniei. Foa~x No. 2. Description of Mill.............Corn Mill. Class of Machinery..............B. M illstones, b _ _ _ __ _ _ _ __ _ _ _ _ _ No. of Pairs Worked. * orig ie Urindi.-0 No. of No. of 'Value of Observations. Qriudi'g Shelling~ n Months Hours Water-power. _ _ _ Sh elIng;.5 perY sar. per Day. _ _ _ _ _ _ _ _ _ _ _ _ I ~~ ~~~~ a. d. 1 ij- 1~~~~i 6 16 2 18 6 In this mill there 1j 3 7 0 12 0 are two pairs of 1 ii- ~~~~~~~~~stones, but no. I - - -. -. ~~~~fans, sifters, or ______ elevators. U 72B42 72is42 ~GRIFFITH 5t SYSTEM OF VALUATION. FoRm No. 3. Description of Mill..............Corn Mill. Class of Machinery..............C. No. of Pairs Worked. v Working!Grindig ' No. of No. of W~ater- Observations. (3rindi'gShellin- I anld ) - 1otsiours p)ower. 1.5h e I Iin perYt-ur per Day.______ In this mill there are ~e s. two pairs of stones, - - 1 ~ 4 16 17 only one pair can be worked at a time; - - 1 - ~~~4 8 0 9 there are fans and sifters in use. but no elevators. This mill works merely for the supply of the neigh borhood, and is distaut four miles from a market town. When there are two or more mills in a district, compare the value of one with the other. Three stocks in a flax, mill is equal to the power necessary to work a pair of millstones in a corn mill. Note the quantity ground annually as a further check, for it has been ascertained that a bushel of corn requires a force of.31,500 lbs. to grind, the stones being about 5 feet in diameter, and making 95 revolutions per minute. 310s. Ia fine, it should be borne in mind, that for each separate tenement a similar conclusion is ultimately to be arrived at, viz., that the value of land, buildings, etc., as the case may be, when set forth in the colunin for totals, is the rent which a liberal landlord would obtain fromn a solvent tenant for a ternt of years, (rates, taxe.~, etc., being paid by the tenant;) and that this rent has been so adjusted with reference to those of surrounding tenements that the assessnient of rates may be borne equably and relatively by all. The valuattor, therefore, should endeavor to carry out fairly the spirit of the foregoing instructions, which hanve been arranged wit-l a view to Ipromote similarity of system in cases which require similarity ofjudgmient. As it may appear difficult to apply Griffith's System of Valuation to. American cities, on, account of the number of frame or wooden buildings, we give a, table at. p. 72B53, showing the comparative value of frame and brick houses. All the surveyors and larid atgents, to whom we have shown a1nd explaiined this system of valuation, have approved of it, and expressed ahope of see-ing surch a systemn take the place of' the presen h it or mis valuations, too) often made by mnen who ate unskilled in the first rudimeats of surveying and architecture. (31Ot.,) F O R.FORM OF FIELD BOOK. County of Clare, Barony of Bunratty Lower, Parish of St. Patrick, Townland of Shanakyle.-Ordnance Survey, 63. Names. Description. Value per Acre. Nett Annual Value. Original Area. In ordi- t Observations. In ordi-? ithal-I d Observations. Mp Occupiers. Immediate Lessors. Of Tenement Of Soil. loal nd. Buildings. To tions.- Iircumstances. no * /7 IC..P~~ nw. Part 7,,,,,, I. Michael Mason, Patrick Connolly, William Connors, James Dalton, Hamilton Jackson, Esq., William Connors, William Connors, House, Garden, Gardens, House, 0 0 32 0 1 1U u. 13 0 14 0 dW. u. I, John Costelloe, Hamilton Jackson, Esq., IHouse and Land, 3 4 Part 2 it Mattw. Hanrahan, Patk. Kelly, (Pat.) Pat. Kelly, (John,),..,,,, P) to I I ~ ~> >~1 Hamilton Jackson, Esq., House, Office & Land, House, Office & Land, House, Offices & Land, } 27 0 0 13 4 0 12 6 o~ _ 15 0 15 9 1 5 C 2 17 6,, jLand,,, Land,,, Land,,, Land,, 91 33 - 0 6 - I 0 24 - 6 ( - 90 30 0 0 9 9 i i I 1 J } Improved. Old deduction. Too high. Worn. Rather low. Bad; part of deduction. Part 8,, 12 0 16 0 11 0 1 (810u.) High Street. FORM OF TOWN BOOK. Parish of Killarney. Totwn of Killarney. Townland of Xillamey.. Amount Area Value s tabular Amount with Value Yearly Valuat'r' m'edlate. Obervt. No. Name and Description. i. -.t of of Garden Imediate Le. OeratM. N| Nae and Description. | | | | 2Items. ' arden. or Yard._ Muliplier, for | Rent. Esit Lot Daniel Mahony, Ft.In Ft.In Ft.In s. d. ~. s. d. A.. P. ~. s. d... d. 1 House, offices, and yard House and shop,. 1B 27 634 028 78 11 4 4 6 Good front, 4 4 6 40 0 0 Two Christ. Galwey, Has back gateHouse Return,. 1 27 630 022 0 66 0 1113 4 7 Multiplier, 83 in 1861. shops, way to yard. Do., do.,. 1 B —12 020 0 8 0 16 0 61 0 8 8 goodsitu Built some Do., do.,. 10 020 0 4 0 6 10 2 0 14 1 8 ation, offices lately, Kitchen,.. 1B-14 614 016 21 7: 0 13 1 Good 25 0 0 and otherwise Oce (Bake-house),.I B —14 6156 01 0 22 0 3 0 6 10 yard to Rere and offices, 611 to improved the Do.,... B — 7 0 9 0 6 00 4 i0 2 O 0 8 this Multiplier, 2 30 0 0 concern. Addition to Bake-hous, 1B I7 0 129 01 0 43 i0 2 0 7 2concern New portionl. Sheds,. I0 2 0 worth 11 2 6 Stable,.. 2B 10 018 017 0 30 0 2 0 6 3 about 0 10 0 -- 26 4 2 6 0 ______ I 91 9 Richard Murphy,. House, yard, and smail garden. House,. Return.. 1C+ 1B.1C 1C 1C+ 17 613 669 Office. Do.... Old office, Part of adjoining house. Deduct shop, 6 6 17 0 6 14 10.9 Small Front house, I 6 0 6 23 0 31 0 71 1 0 0 garden.all Front hou8e 6 0 616 0 1. 0 3*. 0 4 8 add 3s. Multiplier, 5% 6d. to house. ~7 6 9 017 6 24 0 1 0 2 0 0' 0 056 11 0 0 6 Rere and offices. 0 9 2 _ - - 0 2 0 Multiplier, 2 623 0 21 0 71 013 0 18 4 2 2 28 841 623021 0 4 070 Small garden, 0 3 6 1 158 ~8 7 7 8 0 NoTE.-The Length multiplied by the Breadth and divided by 10. Measures. W. W. Murphy, Tenant has the portion of No. 4 which is over the shop. IC+l 8 6 9 OGItIITHR'S Y8TIM OF VALUATION. 72845 TABLES YOR ASCERTAINING THl ANNUAL VALUE OF HOUSES IN THE COUNTRY: (310v.) I.-SLATED HOUSES, WALLS BUILT WITH STONE, OR BRICK, AND LIME MORTAR. Height. A+ A A- B+ B B- C~ C CFt. Inch a. d. a. d d. s. d. a. d. d. d.. d. 6 0 0 51 0 5 0 4 0 4 0 340 31 0 3 2 1 3 0 605 0 45 0 4 4 0 4 0 31 0 31 21 1 0 540 5 0 5 0 40 4 0 3-0 3 2 1 9 0 6 0 51 0 5 0 4-$ 0 441 0 34 0 31 21 1i 9060540 50404 404 0 842 14 7 0 0 61 0 5 0 45 0 41 0 4 0 30, 24 1i 3 0 6 0 6 0 5. 0 5 0 4- 04 0 34 24 1i 6 0 61 0 61 0 56 0 5 0 4 0 41*0 38 14 9 0 64 0 64 0 6 0 54 0 4410 4^ 0 31 3 14 80 00 6 0 6 0 6 0 5 0 5 04 0 43 1 38 0 7 0 64 0 64 0 5 0 5 40 40 4 3 1 6 0 7W 0 64 0 64 0 5 O 404 0 4 34 1 9 0 7 0 76 0 6; 0 6 050 0 4| 0 4 3 1 -90 0 7 0 74 0 61 0 6 0 5 0 5 0 4 s l 3 0 7 0 707 0 64 0 64 0 54 0 5 0 4 38 I 14 6 0 8 0 7 0 7 0 64 0 6 0 5 60 0 44 31 1i 9 0 81 0 74 0 74 0 6' 0 6 0 5 0 41 31 14 10 0 0 8 0 8 0 78 0 64. 06 0 54 0 54 3 14 630 8i 0 8 o 7 0 0 64 0 61 o06 0 64 3 1 6 0 89 0 8~ 0 7 0 69 0 68 075- 0 53-. 2 9 0 9 O 8 0 7 6 0 67 0 56 0 4O 3S- 2 110 0 91 0 8 0 8 0 71 0 6 0 6 0 51 4 2 30 94 0 84 0 8 0 67 0 6- 0 6 0 56- 4 2 60 9 0 9 0 84 0 7 40 6 064 0 6 4 2 9 0 94 0 9 0 87 0 74 0 7 0 6| 0 53 4 2 12 00 10 0 9 0 81, 0 7^ 0 7 0 6- 0 5 4} 2 6 0 104 0 9- 0 8 0 8 0 7 6 0 60 4 24 13 0 0 104 0 10 0 9 0 81 0 7 -46- 44 24 6 0 11 0 10} 0 91 0 840 0 7 07 0 61 4 24 14 0 0 11 0 10 0 9 0 0 7 0 6j 4 24 60 0 0 1 1 0 104 1 0 0 9 4 0 8 7 0 65 6 2 15 0 1 0 110 1 9 0 8 074 O 6 6 2 61 0 0 114 o 10 0 O 94 o 0' 808 5 46 24 16 1 0 0 11 0 104 0 10 9 08 074 5 24 61 1 0 11 0 11 0 10 0 9} 0 89 0 74 54 2 170 1 14 1 0 0 114 010 0 9 0 8 0 70 54 24 6 I 1 I 01 0 011 010 0 9 08 80 7 56 3 I.-SLATED HOUSES, WALLS BUILT WITH STONE, OR BRICK, AND LIME MORTAR-continued. Height. A~+ Ft Inch s. d. s. 18 0 1 2 1 6121 6 1 2 1 19 0 1 24 1 61 21 20 0 1 2 3 1 6 1 3 1 21 6 1 3i 1 6 1 34 1 22 0 1 33 1 6 1 4 1 23 0 1 44- 1 6 1 4 1 24 0 1 4 — 1 6 1 5 25 0 1 5 1 6 1 54 1 26 0 1 5-4 1 6 1 54 1 6 1 64 1 27 0 1 6 1 6 1 6- 1 28 0 1 6 1 29 0 1 6,1 1 6 1 64 1 300 1 7 1 617 1 31 0 1 7- 1 6 1 72 1 32 0 1 7 1 6 1 74 1 33 01 7-4 1 6 1 8 1 6181 34 0 1 8 1 6 1 841 1 35 0 1 8;1 1 6 1 8 1 36 0 1 8 1 6 1 8.1 1 37 0 1 84 1 6 1 9 1 38 0 1 9 1 6 1 9 1 390 9 1 6 1 9 1 400 1 94 1 6 1 94 1 d. 0o 1 14 1 2 4 2 31 2f1 3. 4 3 41 4 41 343 44 4 4 414 414 5 5 51 -5.1 54 54 6 64 64 6;i 64 7 7 4 7 7 71 74 74 1 74 74 74 7j A- B+ B s. d. s. d. s. d. 0 11-3 0 10V 0 10 1 0 011 0 10 1 0 0 11,1 101 -1 i 011 0 10-, 1 04 0 11- 9 10-1 1 1 11- o 0104 1 1,1 0 11 1 1 1 01 0 11 -1 1 0. 0 11: 1 12 1 0o 0 114I 1 2 11 o 11 1 2I 1 1 0 11 -1 41 1 1 04 1 1 1 1 1 0 12,1l 1} 1 0 1 3 1 2i 1 04 1 38 1 1- 1 0I 1 3 1 2 1 01 1 34 1 2 1 01 -1 3,4 1 2 1 1 1 34 2 1I 1 1 3 1 2 I 1 14 1 4 1 24 1 1 1 4 1 2- 1 1 1 41 1 2-1 1 1 1 1 44 1 3 1 1 1 4.4 1 31 1 2 -1 4~ I 3:, 1 2 1 44 1 34 1 2 1 5 1 3. 1 2 1 5 1 31 1 24 1 '5 1 3- 1 21 1 51 1 34 1 2 -1 5t 1 4 1 21 -1 514 1 4 1 24 1 5- 1 4 1 21 1 54 1 4 1 24 1 5 1 4 1 24 1 54 1 44 1 24 1 54 1 44 1 24 1 54 1 41 24 1 6 1 44 1 3 1 6 1 44 1 3 1 64 1 44 1 3 1 61 1 44 1 3 1 6j 1 44 1 3 I _ B — s. d. 0 9 0 9 o 94 -0 94 0 91 0 4 0 (, 0 10 0 10 0 104 0 10i o lot 0 10i 0 101 0 10-3 -0 101 4 0 11 0 11i 0 11; 1 0 -0 114 1 0 1 0 1 0 1 0 -1 01 -1 04 1 0o 1 04 1 1 1 1 I1 0 1 1 1 1 -1 1 1 14 1 1 1 14 1 1 1 14 1 1. 1 14 1 14 c+ s. d. 0 74 0 8 0 81 0 8. 0 82 o 8.4 0 89 0 9 0 9 0 9 0 9. 0 94 o 9 -0 92 0 10 0 10 0 101 0 101 0 10(4 -o 104 o 10o 0 10I 0 10| o 10o 0 101 0 11 0 11 0 111 -0 11-1 0 11I 0 11 0 114 o 114 0 114 0 114 o 113 0 11 0 114 0 114 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 - I C d. 6 6 64 61 64 6B 61 63 -64 q64 64 7 74 72 1 78 1 71 s3 s~ 4 8 9 9' 8 8 8 8 8 -81 84 84 8-4 84 84 84 84 9 9 9 9 9 9 9 9 9 I cd. 331 3 3 3 31 -34 3a 31 4 31 04 34 31 31 31 34 31 4 31 3 4 4 4 4 4 4 4 433 4 41 4 4 -41 41 44 4 4t 4 4 4 4 41 4 4 4 44 I - I l 72B46 72B47 GRIFFITH'B SYSTEM OF VALUATION. (310w.) BRICK Height. A-+Ft Inch 60 3 -6 9 -3 6 -9 -80 -3 -6 9 -90 -3 -10 - 3 -6 -9 -11 0 3 -6 -9 -12 0 -6 -130 - 6 -140 - 6 -150 - 6 -160 - 6 170 - 6 -180 - 6 -19 0 -6 20 0 - II.-THATCHED HOUSES, OR STONE WALLS, BUILT WITH LIME MORTAR. A A- B+ B B- C+ C Cd. d. d. d. d. d. d. d. 4 8 33 3- 31 24- 2 1 a 1 24 14 I 4 42 -44 -5 5 51 54 51 54 4 6 64 7 74 63 -74 74 74 71 l4 8 11 84 9i 94 9 10 101 10i 104 11 114 114 11t 4 4 44 45 44 4t 4 5 6 5',4 64 6 61 64 64 64 74 7 71 8i 74 8 8s 4 9 94 9i 10 101 104 loi 104 104 3| 4 4 4 41 -4 42 4a4 41 44 5 5 5 5~. 5' 54 5i 54 6 6 6t 64 61 62 2 64 7 71 84 84 9] 9, 91 10 9o 10 31 34 4 341 4 4 4 -4 4~ 4| 434 44 44 5 5 5~ 54 54 5~ 6 53 4 54 6 6 61 6 2 64 64 7 7i 7i 74 8 8 84 4 84 84 9 9 3 3 34 3-4 31 34 34 34 34 4 4 4 4 44 414 46 44 44 4t 5 5 5 5i53 4 6 6 641 643 64 7 74 7i 74 74 21 24 24 3 3 34 34 34 34 34 343 4 4 4 4 4~ 41 44 6 44 46 44 -4 5 5 65 64 64 64 6 6 64 6i 64 6i 64 14 1.2 4 2 2 2 2 2 24 21 24 24 24 24 2 -23 32 34 24 24 24 24 34 34 34 34 4 34 44 44 44 44 1' 14 14 1i 1i 1i 14 1 14 14 14 14 13 1i ia 4 2 2 2 2 2 24 2i 2t 24 21 24 24 24 24 21 2t 3 3 3 34 3i I I I - - -c-. _. 72B48 GRIPFITH'S SYSTEM Of VALUATION. (310z.) IIL-THATCHED HOUSES, PUDDLE MORTAR WALLS,-DRY WALLS, POINTED,-MUD WALLS OF A GOOD KIND. Height. A+ A A- B+ Ft. Inch. 60 3 6 9 70 3 6 9 80 3 6 9 9 0 3 6 9 10 0 3 6 9 11 0 8 6 9 12 0 6 13 0 6 140 6 150 6 16 0 6 17 C 6 18 C 6 19 C C 20 C d. 3 34 34 31 33. 4 34 4 4 4. 4-6 44 44 41 6 5 5} 6 6 6 6~ 61 65 64 61 7 71 74 74 71 71 8 81 8s 84 d. 21 3 3 31 34 41 -3 -23 34 -4 33 4 4 4 4 41 44 44 6 5 5} 5} 6 6 6{ 64 6t 7 71 71 74 7t 8 8 B d. 24 21 21 3 3 31 34 34 3t 31Y 3t 34 4 4 4.4 4~ 4} 2 43 41 5 6 51 6t 5t 6 6 61 6} 61 61 6t 7 7 7} 7t 7~ Bd. 21 21 2-5 -24 -21 21 3 3 3t 3 3 -31. 4 48 4 31 34 31 4 4 4 41 41 41 44 5 5 51 5} 6 56 5i 6 6 61 61 6i c-jc:i d. 2 2 2 2 2{-1 21 2- 214 21 21 2-1 24 24 3 23 34 21 21 3 3 3 31 31 31} 34 31 4 34 43 43 4 4 4-1 41 4j 4 4t 6 5 6 EaX d. 1-4 4 14 14 14 14 2i 21 11 4 2 2 2 2 2 2 21 2t 21 2} 32 24 32 32 24 21 21 32 31 34 3 81 d. t t 1 1 1 1 1 1 1 1 1 1 It 1| i~ 1~ 1; 1 -it 1t 11 11 1i 1i 1t 2 1 1 2 I2 2 2 OQRXFITH'9 *YSTEM OF VALUATION. 72M49 310y. IV.-BASEMENT STORIES, OF DWELLING IIOUSES, OI CELLATtS, USED AS DWELLINGS. lIcight. A —iFt. Tnchb!,( 6 0.; 3 - 9 70 Q 1 3 6 4 9, 9 0 41, 3 41 C4', 9 4 30 0 4 6 11 0 5 A d. 0, 31 '-). 4 4 4. 41 t', 4 A — (. o I -O C 1 0 _ I 4 1.1, 0 1 3 O., 4 4 41 4. l; -I- 11 1B c —_ C C (7. 01 i, I 6)l 3., 01 3.1 3." 1 94 0 3 4 4 4 (7 01 0'1 0) ol LI C) 1 01 01 9,, o.~ n". V i 91 C).1 3 1 3 1 ': tJ., d. 0 11 0 1 C) 1l 31 31 C) I C) 1 3 -)I 3} ~.j d1. - 11 I I t. i't 11 I 1:' 14 -2 2 01 - i 2,22 01. 2 0: -, 1) 0 d. 11 1' 1 1 1.i 1 t 11 i} 2 -L 2 d. 4 4 4 1 1 1 1 1 1 1 It1-,:1 1 1' 11. 1.I 11 -4 I t Where houses are built of wood, as in America, we deduct 10 per cent. from the value of a brick house of tlec same size and location, where the winters arc cold. In the Southern States, where the winters are warm, we deduct 20 per cent. from the value of a brick house similarly situated. We value a first-class frame or wooden house as if it was built of brick, and then make the above deductious, or tlart Ilhicih local wlodifyng circumstances willpoint out, such as climate, scarcity of timber, brick, lime, etc. 18 1): 72B50 GRtlFITH'S SYSTEMI OF VALUATlON.. OFFICES. The rate per square for offices of the I., II., III. and IV. Classes, is half that supplied in the foregoing Tables; Offices of the V. Class have the rate per square as follows: 310z. V.-OFFICES THATCHED, WITH DRY STONE WALLS. Hleight. A+ A A- B B B- c- C C-.Ft.. I.ch.. d.. d. d. d. d. d. 5 10 1 1 1 4 i 6 - - 1 14 14 1 4 4 I 9 - _ - 14 14 14 1 4 4 4 6 0 _ 14 14 1 1 4 i 4 31 - -_ 14 14 14 1 a 4 4 i 6 - 4- 14 14 14 1 4 4 7 0 - - 2 1 14 1 1 2 4 3 - - 2 14 14 1t 1 i 6 - _ 2 14 14 14 1 - + '39 - - 24 2 1- 14 14 4 4 80 - _ 24 2 14 14 14 a 3 - - 24 j 2 1 14 14 4 4 390 2 2 14- 1 36 - _ - 2 ~2 2 4a 14 4 4 6 -9 - - 24 22 14 1 1 i 10 _ - 2i 2 2 2 2 1 1 6 - _ 2 24 24.2 14 1 4 10 - 24 24 24 2 14 1 4 6 _- I- _ 3 2 24 2 14 1 12 0 3 24 24 2 1 1 6 _ _ 34 3 24 24 14 1 4 18 0 _ - 38 3 24 24 14 1 a 6 - - 34 3 24 24 2 1 4 14 0 - - 32 34 2 2 2 1 6- - 3 3 3 2 2 1 16 0 - - 3 34 3 24 2 14 {.: W.~ * GRIMIFTITS SYSTEM Or VALUATION.721 72s6l 310A. RIOUSES IN TOWNS. TABLES for ascertaining, by inspection, the relative Talue of any portion of a Building (nine square feet, or one yard,) and of any height, from I to V stories. SIGNIFICATION OF THlE LETTERS. rA+ Built or ornamented with cut stone, of superior solidity and I fnish. 1ST jA Very substantial building and finish, without cut stone CLASS. 1 ornament. A- Ordinary building and finish, or either of the abeve, when built 2415 or 30 years. 2ND (B- 'Medium, in sound order, and in good repair. CLASS. B 'Medium, slightly decoyed, but in repair. (B- Mlediumi, deteriorated by age, and not in gdod repair. 3RD C+ Old, but in repair. CLASS. C Old, and out of repair. (C-Old, and dilapidated-scarcely habitable. TABLE PRtICES FOR HOUSES, AS DWELLINGS, SLATED. Fiusir CLASS. SECOND CL'.SS. THIRD CLASP. ~Stories A+- A A- B-i B B- c+ o ca. d. s. d. s. d. a. d. a.. ad. s. d. a. d. a.d. 1 1 6 1 514 12 1 0 1010 0 806 04 II 2 62 4 222 0 19 16 1 3 10 08 IIL 3 0 910 2 82 623 2 0 1 9 14 010 lV 3 4 8 3 3 0 2 9 2 6 2 4 2 0 1 7 1 0 V 37 3 63 32 92 92 62 2 191 1 BASEMENTS AS DWELLINGS. 0 10 090 8 07 0 6 06504 08302 TABLE PRICES FOR OFFICES, SLATED. FIRST CLASS. SECOND CLASS. THIRD CLASS. Stories A~ A A- B-i- B -B- -- C - Ca. d. a. d. a. d. a. d. s. d.. d.. d. a. d. a. d. a. d. I- 0 9 08 0 807 0 6 0 604 08302 i1 3 121 1 10 010 0 8060 5 04 11116 1 51413 1 0 0100 8 06 06 IV 1 5 1 7 1 6 1 4 1 2 1 0 0 9 0 7 0 6W V 191 8 17 116 14 1 10 10 08 06 CELLARS AS OFFICES. 0 6 0650 61040 3j0830 2 0 Ij 0 1. i t|^??^^^ ":_,: *:.........:::...... 'v. -.. ' *-....-. ' 72s52' GEOLOGICAL FORMATION OF THE EARTH. 810B. Ro B' riginally horizontal, are now, by subsequent changes, inclined lo t lhorizoa: some, ale found contorted and vertical; often inclinrid both ways from a summit, and forming basins, which God has ordaJl;etl,, be great reservoirs for water, coul and oil, from which man draws sw,erl,' ar.es.ian wells. to fcrilii e the sandy soil of Algiers, and to supply bhn Wi', ifuela td lilgl., on the almost woodless prairies of Illinois. Uttfrrtlmi,' t iuks. are those which do not lie in beds, as granite. S!i',tli.i " -k. lie in be.Ji as limestones, etc. Dy.tcc. i:,re wlel e fis -lur';s in the rocks are filled with igneous rocks, such a' lav i. tr-, p rocks. Dy) tcs seldom have branches; they cross one anoe. it a:i naie sometin!es several yards wide, and extend from sixty to seveuty nliles in E;ngllid and Ireland. Vein-.- fcrdlrs or lodes, aie fissures in the rocks, and are of various thickne-isc; are parallel to one another in allernate bands, or, cross one anothc'r as iirt wo k. Mltall'e v,-'i o, e principally found in the primary rocks in parallel bands. aund selo n i'!o:llcd, as svc::dl veins or lodes are in the same locality. Those lodes or veins which iniersect others, contain a different mincr;,l. (jcanue or m7n '.,, is the stony mineral which separates the metal from the adjo i.1.f' roc:'..Mll lic i, iicat!inms. a ee tiLn c;nFne nd numerous cavities in the ground, or o101s on timei sin i 'tm. (,,.:lt>(,ndim!g to 4hose formed underneath by the aCei;ol ofCi o wvai-.I. Ti ci tfe t/: f!e,':,, is supposed to be four and one-fourth miles, and arraTigcl as follows by l:. -:Sult and others: Fotima'an CG i.p. 1. r,', V rC'hle c,'-ijl. Foin.: ion. A\liu.l dcposlts filling estuaries. d II. Up-e:' 'I1: ia- 31'Miln-n vo\'-mnoe, 1)) - ti c t, ilint and burning. ~., 'orl Io1','i ce L, i-c rt' il' lot Sl3lll.:rt ili l.i ' andl 1, '11i. ',!, I:. ji, nl,!tJ;ll colitaiilliig f'os i] bones. o III. I; -I': II( i \:,l,r 'lm, 'loI, bunml toncl, scmetimes contain'e. i.t.. i. i i. iltiitOI oiailc of l ta bleau. ^ IV. TI,'-r 31nrls Mfit f grium, fos.-is of the mamniiftrse. 'g T~.;.~, Co:. i. (: t ni..(tla.,.* ' Pl'las; ic clay;x ii li, ni-. V. l'pr Extl-ri.;;-: l;I(ncone straltum called chalk, with interpos* O Cri.i ots. i;, I;,: I'S O l 0 lICx. VI. lT.i-ver Tiif; c'onls cl.;k ofTo'liaine c:ndl.orsandlstonc,gcnerally c5 C at? cetiS. g ':.'c. 'ic; igii)oits s:ands. VII. Oo!i'ic or Calcareonu e srat. more or lcrs compact nand marly, o Juri.si. and:.1 i;in, xl\\i la rs ifclai;. Tie uplper strata of - X Li;,s. ilis.roul is, n' m cdL Onlile, and tie other, Lias..^ VIII. Trias. rVa.ie.acl-d m li l<. offt n cont lining masses of gypsum '' a'.: -, 'al ld rock sa '. limestone very iossili'erous. A <af:c~~s.-Sandsone of various colors.:.;a IX X. Sandl one. Cotnlomerat.-:nd nsandtone. X. 1'errnm u. Il.incl one miscxd with slate. y:0' ', ' ' Linlci one cotnmlonerate and sandstone, termed the new ]i,?0';: (,/0~ -: 'red s;ndstlole.....:....XI. Carboniferous Sandstone, slates with scams of coal and carbonate of iron, (cl;ay iron stone.) O'- SX *Carboniferous or mountain limestone, with seams of coal. | XII. Devonian. Heavy beds of old red sandstone, with small seams of anthracite (or hard coal.) XMI. HSilurian. Limestone, roofing slate, coarse grained sandstone oalled:;j:s??,' i'i ~, 6 greywacke. i ~ -j:: XIV. Cambrian. Compact limestone, argillaceous shale or slate rocks having often a crystalline texture. tl: -IVC. Prl tmamry Granite and gneiss forming the principal base of tbh; ooI s. interior of the globe, accessible to our observation. DI5CRIPTION 0? ROCKS ANID MINERALS. 7261S 810c. Quartz, silica or silicic acid, is of various forms, color and transparency, and is generally colorless, but often reddish, brownish, yellowish and black. It is the principal constituent in flint, sea and lake shore gravel, and sandstones. It scratches glass: is insoluble, infusible, and not acted on by acids. If fused with caustic potash or soda, it melts into a glass. Vitreous quartz, in its purest state, is rock-crystal, which is transparent f and c /less. Cah onic quartz, resembles rock-crystal, but if calcined it becomes white. It is more tenacious than vitreous quartz, and has a conchoidal fracture. Sand, is quartz in minute grains, generally colored reddish or yellowish brown, by oxyde of iron, but often found white. Sandestone, is where the grains of quartz are cemented together with calcareous, siliceous or argillaceous matter. Alumina. Pure alumina is rarely found in nature. It is composed of two equivalents of the metal aluminum and three of oxygen, and is often found of brilliant colors and used by jewellers as precious stones. The sapphyre is blue, the ruby is red, topaz when yellow, emerald when green, amethyst when violet, and adamantine when brown. On account of its hardness, it is used as emery in polishing precious stones and glass. It is infusible before the blowpipe with soda. Potash or Potassa, is the protoxide of the metal potassium, and when pure =: K 0 or one equivalent of each. Soda = No 0 _ protoxide of the metal sodium. Lime = Ca 0 - protoxide of the metal calcium. Magnesia = Mg 0 protoxide of the metal magnesium. Felspar, is widely distributed and of various colors and crystallization. In granite, it has a perfect crystalline structure. As the base of porphyrics, it is compact, of a close even texture. In granite felspar, the crystals of it is found in groups, cavities or veins, often with other substances. In porphyry, the crystals are embedded separately, as in a paste. It has a clear edge in two directions, and is nearly as hard as quartz. It is composed of silica, alumina and potash. Common Felspar, is composed of silica, alumina and potassa. (See table of analysis of rocks.) Albite-soda felspar, differs from felspar in having about eleven per cent. of soda in place of the potash, and in its crystallization,which belongs to the sixth series of solids, the three cleavages all meeting at oblique angles; yet the appearance of felspar and albite are very similar, and difficult to distinguish one from another. Their hardness and chemical characters are the same except the albite, which tinges the blowpipeflame yellow. It forms the basis of granite in many countries: especially in North America, and is characterized by its almost constant whiteness. Labradorite, a kind of felspar, contains lime, and about four per cent. of soda. It reflects brilliant colors in certain positions, particularly shades of green and blue; but its general color is dark grey. It is less infusible:?-: than felspar or albite, and may be dissolved in hydrochloric acid. It is: abundant in Labrador and the State of New York. Mica. It gleaves into very thin transparent, tough, elastic pla t.s!i toamoniy whitish, like transparent horn, sometimes browu or blikI. -It **...'.... D: A..: - *:, 72B54 DESCRIPTION 01 ROCKS AND MTNERALB. is principally composed of silica and alumina, combined with potassa, lime, magnesia, or oxyde of iron. Quartz or silica, has no cleavage-glassy lustre. Felspar, has a cleavage, but more opaque than silica. Mica, is transparent and easily cleaved. Granite, is of various shades and colors, and composed of quartz, (silica) felspar and mica. It forms the greater portion of the primary rocks. In the common granite, the felspar is lamellar or in plates, ande text- ure granular. Porphy ritic, is where crystals of felspar is imbedded in fine grained granite. It is red, green, brownish and sometimes gray. Hornblende, is of various colors. That which forms a part of the basalts and syenites, is of a dark green or brownish color. It does not split in layers like mica when heated in the flame of a candle. Its color distinguishes it from quartz and felspar. It has no cleavage, and is composed of silica, lime, magnesia and protoxide of iron. Augite, is nearly the same as hornblende, but is more compact. When found in the trap-rocks, it is of a dark green, approaching to black. Gneiss, resembles granite; the mica is more abundant, and arranged in lines producing a lamellar or schistose appearance; the felspar also lamellar. It has a banded appearance on the face of fracture, the bands being black when the color of rock is dark gray. It breaks easily into slabs which are sometimes used for flagging. Porphyritic gneiss, is where crystals of felspar appear in the rock, so as to give it a spotted appearance. Protogine, is where talc takes the place of mica in gneiss. Serpentine, is chiefly found with the older stratified rocks, but also found in the secondary and trap-rocks. It is mottled, of a massive green color, intermixed with black, and sometimes with red or brown; has a fine grained texture lighter than hornblende; may be cut with a knife, sometimes in a brittle, foliated mass. It is composed of about silica 44, *. magnesia 43, and water 13. Sometimes protoxide of iron, amounting to ten per cent., replaces the same amount of magnesia. Syenite, resembles granite, excepting that hornblende, which takes the place of mica. It is not so cleavable as mica, and its laminae are more brittle. It is composed of felspar, quartz and hornblende. The felspar is lamellar and predominates. There are various kinds of syenites, as the Porphyritic, where large crystals of felspar are imbedded in fine grained syenites. Granitoid, is where small quantities of mica occur. Talc, has a soft, greasy feeling, often in foliated plates, like mica, but the leaves or plates are not elastic. The color is usually pale green, sometimes greenish white, translucent, and in slaty mases. The last description from the township of Patton in Canada, and analyzed by Dr. Hunt, for Sir William Logan, Director of the Geological Survey of Canada, gives in the report for 1853 to 1856, the following: Silica, 59.50; magnesia, 29.15; protoxide of iron, 4.5; oxyde of nickel,.traces; alumina, 0.40; and loss by ignition, 4.40; total = 97.96. A soft silvery white talcose schist from the same township, gave silica, 61.60; magnesia, 22.86; protoxide of iron, 7.38; oxyde of nickel, traoes; lime, 1.26; alumina, 8.60; water, 3.60; total - 99.69. DESCRIPTION OF ROCKS AND MINERALS. li IB6U Soapstone or steatite, is a granular, whitish or grayish talc. Chlorite, is a dark or blackish green mineral, and is abundant in the altered silurian rocks, sometimes intermingled with grains of quartz and fesphatic matters, forming chlorite sand, stones and schists or slates, which frequently contains epidote, magnetic and specular iron ores. Massive beds of chlorite or potstone, are met with, which, being free from harder minerals, may be sawed and wrought with great faciliy. A specimen from the above named township (Patton) was of a pale greenish, gray color, oily to the touch, and composed of lamellae of chlorite in such a way as to give a schistose structure to the mass. Dr. Hunt, in the above report, gives its analysis: silica, 39.60; magnesia, 25.95; protoxide of iron, 14.49; alumina, 19.70; water, 11.30; total = 101.04. Green sand, has a brighter color than chlorite, without any crystallization. Limestones, are of various colors and hardness, from the 'friable chalk to the compact marble, and from being earthy and opaque, to the vitreous and transparent. Carbonate of lime, when pure, is cale spar, and is composed of lime, 56.3; and carbonic acid, 43.7. Imtpure carbonate of lime, is lime, carbonic acid, silica, alumina, iron, bitumen, etc. Fontainbleau limestone, contains a large portion of sand. Tufa, is lime deposited from lime water. Stalactite, resembles long cones or icicles found in caverns. Satin spar, is fibrous, and has a satin lustre. Carbonate of magyesia or dolomite, is of a yellowish color, and contains lime, magnesia and carbonic acid, and makes good building and mortar stone. Carbonate of magnesia, (pure) is composed of carbonic acid, 51.7, and magnesia, 48.3. Magnesian limestone, dolomite, (pure) is composed of carbonate of lime, 64.2, and carbonate of magnesia, 46.8. The following is the analysis from Sir W. Logan's report above quoted, of six specimens from different parts of Canada. No. I. From Loughborough, is made up of large, cleavable grains, weathers reddish, with small disseminated particles, probably serpentine, and which, when the rock is dissolved in hydrochloric acid, remains undissolved, intermingled with quartz. No. II. Is from a different place of said township. It is a coarse, crystallinlimestone, but very coherent, snow-white, vitreous and translucent, in an unusual degree. It holds small grains disseminated, tremo-,lite, quartz and sometimes rose-colored, bluish and greenish apatite and yellowish-brown mica, but all in small quantities. No. III. From Sheffield, is nearly pure dolomite. It is pure, white in color, coarsely crystalline. No. IV. From Madoc, is grayish-white, fine grained veins of quarta, Which intersect the rock. No. V. From Madoc, fine grained, grayish-white, silicious, magnesian limestone. No. VI. From the village of Madoc, is a reddish, granular dolomite. The following table shows the analysis of these specimens:....., _...-<~ e '.; i ' v,/; ^ff fcs ^ ^^^' ^ 5 i '.'. ' f S * - 0 2- hew i' I n 7U56 72e56 ~DESCRIPTION OF ROCKS AND MINERALS. i.. IV. V. VI. Spcfcgavt...................... 8 ~; 2.8491 2757 2.834 Carbonate of Lime.............55. 52 57 46.,47 151.90 57.37 AlMagnesia........... ii 4O7 40.17 1 1.8t)9 34.06 Peroxydc of Iron...................0. 2 J.-.... 1 32 Oxyde of Iron and Phosphate. ( ~ ~ ~..............;....... Quartz and Mica.............. 0................... Insoluble Quartz.7.............10i.lo.................... Quartz.................................;2.G 1 8.C00 7.1I0 IMAGXESLAN 31OW[LAUS. Lbnestones~, containing 10 to 2.5 per cent. or cl-ay, arc more and more hydraulic. That which contains 33 p!- ecuki. i)f clay, liar~lens or sets immediately. Good cement mixed wit h t vo it u,(f cle:ar sand arid made into small balls as large as a heci's egg, ZsltwZ)C'-id 51It froml mie 'gild a half to two hours. If the ball cruirbics in. w~i-, too m-11Itch 'jl-lm s present. Where the gromnd is wet, it is,- is' y ixed-oti re r (iof s~i el to one of cement, but where the work, is:-obmcri-cd iii waiter, then the best cement is required anid used in e1 ral pai is, arid often more, as in the case of Roman cement. By taking carbonate of liiae and clay in the required proportions and calcining them, we have tan artificial cerneuL". E~xample: Let the carbonate of lime produce 45 pe et. of lime, thea is it evident that by adding 15 lbs. of ttire dry clay to every 100 lbs. of carbonate of lime, and laying the materials in alternate layers and calcining that, wve produce a cement oif the rcqui4~ed strength. The litnestones should be brok~en as small as possible; the whole, whent caleined, to be ground together. Cement used in Paris, is miade by mixing fat linie and clay in proper proportions. Artificial ccnnent, is made ini France, by mixing 4 parts of chalk with one of clay. The whole is ground into a Pulp, and whent nearly dry, it -is made into bricks, which are dried in the air and then calcined *o frnrnaceE at a proper degree of heat. The temperature must not be too elevated. (See Regnault's Chemistry, Vol. I, p. 617.) Plaster of Paris, is composed of lime, 26.5, sulphuric acid, 387.5, and water, 17. It is granular, sulphate of lime, slakes without swelling, set5t hard in a short, time, but being partially soluble in water, should be only used for outside or dry work. Water lime, is composed of carbonate of lime, alumina, silica and oxyd' of iron. It sets under water. Water cements, differ from water lime in having more silica anc alumina. It must be finely reduced. The English engineers use thil and fine sharp sand in equal parts. DESCRIPTION OF ROCKS AND MINERALS. 72B57 Building stones. Felspathic rocks, such as green stone, phorphyry and syenite, in which the felspar is uniformly disseminated, are well adapted for structures requiring durability and strength. Syenite, in which potash abounds, is not fit for structures exposed to the weather. Granite, in which quartz is in excess, is brittle and hard, and difficult to work. An excess of mica makes it friable. The best granite is that in which all its constituents are uniformly disseminated, and is free from oxides of iron. Gneiss makes good building and flag stones. Limestones, should be free from clay and oxides of iron, and have a fine, granular appearance. Sand, is quartz, frequently mixed with felspar. Coarse sand, is that whose grains are from one-eighth to one-sixteenth of an inch in diameter. Fine sand, is where the diameter of the grains are from one-sixteenth to one twenty-fourth of an inch. Mixed sand, is where the fine and coarse are together. 'it sand, is more angular than sea or river sand, and is therefore prefered by many builders in France and America, for making mortar; but in England and Ireland, river sand, when it can be procured, is generally used. Pit sand should be so well washed as not to soil the fingers. By these means, any clay or dirt present in it is removed. Sand for casting, must be free from lime, be of a fine, siliceous quality, and contain a little clay to enable the mould to keep its form. Sandfor polishing, has about 80 per cent. of silica; is white or grayish, and has a hard feeling. Sand for glass, must be pure silica, free from iron. Its purity is known by its white color or the clearness of the grains, when viewed through a magnifying glass. Fuller's earth, has a soapy feeling, and is white, greenish-white or grayish. It crumbles in water, and does not becomeplastic. Its composition is, silica, 44; alumina, 23; lime, 4; magnesia, 2; protoxide of iron, 2; specific gravity, about two and one-half. Clay, is plastic earth, and generally composed of one part of alumina and two parts of quartz or silica. Clay for bricks, should be free or nearly so from lime, slightly plastic, and when moulded and spread out, to have an even appearance, smooth and free from pebbles. Clay free from iron, burns white, but that which contains iron, has a reddish color, the protoxide of iron in the clay becoming peroxidized by burning. Pipe and potters' clay, has no iron, and therefore burns white. Fire brick clay, should contain no iron, lime or magnesia. Marl, is an unctuous, clayey, chalky or sandy earth, of calcareous nature, containing clay or sand and lime, in variable proportions. Clay marl, resembles ordinary soil, but is more unctuous. It contains potash, and is therefore the best kind for agricultural purposes. Chalk marl, is of a dull, white or yellowish color, and resembles impure chalk; is found in powder or friable masses. Shelly marl, consists of the remains of infusorial animals, mixed with the broken shells of small fish. It resembles Fuller's earth, usually of a bluish or whitish color, feels soft, and readily crumbles under the fingers. It is found in the bottom of morasses, drained ponds, etc. Slaty or stony marl, is generally red or brown, owing to the oxyde of iron it contains; some have a gravelly appearance, but generally resembles hard clay. 19 310c. TABLE SHOWING THE COMPOSITION OF ROCKS. EARTHIS. NAME OF SUBJECT. Silica. Alu- Lim Silica. Lime. mina. nesia. f Quartz rock..0......................................... 82 9 0.4......... Granite............................................... 5 13 0.4 1 Felspar........................................ 64 19 0.7 0.5 Com m on........................................... 65 18.13................. " Labrador............................................. 55.8 26.5 11.0......... M a" Albite........................................ 69.1 19.2................. M ica............................................................... 46 6 0.3 5 c Slate................................................... 73 13 0.2 2.(.......................................... 46.3 36.8.................. P otash.................................................... 46 1 31.6................. - " M agnesian........................................... 40.0 12.7......... 15.7 Hornblend, basaltic......................................... 42.24 13.92 12.24 13.74 " syenitic................................. 45.7 12.18 13.83 18.79 Schorl, Devonshire......................................... 35.2 35.5 0.58 0.70 Tourmaline, Sweden..................................... 37.65 33.46 0.25 10.98 LAugite, Sweden......................................... 53.36......... 22.1 4.99 Greenstone.................................................... 55.0 15 7 9 I'Basalt.......................................53.0 19 5 2 Chlorite slate................................................... 64.0 9 0.2 7 Limestone, carbonate of lime........................... 5.0 0.7 40 00......... " sulphate of, or gypsum............................... 32.9......... " calcined...................................41.5....... " magnesian......................... 10.09 3.40 25.09 12.89 dolomite or carbonate magnesia............... 22.1 " hydraulic, N. Y............................. 1350 26.24 18.80." unburnt, '.............................. 11.76 2.73 25.0 17.83 burnt,..1656 10.77 39.50 22.27 unburnt, Ulster, N. Y............... 15.37 913 25 50 12.35 burnt, "....................22.75 13.40 37.6 16.65 " good French magnesian............... 21.0........ 40.0 21; " good French cement stone.............. 5 0 2 22.2 20 I moderately hydraulic..................... clay 101 carb. 86,carb.l.1 highly hydraulic............................ clav 190 77 ' 3. puzzolana of Italy.......................... 44 15 8.8 4.7 " phosphate of lime........................................... 75 OXIDES. Iron. Manvanese. 04........4 2 0.1 0.7...... per. 1.3................... 6..' 8. 0.6 4 03 4.5........ 8.7 1.4 19 0.63 14 59.33 7.32.22 m17.86.43 m 9.38........ 17.38.09 15.......................... 1.0.................... 1.50......... alumina......... 225......... 3.30......... 12......... ALKALI. Potash Potash. Soda. & Soda. 7.................. 7.. 7................. 13................... 16.7................... 4............ 11.7 10.................. 8.3........................61....................................................................................... 2.09 2.................. 0.70 2.18 1.4 3.0......... ACID_. Sul- CarFluori. phuric. bonic. uoric........ 1...... MISCELLANEOUS........................................................................................................................................ 46.3 58.5 0.61............................................................................................................ 47.4 39.8 39.33 10,9 34.2 5.0 22 28.1...................................................................................................................... 1 0.5 0.7 1.12 2.10......... 1.50.0.7..................... 0.7................................... -..............................................0........................................................... *................. -............. Water, 0.5.... Water, 1.8 '" 1.0 Titanic Acid, 1.63 Boracic Acid, 4.11 Plaster of Paris, 20.8 Cement,"1.18 * " 1.08 " 1.20 " 1.30 Plater of Pari, 10.8 Cemehosnt, cid, 1.18 Phospho. Acid, 25. 310D. TABLE SHOWING TRE COMPOSITION OF GRASSES AND TREES. EARTHS. j OXIDE. ALKALIES. ACIDS. PHOSPHATES. CHLORIDES. I NAME OF SUBJECT. Silica.. Mag- biu l- | ar-c I hos | Ipron. l Magne Chlorine Chlir. of'ChloratelMiscellan'ous. ne odium.'Potas'm. Lucerne............................... 3.46 Upright brome grass............... 38.48 Crested dogstail..................... 40.11 Orchard grass, seed ripe.......... 32.18 Meadow soft grass..................28.31 Meadow barley grass................23 Timothy grass.................... 31.09 Yellow oat grass.................... 35.20 June grass......................... 32.9.3 Hard Fiscue......................... 28.53 Downy oat grass.................... 36.28 W hite Clover...................... 3.68 Red Clover................. 7..... 7 Sanfoin, in seed.................... 3.49 Italian rye grass, in flower......59.18 M eadow hay............3.......... 38 50.57 10.38 10.16 8.14 8.31 5.04 14.94 7.98 5.63 10.31 4.72 26.41 33 29.67 9.95 23 3.64 4.99 2.43 3.47 3.41 2.42 5.30 3.07 2.71 2.83 3.17 8.15 8 4.59 2.23 7 0.63 0.26 0.18 0.23 0.31 0.66 0.27 2.40 0.28 0.78 0.72 1.96 0.4 0.58 0.78 1 14.03 20.33 24.99 33.06 34.83 20.26 24.25 36.06 31.17 31.84 31.21 14.83 3 29.61 12.45 1 6.44.................................... 3.40.................I 0.73 3.72 6t 1.25 3.98 4.23......... 5.46 0.55 3.20......... 3.96 2.88 4.41 1.82 4.29......... 4.86 4.02 4........ 4.26 0.40 3.41 1.38 3.37......... 7.21 18.03 3 15.20 2.33......... 2.82......... 2 1..... 13.68 7.53 7.24 6.41 8.02 6.04 11.29 9.31 10.02 12.07 10.82 11.53 8.02 7.97 6.3 -6......... 3.3......... 3.11..............3.24......... 1.........25 1.25 ~....... 1.31.:......................... 5.66......... 4.95 2......... 2......... I................................... 0.70......... 11.25......... 4.05......... *...*............... Ash, 5.11. " 6.38. " 5.51. " 6.37. " 5.67. " 5.29. " 5.28. " 5.94. " 5.42. " 5.22. Ash, 8. " 6.50. " 6.97. 6 6.:::.........1.....;.... Apple tree, root..................... " bark................... " outside wood......... "c heart wood........... Cherry tree, wood.................. "' bark.................. Peach tree, bark of trunk........ " wood of trunk........ Pear tree, bark..................... " sapwood................. 1.46 1.26 0.45 0.20 2.06 19.98 4.15 1.35 0.40 O..3O 12.13 1.86 15.56 2.06 28.69 41.95 42.17 23.26 30.36 12.64 0.16......... 2.56......... 3.52......... 2.93......... 9.19 0.07 5.10 0.20 2.16......... 6.40......... 9.40......... 3.001 0.31 15.07 0.44 3.29 2.75 20.78 7.46 0.40 7.11 6.20 22.25 21.99 1.5:4 3.33 1.62 8.40 14.53 14.5:3 11.15 1.84........ 0.42 13.96 31.35 38.39 49. 4;........ 3.60......... 12.21 15. 79........ 24.4........ 22.17 38.'983................... 3.29......... 773................ 0.80........ 3.26.,,......... 4.19................................ 1.5 1................................... 1.80 3 7 -2 *))9 - e-1 -*-~l-~~9-@@e 150 372..............1.......... 0.50 37.0.................................... 0.30 0.33 0.51.........70...... 1.170 0.11.................. 0.62 0.04 0.16 0.70 1........... Org. mat.l.20......... do& coal4.61......... )Do 3.55......... Do 3.61 Og....... mg. t.3.30.........Do 5.20 '....... Loss, 3.81 1*@@@****@1*-6* * w *~'........ 1.841 310. ANALYSIS OF TREES i.,., _ NAMES. 't I i I 0 Plum tree, outside wood..45... 15.56 3.52...... 3.29 3.33 " heart ".20... 2.66 2.93...... 2.75 1.66 " root " 1.46... 11.64.16.......15.07,22.00 Chestnut, bark............. 1.20... 51.60.60...... 1.36.33," outside wood.. 1.43... 40.76 5.77...... 4.56 1.41 i" inside " 1.73... 38.20.51...... 2.73 1.98 Beech, red, bark........... 3.30 2.23 52.29.82... 3.85.13...," outside wood...... 1.45... 31.56 5.44...... 12.1315.58,, heart "...... 1.60... 31.82 1.44...... 4.04 25.53 Butternut, bark............30...37.681.0.08..... 1.00 11.27,, outside wood. 4.80... 38.98 3.52....... 4.42 5.61 " heart " 5.40... 43.02 4...... 1.00111.82 Basswood, bark... 4.60... 41.92 2.24..... 1.2612.77,, outside wood.. 2.10... 38.86 7.36...... 10.12 2.88," heart " 1.40... 45.24 7.44...... 4.05 10.41 Elm, (white) bark........ 1.75... 27.46118.10...... 3.79 1.65 cc outside wood................................ Maple, bark..................15... 49.33 3.64...... 88 7.75, outside wood.......50... 31.86 8.40.......87...,, heart "c.......55 43.14 7.24...... 4.21... Oak, (white) sapwood..... 1.01... 30.35.36...... 13.41..., heart wood........... 1.18... 43.21.25...... 9.68.. twigs "........... 1.15... 34.10.50...... 9.74 6.89 (white swamp) bark 2.00...52.26.25......46 trace, outside wood........ 1.50... 30.22.50...... 20.49 3.15, heart "..........50... 35.57.51...... 14.79 3.69 Hickory, outside wood... 4.48...... 6.20...... 7.40.08,, inside "... 6.1...... 8.60...... 20.19.09 " heart ('... 1.30..... 4....... 12.21.06 Pine, pitch................... 7.50.. 13.60 4.35...... 14.10 20.75," scotch fir............ 6.59... 23.18 5.02...... 2.20 2.22 Rose bush, bark............ 3.30... 22.56 2.86...... 5.12 8.52 Birch, soluble compound 1.00............ " insoluble < 5.50... 52.2....5 3.5... Lime tree, bark............ 2.27... 60.81... 1.24... 16.14 4.53,, wood........... 5.26... 29.93... 7.97... 35.80 5.23 Mulberry, (white) soluble........................ 52 11.5, insoluble....... 2.9... 4.6.5 1.3......, chinese, soluble 1.0............... 68,, insoluble........ 13.1... 7.2............ Datura stramonium........ 5.21... 4.11 17.56pr 3.94... 20.2214.24 Sweet Flag................... 2.39... 7.70... prl.91... 6.9082.93 Common Chamomile...... 6.80... 3.67... pr 3.28... 9.66130.58 Cockle......................... 2.39... 6.14... pr 1.21... 13.20!22.86 Foxglove..................... 12.78... 6.53 3.70 3.19... 10.89143.53 Hemlock..................... 2.62.. 8.39. 9,64 2.40... 12.8021.69 Blue Bottle........ 3.29..... 4.56 1.61... 7.32 36.54 Strawberries................12.05...14.21 trace 11.12... 21.07 27.01 Poppy..................... 1.41 5.06... 1.21... 6.85 33.11 72B60 AND WEEDS, ETC. p.. c trace trace '' ''4 2.90.20 17.44 1.30 8.610.30 phos- 1.96 17.23.85 22.04.40 2.25.30 2.20 3.40.59 3.41 8.50.20 17.95 1.2C 8.96 1.30 0. trace phates.02.15. 06.28.30 2.60.04.02 1.80.22 t).1. O 16 A Z3 0 co 0..0 0 0.0:8.0 06 0 4.0 0 MISCELLANEOUR. 13.13 5.7 0 5.09 F I0 P0.3~2.73 1.34 32.25 13.30 23.60 14.44 11.45 6.34 11.10 171.03 15.30 12.21 22.17 1.84.31.50.47.62.74 13.73 21.43.88.27.14 12.02 1.50 1.17 1. 03 4.24.47.25.30.89 4.64 5.263 3.45 2.23 5.00 2.00.75 5.30 8.00 8.00 5.06 4.60 2.39 3.91 3.43 2.69 8.15 2.26 15.79 38.98 39.90 23".8 4 29.52~ 40.41 24.39 24.59 32.12 20.02~ 4.48 2.5.88 16.64 17.96 139.44 37.12 87.25 33.33 8.95 19.29 17.55 40.34 32.92 34.41 29.57 21.41 33.63 17.50 36.48 28.7-0 17.00 3 1 2.3 22. 18.7 5.62 8.50 8.96.05.24.10.06.07 2.30.33.51.11.15.24.08.08 2. 78.39.16.08 3.20 2.21 1.49 2.84 9.03 16.61 2.78 Org. mat. 3.20, coal,.35 "6 3.60. " 1.20. ". " 1.74. " 3.20. " 1.50, coall1.50 " 1.86. " 2.80. ".80. " 3.40. " 3.20. 1.70. " 2.53. " 2. " 2. " 1.50. " 2.40. " 1. 930. " 5.70. " 7.10. " 5.90. " 2.13. "2.70~. Water, 4. Hydrochloric acid, 4. "s i 2.04. Iodide of Sodium,.34. Ohlor. of Potass'm 14.66. "9 c 7.15. "t i 7.55. "9 9 11.88. it I 3.40..90 2.75 4 4.02 4.85 5.4 34.72 11.48 16.01 29.27 15.65 24.96 15.49 8.59 23.37 6. 72B61 310e. ANALYSIS OF GRAINS AND STRAWS, ~. ~ o. NAMES. I ~ ~) m |.o.. Barley, grain, mean of 10................ 2t.49 2.58 8.55 1.43 19.77 3.9!3 "< straw, mean of 3................. 54.56 8.08 4.13 1.3 18.40.68 " grain, at Clevesj...................199 3.3 10.05 1.93 3.9116.79 " grain, at Leipsic.................. 29.10 1.67 G.91 2.10 20.91... Buckwheat, grain........................69 6. 6610.38 1.05 8.74 30.10 t grain......................... 7.06.14 2.66... 23.33 2.04 "t straw...................... 4.37 22 40.37 1 10.37 1.94 Maize or Indian Corn, grain........... 1.44 1.44 1.22.3032.48.. " straw, mean of 2.................. 26.97 7.97 6.64.81 9.62 26-30 Millet, grain, (Giessen).................... 59..86 7.(6.63 9.58 1.31 Oats, grain, mean of 7..................... 47.08 3.92 7.70.6416.76 2.49 straw, mean of 2...................... 48.42 8.07 3.78 1.83 19.14 9.69 t potato, grain.......................... 50.03 1.31 8.25.27 19.70 1.35 Rice, grain.................................... 3.35 1.27 11.69.45 18.48 10.67 " straw................................... 74.09.73 4.49.67 10.27 3.82 Rye, grain, by Way and Ogden.......... 9.22 2.(61 12.81 1.04133.83.39 grain, mean of 3..................... 3.3 4.19 11.17 1.25 26 7.91 " grain, by Liebeg........................69 9.06 2.41.4011.43118.89 " straw, "<.........6...... 4.50 6 10 2 17.19... Wheat, grain, mean of 32................ 3.35 3.40 12.30.79 29.97 3.90 " straw, mean of 10................. 67.88 6.23 2.74.7412.14.60 Flax, whole plant in Ireland............. 21.3512.83 7.79 6.08 9.78 9.82 " best in Belgium..................... 2.68 18.52 3.93 1.1022.30 14.11 Hemp, whole plant, mean of 4........... 8.20 42.91 5.47 2.71 9.93.50 Linseed..................................92 25.98.22 3.67 25.85.71 Rape, seed.................................... 1.11 12.91 11.39 2.56 25.18... <" straw...............................89 20. 9)5.62... 8.13 19.82 Beet, Mangel Wurzel, (yellow).......... 2.22 1.78 1.78 3 23.5419.08 4 It It 'long red....... 1.40 1.90 1.79.52121.68 3.13 " mean of 4............................. 4.44 3.65 2.97 1.24 30.80 12.19 long blood root.................... 1.85 1.50 1.15... 13.10 53.65 < tops............................ 1.99 8.65 8.06.9621.36 7.01 Carrot, (white Belgian root,)........... 1.19 8.83 3.96 1.10(32.44 13.52 " tops................................ 4.50 32.4 2.92 2.40 7.12 10.97 " fresh root, (New York report.).65 3.65 1.60... 8.50 40.25 Artichoke, Jerusalem...................... 15.97 2.82 2.81 6.3954.67... Cauliflower, heart........................... 1.92 2.96 2.38 1.69134.39 14.77 Parsnip....................................... 4.1011.43 9.94.... 36.12 3.12 Potato, mean of...................... 4.23 2.07 5.28.557.75 1.8 " tops.................................... 3.8516.9 7.09 1.0528.0216.24 Tomato.......................................01 trace 0.10....07.09 Turnip, white globe........................ 1 8.69 4.56 1.44 42.83 2.66 swede...............................28 10.67 4.65.38 47.46 3.93 " mean of 10...................... 3.43111.14 3.61 1.09 36.98 6.76 " tops..................................8623.27 3.09.8;628.65 5.41 Beans, mean of 6........................... 2.55 19.30 5.91 2 28.87 6.64 (( straw................................. 7.0519.99 6.69.22 3.08 1.60 Peas, mean of 4...............................52 5.36 8.54.98 36.30 7.11 '" straw...................................20.03 54.91 6.88.40 4.73... Lentils.................................. 1.07 5.07 1.98 1.61 27.84 6.65 Vetch or tare................................. 01 4.9 8.49.75 30.57 9.56 " " straw....................... 8.6638.33 6.36.1735.49 1.02 72B62 VEGETABLE AND LEGUMINOUS PLANTS. 1. 08 2.13.26 2.16 7.30 6.78 2.77 1.19.35 1.29 3.26.10 3.56.17.51.83s.33 3.88 2.6f).5 6.83 1.28.91.53 7.60 3.68 3.14 3'.03 1.65 5.80 6.5 5 6.20 4A1 )0 2.70 11.16 6.50 13.64 6.88.01 12.6 12.16 12.43 12.52 1.91 1.09 4.39 6.77 4.1 2.39 35.20 3.26 4 0. 63 33.48 50.07 57.60 9 44.87 17.08 18.19 18.19 2.56 18 87 5 3.38)6 1.09 3 9.92 -46'.34 51.81 3.82 46 5.43 10.84 8.81 5.2)6 40.11 4 5. 96 4. 76 4.49 1.65 4.19 9. 8 5 5.15 8. )55 1.67 10.55 13".2 7 2 7.8.5 18.66 12.57 7. 62).08 8.61 9.2 9 2 1.'66 7.24 33.52 4.83 29.07 38.08 5.49 6 0 0 10 Q.............20 2.99............... 4.0.0.t, 0 T.47 1.43 3.20 MISCELLANEOUS..07.57.09.22 1.41 1.65 2.20 16.31 18.14 1 6. 27 17.82 28.2 dedu'ct.04............ 4.58...................81............ 1 .. 2.83.01... i... I... 16.05............... Oxyde Mang. and Alumina,.8. Chloride potassium,.14. Chloride potassium,.26. IPhosphate of Iron, 1.15. it "t.70. Carbonic acid deducted. Phosphate of Iron, 8.71. 24.55 49.51 24-55 33.96 6.50 13.67 3.3 2.86 5.54 7.10 7:85 IChloride potassium,.59. 1.35 4.26 2.16 '6.13 2 12.75 It.36. 310o. ANALYSIS OF THE ASHES OF MISCELLANEOUS ARTICLES. EARTHS. OXIDE. ALALIES. ACIDS. CHLORIDES. NAME OF SUBJECT... MagSul- Car- hos- ChlChoride MISCELLANEOUS. __________ S i nesia. | io. Poasn. oda. phuric. bonic. phoric. rine. Sodium. Onion, bulb................................. " stalk................................. Coffee, bean............................... Cabbage, leaves............................ " cow.............................. " stalk........................... Brocoli, heart.......................... " leaves............................ Cucumber.................................. Radish....................................... Tobacco, leaves, mean of 10........... Hops........................................ " whole plant......................... Vine, grape, mean of 3.................. Sugar-cane, stalk......................... " whole plant, mean of 2. Sorgho, Bagasse........................... Orange, whole fruit...................... Cherry, whole fruit...................... Apple......................................... Gooseberry................................ Pear......................................... Chestnut.................................... Celery...................................... 3.04 10.77 2.95.75 1.66 1.04.69 1.83 7.12 8.17 21.50 17.88.88 17.64 45.68 14.40 5.24 9.04 4.32 2.58 1.49 2.32 3.85 12.66 25.10 3.58 20.97 15.01 10.61 470 26.44 6.31 8.78 41.80 15.98 14.15 36.26 2.34 7.61 11.80 22.99 7.47 4.08 12.20 7.98 7.84 13.11 2.70 trace 9.01 5.94 2.39 3.85 3.93 3.43 4.26 3.53 12.18 5.77 5.34 6.91 3.93 9.87 9.80 6.55 5.46 8.75 5.85 5.22 7.84 13.11 *12.29 *10.61 *.55.60.70.41 *2.12 6.21 *2.06 *2.19 4.41 5.12 2.71 2.12... trace 1.74 3.74 2.65 8.65 *1.96 1.95 *2.66 32.35 13.98 42.11 11.70 40.86 40.93 47.16 22.10 47.42 21.16 17.42 25.18 19.41 27.88 32.93 15.12 8.10 38.72 51.85 35.68 38.65 54.69 39.36 43.17 8.04 14.43 11.07 20.42 2.43 4.05... 7.55 4.60.25.70 8.96.77 9.60 7.64 1.12 26.09 9.27 8.52 19.18... 8.34 10.50 21.48 7.27 11.11 10.35 16.10 7.71 4.06 5.41 8.28 2.70 7.97 7.76 28.70 2.95 5.09 6.09 5.89 5.69 3.88 5.58 *......e. 16.68 6.33 *... *... 11.01.e....... trace... *.. *........ 15.09 11.24 12.37 12.52 19.57 24.53 16.62 14.97 40.09 2.23 12.13 14.64 13.18 7.37 6.34 13.42 14.17 14.21 12.34 15.58 14.28 7.83 11.58 o...:.... 5.77...... *...*-....... *3.70.*............70 1.08 4.49 trace 1.67 o.o 2.08 trace... 9.06 7.07 5.11 7.24 3 1.39 17.12 4.40 2.02 *.. 1.23 4.82... Note.-In the Iron * signifies Phosphate. U. S. Patent Office. Cameron. Chloride potassium, 6.22. " 4 4.19.. 1.29. S 3.10. 1.67. 10.07. 7.49. Jackson. Oxyde manganese, 1.92 8101. PERCENTAGE VALUE OF MANURES. SUBSTANCES. Water. Nto I Farm yard manure... Wheat straw....... Rye straw......... Oat straw......... Barley straw....... Pea straw......... Buckwheat straw.... Leaves of rape...... it potato..... "6 carrot..... 69 oak....... it beech..... Saw dust fir........ 99 oak........Malt dust........ Applerfue Hop" Beet root refuse..... Linseed cake....... Rape cake......... llempseed cake... Cotton seed cake..... Cow dung......... "urine........ excrements..... Horse excrements.... urine........ "excrements.... Pigs' urine.... Pigs' excrements.... Sheeps' excrements... " urine....... dung....... Pigeons' dung...... Human urine....... (6excrements.... Flemish manure..... Poudrette from Belloni Do. from Berry in 1847 Do. from Montfaucon.. Do. in 1847........ Blood, liquid....... coag. & pressed Blood, steamed...... Bones boiled....... unboiled..... " dust........ Glue refuse........ Sugar refineries..... Ox hairs.......... Woolenras Guano, Peruvian..... " African...... Soot of wood....... iscoal........ Oyster shells....... 68.21 70.5 12.3 12.4 21.0 11.0 8.5 11.0 12.8 76.0 70.9 25.0 39.3 24.0 26.0 6.0 6.4 73.0 70.0 13.4 10.5 5. 0 11.0 85.9 88.3 84.3 75.3 85.0 75.4 97.49 91.4 57.6 86.5 67.1 61.8 93.3 91.0 13.6 41.4 28.0 81.0 21.4 73.5 8. 11.3 25.6 25. 5.6 15.6 17.9 2.45.41.35.36.26 1.95.54.86 2.30 2.94 1.57 1.91.31.72 4.90.63 2.23 1.26 6. 5.50 4.78 4.52 2.30 3.80 2.59 2.21 14.47 3.02 ii. 5.17 1.70 9.70) 2.79 9.12 21.6 4 14.67 2.29 2.67 2.47 15.58 15.50 17. 5.59 7.58 8.89 7.92 3.27 2.44 15.12 20.26 6.31 8.25 1.31 1.59 0.40 I E 1,tuog, n atph's ac' d1 I SEL N O. trisaedry atatel ISELNO..61.72.36.30.28.23 1.79.48.75.0,).85 1.18 1.18.23.54 4.51.59.56.38 5.20 4.9_2 4.21 4.02.32.44.41.55 2.04.74.23.54.72 1.31.91 3.48 1.46 1.33.20 3.85 1.98 1.56 1.78 2.95 12.18 4.51 6.22 2.13 17.98 4.71 6.19 1.15 1.35.32 I"U 2.00.22.21.204 3.830 4.034 1.04.740 3.83 1.08 2.74 3.655 1.52.03 1.32 5.88 3.88 2.85 1.08 4.80 1.63 1.68 24. 22.20 24. 26.. 17. lieclielburn. Grignon, France. Alsace. Recently collected. Air dried. Solid excrements. Solid and liquid. Fresh excrements. Solid and liquid. Liquid manure. Sauburan. Slaughter house. Commercial. From the press. Wahl's, Chicago. 110 72B(j5 72B66 SEWAGE MANURE. SEWAGE MANURE. 310j. The value of this manure is now fully established. Dr. Cameron, Professor to the Dublin Chemical Society, has recently shown that "100 tons of the sewage water of Dublin containNitrogen, 16 Ibs., worth 10s. 8d. Phosphoric Acid, 4.2 " Is. 4-d. Salts of Potash, 5.1 " 7Td. Salts of Soda, 14.2 " 2-d. Organic matter, 75 " 4d. Taking the population of Dublin at 300,000, the value of the sewage is worth more than ~100,000, or two-thirds of the local taxation of the city." He calculates the value of the night soil at ~3000, and the urine at ~85,000, showing one to be thirty times as valuable as the other. Those who have seen the river Thames or the Chicago river made the receptacle of city sewage, will admit that God never intended that liquid manure should pass into these streams causing disease and death, but that they should be made available in fertilizing the neighboring fields, as in Edinburgh and various other places. We recommended a plan of intercepting sewers for Chicago in 1854, by which the sewage could be collected at certain places, and from thence wasted into Lake Michigan far from the city, or used for irrigating the adjacent level prairies. The plan was rejected, but the consequence has been that an Act passed the Legislature of Illinois in 1865, creating a commission for cleansing the Chicago river, at an expense of TWO MILLIONS OF DOLLARS. The commissioners have now (30th June, 1865,) commenced their preparatory survey. In Chicago the people are obliged to connect their water-closets with the main sewers, thereby making the sewers gas generators on a large scale. Public water-closets are built at the crossings of some of the bridges, and private ones without traps or syphons are built under the sidewalks. This system of sewerage begins to show its bad effects, and will have to be abandoned at some future day. To any person who has spent one hour in a chemical laboratory, it will appear that noxious gases will soon saturate any amount of water that can be held in a trap or syphon, and that no contrivance can be adopted to exclude permanently the poisonous effluvia of sulphide of ammonium and sulphuretted hydrogen. It will cost London thirty millions of dollars to build the intercepting sewers commenced in 1858. Paris commenced a similar work in 1857, and Dublin is now about to do the same. About April, 1865, an Act passed the English House of Lords for the utilitization of town sewage, which was supported by the first vote of the PRINCE OF WALES. The great LIEBEG has commenced operation on the London sewage. He has it free of charge for ten years; to that in a few years the value of sewage will be as well known to the Americans and Europeans as it is now to the Chinese. Then there will not be a scientific engineer who will advocate the converting of currentless streams and neighboring waters into cesspools. The sanitary and agricultural conditions of the world will forbid it. (See also sections on Drainage and Irrigation.) DESCRIPTION OF MINERALS. 7 2B67 DESCRIPTION OF MINERALS. 310K. ANTIMONY. Stibnite, or gray sulphuret of antimony. Comp. Sb73, S27. Found chiefly in granite, gneiss and mica, with galena, blende, iron, copper, silver, zinc and arsenic. Found columnar, massive, granular, and in delicate threads. Fusible. Gravity, 4.5. Lustre, shining. Fracture, perfect and brittle. Color, lead to steel gray; tarnishes when exposed. White Antimony. Contains antimony, 84. Found in rectangular crystals, whose color is white, grayish and reddish, of a pearly lustre. H2.5. Gravity, 5 to 6. Sulphuret of Antimony and Lead. Found rhombic, fibrous and columnar. Color, lead to steel gray. I -_ 2 to 4. Specific gravity, 5 to 6. ARSENIC, White. Sometimes found in primary rocks with Co. Cu. Ag. and Pb. Color, tin white. Is soluble. G., 3.7. Fracture, conchoidal. Lustre, vitreous. Native Arsenic. Found in Hungary, Bohemia, and in New Hampshire with lead and silver. Color, tin white to dark gray. A - 3.5. Gravity, 5.7. F = imperfect. Orpiment or Yellow Sulphuret of Antimony. Found in Europe, Asia and New York. Foliated masses and prismatic crystals. Color, fine yellow. II = 1.5 to 2. Gr., 3 to 3.5. F = perfect. Lustre, pearly. Realetr or Red Sulphuret of. Found in Europe, with Cu. and Pb. Color, red to orange. II = 1.5 to 2. Gr., 3 to 4. Lustre, resinous. F = imperfect. Massive and acicular. BISMUTH. Native. Found in quartz, gneiss, mica, with Co. As., Ag. and Fe. Color, silver white. Found amorphous, crystallized, lamellar. H = 2 to 2.5. Gr. = 9. F = perfect. Lustre. Metallic. Sulphuret of Bismuth. Comp., Bi. 81, S19. Found as above. Massive acicular crystals. II = 2.3. Gr., 6.6. Color, lead gray. COBALT. Smaltine. Found in primary rocks, with As. Ag. and Fe. Massive, cubes and octohedrons. H - 5. Gr., 6 to 7. Color, tin white to steel gray. L = metallic. Fracture uneven. Arsenical Cobalt. Found, as in the latter, massive, stalectical and dentrical. Comp., Co. + As. + S. Color, tinge of copper red. Gr., 7.3. F - brittle. Bloom or Peach Cobalt. Found in oblique crystals. Foliated like mica. Color, red, gray, greenish. H - 1.5 to 2. Gr., 3. Lustre, pearly. Fracture, like mica. COPPER. Native. Nearly pure. Found in veins in primary rocks, and as high as the new red sandstone, in masses or plates. Aborescent, filiform. Color, copper red. H = 2.5 to 3. Gr., 8.6. Sulphuret of. Comp., Cu. 76.5, S22 + Fe..50. Found in great rocks, especially the primary and secondary ones. In double, six-sided pyramids, lamellar, tissular, long tabular, six-sided prisms. Color, blackish steel gray. Gr., 5.5. Fracture, brittle and brilliant. Sulphuret of Copper and Iron. (Copper pyrites.) Comp., Cu. 36, S32, Fe. 32. Found in veins in granite and allied rocks, graywacks, and with iron pyrites, carbonates of Cu. blende, galena. Color, brass yellow when hammered. H = 3 to 4. Gr., 4. Found in various shapes, Tetrahedral, octohedral, massive, like native and iron pyrites, 72B68 DESCRIPTION OF MINERALS. Gray Sulphuret of Cu. and Iron. Comp., Cu. 52., Fe. 23. The same location and associates as the last. It is not magnetic like oxide of iron, nor so hard as arsenate of iron. Color, steel gray to black. Lustre, metallic. F = brittle. Found amorphous, disseminated, crystallized in small tetrahedral crystals. Copper Pyrites, most prevalent. Comp., Cu. 76.5, S22, Fe..5. Found similar to sulphuret of copper. Color, brass yellow. Found in small, imperfect crystals in concretion and crystallized lamellar. F = uneven. Lustre, metallic. Gr., 4.3. Red Oxide of Copper. Contains 88 to 91 of copper. Found with other copper ores. It is fusible and effervesces with nitric acid, but not with hydrochloric acid. Color, red. F = generally uneven. H = soft. Found amorphous, crystallized, in cubes and octohedrons. Blue Carbonate of Cu. Comp., Cu. 70, C02 24, HO6. Found in primary and secondary rocks. Is infusible without a flux, and gives a green bead with borax in the blow pipe flame. It is massive, incrusting and stalactical. Color, blue. F = imperfectly foliated. Green Carbonate of Copper. Found with other copper ores, in incrustations and other forms. Color, light green. L = adamantine. H =, to 4. Or., 4. NICKEL. Arsenical. Comp., As. 54, Ni. 4.4. Found in secondary rocks, as gneiss, with cobalt, arsenic, Fe., sulphur and lead, and is massive, reticulated, botryoidal. Gives out garlic odor when heated. Color, copper red, which tarnishes in air. H = 5. Gr., 7 to 8. L = metallic. Nickel Glance. Found with arsenic and sulphur, massive and in cubes. Comp., Ni. 28 to 38. Color, silver white to steel gray. H = 5. Gr., 6. White Nickel. Comp., Ni. 20 to 28, As. 70 to 78. Color, tin white, found as cubic crystals. Placodine. Ni. 57. Color, bronze yellow. Found tabular, obliqe and in rhombic prisms. H = 5 to 6. Gr., 8. Antimonial Nickel. Ni. 29. Found in hexagonal crystals. Color, pale copper red, inclined to violet. Nickel Pyrites. Contain Ni. 64. Color, brass yellow to light bronze. Found capillary and in rhombohedral crystals. Green Nickel. Contain 36 per cent. of oxide of nickel. Found with copper and other ores of nickel. Color, apple green. ZINC. Blende. Mock-lead. Block Jack. Found in veins in primary and secondary rocks, with Fe. Pb. and Cu. Comp., zinc 67, Pb. 33. Found massive, lamellar, granular and crystallized. It decripitates if heated, and is infusible. Color, yellow, brown or black. Lustre, shining and adamantine. F = brittle and foliated. Gr., 3 to 4. Carbonate of Zinc. (Calamine.) Comp., zinc, 64.5, carbonic acid, 35.5. Found in beds or nests in secondary limestones, and in veins, with oxides of iron and sometimes lead. Crystallized, compact, amorphous, cupreferous and pseudomorphous. Color, gray, greenish, brown, yellow and whitish. L = vitreous and pearly. F., brittle. Gr., 4 to 4.5. Red Oxide of Zinc. Comp., zinc 94, protoxide of manganese 6. Found in iron mines and limestones. Massive and disseminated. Cleavage like mica. Color, deep or light red with a streak of orange yellow. Lustre, subadamantine and brilliant. DESCRIPTION OF MINERALS. 72B69 Sulphate o' Zinc. Found in rhombic prisms. Color, white. L vitreous. F., perfect. Gr., 20.4. MANGANESE. Binoxide of. Comp., Mn02 = Mn 64 + 036. Found in veins and masses in primary rocks, with iron. Forms a purple glass with borax in the blow pipe flame. Color, dark steel gray, with a black streak. L =metallic. F., conchoidal and earthy. II = 2 to 2.5. Gr., 4 to 5. Found massive, and in fibrous concretions. Crystallized. Infusible alone. Phosphate of angangeese. (Triplite.) Protoxide Mn. 33, protoxide of Fe. 32, and phosphoric acid 33. Gives a violet gloss with borax. Color, yellowish, streak of gray or black. L = resinous and opaque. H5 to 5.5. Gr., 3 to 4. Bog Ore of Mn., or add. Found in low places, formed from minerals, containing manganese. Comp., Mn. 30 to 70, protoxide of iron 20 to 25. Color, brownish black. Lustre, dull and earthy. H = 1. Gr., 4. TIN. Oxide qf. Comp., tin, 77.5, 021.5, oxide of iron.25, and silver.75. Found in the crystalline rocks with Cu. and iron pyrites. Found in various places, especially in Cornwall in England. Color, brown or black, with a pale gray streak. Found lamellar, in grains and massive. Decripitates on charcoal. L =adamantine. F., indistinct and brittle. H - ( to 7. Gr., 6.5 to 7. Sulphuret of Tin, or Pyrites. Color, steel gray or yellowish. Streak, black. F =brittle. H4. Gr., 4. Comp., tin 34, S25, Cu. 36 and Fe. 2. PLATINUM. Found only in the metallic state, with various metals, such as gold, silver, iron, copper and lead, and disseminated in rocks of igneous origin, as the primary. Often found in syenite with gold, but it is principally found in alluvium or drift. Color, very light steel gray to silver white. Lustre, glistening. It is found in grains and rolled pieces, seldom larger than a pea. Resembles coarse iron fileings. It is malleable; infusible, excepting in the flame of the oxyhydrogen blowpipe. GOLD. Found in granite, quartz, slate, hornstone, sandstone, limestone, clay slate, gneiss, mica slate, and especially in talcose slate, rarely in graywack and tertiary slate, but never in serpentine. Associated with Cu., Zn., Fe., Pb., Baryta., antimony, platinum. Where it is found in primary rocks, it is frequently in schiste. Color, yellow. Seldom found massive; often disseminated, capillary, amorphous, dentritic, crystallized in cubes, octohedrons, rhomboidal, dodecahedron and tetrahedron. Lustre, glistening and metallic. Fracture, hackly and tissular. H - 2.5 to 3. Gr., 19.4. It is malleable and unaltered by exposure, and is easily cut and flattened under the hammer, which distinguishes it from copper and iron pyrites, which crumble under the hammer. SILVER. Sulphuret of. Comp., Ag. 87, S13. It is soluble in nitric acid. Found in primary and secondary rocks, with other ores of silver. Gives off sulphurous odor when heated in the flame of a blow pipe flame. Found in cubes and octohedrons, reticulated. Imperfect at cleavage, is malleable, amorphous and in plates. Color, blackish, lead gray, with a shining streak. L = metallic, F. fliat and conchoidal. H2.3. Gr., 7. Silver, native. Usually alloyed with gold, bismuth and copper. Found in primary and secondary rocks, often in penetrating crystals, or amorphous in common quartz, with copper and cobalt. It is fusible into a globule. Color, silver white, but often gray or reddish. It is seldom found massive, but often in plates and spangles, dentiform, filiform and 72B70 DESCRIPTION OF MINERALS. aborescent. Crystallized in cubes, octohedrons, lamellar and ramose, with no cleavage. L= splendent to shining. F., fine hackly. 112.5 to 3. Gr., 10.4 Sulphuret of Silver and Antimony. Comp. S16, Sb. 14.7, Ag. 68.5, Cu. 6. Found in the primary rocks, such as granite and clay slate, with native silver and copper. It is found massive and in compound crystals, having an imperfect cleavage. Color, iron black. L = metallic. F., conchoidal. H2.2. Gr., 6.3. Chloride of Silver. Comp., Ag. 75, chlorine 25. Found in the primary rocks with other ores of silver. Massive, seldom columnar, often incrust-' ing, in cubes, with no distinct cleavage, also reniform and acicular. Color, pearly gray, greenish, blue or reddish, with a shining streak. Lustre, resinous to adamantine. Mercury, native. Found in Austria, Spain, Peru, Hungary and California. Found in fluid globules. Color, tin white. Gr., 13.6. Sulphuret of Mercury, or Cinnabar. Comp., mercury s. 14.75. Found chiefly in the new red sandstone, sometimes in mica slate, limestone, gneiss, graywack, beds of bituminous shale of coal formation. In California, at the Almaden mines, it is found in greenish talcose rock. Color, brownish black to bright red, cochineal red, lead gray, sometimes a tinge of yellow. Found massive, six-sided prisms, sometimes fibrous, with a streak of scarlet red. It evaporates before the blow pipe and does not give off allicaceous fumes. L = metallic to unmetallic. Fracture, perfect, fibrous, granular or in thin plates. H2.3. Gr., 7 to 8. LEAD. Native. Rarely met. It has been found in the County of Kerry in Ireland, Carthagena in Spain, and Alston moor, in the County of Cumberland, England. Sulphuret of Lead, or Galena. Comp., Pb. 86.5, S13.8. Found in veins, beds and imbedded masses, in primary and secondary mountains, but more frequently in the latter, particularly in limestone. The indications are calc spar, mineral-blossom, red color of the soil, crumbling of magnesian limestone and sink-hole appearance of the surface. Color, leaden or blackish gray. Found amorphous, reticulated and crystallized in cubes and octohedrons, with a perfect cleavage, parallel to the planes of the cubes. L = metallic. F., lamellar and brittle. Gr., 7.6. Sulphate of Lead. Comp., Pb. 73, sulphuric acid, 27. It is produced from the decomposition of galena, and found associated with galena. Color, white, sometimes green or light gray. Found massive, granular, lamellar, and often in slender crystals. L = vitreous or resinous. F., brittle. 112.8 to 3. Gr., 6.3 to 6.5. JMlinium or RedLead. Found with galena in pulverulent state. Color, bright red and yellow. Gr., 4.6. Phosphate of Lead. Comp., Pb. 78.6, phosphoric acid 19.7, hydrochloric acid 1.7. Color, bright green or orange brown. Found in hexagonal prisms, reniform, globular and radiated. Streak, white. 1I3.8 to 4. Gr. 6.5 to 7. Chromate of Lead. Found in gneiss. Color, bright red, with a streak of orange yellow. Found massive and in oblique rhombic prisms. Black Lead, Plumbago, or Graphite. Found in gneiss, mica, granular limestone, clay slate, and generally in the coal formation. Color, iron DESCRIPTION OF MINERALS. 72B71 black. Lustre, metallic. In six-sided prisms, foliated and massive. H = 1 to2. Gr., 2. IRON. Native. Is found in meteorites, alloyed with nickel. It is massive, magnetic, malleable and ductile. F =hackley. H4.5. Gr. 7.3 to 7.8. A specimen in Yale College contains Fe. 9.1 and Ni. 9. Iron Pyrites, or Bisulphuret of Iron. Occurs in rocks of all ages and in lavas. Found usually in cubes, pentagonal, dodecahedrons or octohedrons. Also massive. Color, bronze yellow, with a brownish streak. Lustre, metallic and splendent. Brittle. H = 6 to 6.5. Gr. 4.8 to 5.1. Strikes fire with steel, and is not magnetic. Comp., Fe. 45.74, S54.26. Auriferous Iron Pyrites. Is that which contains gold. Magnetic Pyrites, or Sulphuret of Iron. Found massive, and sometimes in hexagonal, tabular prisms. Color, bronze yellow to copper red, with a dark streak. F = brittle. H3.5 to 4.5. Gr. 4.6 to 4.65. Slightly magnetic. Comp., Fe. 59.6, S40.4. This ore is not so hard as the bisulphuret of iron, and is of a paler color than copper pyrites. Magnetic Iron Ore. Found in granular masses, octohedrons, dodeca- hedrons, granite, gneiss, mica, clay slate, hornblende, syenite, chlorite, slate and limestone. Color, iron black, with a black streak. F = brittle. H5.5 to 6.5. Gr., 5 to 5.1. Highly magnetic. Comp., Fe. 71.8, oxygen 28.2. This is the most useful and diffused iron ore. Specular Iron Ore, Peroxide of Iron. Found massive, granular, micaceous, sometimes in thin, tabular prisms. Color, dark steel gray or iron black. Lustre, often splendent, passing into an earthy ore of a red color, yielding a deep red color without lustre. H =-5.5 to 6.5. Gr., 4.5 to 5.3. Slightly magnetic. The Specular Variety. Has a highly, metallic lustre. Micaceous, Specular Iron Ore. Has a foliated structure. Red Ochre. Often contains clay, is soft and earthy. It is more compact than red chalk. Bog Iron Ore. Occurs in low ground; is loose and earthy; of a brownish, black color. Clay Iron Stone. Has a brownish red, jaspery and compact appearance. Comp. of specular iron are Fe. 69.3, oxygen 30.7. The celebrated iron mountains of Missouri are composed of specular iron ore. One of the mountains is 700 feet high. There, the massive, micaceous and ochreous varieties are combined. Chromate of Iron. Found massive and octohedral crystals, in serpentine rocks, imbedded in veins or masses. Color, iron and brownish black, with a dark streak. L = sub-metallic. H5.5. Gr., 4.3 to 4.5. When reduced to small fragments, it is magnetic. Comp., chromium 60, protoxide of iron 20.1, alumina 11.8, and magnesia 7.5. Carbonate of Iron. Found principally in gneiss and graywack, also in rocks of all ages. Found massive, with a foliated structure, in rhombohedrons and hexagonal prisms. Color, light gray to dark brown red; blackens by exposure. L = pearly to vitreous. H3 to 4.5. Gr., 3.7 to 3.8. Comp., protoxide of iron 61.4, carbonic acid 38.6. This ore is extensively used in the manufacture of iron and steel. These, with the magnetic, specular, bog ore and clay ironstone, are the principal sources of the iron commerce. 72B72 EXAMINATION OF A SOLID BODY. EXAMINATION OF A SOLID BODY. 310L. Note its state of aggregate, hardness, specific gravity, fracture, lustre, color, locality and associates. Heat a portion of the substance, (reduced to a fine powder) in a test tube; if no change of color appears, it is free from organic matter. It isfreefrom water, if there is no change of weight. If organic matter is present, it blackens first, then reddens. No organic matter is present, if it entirely volatilizes. It is a compound of two or more substances, when only a portion volatilizes. It is an alkali or alkaline earth, if it fuses without any other change. Is it'soluble, insoluble, or partially soluble in water? Is it soluble with boiling dilute hydrochloric acid? Take two portions of the substance, burn one part, and to the other, add dilute hydrochloric acid; if no effervescence takes place until we put dilute acid on the burnt substance, it shows the presence of an organic acid. The substance may be either a borate, carbonate, chlorate, nitrate, phosphate or sulphate. Borates. The alkaline borates are soluble in water, the others are nearly insoluble. They are decomposed in the wet way by sulphuric, nitric and hydrochloric acids, thus liberating boracic acid. If the mixture of any borate and fluorspar be heated with sulphuric acid, fluoride of boron is disengaged, recognized by the dense, white fumes it gives off in the air, and its mode of decomposition by contact with water.-Regnaults. Otherwise. From moderately, dilute solutions of borates. Mineral acids separate boracic acid, which crystallizes in scales. Otherwise. Heat the solution of a borate with one-half its volume of concentrated sulphuric acid and the same of alcohol. Kindle the latter. The boracic acid imparts a fine green color to the flame. Stir the mixture whilst burning. Melt the borate with two parts of fluorspar and one of bisulphuret of potash in a dark place; the flame at the instant of fusion is tinged green. Carbonates. Dissolved in cold or heated acids, disengage carbonic acid with a lively effervescence, which, if conducted through a tube into lime water, gives the latter a milk-white appearance. This gas will also slightly redden blue litmus paper previously moistened; but heat restores the blue color. If the gas is collected in a tube, and a small lighted taper let down into it, it will be extinguished. An engineer constructing tunnels or subterraneous works, will find the above tests sufficient to warn him of approaching danger from "foul air" or "choke damp." Water absorbs an equal bulk of this gas, hence the benefit of workmen throwing down a few buckets of water into a well, previous to going down into it after recess. Although the above tests will detect the presence of carbonic acid in subterraneous work, where the air may be impure, it requires the greatest caution on the part of the engineer to preserve the health of the workmen. Carbonic acid, is inodorous and tasteless. Sulphuretted hydrogen has the odor of rotten eggs, and is often found in subterraneous works. BLOW PIPE EXAMINATIONS. 72Ba7 Alkaline carbonates are soluble, the other carbonates are not. Nitrates. All nitrates, excepting a few sub-nitrates, are soluble in water. A solid nitrate, heated with concentrated sulphuric acid, evolves fumes of nitrous acid, sometimes accompanied by red-brown vapors of peroxide of nitrogen. Otherwise, heat the nitrate with concentrated sulphuric acid, then put in a slip of clean metallic copper, red vapors of peroxide of nitrogen are evolved. Otherwise, to a solution of a nitrate, add its bulk of concentrated sulphuric acid. When cool, suspend a crystal of protosulphate of iron, (green copperas.) After sometime, a brown ring will appear about the crystal. The liquid in this case must not be stirred or heated. Phosphates. Generally dissolve in nitric and hydrochloric acids. Sulphuric acid does not give any reaction, but generally decomposes them. With phosphates soluble in water, nitrate of silver gives a lemonyellow phosphate of silver. Is soluble, with difficulty, in acetic acid. Phosphates. Insoluble in water, are dissolved in nitric acid, then this solution is neutralized by ammonia; to this neutral mixture, the nitrate of silver test gives the above yellow color. Sesquioxide of Iron. In an alkaline solution of a phosphate, gives an almost white gelatinous precipitate of phosphate of sesquioxide of iron. Insoluble in acetic acid. Molybdate of Ammonia, added to any phosphate solution, and then nitric or hydrochloric acid added in excess, a yellow color soon appears, and subsequently a yellow precipitate. This is a very characteristic test. 9 substance ought to be first dissolved in nitric acid, and then nearly neutralized before adding the molybdate of ammonia. Sulphates. Nearly all the sulphates are soluble in water. They do not effervesce with acids. This distinguishes them from carbonates. The sulphates of baryta, strontia and lead, are nearly insoluble; that of lime is slightly soluble. From all the soluble sulphates, nitrate of baryta or chloride of barium, throws down a white precipitate insoluble in nitric acid, which is a characteristic property of the sulphates. In applying this test, the solution ought to be neutral or nearly so. This can be done by adding Magnesia to the solution so as to render it equal to sulphate of magnesia, MgO, S03. BLOW PIPE EXAMINATIONS. 310M. IHeat aportion of the substance on charcoal, in the inner flame of the blow pipe. If potash or soda, the flame is tinged yellow. If an alkaline earth, (barium, calcium, strontium, magnesium,) it will radiate a white light, and is infusible. Now moisten this infusible mass with nitrate of cobalt and heat again. If the flame becomes blue, alumina is present. If green, oxide of zinc. If palepink, magnesia; but if silica, it will fuse into a colorless bead, on the addition of carbonate of soda. i11 r I II I r r 72B74 QUALITATIVI ANALYSIS. If a bead, or colored infusible residue is formed, mix it with carbonate of soda, and heat on charcoal in the inner flame of the blow pipe. If tin, copper, silver or gold, are present, a bead of the metal will be formed, without any incrustation on the charcoal. If iron, cobalt or nickel, are present, the metal will be mixed up with the carbonate of soda, giving the bead a gray opaque appearance. If zinc or antimony, it will give a white deposit around the bead. If lead, bismuth or cadmium, a yellow or brown deposit. QUALITATIVE ANALYSES OF METALLIC SUBSTANCES. 310N. Let M = equal the mass or substance to be analyzed. We reduce it to a fine powder and boil with hydrochloric acid, so as to reduce it to a chloride, but if we suspect the presence of a metal not soluble by the above, we boil it with aqua regia (= nitro-hydrochloric acid) until it is dissolved; then we evaporate and boil again with dilute hydrochloric acid and evaporate to dryness, and so continue till every trace of nitric acid disappears. We have the metals now reduced to chlorides, which are soluble in distilled water. The solution is now set aside for analysis, which is to be acid, neutral or alkaline, as the nature of the reagent may require. The solution is acid if it changes blue litmus paper red, and alkaline, if it changes red litmus paper blue, or turmeric paper brown. Taylor gives nitro-prusside of sodium as a very delicate test for alkali. He " passes a little hydrosulphuric acid into the solution to be examined, and then adds the solution of the nitro-prusside of sodium, which gives a magnificent rose, purple, blue, crimson color, according to the strength of the alkaline. This will incte an alkali in berates, phosphates, carbonates, and in the least oxideable oxides, as lime and magnesia." The metals are divided into groups or classes. CLASS I. Potash = KO, soda NaO, and ammonia NH3. None of these, in an acidified solution, gives a precipitate with bydrosulphuric acid, hydrosulphate of ammonia, or carbonate of soda. CLASS II. Magnesia, MgO. Lime, CaO. Baryta, BaO. Strontia, SrO. None of these gives a precipitate with hydrosulphuric acid, or hydrosulphate of ammonia. Carbonate, or phosphate of soda, with either of this class, gives a copious white precipitate insoluble in excess. CLASS III. Alumina - A1203. Oxide of nickel NiO. Oxide of zinc ZnO. Oxide of cobalt CoO. Oxide of chromium. Protoxide of iron FeO. Protoxide of manganese MnO. Per oxide of iron Fe203. In neutral solutions these metals are precipitated by hydrosulphate ol ammonia. In a slightly acid solution, hydrosulphuric acid gives no precipitat excepting with peroxide of iron, with which it gives a yellowish white prec. CLASS IV. Arsenious acid AsO3, arsenic acid AsO5, teroxide of anti m ony SbO3, oxide of mercury HgO, peroxide of mercury HgO2, oxide of lead, copper, silver, tin, bismuth, gold and platinum..All of this class are precipitated from their acid solution by hydrosul QUALITATIVI ANALYSIS. 72st5 phuric acid. We can thus determine to which of the four classes of metals the substance under examination belongs. POTASH, in a solution of chloride of potassium. * Bichloride of platinum, in a neutral or slightly acid solution, gives a fine yellow crystalline prec., = KC1. Pt. C12, sligtly soluble in water, but insoluble in alcohol; somewhat soluble in dilute acids. When the solution is dilute, evaporate it with the reagent on a water bath, and then digest the residue with alcohol, when the above yellow crystals will appear. Tartaric acid. Let the solution be concentrated, then add the reagent, and agitate the mixture with a glass rod for some time, and let it remain, when a white prec, slightly soluble in water, will appear, the prec = KO. H0. C8 H4 01o. Blow Pipe flame. Wash the platinum wire in distilled water, then place a piece of the salt to be examined on the wire, which will give a violet color to the outer flame. Alcohol flame, having a potash salt in solution, gives the same reaction as the last. SODA, in a solution of sulphate of soda. Bichloride of platinum, added as for potassa, then evaporated, will give yellow needle-shaped crystals different from that by potassa. The preo. is readily soluble in water and alcokol. Antimoniate of potash. Let the solution and the reagent be concentrated, and the solution under examination slightly alkaline or neutral; then apply the reagent, which, if soda is present, will produce a white crystalline ptec. of antimoniate of soda, Blow Pipe. Hold the salt on the platinum wire in the inner or reducing flame, it will impart a golden yellow color to the outer, or oxidizing flame. OXIDE OF AMIIONIUMr, NH40, in a solution of chloride of ammonium. Bichloride of platinum gives the same reaction as for potassa. If we have a doubt whether it is potassa or ammonia, ignite the precipitate and digest the residue with water, then, if nitrate of silver be added, and gives a precipitate, it shows the presence of potassa. In this case we must take care that all traces of hydrochloric acid are removed. Heated in a test tube. If the substance be heated in a test tube with some hydrate of lime, or caustic potassa or soda, it will give off the peculiar odor of ammonia, and changes moistened turmeric paper brown and red litmus paper blue. If this does not happen, we say ammonia is absent. BARYTA, = BaO, in a solution of chloride of barium. Sulphuric acid. White prec. in very dilute solution, insoluble in dilute acids. Sulphate of lime, in solution, gives an immediate prec., requiring 600 times its weight of water to dissolve it. Oxalate o wmonia. White prec. readily sol. in free acids. This is the same rein as for lime, but it requires a stronger solution of baryta than of lime. Flame of alcohol, containing baryta, is yellowish, and is different from that of lime, which has a reddish tinge, and strontia, which is carmine. Blow Pipe, in the inner flame, the substance strongly heated on plati* Those marked with an sterisk are the most delicate tests. -, e 72B76 QUALITATIVE ANALYSIS. num wire, imparts a light green color to the outer flame. If the substance be insoluble, first moisten it with dilute hydrochloric acid. LIME, = CaO, in a solution of chloride of calcium. Oxalate of ammonia. Let the solution be neutralized with muriate of ammonia; then add the reagent, which will give a copious white prec. of oxalate of lime, soluble in hydrochloric acid, but insoluble in acetic.acid. This detects lime in a highly diluted solution. Sulphuric acid, dilute. In concentrated solution gives an immediate prec. soluble in much water, which is not the case with barytt. Blow Pipe. Heated in the inner flame, gives an orange red color to the outer flame. Moisten an insoluble compound with dilute hydrochloric acid before this test. Burnt with alcohol, the flame will be a reddish tint, but not so red as that given by strontia. STRONTIA = SrO. In a solution of chloride of strontium. Oxalate of ammonia, in concentrated solution, a white prec., but not in dilute solution. This distinguishes strontia from lime. Sulphate of lime. The prec. will be formed after some time even in a concentrated solution. This distinguishes strontia from baryta. (See above.) Sulphuric acid gives an immediate prec. in a concentrated solution, but only after some time in a dilute one, where the prec. will be minute crystals. In the flame of alcohol, stir the mixture, and a beautiful carmine color is produced. Blow Pipe, in the inner flame, an intense carmine red. Moisten the insoluble compound with dilute H.C1 as above for lime and baryta. NOTE. Sulphuric acid gives, with a weak solution of lime, no precipitate; with chloride of barium, an immediate white p.; with a weak solution of strontia, a prec. after some time. The prec. from baryta and strontia are insol. in nitric acid, but that from lime is sol. MAGNESIA MgO., in a solution of sulphate of magnesia MgO. S03. Phosphate of soda, a white, highly crystalline prec. of phosphate of magnesia = 2MgO. HO. P05. In this case the solution must not be very dilute. By boiling the solution and reagent together the prec. is more easily produced. Phosphate of soda and ammonia. In using this reagent, add ammonia or its carbonate, which makes the prec. less soluble. Agitate with a glass rod, which, if it touches the side of the test tube, will cause the prec. there to appear first. The prec. is crystalline, slightly soluble in water, less in ammonia, but readily in dilute acids;.'. the solution must be ammoniacal. Ignite this prec., the ammonia is driven off, and the residue = phosphate of magnesia = 2MgO. P05. Blow Pipe. Moisten the substance with nitrate of cobalt, and heat in the blow-pipe, the compound assumes a pale flesh or roslor. NOTE. Sulphate of lime gives a prec. with baryta and strontia. Oxalate of ammonia gives a prec. with a very dilute solution of lime, but only with a concentrated solution of magnesia and strontia, and in a much stronger sol. of baryta than lime. Phosphate of soda, with lime, a gelatinous precipitate. do do with magnesia. QUALITATIVE ANALYSES. 72B77 Hydrofluosilic acid, in a solution of baryta, gives a white, transparent prec. By evaporating the prec. to dryness, and washing the residue with alcohol, we obtain all of the silico-fluoride of barium undissolved. If the sol. is dilute, the prec. will be after some time. ALUMINA, (A1208,) in a sol. of sulphate of alumina. Caustic Ammonia, (Nil3,) gives a semi-transparent, gelatinous, bulky prec. nearly insol. in excess of the ammonia. Caustic Potash, (KO,) gives a similar prec. soluble in an excess of the reagent, but if we add chlorate of ammonia to the solution, the alumina is again precipitated. Hydrosulphate of Ammonia, added to a neutral solution, gives a white prec. of hydrate of alumina, (A1203, 10) and hydrosulphuric acid is liberated. Phosphate of Soda, white prec., sol. in mineral acids, nearly insol. in acetic acid. Lime Water, precipitates alumina. NOTE. Ammonia in excess precipitates alumina, but not magnesia or the other alkaline earths. CIROMIUM, (Cr203,) in a sol. of sulphate of chrom. HIydrosulph. Acid, in neither acid or neutral solutions, gives no prec. IHydrosulphate of Ammonia, in a neutral solution, gives a dark green prec. insol. in excess of the reagent. Caustic Ammonia, if boiled with the solution, will produce the same as the last. If not boiled, a portion of the prec. will re-dissolve, giving the liquid a pink color. Blow Pipe. Reduce the substance to a sesquioxide of chromium, which will give in the inner flame a yellowish green glass, and in the outer flame a bright emerald green. Heat with a mixture of nitrate of potash and carbonate of soda; a yellow bead is formed. Dissolve this bead in watert acidulated with nitric acid, and add acetateof lead; a bright yellow prec. of chromate of lead is formed. PEROXIDE OF IRON. In a solution of sulphate of iron, FeO. S03. The compound is boiled with nitric acid to oxidize the metal, and then evaporated to dryness. Hydrosulphuric Acid, gives no precipitate. Sulphide of Ammonium, precipitates the iron completely as a black precipitate of sulphide of iron, FeS, which is insoluble in an excess of the precipitant. The above precipitate when exposed for some time to the air, becomes brown sesquioxide of iron. Ferrocyanide of Potassium, (prussiate of potassse,) light blue precipitate of KFe3Cfy2. The precipitate is insoluble in dilute acids. Phi is the most delicate test for iron. Sulphocyanide of Potassium. A red solution, but no precipitate. Tincture of Galls. Bluish black in the most dilute solution. Caustic Potash. Reddish prec. sol. in excess. Caustic Ammonia the same, insol. in excess. Blow'Pipe, heated on a platifum wire with borax in the outer flame, gives a brownish red glass, which assumes a dirty green color in the inner or reducing flame. 72B78 QUALITATIVE ANALY8ES. OXIDE OF COBALT. CoO, in a solution of nitrate or chloride of cobalt. Ammonia, when the solution does not contain free acid, or much ammoniacal salt, the metal is partially precipitated as a bluish precipitate, readily soluble in excess of the reagent, giving a reddish brown solution. Sulphide of Ammonium. A black precipitate of sulphide of cobalt, CoS, soluble in nitric acid, but sparingly in hydrochloric acid. Sesquicarbonate of Ammonia. A pink prec. CoO, C02 readily soluble in excess, giving a red solution. Solution of Potassa. Blue prec changing by heat to violet and red. Ferrocyanide of Potassium. A grayish green prec. Blow Pipe. In both flames with borax, a beautiful blue glass whose color is scarcely affected by other oxides. In this reaction the cobalt must be used in a small quantity. OXIDE OF NICKEL, NiO in a sol. of sulphate of nickel, NiO, S03+7HO. Hydrosulphate of Ammonia. Black prec. from neutral solution, slightly sol. in excess of the reagent, if the ammonia is yellow. The prec. is sol. in NO5 and sparingly in HC1. Hydrosulphuric Acid in acidified sol., no prec., but in neutral sol., it gives a partial prec. * Caustic Ammonia. A light green prec. sol. in excess, giving a purplish blue solution. In this case any salt of ammonia must be absent. Caustic Potash. Apple green prec. insol. in excess. Ferrocyanide of Potassium, greenish white prec. Cyanide of potassium, yellowish green prec. sol. in excess, forming a dull yellow sol. From this last sol., S03 precipitates the nickel. Blow Pipe. Any compound of nickel with carbonate of soda or borax in the inner flame, is reduced to the metallic state, forming a dusky gray or brown beads. In the outer flame the bead is violet while hot, becoming brown or yelow on cooling. OXIDE OF MNGANEGSE = MnO in a solution of sulphate of manganese - MnO, 803 + 7HO. * Hydrosulphate of Ammonia in neutral sol. gives a bright flesh colored gelatinous prec. becoming dark on exposure to the air. It is insoluble in excess of the reagent, but sol. in HC1 and N05. * Caustic Ammonia, if free from muriate of ammonia, gives a white or pale flesh colored = MnO, HO, becomes brown in air. * Caustic Potash, the same as the last, but muriate of ammonia does not entirely prevent the precipitate. Carbonate of Potash, or Ammonia, white prec. which does not darken so readily as the above. It is slightly soluble in chloride of ammonium. Blow Pipe. Mix the substance with carbonate of soda and a little nitrate or potash, and heat in the outer flame; it will give a green color, and produce manganate of soda, which will color water green. If the substance is heated with borax in the outer flame, it will produce a bead of a purple color; this if heated in the inner flame will cause the color to disappear. OXIDE OF ZINC, ZnO in a solution of sulphate of zinc, Zn, SO +7HO. * Hydrosulphate of Ammonia, in neutral or alkaline solution, gives a copious white curdy prec. if the zinc is pure. If iron is present it will be colored in proportion to the iron present in the sol. 4g~c QUALITATIVI ANALYS8. 72B79 Hydrosulphuric Acid in acid sol. no prec. Caustic Ammonia, or Potash, a white gelatinous prec. sqluble in excess. From either solution in excess, hyd. sulph. acid (HS) throws down the while prec. of sulphide of zinc. Corbonate of Potash, when no other salt of potash is present, gives a white prec. = 3 (ZnO, HO) + 2 (ZnO, C02) insol. in excess of the reagent. Blow Pipe, moistened with nitrate of cobalt and heated in the outer flame, gives a pale green color which is a delicate test to distinguish it from manganese, alumina and cobalt. AnSINIc ACID = As05. Boil the compound with HC1, and at the boiling point, add nitric acid as long as red flames of nitrous vapor appear, then evaporate slowly so as not to redden the powder, and expel the acid; then dissolve in distilled water for examination. HS, added to the above sol. slightly acidified with HC1, gives no immediate prec., but if allowed to stand for some time, or if heated to boiling point, a yellow prec. is obtained. Apply the gas several times, always heating to boiling point each time. IIyd. Sulph. of Ammonia, as in the above solution, but a little more acid gives the same prec. but of a lighter color. Ammonia nitrate of Silver. In a neutral solution as first made, add nitrate of silver which gives but a faint cloudy appearance; now add ammonia drop by drop till it gives a yellow prec. of arsenite of silver, which is very soluble in alkali. NOTE. The same prec. is obtained from the presence of phosphate of soda. Reinschs' test, in a solution acidified by adding a few drops of hydrochloric acid is a very delicate test, and considered nearly as delicate as Marsh's. Boil with the acidified liquid in a test tube, a clean strip of copper foil; the arsenic will be prec. on the copper as a metallic deposit. Antimony, bismuth, mercury and silver, give the same reduction as arsenic. In order to determine which is present, take out the copper foil and dry it between folds of filtering paper, or before a gentle heat; place it in a dry test tiube and apply heat; the arsenic being volatile, will be deposited in the upper end of the tube as a crystalline deposit, using but gentle heat. If it were antimony it would not be volatile, and would be deposited as a white sublimate, insol. in water, amorphous, and requiring more heat than arsenic. If it were mercury, it would be in small metallic globules. Marsh's test, is dangerous, excepting in the hands of an experienced chemist. Those who wish to apply it, will find the method of using it in Sir Robert Kane's Chemistry, or in those of Graham, Fowne, Bowman, and others. TxROXIDE OF ANTIMONY = SbO3, in a solution of chloride of antimony = SbC]3. This solution is made by dissolving the gray ore, or bisulphide of antimony in hydrochloric acid; the solution then diluted with water, acidified with HC1, is examined. Hydrosulphuric Acid, gives an orange red prec. of 8bS8, insol. in cold dilute acids, soluble in potassa and sulphide of ammonia. iydrosulphate of Ammonia. Add the reagent in small quantities; it will give an orange prec. of Sb58, soluble in excess.,9,,\.....,..,..a....;. 72B80 QUALITATIVE ANALYSES. Caustic Ammonia, or Potassa. Add slowly, and it will give a white prec. of teroxide of antimony = SbO3, soluble in excess. Water in excess. A white prec. which crystallises after some time, and is sol. in tartaric acid. NOTE. The same reaction is had with bismuth, but the prec. is not soluble in tartaric acid. Apiece of zinc, in a dilute solution made with aqua regia, precipitates both antimony and tin. Apiece of tin, in the above sol., prec. the antimony. TEROXIDE OF BISMUTH, in a solution of nitrate of teroxide of bismuth - BiO3, 3N06. Hyd. Sulph. Acid. A black prec. insol. in cold dilute acids, but sol. in hot dilute nitric acid. Chromate, or Bichromate of Potash, yellow prec. very sol. in dilute nitric acid. Water in excess, added to a solution of sesquichloride of bismuth, slightly acidified with hydrochloric acid, produces a white prec. insol. in tartaric acid, which distinguishes it from antimony. Heat a salt of Bismuth. It turns yellow, but on cooling off, becomes again colorless. Blow Pipe. In the inner flame with carbonate of soda, it forms small metallic globules, easily broken. Blow Pipe. In the outer flame with borax, gives a yellowish bead, becoming nearly colorless when cool. OXIDE OF TIN = SnO, in a sol. of chloride of tin, SnCl. Hydrosulphuric Acid, dark brown prec. in neutral or acid solutions. Insol. in cold dilute acids. If the prec. is boiled with nitric acid, it is converted into the insoluble binoxide of tin. IIydrosulphate of Ammonia, brown prec. sol. in excess if the reagent is yellow. Chloride of Mercury. First a white prec. then a gray prec. of metallic mercury, even in very dilute solution and in the presence of much HC1. Caustic Ammonia, white bulky prec. insol. in excess. Caustic Potash, do. = SnOHO, sol. in excess. Terchloride of Gold =(AuC13) very dilute. In dilute solutions, gives a dark purple prec. known as the purple of Cassius. If this mixture is now heated, it is resolved into metallic gold and binoxide of tin. PEROXIDE OF TIN = SnO2, in a sol. of bichloride of tin - SnCl2. Hyd. Sulph. Acid, bright yellow prec. insol. in dilute. SO3, or HC1, made insoluble by boiling with NCS, soluble in HC1 added to a litte NO6. Sol. in alkalies. Caustic Potassa, or Ammonia, white bulky prec. sol. in excess, especially with potassa. The prec. with ammonia is SnO2,HO, and with potassa = KO, 8nO2. Blow Pipe. In the outer flame with borax, it will give a colorless bead, but if there is much tin, the bead will be opaque. A piece of clean zinc, in a sol. of perchloride of tin, will precipitate the tin in the metallic state in beautiful feathery crystals; which under the microscope appear as brilliant crystalline tufts. OXIDE OF MEnRURY =- HgO, in a solution of bichloride of mercury, (corrosive sublimate) - HgC12. QUALITATIVE ANALYSIS. - 72B 81 J 1Hydrosulphuric Acid, added slowly, gives a white or yellow prec. If added in excess, it gives a black prec. of HgS, insol. in dilute S03, HC1 or N05. It is soluble in aqua regia with the aid of heat. If the precipitate be dried and heated in a test tube, metallic mercury is produced. Chloride of Tin, add slowly, a white prec. of Hg2Cl = subchloride of mercury will appear, this prec. becomes gray with an excess of the reagent. If we boil this precipitate in its solution, the mercury is reduced to the metallic state. * Iodide of Potassium, add drop by drop, gives a beautiful red prec. soluble in an excess of either the solution or reagent. HIeat a strip of copper, the mercury will be deposited on it which when rubbed will appear like silver. If the strip be heated in a test tube, the mercury will appear in minute globules in the cool part of the tube. OXIDE OF LEAD = PbO, in a solution of nitrate of lead, = PbO, N06, * made by dissolving the substance in nitric acid, and allowing it to crystallise. We may also use a solution of acetate of lead. Acetate of lead is formed by dissolving oxide of lead in an excess of acetic acid, then evaporate to dryness, the salt is acetate, or sugar of lead. The following reactions take place with nitrate of lead: Hydrosulphuric acid, in neutral or slightly acid solution, gives a black prec. of sulphide of lead = PbS, but if boiled with nitric acid, it becomes PbO + SO3. Caustic Ammonia, a white prec. insol. in excess. Other ammoniacal salts must not be present. Dilute, S03, a white heavy prec. nearly insol. in acids, but soluble in potassa. Now collect the prec. and moisten it with a little hydrosulphate of ammonia, it will become black. This distinguishes lead from baryta and strontia, which are insoluble. Carbonate of Potassa, white prec. insol. in excess. Prec. = PbO, CO2. Iodide of Potassium, beautiful yellow prec. If this is boiled with water and allowed to cool, beautiful yellow scales are formed. Chromate of Potassa, fine yellow prec. insol. in dilute acids, but sol. in potassa. Hydrochloric Acid, a white prec. Boil the solution and let it cool, then needle-shaped crystals will be formed. OXIDE OF SILVER, AgO, in a solution of nitrate of silver. Hydrochloric Acid, or any soluble chloride, a white curdy prec. of chloride of silver, insol. in water and nitric acid, sol. in ammonia. This becomes violet on exposure to light, and is sparingly sol. in HC1. Common Table Salt, gives the same prec. Hyd. Sulph. Acid, and Hyd. Sulphate of Ammonia, gives a black prec. insol. in dilute acids, but sol. in boiling nitric acid. Caustic Ammonia, brown prec. sol. in excess. Caustic Potassa, brown prec. insol. in excess. Phosphate of Soda, a pale yellow prec. sol. in N05 and ammonia. * Chromate of Potassa, dark crimson prec. NOTE. With lead, the prec. would be yellow. Slip of clean copper, iron or zinc, suspended in the liquid, precipitates the silver in the metallic state. NOTE. Silver is precipitated by other metals more electro-negative, such as tin, lead, manganese, mercury, bismuth, antimony, and arsenic. 112 1wfi-, \X @, 4 t: 72B82 QUALITATIVf ANALTYII. OXIDx 0P COPPER. CuO, in a solution of sulphate of copper = CuO, S03 + 6HO. Hyd. Sulph. Acid, in a neutral, acid or alkaline solution, gives a black preo = CuS, insol. in dilute 803, or HC1, but sol. in moderately dilute nitric acid. Insol. in excess of the reagent. Hyd. Sulphate of Ammonia. The same as the last, excepting that the reagent in excess dissolves the prec. Caustic Ammonia, added slowly, precipitates any iron as a greenish or red brown mud, and the supernatant liquid is of a fine blue color. With nickel, ammonia gives a blue but of a pale sapphire color, whilst that of copper gives a deep ultramarine. Caustic Potassa, blue prec. insol. in excess. If the potassa be added in excess and then boiled, the prec. will be black oxide of copper = CuO. Ferrocyanide of Potassium - Prussiate of Potassa, gives a chocolate colored prec. = Cu2, FeCy3, insoluble in dilute acids. This is a very delicate test. The prec. is soluble in ammonia. Potassa decomposes it. Before adding this test, acidify the solution with acetic acid or acetate of potassa. If but a small quantity of copper is present, no prec. will be produced, but the solution will have a pink color. Iron or Steel perfectly cleansed in a neutral sol. or one slightly acidified with S03, will become coated with metallic copper, thus enabling us to detect a minute quantity of copper, which is sometimes entirely precipitated from its solution. This detects 1 of copper in 180,000 of solution. Blow Pipe. In the outer flame with borax while hot, the copper salt is green, but becomes blue on cooling..TEROXIDE OF GOLD = AuO3 in a solution of terchloride of gold. Hydrosulphuric acid, black prec. of tersulphide of gold = AuSs, insol. in mineral acids, but sol. in aqua regia. Sulphate of Iron, bluish black prec. becomes yellow when burnished. Oxalic acid, if boiled, a prec. of a purple powder, which will afterwards cohere in yellow flakes of metallic gold when burnished. Chloride of Tin, with a little bichloride of tin, gives a purple tint, whose color varies with the quantity of gold in the solution, and is insol. in dilute acids. In using this test, first add the golden solution to the chloride of tin, and then add the solution of bichloride of tin, drop by drop. If ohly a small quantity of gold is present, the solution will have but a pink tinge. Tin-iron Solution. This reagent is made by adding sesquichloride of iron to chloride of tin, till a permanent yellow is formed. Pour the golden solution, much diluted in a beaker, and set it on white paper. Now dilute the tin-iron reagent, and dip a glass rod into it, which remove and put into the gold solution, when, if a trace of gold is present, a purple or bluish streak will be in the track of the rod. This may be used in acid solutions.:,-, BINOXIDE OF PLATINUM = PtO2, in a solution of bichloride of platinum. Hyd. Sulphuric Acid, black prec. when boiled. Insol. in dilute acids. Se ";. Chloride of Ammonium. After several hours, a yellow crystalline prec.;...... as lightly sol. in water, but insol. in alcohol. hloride of Tin, in the presence of hydrochloric acid, is a dark brown - olr; but if the solution is dilute, the color is yellow. i 1. 4 V.1 " I, 111 s I, t w,. At,~ #Iztu - LfAS`:wr i.,,t u B; '.1 4. I. ', - 72B88 310o. QUANTITATIVB ANALYSES. The mineral is finely pulverized, in'an agate or steel mortar. The pestle is to have a rotary motion so as not to waste any part of the mineral. When pulverized, wash and decant the fine part held in the solution, and again pulverize the coarse part remaining after decantation. If the mineral is malleable, we file off enough for analysis. Digesting the mineral, is to keep it in contact with water or acid in a beaker, and kept for some time at a gentle heat. If the mineral is insol. in water or HC1, we use aqua regia, (nitro-hydrochloric acid) composed of four parts of hydrochloric acid and one part of nitric acid. Aqua regia will dissolve all the metals but silica and alumina. Filtering papers, are made of a uniform size, and the weight of the ash of one of them marked on the back of the parcel. Filtering.-One of the filtering papers is placed in a glass funnel which is put into a large test tube or beaker, and then the above solution poured gently on the side of the filtering paper, wash the filter with distilled water. The filter now holds silica and alumina. Burn the filter and precipitate or insoluble residue, the increase of weight will be the siliceous matter in the amount analyzed, which may be twenty-five, fifty or one hundred grains, perhaps fifty grains will be the most convenient; therefore, the increase of weight found for siliceous matter if multiplied by two, will give the amount per cent. Decanting, is to remove the supernatant liquid from vessel A to vessel B, and may be easily done by rubbing a little tallow on the outside of the edge of A, over which the liquid is to pass, and holding a glass rod in B, and bringing the oiled lip of A to the rod, then decant the liquid. The Engineer is supposed to have seen some elementary work on Chemistry or Pharmacy. Fowne's, Bowman's and Lieber's are very good ones; from either of which he can learn the first rudiments. The following table shows the substances treated of in this work, showtng their symbols, equivalents or atomic weights and compounds. 310p. TABLE OF SYMBOLS AND EQUIVALENTS. Name. Aluminum............. Antimony.............. Arsenic i Arsenic................. Barium Bariumuth................ 4( Bismuth............... Cadmium.............. Calcium........... Carbon............. c< 3ymbol. -.1. Al Sb As Ba Bi Sc Cd Ca C,c, vEqui- Compound. valt. 14 A1208, Alumina........................... 14 A12C13, Chloride of Aluminum........ 14 A1203, 3S03, Sulphate of Alumina... 129 Sb03, Oxide of Antimony............. 76 AsO3, Arsenious Acid................. 75 As05, Arsenic Acid...................... 69 BaO, Baryta.............................. 69 BaC1, Chloride of Barium............. 107 Bi208, Sesquioxide of Bismuth....... 107 Bi2O8, 3N06, Nitrate of Bismuth..... 107 Bi2, Cl8, Sesquichloride of Bismuth. 56 CdO, Oxide of Cadmium................ 66 CdS, Sulphide of Cadmium........... 20 CaO, Lime............................. 20 CaO,......... 20 CaCl, Chloride of Lime................. 6 C02, Carbonic Acid...................... 6 CO, Carbonic Oxide..................... 6 CS2, Sulphide of Carbon.............. 36 C105, Chloric Acid................. 36 HCl, Hydr!~loric Acid................ Equival't. __, 62 136 172 163 99 116 77 106 238 400 822 64 72 28 66 22 14 88 76 87................. Chlorine.............. Cl *. *. 0..... *" <., Jc ~ I c I t " ~t Y~~:~ -: I ni.c-:~ — I, ;!:. ::t ~~:,- i~: ii~ vl...~..,1 i:_ ~tl~ -; ~r ~~~ 72s84 TABLE OF SYMBOLS AND EQUIVALENTS. Name. Sym Equ. p Equibol. val't. Compound. valt. Chromium.... C 2.........C Cr203, Sesquichloride of Chromium. 80 <............. 28 Cr203, 3803, Sulphate of Chromium. 200 Cobalt.............. Co 30 CoO, Protoxide of Cobalt...............38............... 30 Co203, Sesquioxide of Cobalt......... 84 Copper, (Cuprum)... Cu 32 CuO, Suboxide of Copper.............72 "<..."' " 32 CuO, Black Oxide of Copper..........40 <...'" 1 " 32 CuO, S03, Sulphate of Copper........ 80 Fluorine................F 18 HF, Hydrofluoric Acid................ 19 Gold, (Aurum)........ Au 200 AuO, Oxide of Gold..................... 208 t........I" 200 Au03, Ter oxide of Gold............. 224 t......... L 200 AuC13, Ter chloride of Gold...........308 Hydrogen.............. H 1 HO, Water.............,9...... 9....... "...1 H02, Binoxide of Hydrogen........... 17 Iodine..................I 126 IO5, Iodic Acid.................. 166 <<..............." 126 HI, Hydriodic Acid.................... 127 Iron, (Ferum)........ Fe 28 FeO, Protoxide of Iron.................36 I"....... 28 Fe203, Sesquioxide of Iron............ 80 Lead, (Plumbum)... Pb 104 PbO, Protoxide of Lead................ 112....I 104 Pb304, Red Oxide of Lead............. 344 t.... " 104 PbCl, Chloride of Lead................ 140 Magnesium............ Mg 12 MgO, Magnesia........................... 20 "............ "12 MgCl, Chloride of Magnesium........ 48 ar,_ ____ __ l.*. r ivanganese............ eeeee..ee. ee. Il Mercury........... ~..~.. ~.o...... ~............~~. Nickel................... Nitrogen.............. Oxygen.............. Phosphorous......... Is ~~..~~~... Platinum............... Potassium, (Rolium) Silicon............ Silver, (Argentum).. Sodium, (Natronium Sodium, (Natronium) * t* i t fI~tmnrrfrm, MIV (( 1 Hg Pt Ni cc N 0 P <( Pt ~I 28 28 28 28 202 202 202 202 30 30 14 14 14 8 32 32 32 99 99 40 40 - MnO, Protoxide of Manganese....... MnO2, Binoxide or Black Oxide of Manganese........................ MnO3, Manganic Acid.................. Mn207, Permanganic acid............. HgO, Protoxide of Mercury........... HgO2, Red or Binoxide of Mercury. HgCl, Chloride of Mercury............ HgCl2, Perchloride of Mercury....... NiO, Oxide of Nickel.................... Ni203, Sesquioxide of Nickel.......... NO5, Nitric Acld......................... N02, Binoxide of Nitrogen............ NH3, Ammonia.......................... Air = 23.10 of 0, and 76.9 per cent of N........................... P05, Phosphoric Acid................... P03, Phosphorous Acid................. PH3, Phosphoretted Hydrogen....... PtO, Protoxide of Platinum........... PtO2, Binoxide of Platinum........... IKO, Potash................................ KCl, Chloride of Potassium........... SiO3, Silicic Acid or Silica............ AgO, Oxide of Silver.................... AgCl, Chloride of Silver............... NaO, Soda............................... NaCl, Chloride of Sodium.............. ci-rn oii. ---r 36 44 52 112 210 218 238 274 38 84 54 30 17 72 56 35 107 115 48 76 46 116 144 32 60 - - Si Ag cc Na..r 22 108 108 24 24 AA vuvu......... J- v, o0rU nj, uIu ia......... I.................... od ~"............ 44 SrCl,...................................... 80 Sulphur............. S 16 803, Sulphuric Acid................... 40 - "............ 16 HS, Hydrosulphuric Acid............. 17 Tin, (Stannm)...... Sn 69 SnO, Protoxide of Tin.................. 67...... <9 69 Sn02, Peroxide of Tin.................. 75 Zinc.................... Zn 82 ZnO, Oxide of Zinc..................... 40......." 32 ZnCl, Chloride of Zinc.................. 68 '.;. *:f... l. *. ' * *..., '...* ^: 310Q. TABLE, SHOWING THE ACTION OF REAGENTS ON METALLIC OXIDES. o Be ifHvd. Sulph. Acid, Hyd. Sulph. of Am- Carbonate of Soda, Carb. of Ammonia, Caustic Potash, Caustic Ammonia, Ferrocy. of PotassName ofBase or Metal. S, in acidified sol. monia, NH4S, HS. NaO, CO2. 2N11O, 3CO2. K(. NH,. ium, K2FeCyaS Alumina................ Antimony.............. Baryta.................. Bismuth............... Cadmium......... Calcium, (lime)....... Chromium............ Cobalt................. <s.................. Copper, oxide of...... Gold................. Iron, peroxide of.... Lead, oxide of....... Magnesia............... Mercury, per oxide.. Manganese............ Nickel.................. Platinum............... Siver................. Strontia................;: - Tin, per oxide........ Zinc, oxide of...... ' *.. -.''.i,,. IA'v;.stafh~~;<f.-.......... *.. No reaction......... Orange red SbS3... 0 Brn to blk BiS3... Bright yellow CdS 0 0 0 0 Black CuS.......... 0 Black AuC13........ Yellow white....... Black, PbS........ 0 W becomes blk..... 0 0 Br'h blk PtC12..... Black........... 0 Yellow............... 0 White, insol. in xs. Or red sol. xs...... 0 Brown to black.... Br't yel. insol. xs. 0 Greenish blue...... Black, CoS......... 0 Black................ 0 Br'n-black sol: xs. Black................ Black insol......... 0 W. becomes blk... Flesh col. insol..... Black NiS........... Bro'h bl'k sol............................. Bhlck insol......... 0 Yellow sol.......... White............... W. insol xs........ W. sparingly sol.. W. ins6l. xs......... W. insol. xs......... W. insol. xs......... W. insol. xs......... Green............... Pink insol........... Bluish if boiled.... Greenish blue...... Dark br'n if boiled 0 Rust colored..... White insol......... White insol......... Reddish br'n insol. White insol........ Pale green insol... Yellow white....... With carb potassa White insol......... White insol......... White insol......... White insol........ W. insol............. W. spar. sol........ W. insol............. W. insol............. W. insol............ W. insol............. Green.............. Pink spar sol....... In excess............ Greenish blue...... Sol. in xs............ Yellow insol........ Rust col. insol...... White insol......... 0 W. insol............ White insol......... Pale green sol...... Yellow.......................White so.............. White sol............ White insol........ White insol......... White sol............ W. sol. in xs........ W. spar. sol........ 0 W. insol............. W. isol............. 0 Green sol xs........ Blue insol........... Boiled, a dirty red W. insol. xs......... W. insol............ 0 W. insol.............. White sol. xs...... 0 Gr'n'h blue sp. sol. Blue sol. xs...... Brownish red...... No reaction. White. 0 White. White. Dark br'n if boiled Pale to fine blue... In excess of KO... Sol. in xs........... Yellowish brown.. Yellow insol........ Rust col insol...... Rust colored insol. White sol........... White insol........ White insol......... White insol........ Yellow insol........White insol......... White to brown.... White to brown.... Pale green insol... Pale green sol..... Yellow............... Yellow............... Pale br'n insol..... Pale brown sol.... 0 0 White sol............ White sol........... White sol........... White sol........... xs. = in excess. 0 0 Pale green Or gray. Chocolate Color. 0 Deep blue. White. 0 White. * White. Pale green. 0 White. White. White. 0 For Potassa, Soda and Ammonia, see p. 72B75. %ljl. 8 10SlOa. ANAIYSIS OF VARIOUS SOILS. j -";.: tv -:. NARTHS. OXIDE8. A'CIDS. Same of Soil Water. A S Mag- Potash Ahlorid Humic Organic _________ _water.Alu ^ Silica. Lime. sa Iron. Manga- & Soda. Sul- Car- Phos- Sodium, acid. matter. __mina. mnese. phuric. bonic. phoric. ~~~~~~~~~~~~~~~C~ I~ ~o~ l~om. ~i. Clay, potters'..11..................... 7. 61. 1. W ay, potters'....................................... 11. 27. 61................... 1......................................................................... porcelain........................................ 15. 27. 55. 2......... 1...................................................................... " Stourbridge.................................... 12.6 30.4 57..................................................................... pure....................................................... 40. 60................................................................................... for tiles............................................... 38 to34 62 to66.......................................................................................... loam.....................................................34 to28 66 to72........................... Loamy soil..................................................... 28 to16 72 to84.......................................................................................... Sandy loam...................................................... 16 to 4 84 to96............................................................................................. Sandy soil.................................................... 4. 96................................................................. Marly soil.................................................................s........ to 20o...................................... Fertile pasture, Hanover........................... 1. 9.35 71.85.99.25 5.41.93.01.17..........13........ 8.82 2. "L arable, Ohio..............................5......... 5.67 87.14.56.31 2.22.36.15.03 3.33.06......... 2.37......... Barren soil......................................................45 61.58.32.13.52...................................38.01......... Calcareous soil.............................................. 20....................................................................................... Vegetable mould....................................................................................... o.......................... 5 to 10 Fertile alluvial pjasture...............................03 6.44 84.51.74.53 5.41.45.01.05...................01 3.78.96 Good red clover land.................................... 1.74 93.72.12.70 2.06.32.17.01..........10.05.89.12 Bad " <.......................................... 2.65 92.01.24.70 3.19.48.16 trace..........08 trace.34.15 Very fertile arable in Moravia.............................. 8.51 77.21.96 1.96 6.59 1.52.78.11...............01 1.52 1.11 Good cotton soil, Mississippi...................... 7.82* 80.55......... 1.81 1.45.66.60.21..........04.11......... 4.74 Cottqn soil exhausted2.......6.............................. 24. 85..........76.67..........39.09......... trace................. 6.29 Green sand............................................. 11.5 33.93 48.03......... 1.30.............. 5.61............................................. Shell marl..................................................60 3.10 45.75........ i n........................... 35.95........................... 14.6 Clay marl.......................................... 1.40 3.20 84.9 4.7....................................... 3.70.......................... 2.8 NoTir -Those marked * contain iron not determined. Barren soil, includes insol. humus. * QUANTITATIVE ANALYSES. 72B ANALYSIS OF SOILS. 310s. The fertility of soils -ecomposed of their siliceous matter, phosphoric acid and alkPalie. -he latter ought to be abundant. The surveyor may judge of the soil by the crops-as follows: If the straw or stalks lodge, it shows a want of silica, or that it is in an insoluble condition, and requires lime and potash to render it soluble. If the seeds or heads does not fill, it shows the want of phosphoric acid. If the leaves are green, it shows the presence of ammonia; bu if th c leaves are brown, it shows the want of it. Chemical analysis. By qualitative analysis, we determine the simpl bodies which form any compound substance, and.in what state or combi. nation. Quantitative analysis, points out in what proportion these simple bodies are combined. A body is organic, inorganic, or both. The body is organic, if when heated on a platinum foil, or clean sheet of iron over a spirit lamp, it blackens and takes fire. And if by continuing the heat the whole is burnt away, we conclude that the substance was entirely organic, or some salt of ammonia. Soluble in water.-The substance is reduced to powder, and a few grains of it is put with distilled water in a test tube or porcelain capsule; if it does not dissolve on stirring with a glass rod, apply gentle heat. If there is a doubt whether any part of it dissolved, evaporate a portion of the solution on platinum foil; if it leaves a residue, it proves that the substance is partially soluble in water. Hence we determine if it is soluble, insoluble or partially so in distilled water. Substances soluble in water, are as follows: Potassa. All the salts of potassa. Soda. Do. do. do. Ammonia. (Caustic,) and all the ordinary salts of it. Lime. Nitrate, muriate, (chloride of calcium.) Magnesia. Sulphate and muriate. Alumina. Sulphate. Iron. Sulphates and muriates of both oxides. Substances, insoluble, or slightly soluble in water, are as follows: Lime. Carbonate, phosphate and sulphate of. Magnesian. Phosphate of ammonia and magnesian. Magnesia. Carbonate, phosphate of. Alumina, and its phosphate. Iron, oxides, carbonate, phosphate of. Inorganic substances found in plants, as bases, are-alumina, lime, magnesia, potash, soda, oxide of iron, oxides of manganese. As acids-sulphuric, phosphoric, chlorine, fluorine, and iodine and bromine in sea plants. Take a wheelbarrowful of the soil from various parts of the field, to the depth of one foot. Mix the whole, and take a portion to analyze. Proportion of clay and sand in a soil. Take two hundred grains of well dried soil, and boil it in distilled water, until the sand appears to-be divided. Let it stand for some time, and decant the liquid. Add a fresh supply of water,,and boil, and decant as above, and so continue until the..E,..,W,......~;. 72B88 * QUANTITATIVE ANALYSES. clay is entirely carried off. The sand is then collected, dried and weighed. For the relative propoert nof sand in fertile soils, (see sec. 3091.) Organic matter in the soil. Take two hundred grains of the dry soil, and heat it in a platinum crucible over a spirit lamp, until the black color first produced is destroyed; the soil will then, appear reddish, the difference or loss in weight, will be the organic matter. Estimation of ammonia. Put one thousand grains of the unburnt soil in a retort, cover it with caustic potash. Let the neck of the retort dip into a receiver containing dilute hydrochloric acid, (one part of pure hydrochloric acid to three parts of distilled water;) bring the neck of the retort near the liquid in the receiver, and distill off about a fourth part; then evaporate the contents of the receiver in a water bath; the salt produced will be sal ammoniac, or muriate of ammonia, of which every one hundred grains contains 32.22 grains of ammonia. Estimation of silica, alumina, peroxide of iron, lime and magnesia. Put two hundred grains of the dry soil in a florence flask or beaker, then add of dilute hydrochloric acid four onnces, and gently boil for two hours, adding some of the dilute acid from time to time as may be required, on account of the evaporation. Filter the liquid and wash the undissolved soil, and add the water of this washing to the above filtrate. Collect the undissolved in a filter, heat to redness and weigh; this will give clay and siliceous sand insoluble in hydrochloric acid. Estimation of silica. Evaporate the above solution to dryness, then add dilute hydrochloric acid, the white gritty substance remaining insoluble is silica, which collect on a weighed filter, burn and weigh. Estimation of alumina andperoxide of iron. The solution filtered from the silica is divided into two parts. One part is neutralized by ammonia, the precipitate contains alumina and peroxide of iron, and possibly phosphoric acid. It is thrown on a filter and washed, strongly dried, (not burnt) and weighed; it is now dissolved in hydrochloric acid, and the oxide of iron is precipitated by caustic potash in excess; the prepitate is washed, dried and burnt, its weight gives the oxide of iron, Which taken from the above united weight of iron and alumina, will give the weight of the alumina. The phosphoric acid hereis considered too small and is neglected. Estimation of lime. The liquid filtered from the precipitate by the ammonia, contains lime and magnesia. The lime may be entirely precipitated by oxalate of ammonia. Collect the precipitate and burn it gently and weigh. In every one hundred grains of the weight, there will be 66.29 grains of lime. Estimation of magnesia. Take the filtered liquid from the oxalate of ammonia, and evaporte to a concentrated liquid, and when cold, add phosphate of soda and stir the solution. Let it Stand for some time. Phosphate of magnesia and ammonia will separate as a white crystalline powder. Collect on a filter, and wash with cold water, and burn. In one hundred grains, there are 36.67 grains of magnesia. Estimation ofpotash and soda. Take the half of the liquid. Set aside in examining for silica, (see above,) and render it alkaline to test paper by adding caustic barytes, and separate the precipitate. Again, add carbonate of ammonia, and separate this second precipitate, and evaporr * ' 72189 QUANTITATIVE ANALYSES. ate the liquid to dryness in a weighed platinum dish; heat the residue gently to expel the ammoniacal salts. Weigh the vessel with its contents; the excess will be the alkaline chlorides, which may be separated if required, by bi-chloride of platinum, which precipitates the potassa as chloride of potassium; one hundred parts of which contain 63.26 of potassa, and one hundred parts of chloride of sodium contain 53.29 of soda. Estimation of Phosphoric Acid. For this we will use Berthier's method, which is founded on the strong affinity which phosphoric acid has for iron. Let the fluid to be examined contain, at the same time, phosphoric acid, lime, alumina, magnesia, and peroxide of iron. Let the oxide of iron be in excess-to the fluid add ammonia, the precipitate will contain the whole of the phosphoric acid, and principally combined as phosphate of iron. Collect the precipitate, and wash, and then treat with dilute acetic acid, which will dissolve the lime, magnesia, and excess of iron, and alumina, and there will remain the phosphate of iron or phosphate of alumina, because alumina is as insoluble as the iron in acetic acid. Collect the residue and calcine them. In every one hundred grains of the calcined matter, fifty will be phosphoric acid. Estimation of Chlorine and Sulphuric Acid. These are found but in small quantities in soils, unless gypsum or common salt has been previously applied. Boil four hundred grains of the burnt soil in half a pint of water, filter the solution, and wash the insoluble residue with hot water, then burn, dry, weigh, and compare it with the former weight; this will give an approximate value of the constituents soluble in water. Now acidulate the filtered liquid with nitric acid, and add nitrate of silver; if chlorine is present, it will give a white curdy precipitate, which collect on a filter, wash, dry and burn in a porcelain crucible; the resulting salt, chloride of silver, contains 24.67 grains, in one hundred of chlorine. Estimation of Sulphuric Acid. To the filtered solution, add nitrate of barytes; a white cloudiness will be produced, showing the presence of sulphuric acid. The precipitate will be sulphate of barytes, which collect, wash, and weigh as above. In one hundred grains of this precipitate, there will be 34.37 of sulphuric acid. Estimation of Manganese. Heat the solution to near boiling, then mix with excess of carbonate of soda. Apply heat for some time. Filter the precipitate, and wash it with hot water, dry, and strongly ignite with care. The resulting salt, carbonate of manganese - Mn O. In every one hundred grains of this salt, there are 62.07 o rotoxide of manganese. Analysis of Magnesian Limestone. 310T. Supposed to contain carbonate of lime, carbonate of magnesia, silica, carbonic acid, iron and moisture. Weigh one hundred grains of the mineral finely powdered, and dry it in a dish on a sand-bath or stove. Weigh it every fifteen minutes until the weight becomes constant, the loss in weight will be the hydroscopic moisture. Otherwise. Pulverize the mineral, and calcine it in a platinum or porcelain crucible, to drive off the carbonic acid and moisture. To determine the Silica. Take one hundred grains. Moisten it with water, and then gradually with dilute hydrochloric acid. When it 113,: i J.._i — f v 0 f i t- b, L;LEDIB, 'V,~:; 2,, H E0' A.A,,<''N ',;,-',o~ia~X: 72B90 QUANTITATIVE ANALYSES. appears to be dissolved, add some of the acid and heat it, which will dissolve everything but the silica, which is filtered, washed and weighed. To determine the Iron. Take the filtrate last used for silica. Neutralize it with ammonia, then add sulphide of ammonium, which precipitates the iron as sulphide of iron, FeS. The solution is boiled with sulphate bf soda to reduce the iron to the 'state of protoxide. Boil so long as any odor is perceptible; then pass a current of HS, which will precipitate the metals of class IV. Collect the filtrate and boil it to expel the hydrosulphuric acid gas, then boil with caustic soda in excess, until the precipitate is converted into a powder. Collect the precipitate and reduce it to the state of peroxide, by adding dilute nitric acid; then add caustic ammonia, which precipitates the iron as Fe203, then collect and dry at a moderate heat. In every 100 parts of the dried precipitate, there are 70 of metallic iron. To determine the Lime. Boil the last filtrate from the iron, having made it slightly acid with hydrochloric acid. When the smell of sulphide of ammonium is entirely removed, filter the solution and neutralize the clear solution with ammonia, then add oxalate of ammonia in solution, as long as it will give a white precipitate. We now have all the lime as an oxalate. Boil this solution, and filter the precipitate, and ignite; when cool, add a solution of carbonate of ammonia, and again gently heat to expel the excess of carbonate of ammonia. We now have the whole of the lime converted into carbonate of lime, which has 56 per cent. of lime. Or, dry the oxalate at 212~. When dry, it contains 38.4 per cent. of lime. NOTE. If we have not oxalate of ammonia, we use a solution of oxalic acid, and add caustic ammonia to the liquid containing the lime and reagent till it smells strong of the ammonia; then we have the lime precipitated as an oxalate, as above. If we suspect Alumina, the liquid is boiled with N06 to reduce the iron to a sesquioxide, (peroxide.) Then boil it with caustic potassa for some time, which will precipitate the iron as Fe203, which collect as above. To determine the Alumina, supersaturate the last filtrate with IICl, and add carbonate of ammonia in excess, which will precipitate the alumina as hydrate of alumina, which collect, dry and ignite; the result is A1208 = sesquioxide of alumina, which has 53.85 per cent. of alumina. To determitthe Magnesia. In determining the lime, we had in the solution, hyhlloric acid and ammonia, which held the magnesia in solution; we now concentrate the solution by evaporation, and then add caustic ammonia in excess. Phosphate of soda is then added as long as it gives a precipitate. Stir the liquid frequently with a glass rod, and let it rest for some hours. The precipitate is the double phosphate of ammonia and magnesia. Wash the precipitate with water, containing a little free ammonia, because the double phosphate is slightly soluble in water. When the prec. is dried, ignite it in a porcelain crucible, and then weigh it as phosphate of magnesia = 2MgO, P05. By igniting as above, the water and ammonia are driven off, and the double phosphate is reduced to phosphate of magnesia. In every 100 grains are 17.86 of magnesia. (NOTE. This simple method is from Bowman's Chemistry.) To determine the Carbonic Acid. Take 100 grains and put them into a bottle with about 4 ounces of water. Put about 60 grains of hydro QUANTITATIVE ANALYSES. 72B91 chloric acid into a small test tube and suspend it by a hair through the cork in the bottle, and so arranged that the mouth of the test tube will be above the water. Let a quill glass tube pass through the cork to near the surface of the liquid in the bottle. Weigh the whole apparatus, and then let the test tube and acid be upset, so that the acid will be mixed with the water and mineral. The carbonic acid will now pass off; but as it is heavier than air, a portion will remain in the bottle, which has to be drawn out by an India-rubber tube applied to the mouth, when effervescence ceases. The whole apparatus is again weighed; the difference of the weights will be the carbonic acid. Analysis of Iron Pyrites. 310u. This may contain gold, copper, nickel, arsenic, besides its principal ingredients, sulphur and iron, and sometimes manganese. To determine the Arsenic. Reduce a portion of the pyrites to fine powder; heat it in a test tube in the flame of a spirit lamp. The sulphur first appears as a white amorphous powder, which becomes gradually a lemon yellow, then to tulip red, if arsenic is present. To determine the Sulphur. One hundred grains of the pyrites are digested in nitric acid, to convert the sulphur into sulphuric acid; dilute the solution, and decant it from the insoluble residue, which consists in part of gold. If any is in the mineral, it is readily seen through a lens. This decanted solution will contain the iron, together with oxides of copper, if any is present, and the sulphur as sulphuric acid. Evaporate the solution to expel the greater part of the nitric acid, now dilute with three volumes of water, and add chloride of barium as long as it causes a precipitate. Boil the mixture; filter, wash and ignite the precipitate, which is now sulphate of baryta, in every 100 parts of which there are 13.67 of sulphur. To this sulphur, must be added the sulphur that was found on top of the liquid as a yellow porous lump when digested with the nitric acid. To determine the Iron. Add sulphide of ammonium as long as it will cause a precipitate of sulphide of iron - FeS, whose equivalent is 44; that is, iron 28 and sulphur 16; therefore every one hundred parts of FeS contain 63.63 of iron. But heat to redness and weigh as per oxide of iron = Fe203. In every 100 grains there are 70 of iron. NOTE. Sulphide of ammonia precipitates manganese. To determine the Manganese and Iron separately. Take a weighed portion and dissolve it in aqua regia as above, evaporate most of the acid, and then dilute, leaving the solution slightly acid; pass HS through it, which will precipitate the gold, copper and arsenic, and leave the iron and manganese in solution. Collect the filtrate, to which add chlorate of potassa to peroxide of iron; now add acetate of soda, and then heat to a boiling point; this precipitates the iron, and that alone as peroxide of iron, which collect, wash, dry, weigh, and heat to redness; the result is Fe203, having 70 per cent. of iron. To find the Manganese, neutralize the last filtrate, and add hypochlorite of soda, let it stand for one day, then the manganese will be precipitated as binoxide of manganese = Mn02; collect, dry, etc. In every 100 grains of it, there are 63.63 of manganese. 72B92 QUANTITATIVE ANALYSBS. Analysis of Copper Pyrites. 810v. The moisture is determined as in sec. 310T. To determine the Sulphur. Proceed as in sec. 310u, by reducing 100 grains to powder, then boil in aqua regia until the sulphur that remains insoluble collects into a yellowish porous lump. Dilute the acid with three volumes of water, filter and wash the insoluble residue (consisting of sulphur and silica) until the whole of the soluble matter is separated from it. Reserve the insoluble residue for further examination. Now evaporate the filtered solution so as to expel the nitric acid, and add some hydrochloric acid from time to time, so as to have IICl in a slight excess. From this solution precipitate the sulphur, as sulphuric acid, by chloride of barium, (as in 310u.) Collect the precipitate, wash, dry and weigh, as has been done for iron pyrites. To determine the Copper. To the filtered solution add hydrosulphuric acid, which precipitates the copper as sulphide of copper = CuS. This precipitate is washed with water, saturated with IIS. The precipitate and ash of the filter is poured into a test tube or beaker, and a little aqua regia added to oxidize the copper. Then boil and add caustic potassa, which will precipitate the copper, as black oxide of copper, CuO, having 79.84 per cent. of copper. To determine the sulphur and siliceous matter in the above residue. Let the residue be well dried and weighed, then ignited to expel the sulphur; now weighed, the difference in weight will be the sulphur, which, added to the weight of sulphur found from the sulphate of baryta, will give the whole of the sulphur. The siliceous matter is equal to the.weight of the above residue after being ignited. To determine the Iron. The solution filtered from the sulphide of copper is now boiled to expel the ilydrosulphuric acid, filtered, and then heated with a little nitric acid to reduce the iron to a state of peroxide. To this add ammonia in slight excess, which precipitates the iron as a peroxide. This filtered, dried and weighed, will contain, in every 100 grains, 70 grains of iron; because 40: 28:: 100. Here 28 is the atomic weight of iron, and 40 that of sesquioxide of iron Fe2 03 = 56 + 24= 80, but 80 and 56 are to one another as 40 is to 28. Those marked with an asterisk (*) are the most delicate tests. 310w. Sulphuret of Zinc, (blende) may contain Iron, Cadmium, Lead, Copper, Cobalt and Nickel. The mineral is dissolved in aqua regia. Collect the sulphur as in sec. 310T, and expel the NO5 by adding HIC and evaporating the solution, which dilute with water, and again render slightly acid by IC1. To this acid solution (free from nitric acid) add 1IS, which precipitates all the copper, lead and cadmium, and leaves the iron, manganese and zinc in solution. Let the precipitate = A. To determine the Iron, neutralize the solution with ammonia, and precipitate the iron by caustic ammonia, or better by succinate of ammoniaCollect the precipitate, and heat to redness in the open air, which will give peroxide of iron - FE203, which has 70 per cent. of iron. To determine the Zinc. The last filtrate is to be made neutral, to which add sulphide of ammonium, which precipitates the zinc from magnesia, QUANTITATIVB ANALYSES. 72B93 lime, strontia or baryta, as sulphide of zinc. Pour the filtrate first on the filter, then the precipitate. Collect, dry and heat to redness, gives oxide of zinc = ZnO, having 80.26 per cent. of zinc. We may have in the reserved precipitate A, copper, lead and cadmium. To determine the Cadmium. Dissolve A, in N06, and add carbonate of ammonia in excess, which will precipitate the cadmium. Collect the precipitate and call it B. To the filtrate add a little carbonate of ammonia, and heat the solution when any cadmium will be precipitated, which collect and add to B, and heat the whole to redness to obtain oxide of cadmium, which has 87.45 per cent. of cadmium. To determine the Copper, make the last filtrate slightly acid. Boil the solution now left with caustic ammonia, collect and heat to redness, the result will be oxide of copper CuO, having 80 per cent. of Cu. To determine the Lead. The lead is now held in.solution, render it slightly acid and pass a current of HS, which will precipitate black sulphide of lead; if any = PbS, which collect and heat to redness to determine as oxide of lead = PbO, which has 92.85 per cent. of lead. To separate Zinc from Cobalt and Nickel. The mineral is oxidized as above, and then precipitated from the acid solution by carbonate of soda. The precipitate is collected and washed with the same reagent, so as to remove all inorganic acids. The oxides are now dissolved in acetic acid, from which HS will precipitate the zinc as sulphide of zinc = ZnS, which oxidize as above and weigh. To separate the oxides of Nickel and Cobalt. Let the oxides of nickel and cobalt be dissolved in HC1, and let the solution be highly diluted with water; about a pound of water to every 15 grains of the oxide. Let this be kept in a large vessel, and let it be filled permanently with chlorine gas for several hours, then add carbonate of baryta in excess; let it stand for 18 hours, and be shaken from time to time. Collect the precipitate and wash with cold water; this contains the cobalt as a sesquioxide, and the baryta as carbonate. Reserve the filtrate B. Boil the precipitate with HCl, and add S03, which will precipitate the baryta and leave the cobalt in solution, which precipitate by caustic potassa, which dry and collect as oxide of nickel. The nickel isprecipitated from the filtrate B, by caustic potassa, as oxide of nickel, which wash, dry and collect as usual. To separate Gold, Silver, Copper, Lead and Antimony. 310x. The mineral is pulverized and dissolved in aqua regia, composed of one part of nitric acid and four parts of hydrochloric acid. Decant the liquid to remove any siliceous matter. Heat the solution and atId hydrochloric acid which will precipitate the silver as a chloride, which wash with much water, dry and put in a porcelain crucible. Now add the ash of the filter to the above chloride of silver, on which pour a few drops of N05, then warm the solution and add a very few drops of HCl to convert the nitrate of silver into chloride of silver. Expel the acid by evaporation. Melt the chloride of silver and weigh when cooled. When washed with water any chloride of lead is dissolved; but if we suspect lead, we make a concentrated solution, and precipitate both lead and silver aschlorides by HCI; then dissolve in NO5 and precipitate the lead by caustic potassa as oxide of lead, leaving the silver in solution, which if acidified, *:.;>. '. '.,!,.,,,;,,, 2,,, 7Q2B4 QUANTITATIVE ANALYSES. and HS passed through it, will precipitate the silver as sulphide of silver which heat to redness, and weigh as oxide of silver. To determine the Gold. We suppose that every trace of NO5 is removed from the last filtrate and that it is diluted. Then boil it with oxalic acid, and let it remain warm for two days, when the gold will be precipitated, which collect and wash with a little ammonia to remove any oxalate of ~copper that may adhere to the gold. Heat the dried precipitate with the ash of the filter to redness, and weigh as oxide of gold AuO, which has 96.15 per cent. of gold. To determine the Copper. To the last filtrate diluted, add caustic potassa at the boiling point, which will precipitate the copper. Wash the prec. with boiling water, dry, heat to redness, and weigh as protoxide of copper = CuO. In every 100 grains there are 79.84 grains of copper. To separate Lead and Bismuth. The mineral is first dissolved in N05, then add S03 in excess, and evaporate until the N05 is expelled. Add water, then the lead is precipitated as sulphate of lead, which collect, etc. In every 100 grains there are 68.28 of lead. The bismuth is precipitated from the filtrate by carbonate of ammonia. The precipitate is peroxide of bismuth = Bi203, which collect, etc. This prec. has 89.91 per cent. of bismuth. To determine the Antimony. Let a weighed portion be dissolved in N05. Add much water and evaporate to remove the acid, leaving the solution neutral. Now add sulphide of ammonium, which precipitates the alumina, cobalt, nickel, copper, iron and lead. Collect the filtrate, to which add the solution used in washing the precipitate. Concentrate the amount by evaporation and render it slightly acid Then add hydrochloric acid, which precipitates the silver as a chloride, leaving the antimony in solu'tion, which is precipitated by caustic ammonia as a white insoluble prec. SbOG, which, when dried, etc., contains 84.31 per cent. of antimony. NOTE. The caustic ammonia must be added gradually. For the difference between antimony and arsenic, see p. 72B79. To determine Mercury. 310Y. Mercury is determined in the metallic state as follows: There is a combustion furnace made of sheet iron about 8 inches long, 5 inches deep, and 4 inches wide. There is an aperture in one end from top to within 2 inches of the bottom, and a rest corresponding within 1 inch of the other end. A tube of Bohemian glass is opened at one end, and bent and drawn out nearly to a point at the other. The bent part is to be of such length as to reach half the depth of a glass or tumbler full of water and ice, into which the fine point of the reducing tube must be kept immersed during the distillation of the mercury. Fill the next inch to the bottom or thick end with pulverized limestone and bicarbonate of soda; then put in the mineral or mercury. Next 2 inches of quick or caustic lime, then a plug of abestoes. The tube is now in the sheet-iron box and heated with charcoal, first heating the quick lime, next the mineral, and lastly the limestone and soda. Allow the process to go on some time, until the mercury will be found condensed in the glass of water, which collect4dry on blotting paper, and.weigh.-Graham's Chemistry..:; I/ WATER. 72B95 Otherwise. Dissolve the mineral in HC1. Add a solution of protochloride of tin in Cl in excess, and boil the mixture. The mercury is now reduced to the metallic state, which collect as above. To determine Tin. Dissolve in HC1 and precipitate with HS in excess, letting it remain warm for some hours. Collect the precipitate and roast it in an open crucible, adding a little N05 so as to oxidize the tin and the other metals that may be present. To a solution of the last oxide, add ammonia and then sulphide of ammonium, which will hold the tin in solution and precipitate the other metals of class 3. See p. 72B74: If we suspect antimony in the solution, the reagent last used must be added slowly, as antimony is soluble in excess of the reagent. I~ ~ WA T E R. 310z. Distilled water is chemically pure. Ice and rain water are nearly pure. Distilled water at a temperature of 60~ has a specific gravity of 1000. That is, one cubic foot weighs 1000 ounces = 621 lbs., containing 6.232 imperial gallons = 7.48 United States gallons. NOTE. Engineers in estimating for public works, take one cubic foot of water - 61 imperial gallons, and one cubic foot of steam for every inch of water. Water, at the boiling point, generates a volume of steam = to 1689 times te volume of water used. The volume of steam generated from one inch of water will fill a vessel holding 7 gallons. Water presses in all directions. Its greatest pressure is at two-thirds of the depth of the reservoir, measured from the top. The same point is that of percussion. Greatest density of water is at 39~ 30/, from which point it expands both ways. Ice has a specific gravity of 0.918 to 0.950. The water of the Atlantic Ocean has a specific gravity of 027; the Pacific Ocean = 1.026; the Mediterranean (mean) = 1.05; Red Sea, at the Gulf of Siuz = 1.039. MINERAL WATERS, are carbonated, saline, sulphurous and chalybeate. Carbonated, is that which contains an abundance of carbonic acid,*with some of the alkalies. This water reddens blue litmus, and is sparkling. Saline, is that in which chloride of sodium predominates, and contains soda, potassa and magnesia. Sulphurous, is known by its odor of rotten eggs, or sulphuretted hydrogen, and is caused by the decomposition of iron pyrites, through which the water passes. The vegetation near sulphur springs has a purple color. Chalybeate, is that which holds iron in solution, and is called carbonated when there is but a small quantity of saline matter. It has an inky taste, and gives with tincture of galls, a pink or purple color. It is called sulphated when the iron held in solution is derived from iron pyrites, and is found in abundance with the smell of sulphuretted hydro4 gen. The chalybeate waters of Tunbridge and Bath in England, derive 'their strong chalybeate taste from one part of iron in 35,000 parts of water, or two grains of iron in one gallon of the water. Water traverse "~rc 1~. - jf:i i-: 72B96 WATER. ing a mineral country, is found to contain arsenic, to which, when found *in chalybeate, chemists attribute the tonic properties of this; water. Hoffman finds one grain of arsenic per gallon in the chalybeate well of Weisbaden. Mr. Church finds one grain of arsenic in 250 gallons of the river Whitbeck in Cumberland, England, which water is made to supply a large town. Arsenic has been found in 46 rivers in France. The springs of Vichy, of Mont d'Or and Plombiers, contain the 125th part of a grain of arsenic in the gallon. If lime is present, oxalate of ammonia gives a white prec. If chloride of sodium, nitrate of silver gives a prec. not entirely dissolved in nitric acid. If an alkaline carbonate, such as bicarbonate of lime. Arsenic nitrate of silver gives a primrose yellow prec. An alkaline solution of logwood, gives a violet color to the water if lime is present. The solution of logwood gives the same reaction with bicarbonate of potassa and soda. To distinguish whether lime or potassa and soda are present, we add a solution of chloride of calcium, which gives no precipitate with bicarbonate of lime. Sulphuric acid, is present, if, after sometime, nitrate of baryta gives a prec. insol. in nitric acid. Carbonate of lime is present, if the water when boiled appears milky. Lime water as a test, gives it a milky appearance. Organic matter is precipitated by terchloride of gold, or a sol*on of acetate of copper, having twenty grains to one ounce of water. After applying the acetate of copper, let it rest for 12 hours; at the end of which time all the organic matter will be precipitated. Organic matter may be determined byiadding a solution of peenanganate of potassa, which will remain colored if no organic matter is present; but when any organic substance is held in solution, the permanganate solution is immediacy discolored. We make a permanganate solution by adding some permanganate of potassa to distilled water, till it has a deep amethyst red tint. We now can compare one water with another by the measures of the test, sufficient to be discolored by equal volumes of the waters thus compared. Carbonates of lime and magnesia, also sulphate of lime, act injuriously on boilers by forming incrustations. The presence of chloride of sodium and carbonate of lime in small quantities, as generally found in rivers, is not unhealthy. M. Boussingault has proved that calcareous salts of potable water, in conjunction with those contained in food, aid in the development of the bony skeleton of animals. Taylor says that the search for noncalcareous water is a fallacy, and' that if lime were not freely taken in our daily food, either in solids or liquids, the bones would be destitute of the proper amount of mineral matter for their normal development. Where the water is pure, lead pipes should not be used, as the purest water acts the most on lead. Let there be a slip of clean lead about six to eight inches square immersed in the water for 48 hours, and exposed to the air. Let the weight before and after immersion be determined, and then a stream of sulphuretted hydrogen made to pass through the I --. *1 -;:s HYDRAULICS. 72B97 water and then into the supposed lead solution, which will precipitate the lead as a black sulphide of lead. Taylor says, that water containing nitrates or chlorides in unusual quantity, generally acts upon lead. Water in passing through an iron pipe, loses some if not all of its carbonic acid, thereby forming a bulky prec. of iron, which is carried on to meet the lead where it yields up its oxygen to the lead, forming oxide of lead, to be carried over and supplied with the water, producing lead disease. It is to be hoped that iron supply pipes or some others not oxidizable, will be used. HYDRAULICS. SUPPLY OF TOWNS WITH WATER. 310z. Water is brought from large lakes, rivers or wells. That from small lakes is found to be impure, also that from many rivers. A supply from a large lake taken from a point beyond the possibility of being rendered impure is preferable, provided it is not deficient in the mineral matter required to render it fit for culinary purposes. The water must be free from an excess of mineral, or organic matter, and be such as not to oxidize lead. Solid matter in grains per gallon, are as follows in some of the principal places: Loch Katrine in Scotland, Loch Ness in Annandale, River Thames at London, "( "( Greenwich, cc" " Hampton, Mean of 4 English rivers, Rhone at Lyons, France, Seine at Paris, Garonne at Toulon, Rhine at Basle, 2 Danube at Vienna, 2 Scheldt, Belgium, 23.36 Schuylkill, Philadelphia. 27.79 Croton, N. Y., 16 Chicago river, 20.75 Lake Michigan 2 miles out, 12.88 Cochituate at Boston, 20 St. Lawrence, near Montreal, 9.56 Ottawa, " " 11.97 Hydrant at Quebec, 10.15 20.88 4.49 4.16 20.75 8.01 3.12 11.04 4.21 2.5 Water drawn from wells contains variable quantities of mineral matter, which, according to Taylor, is from 130 to 140 grains in wells from 40 to 60 feet deep. The artesian wells which penetrate the London clay, contain from 50 to 70 grains in the imperial gallon. Catch basin, or water shed, is that district area whose water can be impounded and made available for water supply. One-half the rain-fall may be taken as an approximate quantity to be impounded, which is to be modified for the nature of the soil and local evaporation. Mr. Hawkesly in England collects 48 per cent. of the rain-fall. Mr. Stirrat in Scotland, finds 67 " " In Albany, U. States, 40 to 60 per cent. may be annually collected. The engineer will consult the nearest meteorological observations. ANNUAL RAIN-FALL. 810A*. The following table of mean annual authentic sources. That for the United Statet rological Register for 1855. 114.,: ":.. rain-fall is compiled from _.. i __.. 318 I roIm te Army ieteo'.:. g 1'..::..' l.:. 1 72B98 HYDRAULICS. Penzance, England, 43.1 Plymouth, " 35.7 Greenwich, " 23.9 Manchester, " 27.3 Keswick, Westmoreland, 60 Applegate, Scotland, 33.8 Glasgow, " 33.6 Edinburgh, " 25.6 Glencose, Pentlands, Scotland, 36.1 Dublin, Ireland, 30.9 Belfast, " 35 Cork, " 36 Derry, " 31.1 St. Petersburg, Russia, 16 Rome, Italy, 36 Pisa, " 37 Zurich, Switzerland, 32.4 Paris, France, 21 Grenada, Central America, 126 Calcutta, E. Indies, 77 Detroit, Michigan, 30.1 Ft. Gratiot, " 32.6 Ft. Mackinaw, Michigan, 23.9 Milwaukee, Wis.,. 30.3 Ft. Atkinson, Iowa, 39.7 Ft. Desmoines, " 26.6 Ft. Snelling, Minnesota, 25.4 Ft. Dodge, " 27.3 Ft. Kearney, Nebraska, 28 Ft. Laramie, " 35 Ft. Belknap, Texas, 22 Brazos Fork, " 17.2 Ft. Graham, " 40.6 Ft. Croghan, " 36 6 Corpus Christi, Texas, 41.1 Ft. McIntosh, " 18.7 Ft Filmore, New Mexico, 9.2 Ft. Webster, " 14.6 Santa Fe, New Mexico, Ft. Deroloce, " Ft. Yuma, " San Diego, " Monterey, " San Francisco, California, Hancock Barracks, Maine, Ft. Independence, Mass., Ft. Adams, Rhode Island, Ft. Trumbull, Connecticut, Ft. Hamilton, N. Y., West Point, " Plattsburgh, " Ft. Ontario, Ft. Niagara, " Buffalo, ( Ft. Miflin, Penn., Ft. McHenry, Maryland, Washington City, Ft. Monroe, Virginia, Ft. Johnston, N. Carolina, Ft. Moultrie, South Carolina, Oglethorp, Georgia, Key West, Florida, Ft. Pierce, " Mt. Vernon, Alabama, Ft. Wood, Louisiana, Ft. Pike, " New Orleans, Ft. Jessup, " Ft. Town, Indian Territory, Ft. Gibson, " Ft. Smith, Arkansas, Ft. Scott, Kansas, Ft. Leavenworth, Kansas, Jefferson, Missouri, St Louis, " 19.8 16.6 10.4 12.2 24.5 23,5 37 35.3 52.5 45.6 43.7 54.2 33.4 30.9 31.8 38.9 45.3 42 41.2 50.9 46 44.9 53.3 47.7 63 63.5 60 71.9 50.9 45.9 51.1 36.5 42.1 42.1 30.3 37.8.42 Daily supply of water to each person in the following cities: New York, 52 gallons. Boston, 97. Philadelphia, 36. Baltimore, 25. St. Louis, 40. Cincinnati, 30. Chicago, 43. Buffalo, 48. Albany, 69. Jersey City, 59. Detroit, 31. Washington, 19. London, 30. Reservoirs. The following is a list of some of the principal reservoirs with their contents in cubic feet and days' supply: Rivington Pike, near Liverpool, 504,960,000 cubic feet, holds 150 days' supply. Bolton, 21 millions cubic feet = 146 days' supply. Belmont, 75 million cubic feet = 136 days' supply. Bateman's Compensation, near Manchester, has 155 million cubic feet. Bateman's Crowdon, near Manchester, 18,493,600 cubic feet. Bateman's Armfield, near Manchester, 38,755,556 cubic feet. Longendale, 292 million cubic feet = 74 days' supply. Preston, 4 reservoirs, 26,720,000 cubic feet = 180 days' supply. Compensation, Glasgow, 12 millions cubic feet. Croton, New York, 2 divisions, 24 millions cubic feet. Chicago, Illinois, the water will be, in 1867, taken from a point two miles from the shore of Lake Michigan, in a five-foot tunnel, thirty-two feet under the bottom of the Lake, thus giving an exhaustless supply of ISK -^ '* - * * ': HYDRAULICS. 72B99 pure water. The water now supplied is taken from a point forty-five feet from the shore, and half a mile north of where the Chicago River enters Lake Michigan, consequently the supply is a mixture of sewage, animal matter and decomposed fish, with myriads of small fish as unwelcome visitors. CONDUITS OR SUPPLY MAINS. 310B*. Best forms for open conduits, are semi-circle, half a square, or a rectangle whose width = twice the depth, half a hexagon, and parabolic when intended for sewering. (See sec. 133.) Covered conduits ought not to be less than 3 feet wide and 3~ high, so as to allow a workman to make any repairs. A conduit 4 feet square with a fall of 2 feet per mile, will discharge 660,000 imperial gallons in one hour. The conduit may be a combination of masonry on the elevated grounds, and iron pipes in the valleys; the pipes to be used as syphons. The ancients carried their aqueducts over valleys, on arches, and sometimes on tiers of arches. They sometimes had one part covered and others open. Open ones are objectionable, owing to frost, evaporation and surface drainage. DISCHARGE THROUGH PIPES AND ORIFICES. 1 0c*. Pipes under pressure. Pipes of potter's clay, can bear but a light pressure, and therefore are not adapted for conveying water. Wooden Pipes, bear great pressure, but being liable to decay, are not to be recommended. Cast Iron Pipes, should have a thickness as follows: t = 0.03289 - 0.015 D. Here d - diameter, and t = thickness of the metal. D'Aubisson's HIydraulics. t - 0.0238, d + 0.33. According to Weisbach. Claudel gives the following, which agrees well with Beardmore's table of weight and strength of pipes. t = 0.00025 h d for French metres. t = 0.00008 h d for English feet. Here t - thickness, h = total height due to the velocity, and d = diameter. Lead Pipes, will not bear but about one-ninth the pressure of cast iron, and are so dangerous to health, as to render them unfit to be used for drawing off rain water, or that which is deficient in mineral matter. The pressure on the pipe at any given point, is equal to the weight of a column of water whose height is equal to that of the effective height, which is the height, h diminished by the height due to the velocity in the pipe. Pressure = h - 015,536 v2. Here v is the theoretical velocity. Torricilli,' Fundamental Formula, is V = /2 g h for theoretical velocity. v = m 1/2 g h for practical or effective velocity. The value of 2g is taken at 64.403 as a mean from which it varies with the latitude and altitude. The value of g can be found for latitude L, and altitude A, assuming the earth's radius = R. 2A g = 32.17 (1.0029 Cos. 2 L) X (1 - ants;;..~~~~~~~~~~~~~~~~~~~c 72B100 HYDRAULICS. g = 20887600 (1.0016 Cos. 2 L) v = m '2 gh = 8.026 m V/h = mean velocity. Q = 8.025 A m /h = discharge in cubic feet per second. 8A=- -- sectional area. 8.025 m i/h. -/h Q- from which h is found. 8.=025 m A The value of m, the coefficient of efflux is due to the vena contracts. Its value has been sought for by eminent philosophers with the following result: As the prism of water approaches an outlet, it forms a contracted vein,(vena contracta) making the diameter of the prism discharge less than that of the orifice, and the quantity discharged consequently less by a-multiplier or coefficient, m. The value of m is variable according to the orifice and head, or charge on its centre. Vena Contracta. The annexed figure shows the proportions of the contracted vein for circular orifices, as found by Michellotti's latest experiments. A B is the entrance, and a b the corresponding diameter at outlet; that is the theoretical orifice, A B, is reduced to the practical or actual one, a b. When A B = 1, then C D = 0.50, and a b = 0.787; therefore the area of the orifice at the side AB-1 X.785 and that at ab=.7872 X 0.7854; that is the theoretical is to the actual as 1 is to 0.619.. m =0.619. The values of m have been given by the following: Dr. Bryan Robinson, Ireland, in 1739, gives m = 0.774. Dr. Mathew Young, do. 1788, ".623. Venturi, Italy, ".622. Abbe Bossuet, France, ".618. Michellotti, Italy, ".616. Eytelwein, Germany, ".618. Castel, France, 1836, ".644. Marriot, do ".692. Rennie, England, ".626. Xavier, France, ".615. NOTE. It is supposed that Dr. Robinson used thick plates, chamfered or rounded on the inside, thereby making it approach the vena contracta, and consequently increasing the value of m or coefficient of discharge. Rejecting Robinson and Marriot's, we have a mean value of m -0.622, which is frequently used by Engineers. Taking a mean of Bossuet, Michellotti, Eytelwein and Xavier, we find the value of m = 0.617, which appears to have been that used by Neville in the following formulas, where A = sectional area of orifice, r radius, Q discharge in cubic feet per second, h = heighth of water on the centre of the orifice, and m = 0.617 = coefficient of discharge. s iN.. J ' HYDRAULICS. When h= r, then Q =8.025 m VWX.960 A. Do. 1.25 r, do.. do..978 A. 72B101 Do. Do. Do. Do. Do. Do. Do. 1. 5 r, do. do..978 A. 1.75 r, do. do..989 A. 20r, do. do. *.992 A. 3,r, do. do..996 A. 4 r, do. do..998 A. 5 r, do. do..9987 A. 6 r, do. do..9991 A. Hence it appears, that when h = r, the top of the orifice comes to the surface, and that when h becomes greater or equal to 8 r, that the general equation Q = 8.08 m I/ H X A, requires no modification. The following 6 formulas are compiled from Neville's Hydraulics. In the annexed figure, 1, 8, 4 and 6 are semi-circular, and 2 and S are circular orifices. The value of Q may be found from the following simple formulas, where A is the area of each orifice, and m = 0. 617,-the coefficient of efilux. 2. Q= 4.7553 A1/ 8. Q=03.6264 A iVr. 4. Q=4.9514 V hxA.(1+li.(d. 4.71-2 Ii 2h"i2' 1 r 5 r4 6. Q =4.9514 i/h >( A, (I~ 1 r 1 r 471 1 -- 2 Adjutages, with cylindrical tubes, whose lengths = 2j times their diameters, give m = 0.815. Michellotti, with tubes j an inch to 3 inches diameter and head over centre of 3 to 20 feet, found m = — 0.813. The same result has been found by Bidone, Eytelwein and D'Aubisson. Weizback, from his experiments, gives m = 0.815. Hence it appears that cylindrical tubes will give 1.825 times as much as orifices of the same diameter in a thin plate. For tubes in the form of the contracted vein, mn = 1.00. For conical tubes converging on the exterior, making a converging < of UPj, m = 0.95. For conical'diverging the narrow end toward the reservoir and making the diverg~ijig <= 50 6' m 1.46, and the inner diameter to the outer as 1 is to 1.27. NovE. The adjutagve or tube, must exceed half the diameter (that length being due to the- contracted vein) so as to exceed the quantity discharged through a thin plate. Circular Onifices.Q 3.908 d2 i Cylindrical adjutage as above. Q 5.168 d2 ih 72B102 HYDRAULICS. Tube in theform of vena contracta. Q = 5.673d2 Vh. In a compound tube, (see fig., sec. 310c*) the part A a b B is in the form of the contracted vein, and a b E F a truncated cone in which D G - 9 times a b and E F - 1.8 times a b. This will make the discharge 2.4 times greater than that through the simple orifice. (See Byrne's Modern Calculator, p. 821.) Orifices Accompanied by Cylindrical Adjutages. When the length of the adjutage is not more than the diameter of the orifice, then m = 0.62. Length 2 to 3 times the diameter, m = 0.82. 36 times m = 68. Do. 12 do. m -.77. 43 " m = 63. Do. 24 do. m -=.73. 60 " m -60. 310D*. Orifices Accompanied with Conical Converging Adjutages. When the adjutage converges towards the extremity, we find the area of the orifice at the extremity of the adjutage the height h of the water in the reservoir above the' same orifice. Then multiply the theoretical discharge by the following tabular coefficients or values of m: Let A = sectional area, then Q = m A 1/2 gh =8.03 mA/H. Angle of Coefficients of the Angle of Coefficients of the Convergence Discharge. Velocity. Convergence Discharge. Velocity. 00 0O.829.830 13 24/.946.962 1 36.866.866 14 28.941.966 8 10.895.894 16 36.938.971 4 10.912.910 19 28.924.970 6 26.924.920 21 00.918.974 7 62.929.931 23 00.913.974 8 68.934.942 29 68.896.975 10 20.938.950 40 20.869.980 12 40.942.955 48 60.847.984 The above is Castel's table derived from experiments made with conical adjutages or tubes, whose length was 2.6 times the diameter at the extremity or outlet. In the annexed figure A C D B represents Castel's tube where m n is 2.6 times C D and angle A 0 B = < of convergence. NOTE. It appears that when the angle at 0 is 13j degrees the coefficient of discharge will bejthe greatest. The discharge may be increased by making m n equal to C D, A B = 1.2 times C D, and rounding.or ohamfering the sides at A and B. In the next two tables, we have reduced Blackwell's coefficient from minutes to seconds, and call C = m. Q = 8.03 m A Vh or Q = C A/h, where C is the value of 8.03 m in the last column. h is always taken back from the overfall at a point where the water appears to be still. Experiments 1 to 12, by Blackwell, on the Kennet and Avon Canal. Experiment 13, by Blackwell and Simpson, at Chew Magna, England.::...(/L HYDRAULICS. 72BI~OS 810E*. OVERFALL WEIRS, COEFFICIENT OF DISCHARGE. Value of No. Description of Overfall. Head in inches. Value ofm 8.08 m o C. 1 2 3 4 5 6 7 8 Thin plate 8 feet long. '' I 4 446 " 10 feet long. Plank 2 inches thick with a notch 8 feet long. Plank 2 in. thick, notch 6 ft Pl'k 2 in. thick, notch 10 ft. 44 44 Same as 5, with wing walls Overfall with crest 8 feet. Wide sloping 1 in 12-3 ft. Long like a weir. Same as 7, but slopes 1 in 18 Same as 7 & 8 but 10 ft long 4 4 4 4 Level crest 8 ft w. & 6 long Same as 11 but 10 ft. long. Overfall bar 10 feet long And 2 inches thick. 44 ~4 1 to 3 8 to 6 1 to 8 3 to 6 6 to 9 1 to 8 3 to 6 6 tolO 1 to 3 3 to 6 6 to 9 9 to14 1 to 8 3 to 6 6 to 9 9 to14 1 to 2 4 to 5.440.402.601.435.370.342.384.406.359.396.392.358.346.397.374.336.476.442 8.533 3.228 4.023 8.493 2.971 2.746 8.083 3.260 2.883 3.179 8.148 2.878 2.778 3.191 3.003 2.698 3.822 3.549 1 to 3 3 to 6 6 to 9 1 to 3 3 to 6 6 to 9 1 to 4 4 to 8 1 to 3 3 to 6 6 to 9 3 to 7 7 to12 1 to 5 5 to 8 8 tolO 1 to 3 3 to 6 6 to 9.342.328.311.362.345.332.328.350.305.311.318.330.310.306.327.313.437 499.606 2.746 2.634 2.497 2.907 2.737 2.666 2.634 2.810 2.449 2.497 2.553 2.649 2.489 2.467 2.626 2.613 8,509 4.007 4.055 BLACKWELL'S SECOND EXPERIMENTS. Overfall of cast iron, 2 inches thick, 10 ft. long, square top. Canal.had wing walls, making an angle of 45 degrees. Head in feet. Coefft. m1Head in ft.1Coefft. r Head inft. Coefft. m.083 to.073.083 to.088.182 to.187.229.244.240.242.245.250 to.252.833.591.626.682.665.670.655.653.654.725.745.344.359.365.361.375.416.423.451.453.495.743.760.741.750.725.780.781.749.761.728.600.516.521.678.639.667.734.745.760.749.748.747.772.717.802.737.750.781 - --- From the above we have a mean value of m= 0.723. 72B104 - HYDRAULICS. The reservoir used on the Avon and Kennet canal, in England, contained 106,200 square feet, and was not kept at the same level, but the quantity discharged for the experiment was not more than 444 cubic feet, which would reduce the head but.06 inch. In the Chew Magna we have an area of 6717 square feet kept constantly full by a pipe 2 inches in diameter from a head of 19 feet. The inlet of the pipe to the overfall being 100 feet, consequently the water approaches the fall with a certain degree of velocity, which partially accounts for the difference in value of m, in experiments 13 and 6. Poncelet and Lebros' experiments on notches, 8 inches long, open at top: Size of Notches. Coefficient m. Size of Notches. Coefficient m. 8 X 0.4.636 8 X 3.2.695 8 X 0.8.626 8 X 4..92 8 X 1.2.618 8 X 6..690 8 X 1.6.611 8 X 8..686 8 X 2.4.601 8 X 9..677 From these small notches we have a mean value of m.603. -Du Buat's experiments on notches 18.4 long, give a mean coefficient m =.682. Smeaton and Brindley, for notches 6 inches wide and 1 to 6j high, give m.637. Rennie, for small rectangular orifices, gives as follows: Head 1 to 4 feet, orifice 1 inch square, mean value of m =.613. t" " "' 2 inches long and 3 high, m =.613. " " " 2 inches long and Q deep, m =.682. The following table is from Poncelet and Lebros' experiments on covered orifices in thin plates. Width of the orifice.20 metre (about 8 inches) 1 = length, and h = height of the orifice. 8101*. HEIGHT OF THE ORIFICES. Head on cen- 0.20 m 0.01 m 0.05 m 0.08 m 0.02 m 0.01 m tre of orifce. 1 h. 1 2h I 4h 1 6.7 h 1 10h 1 20 h m m m m m m m 0.02........................660.698.03.............688.660.691.04........... 612.640.659.686.06............617.640.669.682.06 *......90.622.644.668.678.08.......600.626.639.667.671.10.......605.628.638.666.667.12,672.609.630.637.664.664.16.686.611.631.636.663.660.20.692.618.634.634.660.666.80 *.698.616.682.632.646.660.40.600.617.631.631.642.647.60.602.617.631.630.640.643.70.604.616.629.629.637.638 1.00.606.615.627.627.682.627 1.80.604.613.623.623.626.621 1.60.602.611.619.619.618.616 2.00.601.607.613.618.613.613 8.00.601.603.606.607.608.609 C. ~ I I HYDR 1 AU LICS. 72 t: 105 HIIere the water takes the form of the hydraulic cure, nearly that of a parabolic, and its sectional area - 2 l/I. The co-efficient increases as the orifice approaches the sides or bottom. Let C = coift. of perfect contraction, and C' -- co:fl. of partial contraction, then C' = C +, o q n. —Ne'ille. The presence of a coursoir, mill-race, or channel, has no sensible effect on the discharge, when the head on its centre is not below.50 to.60 metres, for orifice of.20 to.15 metres high,.:0 to.40 for.10 mletres high, and.20 for.05 metres high. The charge on the centre is seilom lbelow the al)ove. ---r-ilwin's Aide,l tmoire, p. 27. 310f. ExatInpl 10: IFro./t z~eville's lyt(rablict, p. 7.-W\hat is the (lischarge in cubic feet per minute fiom an orifice 2 ft. 6 in. long, and 7 in. deep; the upper edge bleing 3 in. under the surface of apparent still water in the reservoir. l. = 2.5 ft. x 7" —: area, S of orifice L --- 1.458 square feet. II = half of 7"' - 3 -: 6.5 in. -—. 0.541666 ft. --.iurface of tle water in the reservoir a!ove the centre of the orifice. 'The square root of 0.541(66( -- \ II -- 0.736. Itead on centre of orifice -= 6.5 in. —: 165 metres. Ratio of length of orifice to its height -—: 4. Then opposite, 165 m(etres, and unler / — 4 i/, find t//t -- 0.616 8.0 x 0.616 x 1O..458 x 0.736:- cubic ft. per secondl. ) -= 4S1.S x 0.(616 x 1.45S x 0.73;6 --- cubic ft. per minute. sV'rt,il/e makes //z — ( 0.628, and(l ) — 30.4 cubic feet. M. I)oileau, in his 7)'aie (dc lat if1Aese di's t'l. toflll'tllCst./, ( Paris. 1854,) recommends Poncelet and Ieleros' value of iti in the general formula. Q = m A '2)gh or( in Ih 2,, Cwomplele conlt-/aionz is wlihen the orifice is remove(l 1.5 in. to twice itslesser diameter of the fluid vein. The Frencl make im: —.625 for sluices near the bottom, discharges either above or under the water. Caste! has found that 3 sluices in a gate did not vary tlhe value of i. 310g. ILet R =-yh(y, mean depthi; V\- surface velocity, by Sec. 312; 1.) -- dialm.; r --- radius of circular orifices;. - mean, and w:-= l)ottom velocities; ( ~ — discharge in cuilic feet per second; 'L - time in seconds A == area of section of conduit; I:- the head; per unit = — height dividedl ly the horizontal distance between the reservoir and out-let. ' == 0.90 \ for rectangular canals, and — 0 0.903 V for those with earthen slopes. - -.oi/lca. 7.S 80 V for large cha:nels,,y I'-roy., -=. 0.835 V for large channels, by Xi/nes, 'tnk/, atnd 1' /'ttni. V surface, W --- bottom velocities. 7' — 0.80 V, and( \\ -=.60 V, by Conference on I)rainage anl( Irrigation at Paris in 1849 and 1850. ( = 8.025 in A \' /h is the general formula wlhere A - sectional area. ( -- quantity in culic feet; h -- height of reservoir; i — = co-efft. of efflux. ) = 8.025 t/ A T \ /h in time 'T. R I = 0.00002427 V + 0.000111416 V2 all in feet, Eytelwein; from which he gives V = Io ' 1J.' in which formulas he puts R = hy ad, mean depth, f = twvice the fall in feet per mile, and I = inclination, = head divided by the length. 115 72/Bl106 IHYDRAUIIICS. V = I R/ is used by Beardmore and many Engineers. 310,'. For clear, straight rivers, with average velocities of 1.5, Nee,i/i gives V - 92.3,' R 1, and for large velocities V - 93.3,' R 1. Ie s.ays that co-effts. decrease rapidly when velocities are below 1.5 ft. per second. In his second edition of his valuable treatise on hydraulics, he states that the best formula proved by experiments for discharges over weirs is. 2 73 (2 = ] 06 (3 /I - V a )/3 a Ir. I ere V = velocity of approach. 310h. i/. oz'a Boilean, in his h /i'. (i de la A.Tes/tre ces cauxt coztranl/es, 1). 345: For dichlarge through orifices, O0 sectional area of reservoir at still water, it = — diff. of level between the summit of the section 0 and that of the section (reintots (' ar'a.) where the ripple begins. Is /1/0 ( 2 ( _ V 2,'- = 8.025 A / -- A2 ~, ()2 -A 0 In his tal)les he makes tie value of an, coi'fft. of contraction for short 'csidlS, or e dy, ' — 0.622, 0.600 when it attains the summit, and 0.688S when the orifice is surrounded by the remtois. 310;. Let (,) - tl quian'ity in feet per second. Q = 8.02.)5 It \ effective discharge in cubic ft. per second, /' = variable. Q = 4.879 A h A orifice surrounded on all sides, z - 0.608 5Q =.04S A I' / orifice surrounded on three sides, s =- 0.629 ( = 5.489 A h orifice coincides with sides and bottom, m -- 0.684 Q = 5.939 A \ /z as last sluice makes angle 60~ against stream, ait = 0.740 O = 6.420 A /' A as last but. sluice makes the angle 45", t = 0.800 = 5.016 A \ sluice vertical, orifice near the bottom, t = 0.625 2 '= 4.2-53 A \ hA 2 sluices, or orifices, within 10 ft. of each other, — = 0.530 Q = 6.019 A / It the flood gates make 160~ with the current, and a = 0.750 that there are 3 sluices guarded to conduct the water into the buckets of a water wheel -= sum of the areas. T v = 5.35 In v' h /= mean vel. for regular orifices, open at top, and is the time required to empty a giveln vessel when there is no efflux, and is double the time required to empty the same when the vessel or reservoir is kept full. T=^ __ ___ =Where S -- sectional area of orifice, and A = that of the 4.013 at S reservoir. -A =. S - ti me required to fall a given depth, II - I4 4.013atSj ) ( 8.0225 i S. S -.025 / i S. + r, ' -- discharge in time t. 4A ( S) = 8.025 t S.' I - /z when reservoir A discharges into A' under water. A S'H T =....- time required to fill the inferior A'. 4.013 mt S___ / A. A'. _ - time to bring both to the same level in canl I 4.013 mz S ~/ A - A' locks. V = 5.35 \' ( a + 0.0349410 w 2 ). Here the water comes to the reservoir with a given velocity, u7. iYI)RAUILICS. 72B107 310i. For D'Ary,'s Formzula, see p. 264. IHe has given for Y2 inch, pipes nm = 65.5 and. -= 65.5 / r s For 1' diameter z, 80.3 ' r s = 1n q' r s 2",,i = 94.8, 4" in =- 101.7, 6" =- 105.3 for 9', m -- 107.8, 12" '- 109.3, 18 - 110.7 24"c diam. — = 1] 1.5 -r s = m \/ r I I rs 2 - for arge gpipes ' == N,- _- 1 18 \ r s 0.000077'26 310i. Neville's,,ncral fior-im/ a fJ/br i/ies aned r'iVrs: ' - 140 (r- i) - (r i)/'5 here r == i y ed, mean depth, and i — inclination. f,-.:ices, in Lowell, Mass.?., has found for over falls, in —.623. (See his valuable experiments imade in Lowell. 7T,':.i'Pson, of Belfast College, Ireland, has found from actual experiimen:-; that for triangular notches, i1 == 0.618, and 0 -0O.317, s- _5 culic feet -.; minute, and h -: head in inches. 'M. Girard syas it is indispen-sible to introduce 1.7 as a co-efiicient, due aqr'.ic plants and irre'ularlities in the bottom and sides of rivers. Then the i-hydraulic mean depth (see Sec. 77,) is found by multiplying the wetted pereter l)y 1.7 and dividing the product into the sectional area. A ve locity of I4 feet per second in sewers prevents deposits.-London 310O. I Spoli,, Zii(uis.-Let ' -- top of edge of vessel, and B == bottoun, ) = orifice in the side, and B S-= horizontal distance of the point where the water is thrown. (See fig. 60.) B 'S -- '2 1v'. 0 B = 20 E, by putting 0 E for the ordinate through 0, making a semi-circle described on F B. 31OK. On the application (of waler as a imotiz'e power: Q = cubic ft. per minute, --- height of reservoir above where the water falls on the wheel, P = theoretical horse-power. 528 I' — = 0.00189 Q( /i, and Q = Avanirlable rite-poiccr'c' --- 12 cubic ft., falling 1 ft. per second, and is generally found - to 66 to 73 per cent. of the power of water expended. Assume the theoretical horse-power as 1, the effective power will be as follows: Over-shot wheels -.68 For turbine wheels,.70 Under-shot wheels,.35 For hydraulic rams in raising water,.80 Breast wheels,.55 Water pressure engines,.80 Poncelet's under-shot.60 Iighl breast wheels,..60 Let 1 = - pressur-e, in lbs., per square inch. 1' - Q, 4333 h and h/ 2.31p ' =.00123 (2 / for over-shot wheels, and Q =- 777 P divided ly / ' --.00113 Q h for high-breast wheels, and Q - 882 P divided by h 1 =.00101 Q, for low-breast wheels, and Q = 962 P divided by h I'-=.00066 Q h for under-shot wheels, and Q = 1511 divided by A 1'.00113 Q k for Poncelet's undershot wheels, and Q = 822 divided by A For under-shot wheels, velocity due to the head x 0.57 will be equal to the velocity of the periphery, and for Poncelet's, 0.57 will be the multiplier. 01. 72BIOS 72B108 1)DRAINAtii AND IRRLGATI()N. 31 0(. I1i,-lh-jressu;re turbines /br- every 1 0-hor-se powper-. h~ 30 40 50 60 70 80 90 100 V:36 42 47 51 55 5 9 63 66 We have seen, S. -E'. of D)edham, in Essex, England, a small stream collected for a few days, in a reservoir, thence passed on an over-shot wheel, and again on an undershot wheel. If p.o-,ssible, let the reservoirs be surroundedl ly shade trees, to preven~t ev-alorationl. 310K. Artlesian JMells may lbe sunk and the wvater raised into tanks to he used for household purposes, irrigating lands, (iriving- small machinery, and extinguiislhifcg fires. 310i.. Reser-voirs arc collected from springs, rivers;, wvells, and raini-falls, impounded on the highecst, available groumi, frdm whence it may he forced to a higher reservoir, from which, by gravitation, to supply inhabitants with water. 310t). landl and City Dr-ainob(e. In dli-aining, a Ihilly distr-ict. -— A main dp(rain, not less than 5 ft. (leep, is made along, the base of thte biill to receive the water coming from it and the adj~acent land s -econdary drains are miade to enter obliquely into the main, these oughlt to be 4 to 5 ft. dIeep, Filled wvith brok-en stonies to a certain height; tiles;. and soles, or pipes;. The first form is termied French dlraining; the last two mentioned are now generally used. In1838 to 1842 we have seen, near Ipswich, Eng-land, drains miale by i(hgging 4 feet d]eep, the bottomi scooped 2 to:3 iniches and filled with strawv made in a rope form, over this was laidI somei b~rushwoo.ld, thene the sod, and then carefully filled. The French (Irains wvere -sometimes 15 inchies deep, 5 inches at bottom and 8 inchies at top, all filled wvith stonie, then coveredl with strluv and filled to the top with earth. in tile droainin- the sole is about 7 inches wide, alwvays ~4 inl. on each side of the tile, and is about 12 to 15 inches, long(, its,, height is- to be one-fourth its (diamieter. The egg, shape is lpreferalble. Never omnit to use the tile, let the g-round be ever so hard. Pipe D;-ains.-1ipes~- of the egg shape are the best; pipes, 2 to 4 in. (liameter have a 4 in. collar. Ini retentive land put 4 feet (leep and 2 7 feet apart; wvhen.:3/,' feet deep, l)ut:33 feet alpart. From the best Elnglishi sources, Nve Find the coml.)arativ~e cost. 2, '2 ft. (leep cost 3,/~ pece addl 11" pence for every additional 6 inlche.5~ inl depth. Profit by thorough dIrainiage is 13 to 20 per cenlt. See Parliamentary R{eport. 310o. in dr-ainin- Cities (and 71-ins our tirst careC is to find an outlet where the sewNage caui be used for- manqure, anwl to avoid discharging it into slu-gish streams. The result.of draininig into the river- Thamnes. and the Chicaguo river with it-s far-faed 1Healy -slough ought to be suifficient warning, to E'ngineers to lbeware of like results. (,Se e S ec. 3 10j. Where the city or- town authorities are not prepared to use the sewage as a fertilizer, and that theie is a river iiear, or through it, let there be intercepting sewers, egg-shaped, with sufficient fall to linsure 2, feet per second, wvhich in London is found sufficient to prevent deposit; should not exceed 4Y2' feet per second. When these main sewers get to a considerable depth, the s~ewa-e is lifted from these into small, covered res DRAINAGE AND IRRIGATION. 72B109 ervoirli, thence to be conveyed to another deep level, and so on until brought far enough to be discharged into the river, or some outlet from which it cannot return. But we hope it will not be wasted; the supply of Guano will fail in a few years, then the people will have to depend on the home supply. SC'Tars under 15 inches diameter are made of earthenware pipes, with collar., laid in cement; 2 foot diameter are 4 inches, or half a brick, thick;; 3 to 5 feet, S inches thick; 6 to 8 feet, 12 inches thick, according to the nature of the earth. Where the soil is quick-sand, the bottom ought to be sheeted, to prevent the sinking of the sewer. As the sewers are made, connecting pipes are laid for house drainage at alout every 20 feet, and man-holes at proper intervals to allow cleansing, Iinshing, and repairing. A plat is on record, showing the location of each sewer, with its connections, man-holes, and grade of bottom, to guide house and yard (drains or pipes, whose fall is one-quarter inch per foot, in Chicago. 310 ). Irriation )f /and. Inz '.it distrcls the land is cut up in about 10-acre tracts; the ditches deep; ponds made at some points to collect some of the water, these ponds to be surroundedl by a fence and shade trees, such as willow and poplar, a place on the North side of it may be sloped, and its entrance well guarded with rails, so that cattle may drink from, but not wade in, the pond, which may be of value in raising fish. a =.).' / 2 af and Q- = - a. Here ' = vel. in feet, a -- area, and f- fall in feet per mile. IA i-rri'gating,, the land is laid off and levelled so that the water may pass from one field to another, and may be overflowed from sluices in canals fed from a reservoir or river. The water from a higher level, as reservoir, may be brought in pipes to a hydrant, where the pressure will be great enough to discharge, through a hose and pipe, the required quantity in a given time. Water or sewage can be thus applied to 10 acres in 12 hours by one man and two boys. The profit by irrigation is very great,-witness the barren lands near Edinburgh, in Scotland, and elsewhere. In England, on irrigated land, they grow 50 to 70 tons of Italian rye grass per acre. Allowing 25 gallons of water to each individual will not leave the sewage too much diluted, and 60 to 70 persons will be sufficient for one acre, applied S times a year. At the meeting of the Social Science Association in England, in 1870, it was decided that the sewage must be taken from the fountain head, as they found it too much diluted, and that alum and lime had been used to precipitate the fertilizing matter, but had failed. They estimated the value due to each person at 8Y3 shillings, but in practice realized but 4 to 5 shillings. lr'. Rawvlinson recommended its application diluted; others advocated the dry earth closet system, which in small towns is very applicable, owing to the facility of getting the dry earth and a market for the soil. 310R. The supply of guano will, in a few years, be exhausted, then necessity will oblige nations to collect the valuable matter that now is wasted. See Sec. 310j. 72uI110 STEAM ElNGINE. 310s. Ott t., 3team Eng-ine. I = horse-power capable of raising 33000 pounds 1 ft. high in 1 minute. P pressure in pounds per square inch. D = diameter of cylinder piston in inches. A = area of cylinder or its piston. S = length of stroke, and 2 S = total length travelled. R = number of revolutions per minute. V - mean vel. of piston in feet per minute. ( = total gallons (Imperial) raised in 24 hours., = quantity raised by each stroke of the piston. C:= pounds of coal required by each indicated horse-power. 2 S A P R If -------- = indicated horse-power. 33000 1) 2 ~ S II -= -- - indicated horse-power for high-pressure engines. 15.6 15.6 I1 1D a — and V — = 128 S * ~-g7 3 D2 2 S II -= --- for condensing engines, from which we have 47 47 1t 3 I) — = and V =- 12S ' S S I) 2 V AdlmiralOt Rule. II = -- - nominal horse-power. 6000 The American Engineers add one-third for friction and leakage. Exancple. The required gallons in 12 hours = 3,000,000; Stroke, 10 feet; number of strokes per minute -= 12; time in. minutes =1440. From the above, we find q -- 173.6 Imperial gallons; d= 22.6 inches-the diameter of the pump, as taken by the American engineers; d — 22, as taken by the English. For much valuable information on the steam engine, see Appleton's (Byrne's) Dictionary of Mechanics, and Haswells' tables. Average duty of a Cornish engine is 70 million lbs., raised one foot high, with 112 lbs. of bituminous coal. Example. From Pole on the Cornish Engine, as quoted by -Hann on the Steam Engine. Cylinder, 70 inches diameter; stroke, 10 feet; pressure per square inch, 45 lbs. during one-sixth the stroke, and during the remainder the steam is allowed to expand. 70 x 70 x 0.7854 -- area of piston -3858 square inches. 10 3848 x 45 x - = pounds raised one foot high -- 288,600. 6 This is the work performed before the steam is cut off. To find tie work done ly expansion.-Find from a table of IIyperlbolic Logarithms for C = 1. 7916, which, multiplied by the work donlj before the steam is cut off, will give the work required, that is, 1,7916 x 288600 Work done after the steam is cut off, 517102 RETAINING WALLS. 7n1 721 I,, I I I 310T. Precssur-e (~f _Fluidls andl Retaining~ Tf al/s. (DEiF-Retaining( Wall is that which sustains a fluid, or that which is liable to slide.) 310. The centr-e of Pr-essur-e is that point in the surface press'ed by any fiuki, to which, if the whole pressure could be applied, the pressure wVould be the sam-e as if diffuised over the whole surface. If to this centre a force equal to the whole pressure lbe applied., it 11 wIlIl keep) it in equilib~rium. 4 -oinst a rectan-lar wa(11 the centre of pressure is~- at two-tlsirds of thle height from the top, and the i ressure I. /. Here w o- specific gravit y of the fluid, and I,ihe leng-th pressedi. in a (ylindrieol vessel or- reserv-.oir the same formula wvill hold good, hy steictituting the circumference for the lnt, 1, of the plane. EIraanp/e.-For a lock-gate 10 ft. long, 8 ft. dle.p, the pressure 64 P - x 10 x 62.5 2-00,000 pounds. AEAalliple. -For a circular reservoir, diameter 20 ft., diepth 10 ft., filled with water, we have 10 x 10 x 20 x 3.1416 x 62.5 P --- -__________~~~:- 196,350 U1)s., the presszure on the sj&les of the reservoir. 'The pressure on the bottom 2- 00 x 20 x.7854 x 62.5 =1.9,635 lbs. Total pressure, 215,985 Its. Dams are built at right angles to the stream en-tering tlse reservoir. All places of a porous 'nature are made impervious to water isy clay or masonry laid in cement; top to be 4 ft. above the water; witin ordinary cases, equal to one-third the height; the inner- slope, next the water, to be 3 to 1; the outer slope 2 to 1. In low Damns, width at top equ"_al to the hieight. Dams, in 01lasonr-y, by the Frenich Engineers, Alor-in anad RornezClef, bottom 0. 7 h, at middle, 0.5 /Ii and top, 0. 3 hi. 310/. Thickness of rectangular walls is fotund from '/1000 0.865 (11 - hi). Here 1000 =-weight of a cubic ft. of water. f weight of 1 cubic foot of masonry, and t req-uiredI thickness, 11 total height, and hli height from tolp of dami to wvater. 1fzundtfzions of Basins ohnl Damis are to rest on solid clay, somnetimnes on concrete, laid with ptudlledl clay. The side next the wvater is laid with stones 12 inches deep, laid edgewise; sometimes they are laid wvith brick. in cement, the outer face covered with sod. A puddled wall is brought tip the middle whose base ==one-third the height, and tLop ==one-sixth the height; the top is made to curve, to carry off the rain water. Wb~ste-zoeir is regulated wvith a wvaste-gate, and made so as to carry off the surplus water; the sluice or gate may be made self-acting. Byroo~sls receives the surface water from the waste-weir, and from the supply streams when not required to enter the reservoir in times of heavy rains audi when the wvater lbecomes mudldy. 310m~. Cascade. Letf = fall from crest of weir, hl, as usual, the hei-ht 4 -~~ of still water above the crest of the weir, v ==5.35 V! 1 and( r ~v, dlistance to which the water will leap; this distance is to 1)0 covered withs large stonies, to b)realc: th~e fall of the water. 7 2j; 1 12 RE.TAINING NVALLS. 31 I0tL. A'eeaining- tJVz/s are sometimes built along the base of the darn. S/. Fel-e Reserv,,oir, destined to feed the Languidoc Canal, in France, -contains 1341 million gallons of water; the dam at its highest Part is 1006,2 feet. One re-servoic in ehiient Eg11YPI contains 35,200 million culbic feet of wvater. Somie are in Spaini holding 35 to 40 million cubic feet-similar ones are founit in France. The Ch/inese collect water into large reservoirs *for the supply of towns and cities, and the irrigation of their lands. The Ilindoos heave built immnense reservoirs to meet the periodlical scar 1ci ty of raini, wAhich happensd once in- about five years. One of their r-es-ervoirs, the Veranumi, contains an area of 35 square miles, madle by a dami 12 miles; long. TFhe evaporation in India for S months is,~inch in depth per day. On.e-fourth of an inch mna' be a safe calculation ini mildler or colder clim-ates:. in Din~s t~/ Maisonry,, buttressies are madle at every 18 to 210 feet. TDepth =-the thickness of the wall, and length dloublie the thicknes-s. Mahan and liarloxe,, in their 'Treatise on Engineering, say, ''It is better to put the material uniformlyv into the wall." oOI 0UT. i'O find the thickness g!f a rectang-ular- wa/i, A B), to resist its lying~ turned or'er on thic Point D. (See Fig. 70.) Let the perpendicular, E F, pasas through the Centre of the rectangle; by Sec. 313 it pase~s through the centre of gravity C,. makes C j) == one-third of B3 C. We have the vertical pressure weight of the wvall, and the lateral pressure equal to that of the pressing fluid or mass. Let -v ' specific gravity of the wvater, and IV that of the wall. We have the pressure of the fluid represented by 11 1) =C 1', and that of the wall by I) F, and TF D II is a bent lever of the first order. I)C' B C By Section 319c, P) W 2 3 )x B C I) Cx W andl — ___ ~-___~ clear of fractions. 3 3 D C x WV,th e ne P -__ __ 2 B C P x 2 B C an1d J1) C ==A B U_ 3 W We have the value of P x 2 B C per lineal foot, and find the value of 3 W for height, B C, and one foot thick, which, divided into P x 2 B C, will give the value of A B or 1) C when on the point of turning over. L'et W v Aweig-ht of material, and S ==weight of water; h = height of wall that of the water, and b — breadth of wvall required, then we heave lx2 I'F -. 62, lbs. =pressure of water against the wall, and 31bx hbw 3b42Nw 2 h 2 lI 3 1) 2 Av 62. 5 - =___, 2 2 REVETMENT WALLS. 72B113 62.5h2= 3b2W __ 62.5 h2 ) 4 /62.5 b = - ---- h / ' ( 3W ) 3W /3 h=b / / 62.5 Example. -Height of dam and water = 20 ft.; specific gravity of wate = 622 lbs., and that of the masonry 120 lbs. —to find thickness b. 62.5 x 20 x 20) 2 b \ - -8.33 feet. 3 x 120 As this formula gives but the thickness, to form an equilibrium, add one foot to the thickness, for safety. Rondelet recommends, to find the required thickness of 1,8 times the calculated pressure, which in this case would be 28800, which divided by 263, gives b2 79.33088, whose square root = 8.91 feet. We prefer to use Roundelet's formula for safety. 310v*. REVETMENT WALLS. In retaining walls we have to support water, but in revetment walls we have to support moveable matter, such as sand, earth, etc. (See fig. 71) Let C = tangent squared of half the angle of repose, which may be taken at 22Y2 deg., which angle is called the angle of rupture, as shown by Coulomb and others. The angle of V D W is the angle of repose, and the angle W D S being half the angle, w D S is the angle of rupture, and the line D S - line of rupture. Assume the angle W D S = 223~ whose tangent squared equals.41421 x.41421 = 0.1715699, nearly 0.1716, which we take for the coefficient of c in the following formula: b = width at top ( cw) Y i 3W )2 h 2 W c b= hx - And h = b AndP =- x ( 3 W ( cwv 2 2 0.1716w 2 i 3W W) 4 0.1716h2w b = h <, -- -- And =/ b - And P= ( 3W h 3 ( 0.1716 c 2 Here Tw = specific gravity of the material to be sustained, and W = that of the wall C = 0.625 for water. 0.410 for fine dry sand. 0.350 earth in its natural state; and for earth and water mixed, 0.40 to 0.65. To the value of b thus found the English engineers add for safety about one-sixth of it. 310u1. When the wall /has an external batter. Let t equal the mean thickness; then we have: / / z, t = ch / — = ch /- for a vertical wall. v w t w / z w t = 0.95 ch / —=ch / batter 1 in 16. W Vw t = 0.90/ —, 1 in 14. V W t = 0.86 -,, 1 in 12. V W 116 72B114 REVETMENT WALLS. / w t = 0.83/ -- 1 in 10. V w / 70 t = 0.80/ —, 1 in S. / W t =.76 ch/ — 1 in 6.! W From the mean thickness t, take half the total batter, and it will give the thickness at top; and to t add the half batter it will give the thickness at the base. 310u2. Where there is a surcharge running back from the walls at a slope of 1yz to 1. Column A for hewn stone or rubble laid in mortar. B for well scrabbled ruble in mortar, or brick. Col. C, well scrabbled dry rubble. Col. D the same as A. Col. E the same as B. Columns A, B, and C are from the English. Cols. D and E are from Poncelet. H = total height of the walls and surcharge. h = that of a rectangular wall above the water. Poncelet has the surcharge:WHEN. A 1B C D E H h 0. 35h.40/i.50.35/h.45A/ H = 1.2h.46/i.51.61.44.55/z H = 1.4h.51/.56/h.66h.53i.67h H =1.6h.54/.59/i.69h.62/.78h H - 1.8h.56.61.71//.767/h.85h H = 2.h.58/.63.673/.71/.93/ W\ALLS OF DAMS. 310u3. Morin in his Aide 3Memoire, gives for thickness at base t = 0.865 (HI-h). /1000. Here H = height of the wall and h = height from the surface of the water to the top of the wall. 1000 =specific weight of one kilogramme of water, and p = specific weight of one kilogramme of the masonry. Example wall four metres high. h = 0.50 m.p = 2000, t = 0.865. x (4.0 met -.0.50). / 1000 = 2,04 metres. - 2000 310u4. DRY WALLS are made one-fourth greater than those laid in mortar. 310u5. Line of resistance in a wall or pier. (See fig. 71.) Let PQ = the direction of the pressure P, which is supported by the wall. The line EF passing-through the centre of gravity meet PQ at G. Make GL = the pressure P, and GH = pressure by the weight of the wall ABCD. Complete the parallelogram GHKL. Join GK and produce it to meet the base CD at M. Then M is a point in the line of resistance. 310u6. The celebrated Vaubamr in his walls of fortifications, makes 4a MF = o of CF. F being where the line through the vertical of the centre of gravity of the wall intersects the base. Let w = weight of the wall. h = BD. b = AB. a = angle PGE. d =,SE and x = MF. = P /isin a - d cos a wbh + P cos a REVETMENT WALLS. 72Bsl15 310u6a. The greatest height to which a pier can be built, is when the line of resistance intersects the base at C, that is, when H is a maximum, x = Yb MF must not exceed from 0.3 to 0.375 the thickness of CD. Vaubam in his walls of fortifications makes the base 0.7h. At the middle 0.5h, and at the top 0.3h. 310u6b. In fig. 72. Let CE - nat. slope. G = centre of gravity of the triangular piece to be supported. Draw FGR parallel to CE, then the triangular wall BCR will be a maximum in strength. And by making BA = 1,5 to 2 ft. and producing EB to 0, making AO = OR and describing the curve AKR the figure ABCRK will be a strong and graceful wall. 310u7. (See fig. 72.) Rondelet's Rules.-Assume the nat. slope to be 45 degrees. In the parallelogram BCDE draw the diagonal CE. When the wall is rectangular, then BA= CR== one-sixth of CE. When the wall batters 2 inches per foot AB=one-ninth do. do do do 1 1-2 inches per foot AB= one-eight do. The English Engineers, make their walls less than the French. They put 1-15 1-10 respectively where Rondelet has 1-8 and 1-9. When the batter is one inch per foot, the English make AlB= one-eleventh of CE. For dry walls, make AB=2-3 of CE, never less than one-half; and in order to insure good drainage, ought to be built of large stones, and batter three inches per foot. 310u8. Colonel Wurmbs in his Militaiy Architecture, gives a / nh T = 0.845 h.tan. ' —, and t = T+ 2 W 10 Here T = thickness of a rectangular wall and t = that of a sloping one at the base, n = ratio of batter to h and a = half the complement 2 of the angle of repose = WDS. (fig. 71.) 310u9. Safety pressure per square foot. White marble 83,000 lbs.; variegated do. 129,000 lbs.; veined white do. 17,400 lbs.; Portland stone 30,000 lbs.; Bath stone 17,000 lbs. Pressure on-The Key of the Bridge of Neuilly, Paris, 18,000 lbs. Pillars of the dome of the Invalides, Paris, 39,000 lbs. Piers of the dome of St. Paul, London, 39,000 lbs. Do. of St. Peter's, in Rome, 33,000 lbs.; of the Pantheon, in Paris, 60,000 lbs. All Saints, Angiers, 80,000 lbs. Rankine gives on firm earth 25,000 to 35,000. do on rock a pressure equal to one-eighth of the weight that would crush the rock. Fox on the Victoria R. R., London, clay under the Thames 11,200 lbs., and for cast iron cylinders filled with concrete and brickwork 8,960 lbs. Brunlee on the Leven and Kent viaduct, gravel under cast iron 11,2001bs. Blyth-On Loch Kent viaduct, gravel under the lake 14,000 lbs. Hawkshaw.-Charing Cross R. R., London, clay 17,920 lbs. Built on cast iron cylinders 14 ft. diameter below the ground and 10 ft. dia. above it, sunk 50 to 70 ft. below high water mark, filled with Portland cement, concrete, and brickwork. General Morin, of France, recommends for Ashlar one-twentieth of the crushing weight, for a permanent safe weight. Vicat says that sometimes we may load a column equal to one-tenth of the crushing weight, but it is safer to follow Morin. 4'\ W K *;:;,,,. 72B 1 16 REVETMENT WALLS. OUTLINES OF SOME IMPORTANT WALLS. 310u11. (Fig. 72 a.) Wall built at the India Docks, London. Radius 72 ft. = DB = DE. Wall is 6 ft. uniform thickness. Counterforts 3'x 3', 18 ft. apart. AE = h = 29 ft. The wall at East India Dock, built by Walker, is 22 ft. high, 7 1-2 ft. thick at base and 3 1-2 ft. at top. Radius 28 ft. Counterforts 2Y ft. wide, 7 1-2 ft. at bottom and 1 1-2 at top. Lines of the two walls are on the same line with the top. Their backs vertical. Fig. 73. Liverpool Sea Wall, built in 1806, base 15', top 7 1-2. Front slope 1 in 12. Counterforts 15 wide and 36' from centre to centre. Height 30 ft. Fig. 73 a. Dam at Poona, near Bombay, in the East Indies. Top of dam is 3 ft. above water. 60 1-2 ft. thick at base and 13 1-2 at top. 100 ft high. (Fig. 74.) The Toolsee Dabzt, near Bombay, is built of Basalt, ruble masonry. Mortar of lime and Roman cement. Height 80 ft., thickness at base 50 ft., at top 19 ft. (Fig. 75.) Dublin Quay Wall, 30 ft. high. Counterforts 7 ft. long and 4 1-2 ft. deep, and 17 1-2 ft. from side to side. A puddle wall at the back, built on piles. Sheeted on top to receive the masonry. (Fig. 76.) Wall of Sunderland Docks, England. (Fig. 77.) Bristol Docks. (Fig. 78.) Revetment wall on the Dublin and Kingston R. R. This is in face of a cut and is surcharged. (Fig. 79.) Chicago street revetment walls. Blue Island Avenue viaduct in Chicago. Steepest grade on the streets crossing is 1 in 30, rather too steep for traffic. On the avenue it is but 1 in 40. 310u12. Blue Island dam on the Calumet feeder taken away in 1874. Timber of Oak and Elm. Built in compartments, well connected and the spaces filled with stones. It was down 27 years and did not show the slightest decay in the timber used. 7ones' Falls dam, on the Rideau canal, is 61 feet high, built of sand stone, with puddle embankments behind it. Several other dams made similar to that at Blue Island, are between Kingston and Ottawa (formerly Bytown), in Canada. PILE-DRIVING, COFFER-DAMS, AND FOUNDATIONS. Pile driving machines are of various powers and forms. A simple portable machine may be 12 to 16 feet high, hammer 350 to 400 pounds weight, without nippers or claws, and worked by about 10 men. A Crab may be placed and worked, but where a small engine can be placed it is preferable. The locality and ground will control which to use. The site is bored to find the under lining stratas, both sides of the banks, (if for a bridge,) to be brought to the same level. It is an old rule that a pile that will not yield to an impact of a ton, will bear a constant pressure of 1~ tons. The power of a pile driver may be determined from the following formulas: 310v-1. Screw Piles 6 1-2 ft. in dia. have been driven in India and elsewhere. 4 levers are attached to a capstan, each lever moved by oxen, Hollow Cast Iron Piles.-When these are driven, a wooden punch is put on top to receive the blows and protect the piles from breaking. i-' ' <.- -... PILE-DRIVING, COFFER-DAMS, AND FOUNDATIONS. 72B117 -= velocity in feet acquired at the time of impact. h height fallen through in time s, in seconds. s =time of descent in seconds, w = weight of hammer. _ h.s =\/. -- - - v = 8.82 \ -' I16.083 = V 4.01 - m = 2w 16.083 h Let h = 10 feet, w = 2 tons; Then i = 4 \/ 160.83 = 30.4 tons. v = 25.2 feet. Otherw-ise We determine the safe load to be borne by each pile, and in driving find the depth driven by the last blow = d. W = weight of the hammer in cwts., H = heigth fallen, and L = safe load in cwts. of 112 lbs. W Hi W H L = - and D =81) 8 L Example.-Hammer 2000 bs., fall 35 feet. Safe load L = 44,000 lbs., 2000 x 35 then D = 8 x 40,000 = 0.22 inches, nearly the length to be driven by the last blow. Let w = safe weight that a pile will bear where there is no scouring or vibration caused by rolling pressure on the superstructure. R = weight of ram in pounds. f= fall in feet and d equal depth driven by the last blow. Rh w 8 d this is the same as Major Sander's, U.S. Engineers. 80 w =. (R+0.228 /! h-1) The same as Mr. McAlpine's formula assuming w = one-third of the extreme weight supported. w = 1,500 lbs. x by the number of square inches in the head of the pile. This agrees with the late Mahan and Rankine's formulas for piles driven to the firm ground. w 460 lbs. (mean safe working load) per inch, by Rondelet. w = 990 lbs. per square inch for piles 12 in. dia., by Perronet. w = 880 lbs. do. do. do. 9 do. do. w 0.45 tons in firm ground. According to English Engineers. w = 0.09 tons in soft ground. do. do. do. Piles near, or in, salt water deteriorate rapidly and must be filled with masonry or concrete. Lime stone exposed to sea air also suffers, and ought not to be used, as granite laid in cement can alone remain permanent. Piles are driven, according to the French standard, until 120,000 lbs. pressure equal to 800 lbs. falling 5 ft. 30 times will penetrate but one-fifth of an inch. The most useful fall is 30 feet-should not exceed 40 ft. Where there is no vibration of the pile the friction of the sand and clay in contact with it increases its strength, and is greater under water where there is no scouring, than in dry land. The Nasmith Steam Hammer strikes in rapid succession, so as to prevent the material being displaced at each blow to settle about the'pile. The blows are given about every second. WVhen men are used as a force, there is one man to every 60 lbs. of the weight. Piles driven in hard material are shod with iron and an iron hoop put on top, to prevent splitting. For much valuable information, see a paper by Mr. McAlpine, in the Franklin Journal, vol. 55, pp. 98 and 170.:,, -..... *. ',..,. -'<. WL~1'. 1~"`,l E.::: 0:~.~;., 72B118 PILE-DRIVING, COFFER-DAMS, AND FOUNDATIONS. It sometimes happens that below a hard strata there is one in which the pile could be driven easier, therefore boring must be first used to find the stratas, and observations made on the last three or four blows. 310v. Mr. McAlpine's formula, from observations made at the Brooklyn Navy Yard, gives as follows: x = W +. 0228 V F —. Here x = supporting weight of the pile. W = weight of the ram in tons. F = fall in feet. He says that only 1-3 of the value of x should be used for safety weights. These piles were driven until a ram 2,200 lbs. falling 30 ft. would not drive the piles but 1-2 an inch. They were made to bear 100 tons per square foot. Piles in firm ground will bear 0.45 tons per square inch, and in wet ground 0.09 tons. The greatest load ranges from.9 to 1.35, tons per square inch. 310vl. Cast iron cylinders were first used in building the railway bridge across the Shannon, in Athlone, Ireland; next at Theis, in Austria, and now generally used. Those used in the bridge of Omaha, United States, are in cylinders 10 ft. long, 8' inner diameter; thickness 1Y inches. Flanges 'on the inside 2". These when down are filled with concrete. The lower ends of those sunk in Athlone were bevelled, and sunk by Potts' method of using atmospheric pressure-that is, by exhausting the air in the cylinder, which caused the semifluid to rise and pass off. The pipe of the air pump was attached to the cap of the cylinder. 310v2. Foundations of Timber.-Where timber can be always in water, several layers of oak or elm planks are pined together. We have seen the Calumet dam, on the Illinois and Michigan Canal, removed, in 1874, after being built 27 years, The foundation was of oak logs, pined together, and in compartments filled with stones. The lumber did not show the least sign of decay. Timbers 10 to 12 in. square are laid 21 to 3 feet apart, and another layer is laid across these, and the spaces between them filled with concrete, the whole floored with 3-inch plank. Pile Foundations.-Piles ought to have a diameter of not less than one-twentieth of their length, to be 2. to 3 feet apart, and the load for them to bear, in soft ground, 200 lbs. and in hard, firm ground, 1000 lbs. per square inch of area of head. Piles ought to be driven as they grew -with butt end dOwnwards-all deprived of their bark; a ring is sometimes put on top, to prevent their splitting and riving. Pile-Driving Engine. —When worked by men, there is one man to every 40 lbs. weight of the ram or hammer used. A pile is generally said to be deep enough when 120,000 foot lbs. will not drive it more than one-fifth of an inch. 120,000 foot lbs. pressure is a hammer of 1000 lbs. weight falling 6 feet 20 times. Let W = weight of ram, h = height of fall, x = depth driven by the last blow, P = greatest load to be supported, S = sectional area of the pile, = its length, E = its modulus of elasticity. ( 4ESp2l 4E2S2x2 2ESx ( 4ES/ 2 By this formula P is to be 2000 to 3000 lbs. per square inch of S, and the working load is taken at 200 to 1000 lbs. if~~~ - COFFER-DAMS. 72B119' COFFER-DAMS. 310v3. In building the Victoria bridge, in Montreal, the coffer-dam was 188 ft. long, width 90, pointed against the stream, and flat at the other end. Double sides made to be removable. Depth of rapid water 5 to 15 ft. On the outside at intervals of 20 ft., strong piles were driven, in which steel pointed bars, 2 in. dia. were made to drill to a depth of two feet in the rock, to keep the dam in position. When the pier was built these bars, etc., were removed as required. In floating it to its required place the dam drew 18" of water. For building cofferdams in deep water, see AMr. Chanute's treatise on the Kansas City bridge, on the Missouri. Cofferdam of earlth, where it is feasible, is the cheapest. It has to be built slowly. There are two rows of piles driven, then braced and sheeted, and filled with clay of a superior quality. The Thames embankzment reclaimed a strip of land 110 to 270 ft. wide. Depth of water in front 2 ft. Rise of tide 18Y'. Strata, gravel and sand resting on London clay at a depth of 21 to 27 ft. Depth of wall 14 ft. below low water mark. l)ams were 11 Y ft. long and 25 broad inside, made of two rows of piles 40 to 48 ft. long, 13 in. square, shod with cast iron shoes 70 lbs. each, and driven 6 ft. apart. The sheeting driven 6 ft. in the clay. At intervals of 20 ft., other piles were driven as buttresses and supported by walling at every 6G2 ft. horizontally, and connected with two other piles bolted with iron bolts 2'2 in. dia., with washers 9" dia. and 24" thick. An iron cylinder 8 ft. dia. sunk in each dam as pump wells. WOOD PRESERVIN(;. 310v4. Trees ought to be cut down when they arrive at maturity, which, for oak, is about 100 years, fir, 80 to 90, elm, ash, and larch, 75. Should be cut when the sap is not circulating, which, in temperate climates, is in winter, and in tropical climates in,the dry season-the bark taken off the previous spring. When cut, make into square timber, which, if too large, ought to be sawed into smaller timbers. 310v4a. Natural Seasoning. -By having it in a dry place, sheltered from the sun, rain, and high winds, supported on cast-iron bearers, in a yard thoroughly drained and paved, this requires two years to' fit it for the carpenter's shop, and for joiners, four years. Timber steeped in water about two weeks after felling, takes part of the sap away. Thus, the American timber, rafted down stream to the sea-board, affords a good opportunity for this natural process. 310v4b. Artificial Seasoning, is exposing it to a current of hot air, ploduced by a fan.blowing 100 feet per second. The fan air-passages and chambers are so arranged that one-third the air in the chamber is expelled per minute. The best temperature is, for oak, 105~ Fahr., pine in thiclk pieces, 120~, pine in boards, 180~ to 200~, bay mahogany, 280~ to 300~Thickness in inches, 1 2 3 4 6 8 Time required in days, 1 2 3 4 7 10 each day, only twelve hours at a time. 310v4c. Robert Napier's Process is by a current of hot air through the chamber, and thence into a chimney, is found very saccessful. The air admitted at 240~, requires 1 Ib. of coke to every 3 lbs. moisture evaporated. The short duration of wooden bridges, ties, etc., calls for a method for preventing the dry rot in timber. The following brief account will be sufficient to inform our readers of the means used to this time: I X I ) 144., *.'.":-'e M:..' ' k i; J.* > X" *'-; -*1'u** "^ ' 72B120 WOOD PRESERVING. Tanks are made to hold the required cubic feet, and sunk in the ground level with the surface.-Kyan's Process, patented March, 1832. 'On the Great Western Railway, England, the tank was 84 feet long, 19 feet wide at top, 60 feet long and 12 feet 8 in. wide at bottom, and 9 feet deep. Corrosive sublimate (bichlorate of mercury) was used at the rate of 1 lb. to 5 gallons of water. Cost per load of 50 cubic feet, 20 shillings, sterling; of this sum, one-fourth was for the mercury, one-fourth for labor, and one-half for license, risk, and profit. The solution is generally made of 1 lb. of the mercury to 9 to 15 lbs. of water. Time of immersion, eight days; timber to be stacked three weeks before using. Experiments are reported against Kyan's method. Sir William Burnet's Method-Patented in England, March, 1840. He uses chloride of zinc (muriate of zinc). Timber prepared with this was kept in the fungus-pit at Woolwich dock-yard for five years, and was found perfectly sound. The specimens experimented on were English oak, English elm, and Dantzic fir. Cost-one pound at one shilling is sufficient for ten gallons of water, a load of 50 cubic feet thus prepared in tanks costs, for landing, 2 shillings, preparation, labor, etc., 14 shillings, total, 16 shillings. Bethell's Method.-Close iron tanks are provided, into which the wood is put, also coal-tar, free from ammonia and other bituminous substances. The air is exhausted by air-pumps under a maximum pressure of 200 lbs. per square inch during 6 or 7 hours, during which time the wood becomes thoroughly impregnated with the tar oil, and will be found to weigh from 8 to 12 lbs. per cubic foot heavier than before. The ammonia must be taken away from the tar oil by distillation. Payne's Method-Patented 1841.-The timber is enclosed in an iron tank, in which a vacuum is formed by the condensation of steam, and air-pumps. A solution of sulphate of iron is then let into the tank, which immediately impregnates all the pores of the wood. The iron solution is now withdrawn, and replaced with a solution of chloride of lime, which enters the wood. There are then two ingredients in the wood-sulphate of iron and muriate (chloride) of lime. The timber thus prepared has the additional quality of being incombustible. Boucheri's Method.-Use a solution of 1 lb. of sulphate of copper to 12~ gallons of water. Into this solution the timber is put endwise, and a pressure of 15 lbs. per square inch applied. W v. H yett, in Scotland, impregnated timber standing,-found the month of May to be the best season. From his experiments on beech, larch, elm, and lime, we find that prussiate of potash is the best for beech - lb. per gallon-chloride of calcium the best for larch. Time applied, 17 to 19 days. For further information, see Parnell's Applied Chemistry. A. Lege and Fleury Peronnet, in France, in 1859, used sulphate of copper, which they found to be better and cheaper than Boucherie's method. 310v5. By exhausted steam. -In Chicago, at Harvey's extensive lumber yard and planing mill, the following process is found very cheap and effective:The machinery is driven by a 100-horse power engine, the fuel used is exclusively shavings; the exhausted steam is conducted from the engine house to the kiln, where it is conveyed along its east side in a live steam MORTAR, CEMENT, AND CONCRETE. 72B121 coil of 20 pipes, 2 inches in diameter. The heat thereof passes up and through the timber, separated by inch strips and loaded on cars. The heat passes to the west through the lumber cars, and thence to the northwest corner of the kiln, where it escapes. Connected with the last main pipe (8 inches in diameter,) are condensing pipes, 2 inches in diameter, laid within 4 inches of one another, and connected with a main exhaust pipe 4 inches into a chimney-one of which is over each car. There are five tracks, or places for ten cars in each, about 80 by 60 feet; each car is 16 feet long, 6 feet wide, and 7 feet high, and is moved in and out on a railway; the whole, when filled, contains 200,000 feet of lumber. The temperature is kept, day and night, at 160~ Fahr., and the whole dried in 7 days, losing about half its weight, and selling at about one dollar more per thousand. This makes a great saving in the transportation of lumber from the yard to various places in the west, as the freight is charged per ton. MORTAR, CONCRETE, AND CEMENT. From experiments made by the Royal Engineers, they find that 1120 bu. grazel, 160 bu. lime, and 9 of coals, made 1440 cubic feet in foundation; 4522 bu. gravel, 296 lime, and 301 coal, made 2325 feet in abutments; 3591 bu. gravel, 354 lime, and 30 bu. coal, made 2180 cubic feet in arches. Cost per cubic foot-in foundations, 3id, abutments, 4jd, arches, 54Sd; specific gravity, 2,2035; 16 cubic feet = 1 ton = 2240 lbs. Breaking weight of concrete to that of brick-work, as 1 to 13. At Woolwich that concrete in foundations cost one-third, and in arches one-half that of brickwork. Stoney, in his Theory of Strains, p. 234, edition of 1873, says Rondelet states that plaster of Paris adheres to brick or stone about two-thirds of its tensile strength; is greater for mill-stones and brick than for limestone, and diminishes with age; lime mortar, its adhesion to stone or brick exceeds its tensile strength, and increases with time. On the Croton Water Works. Stone backing. 1 cement to 3 of sand. Brick work, inside lining 1 c to 2 s. At Fort Warren, Boston Harbor, the proportions for the stone masonry were stiff lime paste 1 part, hydraulic cement 0.9, loose damp sand 4.8. At Fort Richmond, hyd. cement 1.00, loose damp sand 3.2. Vicat, a well-known French Engineer, recommends pure limepaste 1, sand 2.4, and hyd. lime paste 1, sand 1.8. Cement for water 7iork. Friessart recommends hyd. lime 30 parts, Terras of Andrenach 30 parts, sand 20, and broken stones 40. Grouting. Sineaton, who built the Eddystone light house, recommends 4 parts of sand, one of lime made liquid. For Terras mortar he substitutes iron scales 2 parts, lime 2 and sand 1 part. This makes a good cement. Iron cement. Gravel 17 parts by weight, iron filings or turnings 1 part, spread in alternate layers. Used in sea work, forms a hard cement in two months. 310v6. Stoney at Sec. 304, edit. 1873, gives the crushing weight per square inch at 3, 6, and 9 months, as follows: Specimens acted on were made into bricks 9 x 4z x 2Y4 inches. They began to fail at five-eights of the ultimate load. At Sec. 688 of Stoney on strains, the working load is taken at one-sixth of the crushing weight. vI. ' E -*....... -.:,',i ., *'. E. *. 1.' 72B122 MORTAR, CEMENT, AND CONCRETE. Vicat gives tenacity (one year after mixture) of hydraulic cement 190 lbs. to 160, and common mortar 50 to 20. Cement for moist climates. Lime one bushel, Y2 bu. fine gravel sand, 2Y lbs. copperas, 15 gallons of hot water. Kept stirred while incorporating. CONCRETE. 310v7. In London, architects use one part of ground lime and 6 parts of good gravel and sand together. Broken bricks or stones are often added. Strong hydraulic concrete, is made of 2 parts of stone and 1 of cement. In the United States, 1 of cement to 3 of broken stone and sand is frequently the proportions. The stones and sand are spread in a box to a depth of 8 inches, the proportion of cement is then spread on the whole and sufficiently wetted. Four men with shovels and hoes mix up the ingredients from the sides to the centre, and mix one time in one direction and again in the opposite one. It is then taken on wheel-barrows and thrown from a height where it is spread and well rammed. One part of the materials before made makes 5 in foundation. Lime must not be mixed when used in sea-walls. Concrete is made into domes and arches. The central arch of Ponte d'Alma, 161 ft. span and 28 ft. rise is made of concrete. Also the dome of the Pantheon at Rome, 142 ft. diameter. Beton is concrete where cement takes the place of lime. In building the harbor at Cherbourg, in France, Beton blocks 52 tons weight, dimensions 12 x 9 x 6 1-2ft., 712 cubic feet, built of stone and cement, mortar made of sand 3 and cement '4. These blocks at nine months old bore a compressive strength of 113 tons, nearly equal to that of Portland stone. The Mole, at Algiers, Africa, built by French Engineers, is made of blocks of Beton, not less than 353 cubic feet each. All the blocks are of the same form, 11' long, 62 ft. wide and 4 ft. 11" high. Composition oJ Beton Afortar is made of lime 1, Pozzuolana 2, makes two parts of mortar. Beton is composed of mortar 1, stone 2. The stones are broken into pieces of about 1 cubic ft. each. Weight per cubic foot of this Beton = 137 lbs. An adjustable frame is made so as to be removable when the block is dry, the bottom is covered with two inches of sand and the sides of the frame lined with canvass to prevent their being washed. They are cast in making a slope on the outside 1 to 1, and on the land side Y to 1. The blocks are put on small wheeled trucks and moved on a tramway to an inclined float, where it is lowered to a depth in water of 3 ft. 3 inches, and placed by chains between two pontoons and floated to the required place in the Mole. PRESERVATION OF IRON. 310v8. The iron is heated to the temperature of melting lead (630~ Fahr.), then boiled in coal tar. Where the iron is to be painted with other parts of the structure, the iron is heated as above, and brushed over with linseed oil-this forms a good priming coat for future coats of paint. Galvanizing with zinc is not successful, being acted on by the acid impurities found in cities, towns, and places exposed to the sea, or sea air. Steel hardened in oil is increased in strength.-Kirkaldy.... ARTIFICAL STONE. 72B123 VICTORIA ARTIFICIAL STONE. 310v9. Rev. H. Heighton, England, uses at his works, Mount Sorrel and Guernsey granite, refuse of quarries, broken into small fragments and mixed with one-fourth its bulk of granite and water, to make the whole into a thick paste, which is put into well-oiled moulds, where it is allowed to stand for four or five days, or until the mass is solidified. After this, it is placed in a solution of silicate of soda for two days, after which it is ready for use. He keeps the silicate of soda in tanks which are to receive the concrete materials, the silica is ground up and mixed with the bath. The lime removes the silica, forming silicate of lime. The caustic soda is set free, which again dissolves fresh silica from the materials containing it. This, in flags of 2 inches thick, serves for flagging. It is made into blocks for paving, is impervious to rain and frost. Mr. Kirkaldy has found the crushing weight to be 6441 lbs. per square inch -Aberdeen granite being 7770, Bath stone, 1244, Portland stone, 2426. 310o10. Ransom's MAethod to prevent the decay of stone, and when dried then apply a solution of phosphate of lime, then a solution of baryta, and lastly, a solution of silicate of potash, rendered neutral by Graham's system of dialysis-this is Frederick Ransom's process. With Mr. Ransom, of Ipswich, England, in 1840 and 1841, we have spent many happy hours in constructing equations, etc. The above process, by Mr. Ransom sets the opposing elements at defiance. Ransom dissolves flint in caustic soda, adds dry silicious sand and lime-stone in powder, forms the paste into the desired forms, and hardens it in a bath of a solution of chloride of calcium, or wash it by means of a hose. Make blocks of concrete with hydraulic cement. When well dried, immerse in a bath of silicate of potash or soda, in which bath let there be silica free or in excess. Here the lime in the block takes the alkali, leaving the latter free to act again on the excess of silica, and so proceed till the block is an insoluble silicate of lime, known as the silicated concrete, or Victoria stone, of which pavements have been made and laid in the busiest part of London; also, as above stated, enormous buildings, such as the new warehouses, 27 South Mary Ave., London. Silicate of Potash is composed of 45 lbs. quartz, 30 lbs. potash, and 3 lbs. of charcoal in powder. Silicate of Soda-Quartz 45, soda 23, charcoal 3. These are fused, pulverized, and dissolved in water. This silica absorbs carbonic acid, therefore it must be kept closely stopped from air. The strength is estimated by the quantity of dry powder-40 degrees means 40 of dry powder and 60 of water. In applying this, begin with a weak solution, make the second stronger. One pound of the silica to five pounds of water will answer well. It is not to be applied to newly-painted surfaces. Mortar and lime stones ultimately produce silicate of lime. If the surface is coated with a solution of chloride of calcium, the chlorine will combine with the soda, making the soluble salt, chloride of' sodium, and there remains on the surface silicate of lime, which is highly insoluble. The surface is washed with cold water, to remove the chlorideof sodium. When applied to stone or brick, add 3 parts of rain-water to a silicate of 33 degrees. A final coating of paint, rubbed up with silicate of soda, will render the surface so as to be easily cleaned with soap and water. 72B124 BEAMS AND PILLARS. This silicate adheres to iron, brass, zinc, sodium, etc. Enormous buildings have been built and repaired by this means. The best colors to be used with it are Prussian blue, chromate of lead and of zinc, and blue-green sulphide of cadmium. BEAMS AND PILLARS. 310v11. The strongest rectangular beam that can be cut out of a log is that whose breadth == cdivided by 1,732, where d = diameter of the log. (See Fig. 80.) In the figure, a e = diameter, make a f= one-third of d, erect the perpendicular f b, join b c and a b, make c d parallel to a b, join a d, then the rectangle, a b c d, is the required beam. See Sections 21, 22. A beam supported at one end and loaded at the other will bear a given load, = w, at the other end. When the load is uniformly distributed, it will bear 2 w. Beam supported at both ends and loaded at the middle = 4 w. Beam supported at both ends and the weight distributed 8 w. When both ends are firmly fixed in the walls, the beam will support fifty per cent. more. The following table are the breaking weights for different timbers and iron-the safe load is to be taken at one-fourth to one-sixth of these:-onesixth is safer. 310v12. TABLE. SPECIFIC GRAVITIES, BREAKING WEIGHTS, AND TRANSVERSE STRAINS OF BEAMS SUPPORTED AT BOTH ENDS AND LOADED IN THE MIDDLE. KIND OF WOOD., lrking Sp cfic Weight ur vity _w Ash, English,, African, - - -, American, -, White,,, seasoned, Black,, - Elm, English, - - -, Canada, - -, Rock, seasoned,, green, - Hickory, American, Iron-wood, American, Butternut, green, -Oak, American, mean of 11,,, Live, - - - Pine, White, mean of 6, -,, North of Europe,,, Red, West Indies, -,,,, American, mean 3, 7 Hemlock, Larch, Scotch, ~Coudie, New Zealand, Bullet-tree, West Indies, - Green-heart, t:> ' Kakarally,,, Yellow-wood, mean of 3, Wallabia, Lancewood, South African, h!t".mean of 4, - L/"'-. Teak, mean of 9, -.,.. j. 760 985 611 642 533 605 703 685 752 746 838 879 772 1034 1120 453 587 621 911 480 550 1075 1006 1223 926 1147 1066 719 1701 274 1377 1265 1857 1000+' 1041 966 1292 1364 1167 1292 '1 ansv Strain. S 2022 2484 1550 2041 8861 551 1966 1819 2312 2049 1332 1800 1387 1806 1513 1456 1387 1799 1944 1142 1193 1873 2733 2471 2379 2103 1643 2305 1898 Barlow. Nelson. t! Lieut. Denison. Moore. Nelson.,, Denison. It Nelson. It,, il Moore. Young. Nelson. Chatham, England. 11 if 1):~g. IP IT i Young. it Nelson. 'p! AUTHORITY. BEAMS AND PILLARS. 72B125 - Let / = length, b = breadth, d = depth, W = breaking weight, loaded. at the centre, S = transverse strain acting perpendicularly to the fibres. 2, b, and d in inches-W and S in pounds. /W 4bd2S S = W= 4bd2 I b= d= 4d2 S 4bS TIMBER PILLARS. BY RONDELET. 310v13. Let w = the weight which would crush a cube of fir or oak. When height = 12 times the thickness of the shorter side, the face= 0.833wu,, 24,,,,,,, 0.500w, 36,,,,, 0. 334zv,, 48..,., 0.1667e I,,60 0.083w,, 72,..,. 0.42 - 1. Example. A white pine pillar 24 ft. long, 12 inches wide and 6 inches thick. Required the breaking weight. From Sec. 3107. The crushing weight of white deal = 7293 72 = 12 x Length - 48 times the shorter side. 525096.166 -1 / 87,516 lbs. Rondelet = 39.07 tons. 310v14. Hodgkinson's formula for long square pillars more than thirty times the sideW = breaking weight in tons, I = length in feet, d= breadth in inches. Note. With the same materials a square column is the strongest, the timber in all cases being dry. d4 W = 10.95 - for Dantzic oak. d4 W = 6.2 2- for American red oak.* d4 W = 6.8 2 for red pine. d4 W = 6.9 - French oak. d4 XW = 12.4 -- for Teak.* Note. These marked * are put in from the values of C. Sec. 319Y6. 310v15. Brereton's experiments on pine timber. For pieces 12 inches square and 20 feet long, he finds the breaking weight in tons 120, for 20, 30 and 40 ft., he finds 115, 90, and 80 tons respectively. Stoney says "this is the most useful rule published," and gives a table calculated from Brereton's curve to every five feet. Ratio of length to the least breadth, 10, 15, 20, 25, 30, 35, 40, 45, 50. Corresponding breaking wt. in tons per sq. ft. of section, 120, 118, 115, 120, 90, 89, 80, 77, 75. 2. Example. White pine pillar 24' ft. by 12" x 16". Ratio 24 ft. to 6 in. = 1-48 tabular number for 50 = 75 and for 65 = 77. or therefore for 48 = 75,8.. _. | i '; *, *; * ~ _ ' v ' 72B126 IRON BEAMS AND PILLARS. 12" x 6" x 75.8 12 x 12 == 37-9 tons. Brereton. By Hodgkinson least side 6" in the fourth power 1296 which multiply by the coefft for red deal 7.8 10108.8 Divide by the square of the length in feet 576 and the quotient will be for red pine and 6 inches square 17.55 tons. As 6":17.55::12" = for 12" x 6" = 35.10 tons. The crushing weight of white deal = 7293 lbs. and of red deal 6586, that is white deal is 1.11 times that of red =35.1 x 1.11 = 38.96 tons. HIodgkinson's. Safe load in structures, includes weight of structure. Stone and brick one-eighth the crushing weight. Wood one-tenth. Cast iron columns, wrought iron structures and cast iron girders for tanks each one-fourth, and for bridges and floors one-sixth. A dense crowd, 120 lbs. lcr sq. ft. For flooring 12 to 2 cwt. per sq. ft., exclusive of the weight of the floor. 310v16. The strength of cast iron beams are to one another as the areas of their bottom flanges, and nearly in proportion to their depths. cad W - - = theoretical weight, which is from 4 to 6 times the weight to be sustained. Here W == breaking weight in tons placed on the middle of the beam. c and a constant multipliers derived from experiments. One-sixth the breaking weight where there is rolling or vibration and onefourth where stationary and quiet, generally taken at 26. a = sectional area of the bottom flange, taken in the middle. d = depth of beam g a (fig. 81) b = length between the supports. The strongest form, according to Hodgkinson, is where the area of the lower flange is six times that of the upper flange. Fairbarn's form is shown in fig. 81, where e d = 1, a b = 2.5, ag = 4, h = 0.42, ef = 0.20 and i k =- 0.25. Area of bottom flange = 1.05 and of top one = 0.20. Here we have the bottom flange area = 5f' times that of the top. Mr. Fairbarn says, at page 32 of his treatise, that "a beam made in the above form, will be safer without truss, bars, or rods than with tflt." At page 65, he shows that the advantage of a truss beam is but twothirds of that of the simple beam as determined by experiments. 310v17. To calculate the strength of a truss beam, dimensions in inches. (26a + 3a ).d W -- tons. Here zo = safe weight, a = area of bottom flange, and b = area of the truss rods, I = the distance between the points of support, and d = depth of the cast metal beam. At p. 51, he states *that when the broad flange is uppermost its strength is 100, and when undermost its strength is 173. Note A. There are various causes which render cast iron beams unsafe for bridges, ware-houses, and factories. The wrought iron beams are lighter, easier handled in building, stronger, and cheaper than cast iron, and are 't/ only aboqt two-fifths the weight of cast iron beams of the same strength. Note B. By comparing thirty principal American trussed bridges, we ', find that their depth is about one-eighth their span, ranging from one-fifth to one-tenth. -3:;.. - A CAST IRON PILLARS. 72B127 310v18. Wrought iron beams. Note C. The box-beam (fig. 82) is the strongest form, weight for weight, best beam (fig. 83) on account of its simple construction, facility of painting; it is recommended by Fairbarn, who says that "taking the strength of a box beam (fig. 82) at 1, that in the form of Fig. 83 would be 0.93, each of equal weight. Beams like Fig. 83 can be made for buildings 60 ft. wide without columns, and with one row of columns they may be 22 inches deep and 5-16 inches thick, with angle iron rivetted. Let W = breaking weight in tons, d = 22" = depth of beam, a area of the bottom flange, I distances between the supports in inches = 360 adc W - IHere = constant = 75 and a == 6" 6 x 22 x 75 that is W = 3- = 27,5 tons in the middle, or 55 tons distributed. Fairbarn gives the weight of this beam equal to 40 cwt. and that of wrought iron, having the same strength, equal to 16 cwt. 1 qr. and 14 its. CAST IRON PILLARS. D 3.5 310v719. W -- m -63 tons. W = breaking weight in tons. D external and ( = internal diameters in inches, and b = length in feet. Hodgkinson gives a mean value of 13 irons = 4.6. To find I) in the power 342. Find the logarithm of I). Multiply it by 3Y2 and find the natural number corresponding to it. 1)3.5 W = 42.6' ~ —63 tons. The thickness of metal in a hollow pillar is usually taken at one-twelfth its diameter. Assuming the strength of a round pillar at 100, then a square pillar with the same amount of material. 93, a triangular pillar with the same amount of material = 110. 310(v20. Gordon's rule is considered the best formula. P == f Here P = breaking weight in lbs., S = sectional area, l +a 2 I length, and h =the least external diameter on the least side of a rectangular pillar, f and a = constants. (All in inches.) For Wrought iron, f = 36,000 and a =.00033., Cast iron, f = 80,000 and a =.0025, Timber, f= 7,200and a =.004. Example 1. Let length = I = 14. Diameter =h -= 8 inches of a timber pillar or column. Sectional area= 50,265 multiplied by the value off 72,000 gives 361908 =f S. 14x 12x 14x 12 /2 8 - x 87 --- = 336 -= ' -. This multiplied by.004 = 1,344 and 1 + 1.344 = 2.344 = the denominator in the formula, which divided into 361908, gives the value of P = 154,397 Ibs. The safe weight to be taken at one-sixth to one-eighth for permanent loads and one-third to one-fourth for temporary loads. 310w. We are to find the weight of the proposed wall with the pressure of the roof thereon, and prepare a foundation to support eight times this weight on rock foundation, and in hard clay the safe load may be taken from 17 to 23 lbs. per square inch. In Chicago, on blue clay the weight is I/ ' -. ' -I*,. '. 72B128 WALLS AND ROOFS OF BUILDINGS. taken at 20 lbs. per square inch. The foundation must be beyond the influence of frost at its greatest known depth. 310wl. Depth of foundation. Let P = pressure per lineal foot of the wall, w = weight of one cubic foot of the load to be supported. W weight of one cubic foot of masonry. f = friction of masonry on argillaceous soil. d = the required depth of the foundation. a = the complement of the angle of repose. Let us take f= 0.30 which is the friction of a wall on argillaceous soil. d 1.4 tan -2 t 2(P-f) (See Fig. 71.) Example. A dam has to sustain water 4 metres high. The specific weight of masonry = 2000 and that of water is = 1000. Let / = thickness at top of wall and T = thickness at the bottom. /= 0,865 x 4 /1000 =2.44 metres. -' 2000 Weight of one lineal metre = 4 x 2.44 x 2000 19520 kilogrames. Friction -f 19520 x 0.30 = 5856 h2 Pressure P = 1000 x — = 1000 x 8 =7000 and 8000(- 5856 == P-f = 2144. Taking the complement of the angle of repose = 60~ a f= tan of half a tang 30~ = 0.578, then fiom the above formula / 288 d-= 1.4 x 0.578 / 20= 1.185 metres, the required depth of foundation. The footing is to be equal to the thickness of the wall at base; that is the base of footing will be twice as wide as the wall, and diminish in regular offsets. The foundationpf St. Peter's, in Rome, are built on frustums of pyramids connected by inverted arches. 310w2. The area of the base of footing must be in proportion to the weight to be carried. It is usual to have one square foot of base for every two tons weight. In Chicago, where clay rests on sand, the bearing weight is taken at 20 lbs. per square inch, but there are buildings where the weight is greater, in some cases as high as 34 lbs. Mr. Bauman, in a small practical treatise on Isolated Piers, makes the. offsets for Rubble masonry 4 inches per foot in hleight. For concrete 3 inches. For dimension stone about the thickness of the stone, but his plan shows the offsets for dimension stone to be four-fifths of the height, and the height to 1-2 the width at the lowest course of dimension stone. WVALLS OF BUILDINGS. - 310w3. Let 7, h and t represent the width, height and thickness respectively in French metres. 2/+h t - 4 = minimum thickness for outer walls. ~p, 48 +h t 48 for walls of double buildings or of two stories.:~:~.~.:. 41,~;~Y"I:; ; i ~~, i+' alr; I~:Y )r 1 ii: ~I~rjl:.~J~: = 36 for partition walls. Example. A building having a basement story 5 metres high, 1st story = 2.50 met. high, and the 2d story = 2.50 met. high. = width - 11 metres. WALLS OF BUILDINGS. 72B129 11+10 48 = 0.44 for basement. 11+5! = 48 - 0.33 for 1st story. t = 112. = 0.28 for 2nd story. These are from Guide de e48 chanique Practique, by Armegaud. 310w4. Rondelet says the thickness of isolated walls ought to be from one-eleventh to one-sixteenth of their height, and walls of buildings not less than one-twenty-fourth the distance of their extreme length. He gives the following table: Kind of Building. Outer Walls. Middle Walls. Partitions. met. met. met. met. met. met. Odd houses, 0.41 to 0.65 0.43 to 0.54 0.32 to 0.48 Iarge buildings, 0.65 to 0.95 0.54 to. 65 0.41 to 0.54 Great edifices, 1.30 to 2.90 0.65 to 1.90 0.65 to 1.95 Rondelet examined 280 buildings, with plain tiled roofs, in France; finds / =- 1-24 of the width in the clear. 310w5. Thickness of walls ly Gwilt. To the depth add half the height and divide the sum by 24. The quotient is the thickness of the wall, to which he adds one or two inches. For Partitions, he says:-To their distance apart add one-half the height of the story and divide by 36 will give t. To this add /3 inch for each story above the ground. 310w6. To connect Stones. Iron clamps are put in red hot and filled up with asphalt. This protects the iron forever. Where the clamps are fastened with lead, the iron and lead in the course of time, decompose one another. Duals of wood dove-tailed 2 inches square, have been found perfect, imbedded in stones as clamps, after being 4000 years in use. In large, heavy buildings, pieces of sheet lead are put in the corners and middle of the stones to prevent their fleshing. 310w7. Molesworth & Hurst, of England, in their excellent hand-books, have given valuable tables on walls of buildings. From these and other reliable English sources we findFirst-class houses, 85 ft. high, six stories. The ground and first story are each one-forty-seventh of the total height. The 2d, 3d, and 4th stories are each 6 inches less; the 5th and 6th stories are each 4Y inches less than the latter. Second-class, 70 ft. high. 'I he ground, 1st and 2d stories are each onefifty-fourth of the total height, and 4th and 5th stories, each 63 inches less than these. Third-class, 52 ft. high. The ground floor is 1-40 of the total height, and the 1st, 2d, 3d, and 4th stories are 6, inches less than these. Fourth-class, 38 ft. high. The ground and first stories are one-thirtyfifth of the total height, and 2d and 3d stories are 4y in. less than these. When the wall is more than 70 ft. long, add one-half brick (6% inches) to the lower stories. The footing is doulble the thickness of the wall, and also double the height of the footing, laid off in regular offsets. The bases must be level. 310w8. n Chicago, there is the following ordinance, strictly enforced since the great and disastrous fire of Oct. 9, A. D. 1871. Outside walls 118 72B130 CHIMNEYS. for two stories, 12 inches thick. If more than two stories above the basement, the basement and first story shall not be less than 16 inches, and the walls above the second story not less than 12 inches, and with the exception of the front walls the others will extend at least 12 inches above the roof. For dwelling-houses the above may be reduced 4 inches. In all buildings over 25 ft. in width, and having no partitions or girders supported by columns or piers, 4 inches must be added for every additional 10 ft. in width of said building. CHIMNEYS. 310w9. Chimneys. That of the Refiningc, Company, in Chicago, is 151 ft. high, 12 ft. square at base. Two courses of heavy dimension stones. Base 16 ft. square. Mortar made of cement and roofing gravel. Pressure on foundation 34 lbs. per square inch. The McCormick Reaper, 160 ft. high, 14 ft. square at base of column, which is circular. It is 25 ft. square at the ground. Flue 6' 8" diameter. Covers an area of 625 square ft. Weighing 1100 tons. Pressure 24 2lbs. per square inch. Built on hard, dry clay. 77zc Tobacco Chimney, in Paris, is 29 metres high. Outer diameter at the bottom 3.45 metres. Inner dia. at the same = 2. ]5 metres. At the top the outer dia. = 1.30 and the inner = 1.03 met. This burns 700 kilogrames of coal, which gives about 150 horse power. Chimneys in France are built from 20 to 30 metres high, rarely 40 metres. M. Darcte recommends one square decimeter to every 3 kilogrames of coal consumed per hour = 0.64 horse power. The surface for the grating three times greater than that for the chimney. Best forms in order are, circular, octagonal, or many sided. Thickness at top usually one brick in length. Thickness at top 0.11 to 0.22 metres, and putting d =.inner diameter and i -= outer diameter at top, we have d == d + 0.22 or d + 0.44. And putting D - bottom diameter and D, = outer dia. at do., we have H = height and m = a tabular constant for slant or inclination. Then D = D + 2 Huc, where m for the interior is taken bet. 0.012 and 0.018 and for the outer dia. m is taken at 0.025 to 0.035. Example. H = 60 metres. d = 0.60 = interior diam. Then D d + 2-m = 0.60 + 120 x 0.015 = 2.40 metres mean I'= 0.60 + 0.33 + 120 x 0.30 = 4.53 took mean thickness and constants. Chimney at St. Rollox, Glasgoiw, 455L ft. high, and 435~ ft. above bottom of the base, which is of concrete, 6 ft. thick. Load per square ft. 6720 lbs. or 3 tons on concrete. Chimney at Mutspratt's Chemical Works, St. H-elen's, near Liverpool, is 406 ft. high. Chimney at West Cumberland, Harmetide Iron Works. Base of concrete 3 ft. thick, made with hydraulic lime. Height above ground, 250; total height, 267 ft. Pressure at a section 2 ft. above the ground. Working load on concrete 3 tons, and on brickwork 8 tons. Chimney at Atkins' Soap Works, near Birmingham, England. Total height, 312 ft. Brickwork. Pressure per square ft. at base, 6 tons. Shot- Tower, Baltimore. Brickwork, 244 ft. high. Working load on base, 63 tons. The crushing weight = 4.8 times the working load. United States Light House, 160 ft. high. Brick. Pressure, 3.7 tons. Crushing weight at base = 8~ times the working or safety load. T1 UNNEI S. 72B131. Pressure on roof for weight of roof, snow, and pressure of the wind, 40 lbs. per square, weather side, and 20 lbs. on the other, under 150 foot span; add 1 lb. for every additional 10 feet, stoney, 524. Greatest pressure of wind observed in Great Britain was 55 lbs. per square foot = 0.382 lbs. per square inch. TUNNEILS. 310wl. Tunnels.-Within brick work, for single track, 20 feet high, 15 feet wide. Double track, 24 feet high, and 24 to 30 feet wide. For canals, 14 to 30 feet high and 14 to 30 feet wide. Alinzium tunnels, 4~ by 3 feet. The form of a horse-shoe, or elliptical, is generally adopted, resting on an inverted arch, excepting that directly under the side walls, which is horizontal. Shafts are sunk to facilitate the lifting of materials and supplying fresh air; they are about 8 feet in diameter. The Mount Cenis tunnel is 7.59 miles long, has no shaft, owing to its great depth below the top of the surface. At each end there is a sump or well, to collect the water of the tunnel, and from which it is lifted. Some are made by sinking cast-iron cylinders, others steined with brick, those of iron ought to be preserved from oxidation. See Sec. 310v8. In sinking a shaft lined with brickwork, a drum curb, made of oak timber, mounted with bevelled iron to enable it to sink. The outer diameter is the same as that of the brickwork. The excavation is made greater than the intended shaft. The drum is lowered horizontally as low as tie excavation will permit, and the brickwork laid in single courses or rings. There are temporary supports to keep the drum in position until another length is excavated, then these are removed. The sharp edge of the drum penetrates deeper, carrying its already built load of masonry, and giving an additional length on top to be built, etc. At the London Thames tunnel, the Wapping-Street shaft was sunk on a drum to 72 feet deep. Tunnels in soft ground must be timbered in length. The cost of brickwork in tunnels is about double of what it is over ground. The Mount Cenis tunnel was made by driving jumpers by atmospheric pressure, using the pressure of five atmospheres, each jumper driven by its own air-cylinders, holes 1 3-16 in. diameter, 80 holes driven in the surface of the tunnel, making a progress of 1~ yards per day. Thames tunnel, built in soft earth by Brunel, 37~ feet wide, 22 feet high, being in two parallel elliptical archways, each 14 feet wide and 17 feet high; thickness at invert, 2~ feet, at the crown 21 feet, sides 3 feet, central wall 3~ feet, the whole laid on a flooring of elm planks 3 inches thick. In constructing this, Brunel used a shield-a machine resembling a man, moving forward step by step and arm after arm. Cost ~12 5s per cubic foot of its bulk, and ~1137 per lineal foot. For a full account of this great feat of engineering, see Weal's Quarterly Papers on Engineering. We believe the mortar made by the ancients was mixed with blood and iron filings. From the Professional Papers of the Royal English Engineers. 310w2. Concrete of lime and stones will not concrete. Godwin gives stones, 2, sand, 1, lime sufficient to mix well, then add boiling wateri use while hot, and ram; the stones not larger than a hen's 72B132 TUNNELS. egg. Gravel means coarse, gravel 5, sand, 3. 3. buckets of gravel, i bucket of lime, and - bucket of boiling water-ready for use in 21 minutes. An arch of concrete, 4 feet thick, was found to be bomb-proof, at Woolwich, England. TUNNELS. 310w3. foosaic Tunnel, (fig. 83c), has shafts, the central one of which is 1030 ft. deep, of an elliptical form. The conjugate diameter across the roadway is 15 ft., and the transverse along the road 27 ft. There are other shafts, some 6' x 6', 10' x 8', and 13' x 8'. Where the shaft is not in rock, it is lined on one side 2' 8" to 2' 2", and on the other side, 2' 4" to 1' 8". The work was carried on the same as Mount Cenis, using the Burleigh rock drill, mounted on two carriages; each carrying five drills, standing on the same cross section, 6 ft. asunder. The explosives used, were nitroglicerine in hard rock, and powder in other places. The compressed air, at the time of the application, was 63 lbs. per square inch, which was 2 lb. less, due to its passage through two cast-iron pipes, each 8 inch. in diameter, through which fresh air was supplied to the workmen. Three gangs of men worked each eight hours per day, excepting Sundays. Average shafts, 26 ft. high and 26 ft. at widest part, sunk 25 feet per month, and in rock, about 9 ft. per month. Tunnelfor one track is 19 ft. from the top of the rail to the intrados of the crown, and widest width = 184 ft. Thickness of the arch =1' 10", horse shoe form. 310w4. The Box Tunnel, (Fig. 83a), on the Great Western Railroad, England, (horse shoe form), is 28 ft. wide at the top of the rail and 244 ft. high. Thickness of arch 2' 3". At 13 ft. above the rail, width is 30 ft. At 20 ft. above the rail, width is 20 ft. At 24. ft., width is 0. Length 9600 ft. in clay and lime stone. Shafts at about every 1200 ft. 310w5. The Sydenham Tunnel, (Fig. 83b). On the London and Chatham Railroad, England. Length 6300 ft. Five shafts, each 9 ft. diameter. Thickness of arch 3 ft. Width at level of rail 22. ft. At 5 ft. above rail 24 ft. At 10 = 23 ft. At 16 = 18 ft. At 204 ft. met under part of the crown. 310w6. 7unnel for one track. (Fig. 83e.) 310w7. BLASTING ROCK. Let P =l bs. of powder required when == the length of line of least resistance, that is, to the nearest distance to the surface of the rock in feet, which should not exceed half the depth of the hole. /3 P O-. One pound of powder will loosen about 10,000 lbs. of rock. Nitroglycerine is ten times as powerful as powder, but extremely dangerous. Dualine is ten times as powerful as powder. Gun-cotton is about five times that of powder. Giant, Rendrock, Herculian, and Neptune, about the same as nitroglicerine. Giant powder is preferable, but is more expensive. In small blasts, 1 pound of powder loosens 4J tons of rock; and in large blasts, it loosens 2 3-5ths. tons. It is usual to use. to i lb. of powder for ton weight of stone to be removed, taking advantage of the veins and fissures of the rock in sinking. A man in one day will drill in granite, by hammering, 100 to 200 in......., churning, 200..,.,. lime stone, 500 to 700 ARCHES, PIERS, ANI) ABUTMENTS. 72B133 310-a8. The bottom of the hole may be widened by the action. Of one part nitric acid added to three parts of water. See Fig. 85, which represents a copper funnel of the same size as the hole. Inside of this is a lead pipe an inch in diameter, reaching to within one inch of the bottom. About the outside of the funnel is made air-tight at the surface with clay around it. At g, above the neck, is a filling of hemp. The acid acting on the limestone in a bore of 21 inches, will remove 55 lbs. of stone in four hours. The frothy substance of the dissolved rock will pass through the copper tube. And after a few hours, the hole is cleaned and dried, and made ready to receive the powder. One lb. of powder occupies 30 cubic inches of space, fills a hole 1 inch in diameter and 38 inches deep. As the square of 1 inch diameter filled with 1 lb. of powder is to 38 inches in depth, so is the square of any other diameter to the depth filled with 1 lb. of powder. See Sir John Burgoyne's Treatise on Blasting. When the several holes are charged they are connected by copper wires with a battery and then discharged. The blowing up of Hell Gate, by Mr. Newton, is the greatest case of blasting on record. At the Chalk Cliff, near Dover, England, 400,000 cubic yards were removed by one blast. Length of face removed, 300 feet. Total pounds of powder, I8,500. ARCHES, PIERS, AND ABUTMENTS. 310w9. Next page is a table showing several bridges built by eminent engineers, giving their thickness at the crown or key of each, as actually existing, and the calculated thickness, by Levell's formulas. We also give Trautwine. Rankine & Hurst's formulas. M. Levelle, in 1855, and since, has been chief engineer of Roads and Bridges in France. We believe that all surveyors and engineers are familiar with the names and works of Trautwine. Rankine & Hurst. C = thickness of the crown. r = radius of the intrados. h = height of the arch. s = half span. v = height of the arch to the intrados, and r the radius of the circle. Then, S2 - V2 2v See Euclid, Book III, prop. 35.* S+10 S+32.809 By Lerelle. C =- 30 for French meters, - 3- 0 for English ft. By Prof. Rankine. C = I 0.12r for a single arch and V! 0.17r for a series of arches. B, Trautzwine. C / r +S + 0-2 feet for first-class work. 4 To this add one-eighth for second-class work, and one-fourth for brick or fair ruble work. By, Hurst. C = 0.3 'r for block stone work.,,, C = 0.4 V r for brickwork and 0.45 V r for rubble work. _ S C = 0.45 V S + -2 for straight arch of brick, with radiating joints. Mr. Levelle finds his formula to agree with a large number of arches now built from spans of 5 to 43 meters, including circular, segments of circles, semicircular, and elipitical. * If two lines intersect one another in a circle, the product of the segments of one = the product or rectangle of the others. 72B134 BRIDGES. BRIDGES, WITH THEIR ACTUAL AND CALCULATED DIMENSIONS. 310-w10. THE CALCULATED ARE BY LEVELLE'S FORMULA. NAMES OF BRIDGES. SEGMENTS OF CIRCLES. Pont de la Concorde, Paris. --- —---- i, de Pasla, i, ---- i, de Courcelles du Nord -------- it des Abbattoirs, Paris --- —--- if de Ecole Militaire, ----- i, de Melisey --- —----- i sur le salat --- —--------------- It de Marbre, Florence, Italy --- —, on the Forth, at Stirling, Scotl'd i, de Bourdeaux, France i, Saint Maxence Sur la Oise,,,, de la Boucherie, Nuremburg,, de Dorlaston --- —------------- du Rempart, R. R. Orleans to Tours --- —--—. --- —-------- de Saint Hylarion, R. R. Paris to Chartres --- —----------- de la Tuilierie, des Voisins,,, y Prydd, Wales --- —----- Cabin John, Washington Aqueduct —. Ballochmyle, Ayr, Scotland --- —----- Dean, Edinburgh,,, -- Ordinary over a double R. R. track — Grovenor, on the Dee ------------- Turin, Italy. --- —------- Mersey Grand Junction ------—. --- Philadelphia & Reading R. R --- —-- SEMICIRCLES. Pont des Tetes, on the Durance ----- i, de Sucres --- —----------------- It de Corbeil --------------------- de Franconville. ----------------., du Crochet --- —---------------- des Chevres ------------------- de Orleans A'Tours --------—. ELIPTICAL. Pont de Neuilly, Paris. --- —-------,, de Vissile Sur le Romanche B ---,, du Canal Saint Denis --- —-----,, de Moielins A' Nojent --- —----,, du Saint du-Rhone --- —--------, de Wellesly a' Limerick, Ireland i, Sur le Loir --- —---------------,, de Trilport-. --- —-------------,,.., Royal, Paris --- —--------------,, Gignac sur le Herault.. --- —---, Alma sur le Seinne --- —-------- t de Vieille Brioude sur le Allier.-, Auss, on the Vienna R. R --- — ~._. I 0, 23.40 5.00 9.80 16.05 28. 11.40 14. 42.213 16.30 26.49 23.40 29.60 26.37 1.20 2.0 4.0 5.0 140 220 181 90 30 200 147.(5 75. 41:3. 0 18 16.82 7.4C 4. 1.5C 20. 38.9 41 9( 12. 18. 34. 2 1.3 24.2( 25.6 24.5( 23.55 48.7: 4:3 54.21 20. 1.93.80.90 1.55 2.99 1.50 1.90 9.10 3.12 8.83 1.95 3.90 4.11 35. 57. 90.5 30. 7.5 42. 18. 14.5 8. 19. 8.41 3. 70 2. 7..i 10. 9. 74 11.69 4.5C 5.13 9. 74 4 3.13 1 8.77 8.44 92 3( 2 13.3( 8.6( 0 21. 6. 6 0.97.52.65.90 1.14.60 1 20 1.46 1.522.65 1.14.40.510.55 1.5 4.16 4.5 3.0 1.83.4 4.90 3..50 1.45.40.5(.35 1. 1.62 1.95 3.0 1.28 1.36 1.0 0).75.50 1. 1.62 1. 1.30 1.20 1.10 1.'395 1.30 7 1.10 i rY.50.66.87 1.29.71.80 1.74.88 1 23 1.11 1.32 1.21.37.40.47.50 5.76 8.42 7.16 4.09 2.09 7.76 6.01 3.5() 2.56 1.6C 0.8.4.56.A0.30 1. 1.6: 1.71.7 1.4 1.0l 1.1 -1.61 1.17 1.1' 1.90 2.1. ) 1.(9 -c 2 3 3 6 1 3 j: 3 2 I6 I H).0.93.55.21.32.45.03.2(.8(.4(.5( 1 '5.5 4 '1 1 I 41 II 0 0, 15 )j 1I 0 r: ir 0 I.7( 0..2(.8( 1.8E 1.2(.54 L.24 L.4( 1.5< 7 )4 I 31 38 0 0.0 15 )3 '5 zD. i'.0..95 '.24 1.68 5.15 L2.2 ).00.74 L.0O 1.58 L.77 t [1 I5 I:9 0) 0 0 1 160 097 132 136 192 083 156 L.70.40. 10 (.15 I 1. 2.3 3.1 1.5 108 3.7 4.4 108 3.4.250 g.375, uz 4.6 5.( 6.4.250 1.9 5.8 6.2.344 = The Line of Rupture in a semicircle arch, with a horizontal extrados, is where the line of 60 degrees from the vertical line through the crown meets the arch. This has been established by Mr. Mery, and Mr. Petit, of France, the latter a Captain of Engineers. Mr. Lavelle, from Petit, gives for semicircular arches, where d = diameter, t = thickness of the arch or key at the crown. When the diameter = 2,m00, 5,m00, 10m,00, 20m,00, then ( = L. Id = 0.40, 0.50, 0.67, 1.00, whose corresponding angles of rupture are 59~. 63~. 64~. and 65~., from the vertical line CD. Lavelle adopts 60~. BRID)GES. 72)B 135 310x. TELFORD'S TABLE.-HIGHLAN I) BRIDGES. to 4) 4-ru P E 0 0 >* 4) 4)I 4... 2~~ 0(5 Sd.6 TM C' 110l 2/. 6/1 T 1. 6 I 0 11 18 4 1.- 30 46.91O 24 6 1.9 4~1.1.0 414- 2.94 1.4 10 3 1.3 3.0 2.6 2.0 1.0 50.. 2.6 6.0 6.01 3.6 1.6 310x. SEGMENT ARCHES. B3ATTER OF PIERS '4 -INCH IN ONE FOOT. 4) 4~~~~~ ~~~...)d t..0 0 ~~~~~~~~~~ U) 4 l0ft 1'. 2" 5' to 20'3' to 3' 9 " 3'. 0' 1'. 3'to 2'.7j 2 3 3'.0O' -15 1.6 5 20 1 1 3. 0 '2. - 7 2.7', 4.6 20 1.6 5 40 3 4. 6 3. 0 2. '.Yi,343 4 6.0 25 1.6 5 40 3 4.10 —3. 93. 0- 411 3.4-L 7.3 30 1.103- 5 40 4. 1'1 6. 4. 1 4. 1, 6.0 4. 11 9.0 35 2.3 10 H40 4.101 6. 4 J 4.10 5. 3 "1 6.4'1 4 6 10.6 40 2.3 o 57 7.1 - 5. 3 4.10 ', 6. 4.l0.L1. 45 2.7 6b 47 7. 6 6. 0 5 7'1 13.0 50 3.0 7.1 8. 3 7. 1 6b 9_ 14.6 55 3.0 710 9. 4 7.10 /. 1 16.0 60 3.0 8. 7 9. 8 8. 3 7 10y I 17.3 310xl. RADIUS OF CURVATURE. Fig. 86-Let AI3CD be a curve of hard substance. WVind a cord oni it from 1) to A. Take hold of the cord at A and unwind it, describing- the oscilatory curve a, 1), c, d. When the cord is unwound as far as B and C, etc., the point or end A wvill arrive at 13, C, etc., and the line BC wviii be the radius of' curvature to the lpoint B, and the line Cc will be the radius of curvature to the point C. The curve ABCD may be made on thick lpasteboard, and drawn on a large scale, by which mechanical means the radius of curvature can be found sufficiently near. The radius of curvature of a circle is constant at every point. 310X2. Tension is the radius of curvature at the crowvn. 310x3. Pier-s. L. B. Alberti says piers ought not to be mnore than onefourth or less than one-flfth the span. The pier of Blackfriar's Bridge, London, is about one-fifth the span. The pier of Westminster Bridge, London, is about one-fourth the span. T1he pier at Vicenza, over tile Bacchilione, Palladio, makes one-fifth the span. Piers generally are found from one-fourth to one-seventh of the span. The end of the pier against the current is pointed and sloped on top, to 72B136 BRIDGES. break the current and floating ice, if any. When the angle against the current is ninety degrees, the action of the water is the least possible, and half the force is taken off. 310x4. The horizontal thrust of any semi-arc. Fig. 87, AEKD. By section 313, find G, the centre of gravity of said arc, or by having the plan drawn on a large scale-about four feet to one inch-the point G can be found sufficiently near. Draw OGM at right angles to AQ, and draw DO parallel to AQ. We find the area A, of AEKD. We have A M from construction, and OM = QD - rise at the arch, and AQ - one-half the span, and the height of the pier, XV, to find the thi:kness of FE - BL. We have OM: AM:: A: T, equal to its thrust in direction of AH on the pier. We have taken the area A to be in proportion to the weight, and make the pier to resist three times the thrust, T. This fourth term F, will be the surface of the pier BEFL, whose height. XY, is given. Therefore, 3T Thickness of the pier out of wctcr. -\' Let AQ = 28, MO - 18, AM -= 9, A = 270, and XV -- 30. 18: 9:: 270: 135 T == thrust on the pier at B. The pier 30 feet high is to sustain for safety three times 135 -= 405 405 30 -- 13.5 ft. -:BL, the required thickness. 310x5. The thrust to overturn the pier about the point L, AM x Ax CB GM= — xA -C which must be = EIB x BL. OM 2AM x Ax CB\! *' BI OOM x EIB ) thickness of a dry pier. ( 7AMxAxCB / BL = (OM- (3'5 iB L- A B) thickness w, when in water. Here we take A, as before, three times the area of AEKD. In circular and elliptical arches, we take AB1 -diameter for circular, and transverse axis for elliptical; CD for rise or versed sine in the circular, and the confugate diameter in elliptical, and DQ for the generating circle of the cycloid. DP -- abscessa, and PC its corresponding ordinate to any point, C, in the curves. Having determined on the span and rise of the arch, and the thickness, DK, at the crown, we find the height, CI, at the point C, corresponding to the horizontal line, PC, an ordinate to the abscissa DP. See the above figure. DK x DQ3 CI = pQ3 For the circle. pQ3 DK x DQ3 CI- p Q3 TFor the ellipse - same as for the circle. PQ3 DK x DQ2 CI (DQ-DP) For the cycloid. DK x (C+DP) CI C - For the catenary. Here C is the tension or radius of curvature at D. The above three forms are practicable. Sometimes for single arches the parabolic arch is used. CI = DK for every point, C, in a parabola. In all cases, CI is at right angles to the line AB. BRIDGES. 72B137 Gwilt, in his work on the equilibrium of arches, says: " The parabola may be used with advantage where great weights are required to be discharged from the weakest part of an edifice, as in warehouses, but the scantiness of the haunches renders them unfit for bridges." 310x6. TrIE CATENARIAN is correctly represented by driving two nails in the side of a wall or upright scantlings, at a distance equal to the required span BA. From the centre, drop a line marking the distance DQ equal to the rise of the arch, and let a light chain pass through the point to ADB, and we have the required curve. Let DP and CP be any abscissa and corresponding ordinate, to find CI from the intrados to the extrados. TO FIND TIlE TENSION AT D. 310x7. Let c -- tension constantly at the vertes. KD = thickness of the arch at crown = a. DP = --- any abscissa x, and PC - y, its corresponding ordinate. x / y2 8x2 691x4 23851x6 \ C =- x ( y2 + 0.3333 - + &C. This is - x, 03333- 45y2 + 3780y4 -453600y6 & This is Dr. H-utton's formula, excepting that the parenthesis, is erroneously omitted.,- /5Z2,V2,V 4 A-4 C,- x ( + 0'3333 - 0'1778 - + 0-1828 T - 00526 T &c. Example given by Hutton. Let DQ -- 40 - x, and one-half the span AQ - 50 - y. Here the tension C = 20 x (1'5625 + 0'3333 - 0-1137 + 0'0749 - 0:0138, &c.) That is C = 20 x 1 8432 = 36 864, as given by Hutton. TO FIND TIIE RADIUS OF CURVATURE AND TANGENT TO ANY POINT C OF THE CATENARIAN. Fig. 90. 310x8. Produce QD to P making OP = CO x!2c + DO + DO2. Join PC, which will be the tangent to the point C. From the point C, draw CW at right angles to Al. And make As c: c- + DO:: c + DO: CR = Rad. of curvature. When the abscessa DO = o: C: c:: c: CR=c. HIence the tension at the lowest point D is equal to the radius of curvature. Let the span = 100 and rise — 40 feet, then radius of curvature for a segment of a circle = 51.25 - radius of curvature.,, Parabola, = 30.125,,, Ellipsis, = 62.5,,, Catenary, = 36.864, The strength of the Parabola at the crown is to the above figures as the rad. of curvature of the other figures, to that of the parabola; hence the strength of the parabola is 2.1 times that of the ellipsis, and P: C:: 36.864:30.129. Parabola is 1.22 as strong as the Catanerian. To find the extrados to the point C. Whose abscissa DO = x and ordinate CO = y are given. Fig. 90. Let KD = a and DO = x and CO = y as above. Then from Hutton: ac + ax ax CI- a + -- c c KV -c-a ax KV X x = -- C C DO: KV:: always as c: c-a. The extrados will be a straight line when a = c, the tension at K. 72B138 BRIDGES. In the above example, where we have found c = 36,864 feet to have the extrados a straight line, would require a = KD, to be nearly 37 feet. Assuming the same span 100, rise =- 0, and putting DK = 6 feet, the extrados and the arch will be as figure 91. This arch is only proper for a single arch, where the extrados rises considerably from the springing to the top. AC = CB is given = a -= -span. CD = h = height. Figure 92. DE = distance of chain to the lower part of the roadway parameter. K and M any points in the curve, from which we are to find the suspension rods KD and MP, etc. CD-DE CD-DE DK = AC x -K2 + and AC x DM2 + DE=MP CD-DE We have AC, a constant quantity;. Let it = c, and divide EG into any parts as Q, P, D, R, etc. Then the length of the rod at R = RS c x ER2 and rod QT = c x EQ2. 310x9. To find the sectional area in inches of any rod, as DK, and the strain in pounds on it, at K. Let W = weight of one lineal foot of the roadway when loaded with the maximum weight. At-I Strain on K.-Let 2 - - 0.0003 be divided into W, it will give the strain in pounds on K. Let this strain be represented by S. Sectional area of the rod DK S= S + 0, 0000893 lbs. CD- DE DK- AC2 x HK2 + DE = length of the rod I)K. Let W = weight of every lineal foot of roadway and its maximum load CD - DE thereon. Strainz = 2 AC-2 - 0.0003, this divided into W, gives the strain on the lowest point D of the chain. Sectional area of chain at I) is found by multiplying the last, by.0000893. Example. Half span AC = 200. DE -2 feet, wt. of one lineal foot of road =- 500. Horizontal distance HK = 100 ft. CD -- 40 ft. 38 x 1002 380000 40-2 200x200 200x200- 9.5 -= HD. And 9.5 + 2 - 11.5 rod KD. (40- 2) 3S x 2 76 2200 x200= 40000 40000 - 0.0019, and.0019 - 0.0003 = 0.0016. 500 And 006- = 3.125.000 Ib. Ib. strain on the lowest point of chain at B. And 31250000 x 0.0000893 = 279 square inches = sec. area at B. 2x9 9 19 100 = 100-.0,190, this squared + 0,0261 + 1 - 1.0262, whose square root -= 1.013, which x by 3125000 = 3165625 lbs. strain on the point K, which x by 0.0000893 = sectional area = 283 square inches of chain at K.. Basis here. Took one-sixth the load for coefficient of safety. A bar of iron 12 feet long and 1 inch square weighs 3.3 lb. The tensile strain to break a square inch of wrought-iron is taken at 6720 lb., the iron loaded with one-sixth its breaking weight. On bridges, the load should not exceed one-twentieth of the weight which would crush the materials in the arch stones; and where there is a heavy travel, should not exceed one-thirtieth. PIERS AND ABUTMENTS. 72B139 PIERS AND ABUTMENTS. 310x10. When the angle at the point of an abutment against the stream is 90 degrees, then the pressure on the pier is but one-half what it would be on the square end. The longer the side of the triangular end of the pier is made the less will be the pressure. Let ABC represent the triangular end against the stream, and C the furthest point or vertex. Gwilt says "that the pressure on the pier is inversely proportional to the square of the side AC, or BC, and that the angle at C ought not to be made too. acute, lest it should injure navigation, or form an eddy toward the pier. Abutments. In a list of the best bridges, we find the abutment at the top from one-third to one-fifth the radius of curvature at the crown of the arch. AMoleswzorth gives the following concise formula: T ==thickness of abutments 6 R 4- ( )2 ) I - 2H Here R = rad. at crown in feet, H height of the abutment to springing in feet, for arches whose key does not exceed three feet in depth. Example. R =20+. H = 10. (120 + 9)? == 11.36 from which take 3, will give the abutments without wing walls or counterforts. Abutments.-To counteract the tendency to overturn an abutment, let the arch be continued through the abutment to the solid foundation, or by building, so as to form a horizontal arch, the thrust being thrown on the wing walls, which act as buttresses. 2d.-By joggling the courses together with bed dowel joggles so as to render the whole abutment one solid mass. 310x0. The depth of the voussoirs must be sufficient to include the curve of equilibrium between the intrados and extrados. The voussoirs to increase in depth from the key to the spanging, their joints to be at right angles to the tangents of their respective intersections and curve of equilibrium. The curve of equilibrium varies with the span and height of the arch stones, the load and depth of voussoirs, and has the horizontal thrust the same at any point in it. The pressure on the arch stones increase from the crown to the haunches. 310xl. SKEW ARCHES. In an ordinary rectangular arch, each course is parallel to the abutments, and the inclination of any bed-joint with the horizon will be the same at every part of it. In a skew arch this is not possible. The courses must be laid as nearly as possible at right angles to the front of the arch and at an angle with the abutments. The two ends of any course will then be at different heights, and the inclination of each bed-joint with the horizon will increase from the springing to the crown, causing the beds to be winding surfaces instead of a series of planes, as in the rectangular arch. The variation in the inclination of the bed-joints is called the thrust of the beds, and leads to many different problems in the cutting. See Buck on Skew Bridges. EAST RIVER BRIDGE, NEW YORK. 310x2. Brooklyn tower, 316 feet high, base of caisson, 102 x 168 feet. New York tower, 349 feet high, base of caisson, 102 x 178 feet. The Victoria Bridge, at Montreal, 7000 feet long, one span, 330 feet and fourteen of 242 feet, built in six years. Cost, $6,300,000. Built by Sir Robert Stephenson. 72B140 BRIDGES AND WALLS. Concrete Bridges.-One of these built by Mr. Jackson in the County of Cork, Ireland, is of cement, one part sand. Clear sharp gravel, six to eight parts. Rammed stones in the piers. He also built skew bridges of the same materials. AfM. MAcClure built one 18 feet span, 3~ feet rise, and 1 feet thick at the key, and 22 feet at the springing. Built in ten hours, with fifteen laborers and one carpenter. Piers are of stone, centre not removed for two months. Proportions of materials used: Portland cement, 1, sand, 7 to 8, 40 per cent of split stone can be safely used in buildings, and 25 per cent in bridges. Stones used in practice, 4 to 6 inches apart. Cottage walls, 9 inches thick. Chimney walls, 18 inches. Partitions, 4 inches. Walls, sometimes 18 feet high and 12 inches thick. Garden walls, Y mile long, 11 feet high, and 9 inches thick. Cisterns, 5 feet deep and,6 x 5 feet 9 inches thick. Cost of one cubic yard of this concrete wall, 12 to 15 shillings, at 3 to 4,dollars. 310.3. These kind of buildings are common in Sweden, since 1828, and built in many towns of Pomerania, where its durability has been tested. It is applicable to moist climates. Where sand can be had on or alear the premises, walls can be built for one-fourth the cost of brickwork. In Sweden, they use as high. as 10 parts of sand to 1 of hydraulic lime. The lime is made into a milk of lime, then 3 parts of the sand is added, and mixed in a pug-mill made for that purpose. After thus being thoroughly mixed the remainder of the sand is added. These walls resist the cold of winter, as well as the heat of summer. The pug-mill is made cylindrical, in which on an axis are stirrers, moved by manual labor, or horse power, as in a threshing machine. One "of these, in ordinary cases, will mix 729 cubic feet in one day. Let us supposeka house, 40 feet long, 20 feet wide, and 1 foot thick. This caisse will mix I to 1 loise, cubic, per day, which will be made into the wall by three men, making the wall all round, 6 feet high, moved upwards between upright scaffolding poles. There is a moveable frame, stayed at proper distances, laid on the wall to receive the beton where two men are employed in spreading it. 310 Ox4. TO TEST BUIDING STONES. Take a cubic 2 inches each way, boil it in a solution of sulphate of soda {Glauber salts) for half an hour, suspend it in a cold cellar over a pan of clear sulphate of soda. The deposit will be the comparative impurities. Rubble work.-The stones not squared. Coursed work.-Stones hammered and made in courses. Ashlar.-Each stone dressed and squared to given dimensions. To prevent sliding -Bed dowels are sunk one-half inch in each, made of hardwood. [Valls faced with stone and lined with brick are liable to settle on the inside, therefore set the brickwork in cement, or some hard and quick setting mortar. The stones should be sizes that will bond with the brickwork. Bond in masonry is placing the stones so that no two adjoining joints:are above or below a given point will be in the same line. The joints must be broken. Stones laid lengthways are called stretchers, and those laid crossways, headers. ANGLES OF ROOFS. 72B141 Brick work.-English bond is where one course is all stretchers and the. next all headers. Flemish bond is where one brick is laid stretcher, the next a header and~ in every course a header and stretcher alternately. Tarred hoop-iron is laid in the mortar joints as bonds. 310x5. ANGLES OF ROOFS, WITH THE HORIZONTAL. CITY. COUNTRY. N. Hollow Roman Sa tes. Latitude. Plain tiles. tiles. tiles. Carthagena, -_- Spain ----— 37' 32' 24' 12' 16' 12' 1.9' 12' 22' 12' Naples, --- —Italy --- —— 40 52 26 12 18 1 2 2 1 12 24 12. Rome, --- —do --- —-4 1 53 27 0 19 0 22, 025 0 Lyons, --- —France, --- —45 48 30 0 22 0 I-!) 4 28 0 Munich --- —Germany- 48 7 Itl 48' 23 484 26 4S 29 48 Viena,- --— Austria — - 48S 5 32 0 24 0 27 0 30 0 Paris, -_-. —France ---— 48.52 32 36 24.36' 27 t3i 30 36 Frankfort,- -— On the Main, 50 8 33 48 25.348 28 48 33 48 Brussels,- -— Belgium, - — 50 52 34 36 26; 39 29.36 32 36 London, --- —England, --— 51.31.35 24 27 24 30 24 33 24 Berlin ---— Germany', -— 52 33:16 306 28 36 31 36' 34 3 6 Dublin,- ----— Ireland, --- —53' 21' 37 48' 29 48 32) 48 35 48 Copenhae en, - Denmark- 55 42 40 48 32 48:35 48 38 48 St Petersburgh Russia ---— 59 f.40 48 24 40 '24 4:3 24 46 24 Edinburgh, - - - Scotland, 55.57 41 12 33 12 36 12 39) 12 Bergen ---— Norway - --- 60( 4821 40 24 432 464 From the above table, we see that the elevation of thie roof increases one degree for every.34ths degree of latitude, from Carthagena to Bergen. Pressure onl Roof' For weight of roof, snow, and pressure of the wind, 40 lbs. per square foot, on the weather side, and 20 lbs. on the other, under 150 feet span. Add 1 lb. for every additional 10 feet.-Stoney,, p. 524. Greatest pressure of wvindl observed in Great Britain has been i55 lbs. pet-r square foot 0. 382 lbs. per square inch, 310x6. TRUSSED BEA.MS AND ROOFS. Let AD b =' half the span. AB =tie-beam resting on the wall-plates. CD = hi = height king-post. AC b length of principal rafters, l(~ to 12 feet asunder. Q = angle BAC angle of minimum pressure on the foot of the rafter-. Secant of the angleQ 1. See fig. 83 A. When Q = 35' 16', the pressure P is a minimum. Moseley's Akchanics, Sec. 302, Eq. 395. Then Ih = 0-7072b Here s =distance between each pair of rafters. / =- I '248b *. = weight of each square foot of roof, IV =I -2248b s w,~ including pressure of the wind and snow, as. dletermined in the locality. W = weight on each rafter. 310x7. [To calculate the parts oj'a common Roof. Let a = sectional area of a piece of timber. dI = its breadth, and I = its length. s span of the roof in feet. p length in feet of that part of the tie-beam supported by the queen-post. King-1post. aI Is x 0-121 for fir, and at = Is x 0-13 for oak. Queen-post. it Ip x 0-27 for fir, and a = 1px 0,32 for oak. The Beam. d IV x 1 47 for fir. Princi 1 pal rafters with a king-post, a'= x 0-96 for fir. 12 sit with two queen-posts, d -= 72B142 ARTIFICERS' WORK AND JETTIES. Straining Beam. Its depth ought to be to its thickness as 10 to 7. 0 d I -d = V ls x 09 for fir. Struts and Braces. d = i l p% x 0'8 for fir, and b = 0'7 d. Purlins. -d = 48/ b 3c for fir, or multiply by 1 04 for oak, and b = 0. 6 d. Common Rafters. d = -b x 0'72 for fir, or 0'74 for oak. Two inches is the least thickness for common rafters, therefore, in this case, d = 0'571 /for fir. 310x8. Lamenated arched beams formed of plank bent round a mould to the required curve and bolted are good for heavy travel and great speed. JETTIES. 310x9. In rivers, at and near their outlets, sand bars are formed where the velocity is less than that of the deep water on either side. The desired channel is marked out, and two rows of piles are driven on the outsides, to which the mattrasses are tied. The space or jetties thus piled are filled with matrasses made of fascines of brushwood, bolted by wooden bolts and boards on the top and bottom of each, sloping from the outside towards the channel. One in New Orleans, now in progress of construction by Capt. Eads, C. E., is from 35 to 50 at bottom, and 22 to 25 at the top, matrasses 3 feet thick. From 3 to 6 layers are laid on one another. Mud and sand assist to fill the interstices. They are loaded with loose stones, and the top covered with stone. The water thus confined causes a current, which removes the bars. Drags may be attached to a boat and dragged on the bars, which will assist in loosening the sand. The mattrasses are built on frames on launchways on the shore, and then floated and tied to the piles. Jetties may be from 10 feet upwards, according to the location. Those of the Delta, at the mouth of the Danube, are filled with stones. See Hartley on the Delta of the Danube, for 1873. General Gilmore, U. S. Engineer's report on the Jetty System, for 1876. General Comstock's, U. S. A., report on the New Orleans South Pass. 310x9. Excavationsfor Foundation, measured in cubic yards, pit measurement. Allow 6 inches on each side for stone and brickwork, and no allowance is made where concrete is used. Where excavation is made for water or gas pipes, slopes of 1 to 4 is allowed. State for moving away the earth not required for backfiling, the distance to which it is to be moved, and inclination, and how disposed of, whether used as a filling or put in a water embankment. This done for first proposed estimate. Filling is measured as embankment measurement, for the allowances for shrinkage add 8 per cent for earth and clay when laid dry. When put in water, add one-third. Bog stuff will shrink one-fourth. See p. 210. 100 cubic feet of stone, broken so as to pass through a ring 1 inch in diameter, will increase in bulk to...................... 190 cubic feet. Do do to pass through a 2 inch ring,........ 182,, Do do,,,, 2 17........ 170... Rubble Masonry.-One cubic yard requires 1 1-5 cubic yards of stone and 1-4 cubic yard of mortar. Ashlar masonry requires 1-8 its bulk of mortar. All contractors ought to be informed that when they haul 100 yds from the pit, that it will not measure the same in the "fill" or embankment. MEASUREMENT OF WORK. 72B143 Isolated Peirs are measured solid, to which add 50 per cent. Brick Walls are measured solid, from which deduct one-half the openings; then reduce to the standard measurement, for example: multiply the cubic feet by 22?., and divide by 1000, to find the number of thousands of bricks, as calculated in Chicago, where the brick is 8 by 4 by 2 inches. NOTE.-One must observe the local customs. The English standard rod is 16'x16t'x131" = 272 superficial feet of the standard thickness of 1~ bricks or 1,,1" = 306 cubic feet. 100 cubic feet brickwork requires 41 imperial gallons of water, or 49 United States to slake the lime and mix the mortar. When the wall is circular and under 25 feet radius, take the outside for the width. Include sills under 6 inch. Cornices. The English multiply the height by the extreme projection for a rectangular wall. In various places in America, the height of the cornice is added. Chimneys, flues, coppers, ovens, and such like, are measured solid, deducting half the opening for ash-pits and fireplaces. Three inches of the wall-plate is added to the height for the wall; this compensates for the trouble of embedding the wall-plates. Stone Walls. Measured as above, and take 100 cubic feet per cord of stone mason's measurement. The cord is 8x4 feet by 4 feet, or 12 cubic feet, or it is measured in cubic feet. The surface is measured by the superficial foot, as ashler hammered cut stone, and entered separate. Chimneys are measured solid, only the fireplaces deducted in England. Slater's Work. Measured by the square of 100 feet. Measure from the extreme ends. Allow the length by the guage for the bottom course or eve. Deduct openings; but add 6 inches around them; also 6 inches for valley hips, raking, and irregular angles. Filling. Measured as above. Add for valleys, 12", eaves, 4". All cutting hip, etc., 3 inches. A Pantile is I'.I " x.( " x I inch, weighs 51 lt, more or less, 1 sq. = 897 lb. A Pantile 101" x 6' " x 8 inch, weighs 2~ lb,.,. =1680 lb. Pantile laths, are 1 inch thick and 1L inch wide and 10 feet long. Plastering. Render two coats and set. Lime, 0'6 cubic feet; sand, 68; hair, 19 lb; water, 2'7 imperial gallons. Measure from top of baseboard to one-half the height of the cornice; deduct one-half for openings, or as the custom may be. Gutters should have a fall of 1 inch in 10 feet. Painting. 1 lb. of paint will cover 4 superficial yards, the first coat, and about 6 yards each additional coat. About 1 lb of putty for stopping every 20 yards. 1 gallon of tar and 1 lb of pitch cover 12 yards first coat, and about 17 yards the second coat. 1 gallon of priming color will cover 50 superficial yards. 11 white paint 11 41, i,, Other paints range from 44 to 50 1 f, Take where the brush touched. Keep difficult and ornamental work separate. Also, the cleaning and stopping of holes, and other extras. Joiner's Work. Measured as solid feet or squares of 100 feet superficial. Flooring by the square of 100 feet superficial. Skirting, per lineal foot, allowing for passages at the angles. Sashes and frames. Take out side dimensions, add 1 inch for any middle bar in double sashes. 72B144 SANITARY HINTS. Engineers and architects ought to discountenance draining and wasting sewage into rivers. The paving of streets with wooden blocks, which is certainly unhealthy, causing malarial fevers. MacAdam stones, heavily rolled, etc., or stone blocks, are better. The French pavement, now used in London, is the best, which is made by putting a coat of asplmlt 2i to 3 inches thick, on a bed of concrete 8 to 10 inches thick. CHICAGO, Oct. 15, 1878. M. McDERMOTT. SANITARY IIINTS.:310x10. The surveyors and engineers are frequently obliged to encamp where they encounter mosquitoes and diseases of the bowels. Oil of pennyroyal around the neck, face, and wrists. Apply around the neck and face, at the line of hair, and around the wrists, two or three times during the day and once or twice at night. This is a pleasant application to use, but disagreeable to the mosquitoes. We used to use a mixture of turpentine and hog's fat or grease, and at other times, wear a veil; both were but of temporary benefit; the first, was a nuisance, and the latter, by causing too much perspiration, was unhealthy. Drinking too much water can be avoided by using it with finely ground oatmeal; by using this, the surveyor and engineer, and all their men using it, will not drink one-fifth as much water as if they did not use it. DIARRHOEA. The best known remedy is tincture of opium; tinct of camphor; tinct of rhubarb; tinct of capsicum (Cayenne pepper); of each one ounce. Add, for severe griping pains, 5 drops of oil of Anisee to each dose. Dose.-25 drops in a little sweetened water, every hour or two, till relieved. Sometimes we put a little tannic acid, which is a powerful astringent. Avoid fresh meat, and use soda crackers. To escape Chills and Fever, use quassi, by pouring some warm water on quassi chips, and letting it stand for the night. Take a cupful every morning. Never allow wet clothes to dry on you, if it can possibly be avoided. Tannic acid and glycerine will heal sore or scald feet. Wafers applied to your corns, after being well soaked in lye water, will cure them. Apply the wafer after being moistened on the tongue; then apply a piece of linen or lint. Repeat this again when it falls off, in two or three days, and it will remove the corn and the pain together. To Disinfect Gutters, Sewers, etc. Take one barrel of coarse salt and two of lime; mix them thoroughly, and sprinkle sparingly where required. This acts as chloride of lime. 7b Disinfect Rooms in Buildings. Take, for an ordinary room, half an ounce of saltpetre; put on a plate previously heated, on this pour half an ounce of sulphuric acid (oil of vitriol); put the plate and contents on a heated shovel, and walk into the room and set the plate on some bricks previously heated. This destroys instantaneously every smell, enables the nurse to go to the bedside of any putrid body and remove it. Where there is sickness, as now in Memphis, etc., it causes great relief to the sick and protection to those in attendance. This is Dr. Smith's disinfectant, used at Gross Isle, Quarantine Station, below Quebec, Canada, in 1848. We have used it on many occasions, with satisfactory results, since then. Clothes hung in a well-closed room for two days, and subjected to this on three plates, would be rendered harmless. CHICAGO, 23d Sept., 1878. M. McDERMOTT. FORCE AND MOTION. 311. Matter is any substance known to our senses. Inertia of Matter is that which renders a body incapable of motion. Motion is the constant change of the place of a body. Force is a power that gives or destroys motion. Power is the body that moves to produce an effect. Weight is the body acted upon. Momentum of a body is the product of its velocity by the quantity of natter in it. Gravity is the force by which bodies descend to the centre of the earth. Centrifugal Force is that which causes a body, moving around a centre, to go off in a straight line. Centripetal Force is that which tends to keep' the body moving around the centre. Let D B represent a straight line; D, A B D, C, A and B, given forces. *. * * If D and C in the same direction act on A, their force = their sum. If D and B in the same line act on A, but in different directions, the effect of their force will equal their difference, as D - B, where D is supposed the greater. If D and C act on A in one direction, and B in the other, then the effect D + C - B. When the forces C and B act on A, making a given < B A C, the single force equal to-both is called the resultant. Resultant of the forces B' and C acting on A is - D; or by representing forces B, C and D- by the lines A B, A C, A D, then the resultant in the above will be the diagonal A D, and A B and A C are its components. Composant or Component Forces are those producing the resultant, as A B and A C. Rectangular Ordinates are those in which the < B A C is right angled, or when a force acts perpendicularly to the plane A C or A B. In the last figure, the force A C forces A in a direct line towards a, and the force A B forces A towards b in the same line; but when both forces act at the same time, A is made to move in A D, the diagonal of the parallelogram made by the forces A C and A B, by making C D = A B, and A C - B D. Parallelogram of Forces is that in which A B and A C, the magnitudes of forces applied to the body A, gives the diagonal A D in position and magnitude. The diagonal A D is called the resultant, or resulting force. Example. The force A B = 300 lbs., the force A C = 100 lbs., the angle B A C = right angle. Here we have A C and A B = B D and C D; V/(A C2 + C D2)-A D; i. e., /(10000 + 90000) = V(100000)= A D = 316.23 lbs. Otherwise, A D =(A B2 + A C- + 2 A B X A C X cos. < BA C)i m 72D FORCE AND MOTION. Let the < B A C = 60~;.-. its cosine =.6; then 3002 = 90000 1002 = 10000 2 X 300 X 100 X 0.5 = 30000 A D2 = 130000.. A D = 360.55 lbs. Having the < B A C, to find the < CAD. AD: A B:: sine < BAC: sine < D A C. A B * sine < B A C. sine D A C = A D Let C A, B A and E A be three forces in magnitude. We find the resultant A D of the forces C A and B A; then between this resultant and the force E A find the line E F, the required resultant of the three forces; and so on for any other number of forces. By drawing a plan on a scale of 100 lbs. to the inch, we will find the required forces. Or, let 0 X and O Y be two rectangular axis, and A O, B O, C 0 and D 0 represent forces, and a, b, c, d = the angles made by the forces A, B, C and D, with the axis O X. Let S = sum of the forces acting in direction of axis O X, and a the sum of the forces acting in the direction of O Y; then we have S = A O ~ cos. a + B cos. b + C O. cos. c + D 0 cos. d. a = A 0 sine a + BO 0 sine b + C O. sine c - D 0. sine d. Resultant - /(S2 + 82). In this case, the forces are supposed to move inclined to the axis 0 X, as well as to 0 Y. Note. In the first quadrant X 0 Y, the sines and cosines are positive; but in the fourth quadrant X 0 W, the sines must be negative. The effect of any force acting on a body is in proportion to the cosine of its inclination. If three forces, B, C and D, act on a point A, so as to keep it in equilibrium, each of these is proportional to the sine of the < made by the other two. (See fig. B.) Let B and C be the components of the resultant D, then D: C:: sine < B A C: sine < B A D. D: B:: sine < B A C: sine < C A D. If we represent the three forces meeting in A, by the three contiguous edges of a parallelopiped, their resultant will be represented in magnitude and direction, by the diagonal drawn from their point of meeting to the opposite angle of the parallelopiped. If four forces in different planes act upon a point and keep it in equilibrium, these four forces will be proportional to the three edges inid diang onal of a parallelopiped formed on lines respectively parallel to the directions of the forces. Polygon of Forces. Let 0 A, 0 B, 0 C and 0 D in fig. B. represent forces in position and magnitude. From A draw A E = and parallel to O B, E F - and parallel to 0 C, F G = and parallel to O D; then the line 0 G =8 resultant in magnitude and direction. The sum of the moments, of any number of forces acting on a body, must be equal to sum of the moments of any number of forces acting in opposite directions, so as to keep the body from being overthrown. FORCE AND MOTION. 72E PALLING BODIES. 312. All bodies are attracted to the centre of the earth, fall in vertical lines, and with the same velocity. Velocity acquired by a body in falling increases with the time. Uniformly accelerated motion is that which augments in proportion to the time from its commencement. If a body falls through a given space in a given time, it acquires a speed or velocity which would carry it over twice that space in the same time. ANALYSIS OF THE MOTION OF A FALLING BODY. Comparative spaces Constant difference. Timeinsecondsfrom fallen through in Velocities acquired alerth ghfts a state of rest. each successive at the end of times a state of rest fH. ___second. nsin second col.==V. 1 1h 2h 1 h 2 3h 4h 4h 3 5 h 6h 9h 4 7h 8h 16h 6 9 h 10 h 25 h 6 11 h 12 h 36 h etc. etc. etc. etc. n (2 n - 1) h 2 n h n2 h Here h = half the initial of gravity, being half the velocity acquired by a body falling in vacuo at the end of the first second. As g, the initial of gravity, is = 32.2,.-. h = 16.1. The value of g varies with the latitude, but the above is near enough. From the above, we find that by putting H = total height, and V = the acquired velocity, V = 12 h = 1/4 h X 36 h = /2 g H. Here 2 g =4 h. Let V = 10 h = i/(4 h X 25 h) = /2 g H = 8.02 i/H, etc. V 2 n h = /(4 h X n2 h) = do. = do. This is the general equation for the velocities of bodies moving in vacuo, from which it appears that Velocities are to one another as the square roots of their heights. Heights are to one another as the squares of their velocities. But as bodies do not move in vacuo, the velocities are less by a constant quantity of resistance, which we put = m. Theoretical Velocity = 8.02 i/H, or as now used = 8.03 i/H. Actual Velocity = 8.03 m l/H, in which m is to be determined by experiments. To find the velocity of a stream of water. Take a ball of wax, two inches in diameter, or a tin sphere partly filled with water, and then sealed, so that two-thirds of it will be in the water. Find the elapsed time from the ball passing from one given point to another. Repeat the measurements until two of them agree. Mean velocity is in the middle of the stream and at half its depth. Let V = surface, and v = mean velocity; then, according to Prony, v = 0.816 V for velocities less than 10 feet per second. (See Sequel for Water Works.) Composition of Motions is like the composition of forces, and the same operations may be performed. If, in fig. A, last page, a body acting on 72p FORCE AND MOTION. A drives it to B in 300 seconds, in the direction A B, and in the direction A C drives it to C in 100 seconds,.. it is driven by the united forces to D in 360.55 seconds. V = t g. Here t - time in seconds, and g - 32.2. vt t2 g v2 v H I- - - —, because t -. Here H = space fallen through. 2 2 2g g Example. Let a body fall during 10 seconds; then we have, V = 10 X 32.2 - 322 - velocity at the end of 10 seconds. 322 H =- -- X 10 - 1610 = space passed through in 10 seconds. 100 X 32.2 Or, H = - = 1610; or, by the third equation for S, (322)2 103684 1 H3[ =- = 1610. 2 X 32.2 64.4 When the velocity begins with a given acquired velocity = c, V = c +- t g. Here c is constant for all intervals. t2 g c + V V2 - C2 H = c t + - = ( ) t = -- for accelerated motion, 2 2 2g When the motion is retarded, and begins with velocity c, then V = c - t g. t2g c-V c2- -t H=c t- - =( t= t= — 2 2 ' 2g V From above we have V = t g;.'. t - g t2 g Also, 11 = c t- —. Substituting the value of t, we have, V2 g V2 H = __ 2g2 2g V2 - 2 g H; but H = the total height = I;. V = /'2 g H = 8.02 V/H -formula for free descent. V2 H =, and by putting m = coefficient or constant of resistance, we 64.4 ~~~V2 find V = =n 1/2 g H, and 11 --- m2 X 2 g V2 Actual velocity V = (8.00 m 1/H) and H = (64.4 Xm) all in feet. CENTRE OF GRAVITY. 313. Centre of Gravity is that point in a mass which, if applied to a vertical line, would keep the whole body or mass in equilibrium. In a Circle, the centre of gravity is equal to the centre of the circle. In a Square or Parallelogram-where the diagonals intersect one another. In a Triangle-where lines from the angles to the middle of the opposite line cut one another (see annexed figure). Where C H, D G and B P cut one another in the same point F, then G F = one-third of G D, and H F = one-third of C H. Hence, the centre of gravity of a triangle is at one-third of its altitude. In a Trapezoid, A B C D, let E F be perpendicular to A B and C D. E F CD - 2 AB WhenEG=- X C- AB let E F= h, AB= b, and C D c; 3 CD+ABB FORCE AND MOTION. 720 thenE G -=- X ( b) 3 c jb Prapekium. Let A B C D be the given trapeziumn; join B and C; find the centre of gravity E of the / A C B, and also the centre of gravity F of the A C B D; join E and F; let E F = 36; let the area of A A C B = 1200, and that of C B D 1500:; then, as 1200 + 1500: 1200:: 36: F G =16; and in general figure, AB DC: A C B:: F E: F Y. In the annexed figure, A K - K B, C G G B, B H = H D, and Y is the required centre of gravity of A B D. Let the figure have three triangles, as A B L D C. Find the centre of gravity N of the BLD; joinYand N; then, ABLDC: A B L D:: YN: Y S. Hence, S = required centre of gravity of A B L D C. Points E, F, N, are the centres of the inscribed circles. By laying down a plan of the given figure on a large scale, we can find the areas and lines E Y and Y S, etc., sufficiently near. 'Otherwise, by Construction. Let A B C D be the required figure. Draw the diagonals A D and C B; bisect BC inF; make DE=AG; join F G, and make F K _ onethird of F G; then the point K will be the required centre of gravity. Cone or pyramid has its centre of gravity at one-fourth its height. Frustrum of a Cone has its centre of gravity on the axis, measured from the centre of the lesser end, at h 3 R2 + 2 Rr+- r2 the distance -( ). Here R = radius of the greater end, 4 R2 + R r + r2 and r = that of the lesser; h = height of the frustrum. Frustrum of a Pyramid, the same as above, putting S = greater side, instead of R, and s = lesser side, instead of r. In a Circular Segment, having the chord b, height h, and area A, given. Distance from the centre of the circle to the centre of gravity on h 1 b 12 A In a Circular Sector C A B, there are given the arc A D B, the angle A C B, A B and the arc A D B can be found by tab. 1 and 5, the radius C D bisecting the are A D B, and putting G = centre of gravity, then its distance from the centre chord C arc D 72a FORCE AND MOTION. Example. Let < A C B = 400, and C D = 50 feet, to find C G. Here the < A C D = 20~, and C A = 50,.. by table 1, its departure A K = 17.10; this multiplied by 2, gives the chord A B = 34.20. By table 6, 40~ =.698132; this multiplied by 50, gives arc A D B = 34.91. 34.907 2 3490.7 Now, C G = 3 — X - X 50 = - = 34.02. 34.2 3 102.6 In a Semicircle, the centre of gravity is at the distance of 0.4244 r from the point C. In a Quadrant, the point G is at the distance C G = 0.60026. In a Circular Ring, E H F B D A, there are given the chords A B, E F = a and b, and the radius C A R, and radius C E = r, and C G 4 sin. c R3 -r3 ' c (R2 2). Here c angle A C B. Centre of Gravity of Solids. 314. Triangular Pyramid or Cone. The point G, or centre of gravity, is at three-fourths of its height measured from the vertex. Wedge or Prism. The point G is in the middle of the line joining the centres of gravity of both ends. In a Conic Frustrum, the distance of G from the lesser end is equal to h 3 R2 + 2 R r + r2 -4 R2( +Rr - - r2 ). Here R = radius of greater base, and r = that of the lesser. In a Frustrum of a Pyramid, the above formula will answer, by putting R for the greater side and r for the lesser side of the triangular bases. The value will be the length from lesser end. In any Polyhedron, the centre of gravity is the same as that of its inscribed or circumscribed sphere. In a Paraboloid, the point G is at i height from the vertex. h 2R2+r2 In a Frustrum of do. The distance of G from lesser end = - ( ). 3 R2 + r2 In a Prismoid or Ungula, the point G is at the same distance from the base as the trapezoid or triangle, which is a right section of them. In a Hemisphere, the distance of the centre of gravity is three-eighths of the radius from the centre. In a Spherical Segment, the point G, from the centre of the sphere - 8.1416 h2 h 2 (r - -). Here h = height, and S = solidity. S 2 SPECIFIC GRAVITY AND DENSITY. 316. Specific Gravity denotes the weight of a body as compared with an equal bulk of another body, taken as a standard. Standard weight of solids and liquids is distilled water, at 60~ Fahrenheit or 15~ Centragrade. At this temperature, one cubic foot of distilled water weighs 1000 ounces avoirdupois. When 1 cubic foot of water, as above, weighs 1000 ounces, 1 cubic foot of platinum weighs 21500 " That is, when the specific weight of water - 1, then the specific weight of platinum = 21.5. One cubic foot of potassium weighs 865 ".'. its specific gravity, compared with water, 0.865. FORCE AND MOTION. 72i 316. To find the Specific Gravity of a liquid. The annexed is a small bottle called specific gravity bottle, which, when filled to the cut or mark a b on the neck, contains, at the temperature of 60~ Fahrenheit, 1000 grains of distilled water. Some bottles have thermometers attached to them; but it will be sufficiently accurate to have the bottle and thermometer on the same table, and raise the heat of the surrounding atmosphere and liquid to 600. Some bottles contain 500 grains. Some have a small hole through the stopper. The bottle is filled, and the surplus water allowed to pass through the stopper. C is a Counterpoise, that is, a weight = to the empty bottle and stopper. To find the Specific Gravity. Fill the bottle with the liquid up to the mark a b (which appear curved), and put in the stopper. Put the bottle now filled into one scale, and the counterpoise and necessary weight in the other. When the scales are fairly balanced, remove the counterpoise. Let the remaining weight be 1269 grains; then the specific gravity 1.269, which is that of hydrochloric or muriatic acid. Density of a body is the mass or quantity compared with a given standard. Thus, platinum is 21J times more dense than water, and water is more dense than alcohol or wood. Hydrometer is s simple instrument, invented by Archimedes, of great antiquity (300 B. C.), for finding the specific gravity of liquids. It can be seen in every drug store. See the annexed figure, where A is a long, narrow jar, to contain the liquid; B, a vessel of glass, having a weight in the bulb and the stem graduated from top downward to 100. Theweight is such that when the instrument is immersed in distilled water at 60~ Fahrenheit, it will sink to the mark or degree 100. Example. In liquid L the instrument reads 70~. This shows that 70' volumes of the liquid L is = to 100 volumes of the standard, distilled, water;.-. 70: 100:: 1: 1.428 = specific gravity of L. The property of this instrument is, that it sustains a pressure from: below upwards = to the weight of the volume of the liquid displaced by such body. Those generally used have a weight in the bulb and the stem graduated, and are named after their makers, as Baume, Carties, Gay Lussac, Twaddle, etc. Syke's and Dica's have moveable weights and graduated scales. To find the Specific Gravity by Twaddle's Hydrometer. Multiply the degrees of Twaddle by 5; to the product add 1000; from the sum cut off three figures to the right. The result will be the specific gravity. Example. Let 10~ = Twaddle; then 10 X 5 + 1000 = 1.050 = specific gravity. 317. To find the Specific Gravity of a solid, S. Let S be weighed in air, and its weight =W. Let it be weighed in water, and its weight = w. Then W -w weight of distilled water displaced by the solid S. Then W W -w = specific gravity. Rule. Divide the weight in the air by the difference between the weight in air and in water. The quotient will be the specific gravity. Let a piece of lead weigh in air = 398 grains, and suspended by a hair in distilled water = 362.4 " Difference = 35.6 This difference divided into 898, gives specific gravity = 11.176, because 35.6: 1:: 398: 11.176 = specific gravity of the lead. 72J FORCE AND MOTIOIN. 318. To find the Specific Gravity of a body lighter than water. Example. A piece of wax weighs in air = B = 133.7 grains; Attached to a piece of brass, the whole weight in air = C = 183.7 Immersed in water, the compound weighs = c = 38.8 Weight of water = in bulk to brass and wax = C - c = 144.9 Weight of brass in air = W = 50 " t" in water = w =- 44.4 Weight of equal bulk of water = W - w = 5.6 Balk of water = to wax and brass = C - c = 144.9 " <( -= to brass alone = W - w = 5.6 " " = to wax alone = C- c — (W -w) = 139.3 That is, C - c + w - W = 139.3. B: C - c w - W:: specific gravity of body: specific gravity of water. That is, W: C - c + w - W: specific gravity of body. 1. B 133.7 Specific gravity of body = — = = 0.9598. C-c+w- W 139.3 The above example is from Fowne's Chemistry; the formula is ours. 319. To determine the Specific Gravity of a powder or particles insoluble in water. Put 100 grains of it into a specific gravity bottle which holds 1000 grains of distilled water; then fill the bottle with water to the established mark, and weigh it; from which weight deduct 100, the weight of the pow. der. The remainder = weight of water in the bottle. This taken from 1000, leaves a difference = to a volume of water equal to the powder introduced. Example. In specific gravity bottle put B~ 100 grains Filled with water, the contents = C = 1060 " Deduct 100 from 1060, leaves weight of water = C - B = 960 " This last sum taken from 1000, leaves 1000 - C + B = 40 " Which is = to a volume of water = to the powder. B 40: 1.:: 100: 2.5 = required specific gravity -- B 1000 - B - C To find the Specific Gravity of a powder soluble in water. Into the specifi gravity bottle introduce 100 grains of the substance soluble in water; the] fill the bottle with oil of turpentine, olive oil, or spirits of wine, or an: other liquid which will not dissolve the powder, and whose specific gravit2 is given; weigh the contents, from which deduct 100 grains. The re mainder = the weight of liquid in the bottle, which taken from 100C leaves the weight of the liquid = to the bulk of the powder introduced. Example. In specific gravity bottle put of the powder = 100 grains Fill with oil of turpentine, whose specific gravity = 0.874 Found the weight of the contents 890 " 890 - 100 = weight of oil of turpentine in bottle = 790 which has not been displaced by the powder. But the bottle holds 874 grains,.-. 874 - 790 - 84 That is, 84 is the weight of a volume of the oil, which is equal to the vo ume of powder introduced. Consequently, 874: 1000:: 84: 96.1 = weight of water = to the volume of powdr introduced. And again, as 96.1: 100:: 1: 1.04 = required specif gravity. 819a. SPECIFIC GRAVITIES OF BODIES..Specific Weighto Specific Weightof SUBSTANCES. Gravity, one cubic SUBSTANCES. Gravity, one cubic ounces. foot in b. ounces. foot in lb. Metals. Brass, common..... Copper wire........... " cast........... Iron, cast............. " bars............ Lead, cast............ Steel, soft............ Zinc, cast............ Silver, not hammer'd "' hammered.... Woods. Ash, English.......... Beech................... Ebony, American.... Elm..................... Fir, yellow............. " white............... Larch, Scotch........ Locust.................. Norway spars......... Lignumvite........... Mahogany............. Maple.................. Oak, live............... English............ "Canadian......... "African............ " Adriatic........... Dantzic............ Pine, yellow......... " white.......... Walnut... n.......... Teak................... Stones, Earth, etc. Brick.............. Chalk................... Charcoal.............. Clay..................... Common soil.......... Loose earth............ Brick work............ Sand.................. Craigleith sandstone Dorley Dale do....... I 7820 8878 8788 7207 7788 11352 7833 6861 10474 10511 845 700 1331 671 667 569 540 950 580 1333 1063 750 1120 932 872 980 990 760 660 554 671 750 1900 2784 441 1930 1984! 489.8 554.8 549.2 450.1 486.7 709.5 489.5 428.8 654.6 656.9 52.8 43 8 83.1 41.9 41.1 35.5 33.8 59.4 36.3 83.3 66.4 46.8 70 58.2 54.5 61.3 61.9 47.5 41.2 34.6 41.9 46.9 118.7 174 27.6 120.6 124 109 112.3 139.5 164.2 I I I I I I Mausfield sandstone. Unhewn stones....... Hewn freestone....... Coal, bituminous.... Coal, Newcastle...... " Scotch........... " Maryland...... " Anthracite...... Granites. Granite, mean of 14. Granite, Aberdeen... " Cornwall...... [" Susquehanna. " Quincy......... " Patapsco...... Grindstone........... Limestones. Limestone, green.... " white.... Lime, quick............ Marble, common...... " French......... " Italian white.. Mill-stone........... Paving do............. Portland do.......... Sand.................... Shale.................. Slate................... Bristol stone......... Common do............ Grains and Liquids. Water, distilled....... " Sea......... Wheat................ Oats.................... Barley.................. Indian corn........... Alcohol, commercial. Beer, pale............ " brown.......... Cider................... Milk, cow's............ Air, atmospheric..... Steam................... I 2338 1270 1270 1300 1355 1436 2625 2662 2704 2652 2640 2143 3180 3156 804 2686 2649 2708 2484 2416 2428 1800 2600 2672 2510 2033 1000 1026 837 1023 1034 1018 1032!.... 146.1 135 170 79.3 79.3 81.2 84.6 89.7 169 164 166.4 169 165.8 165.7 133.9 193.7 197.2 50.3 167.9 165.6 169.3 155.3 151 151.7 112.5 162.5 167 156.9 127 62.6 64.1 46.08 24.58 48.01 46.08 62.3 63.9 64.6 63.6 64.6.075.037 2232 2628 Average Shrink'e One ton, or 2240 lbs. of bulk in Name of Materials used. or incre'se _ cubic feet. _____ per cent. vi n g _,.... - - - -. Bariong Stole,................ ranite....................... Granite........................ M arble,........................ Chalk.. Limestone, filled in pieces,.... " compact,........ Elm,........................ Mahogany, Honduras,........ Spanish,........ ir, Mar forest,............. * " Riga.................... Beech,.............. Ash and Dantzic oak,........ Oak, English,................ Common soil,................ Loose earth................. Clay,. Sand,........................ m2 18.828 18.606 18.070 12.874 14 11.278 64.460 64 42.066 61.650 47.762 61.494 47.168 86.206 18.044 20.661 18.674 20 Lignh sanay earth,............ Yellow clayey "............ Gravelly "............ Surface or vegetable soil,.... Puddled clay,............... Earth filled in water........ Rock broken into small pieces Rock broken to pass through an inch and a half ring,.... Do. do. 2 inch ring, Do. do. 21 do. One cubic yard of the It stone above weighs 2180 lb. Do. to pass through 2 inch,. 2800 lb. Do. to pass through 21 inch ring, 2608 lb..12 shr..10 ".08 ".16 ".26 ".80 " S to j in. 106 " 90 '" 70 " MECHANICAL POWERS. The Mechanical Powers are: the lever, inclined plane, wheel and axle, the wedge, pulley, and the screw. 319c. Lever, are either straight or bent, and are of three kinds. LEVERS CONSIDERED WITHOUT WEIGHT. Lever of the first kind is when the power, P, and weight, W, are on opposite sides of the fulcrum, F. Then P: W:: A F: B F, which is true for the three kinds of levers, and from which we find P X B F W X A F. WXAFand Wz P F* (See Fig.I.) B F A F W XA F P X BF B F,fand A F P w Lever of the second kind is when the weight is between the fulcrum and the power, (Fig. II.) Then P: W:: A F to B F, as above. Lever of the third kind (Fig. III.) is when the power is between the fulcrum and the weight. Then P: W:: A F: B F, as above. Hence, we have the general rule: The power is to the weight as the distance from the weight to the fulcrum, is to the dzstance from the power to the, fulcrum. In a bent lever (Fig. IV.), instead of the distances A F and F B, we have to use F a and F b. Then P: W:: Fa: Fb; or, P:W::F A Xcos. <AFa: F B Xcos. < B F b. Let P A B W represent a lever (see Fig. V.) Produce P A and W B to meet in C. Now the forces P and W act on C; their resultant is C R, passing through the fulcrum at F. LetAF=a,BF~b,<PAB~n,and<ABW==m. Then P: W:: b sin. <in: a sin. < n; And P * a sin. n = W * b sine m. LEVERS HAVING WEIGHT. 31 9d. When the lever is of the same uniform size and weight. Let A Ba lever whose weight is wto. (Fig. VI.) Ca.. 1. Let the centre of gravity, f, be between the fulcrum, F, snd power, P; then wehave, byputting F f d,WN.-A F ~P.B F +-d wi W.AF-dw P.BF+dw. P =.*-,and W AF MECHANICAL POWERS. 72J3 Case 2. When the centre of gravity, f, is between the fulcrum and the weight. Then W.AF + d w =P. B F. P.BF- dw W.AF +dw W-. --------, and P -- -. AF andBF Example from Baker's Statics. Let the length of the lever = 8 feet, A F = 3;.. B F = 6, its weight = 4 lbs., and W suspended at A = 100 lbs. Required the weight P suspended at B, the beam being uniform in all respects. We have the centre of gravity, a, = 4 feet from A, and at 1 foot from F towards P. Then, by case 1, W.AF-dw 100 3-1 X4 300-4 P.BF ----5 = 59 1-5 lbs. BF 5 5 319e. Carriage wheel meeting an obstruction (see Fig. VII.) is a lever of the first kind, where the wheel must move round C. Let D W C = a wheel whose radius = r, load = a b c d = W. The angle of draught, P Q W, = a, and C, the obstruction, whose height = h. Let C n and C m be drawn at right angles, to 0 W and 0 P. Then C m represents the power, and C n the weight; then P: W:: C n: C m: sine < C 0 n: sine C O m. D W - 2 r;.. D n =2r-h; and by Euclid, B. 2, prop. 5, (2r- h). h + 0n2 = C 02 (2rh —h2) =i/(C02 ON2)= Cn;.'. C n 1/(2rh-h2) Sine C O n = — C m. Co r When the line of draught is parallel to the road, then C m = r - h. From this we have P: W:: /2 rh- h2: r - h, 1/(2 r h — h2) And P = W * /(2 - ). A general formula. r- h Example. A loaded wagon, having a load of 3200 lbs., weight of wagon 800, meets a horse-railroad, whose rails are 3 inches above the street, the diameter of the wheel being 60 inches. Require the resistance or necessary force to overcome this obstacle. Total weight of wagon and load, 4000 lbs. Weight on one wheel, 2000.. P = 2000 X 0X 3 = 968.9 lbs., which is about three times 30 - 3 the force of a horse drawing horizontally from a state of rest. Hence appears the injustice of punishing a man because he cannot leave a horse-railroad track at the sound of a bell, and the necessity of the local authorities obliging the railroad companies to keep their rail level with the street or road. 72j4 MECHANICAL POWERS. Of the Inclined Plane. 319f. Let the base, A B, = b, height, B C, = h, and length, A C, - 1. The line of traction or draught must be either parallel to the base, A B, as W Pt parallel to the slant, or the inclined plane, as W P, or make an angle a with the line C W, W being a point on the plane where the centre of pressure of the load acts. When the power P/ acts parallel to the base, we have — P/: W:: BC: BA:: h: b; or, P/: W:: sine < B A C: sine < A C B. W.h P b P' = and W —. b h P b Wh h, and b = - W ' P/ When the line of traction is parallel to the slant. P: W:: h: 1; hence, we have P1 = W h, P1 Wh W, P = -, h 1 P1 Wh h -- and 1 =-. -W'^ - P When the line of traction makes an angle a with the slant, then P//: W:: sine < B A P": cos. < P/ W C, from which, by alternation and inversion, we can find either quantity. Example. W = 20000 lbs., < B A C = 6~, < P/ W C = 4~. Required the sustaining power, P/. sine B A Pa/ W sine B A P sine 4~.06976 p// =. -- W - ----. W. P// W C cos. < P/W C cos. 6~.99452 1395.2 _ 4 --- 2 1413 lbs..99452 Of the Wheel and Axle. 319g. When the axle passes through the centre of the wheel at right angles to its plane, and that a weight, W, is applied to the axle, and the power, P, applied to the circumference, there will be an equilibrium, when the power is to the weight as the radius of the axle is to the radius of the wheel. Let R = radius of the wheel, and r = radius of the axle, both including the thickness of the rope; then we have P: W:: r: R; from which we have Wr PR PR =Wr, and P = — andW= —. (A.) R r Wr PR R - - and r = -. PI W Compound Axle is that which has one part of a less radius than the other. A rope and pulley is so arranged that in raising the weight, W, the rope is made to coil on the thickest part, and to uncoil from the thinner. An equilibrium will take place, when 2 P * D = W (R - r). D = distance of power from the centre of motion. R = radius of thicker part of axis, and r = that of the thinner. 319h. Toothed Wheels and Axles or Pinions. Let a, b and c be three axles or pinions, and A, B and C, three wheels. The number of teeth in wheels are to one another as their radii. P:W:: a b c: A B C: that is, the power is to the weight as the product of all the radii of the pinions is to the product of all the radii of the wheels. Or, P is to W, as the product of all the teeth in the pinions is to the product of all the teeth in the wheels. (B.) Example 1. A weight 2000 lbs. is sustained by a rope 2 inches in diameter, going round an axle 6 inches in diameter, the diameter of the wheel being 8 feet. Wr From formula A, P = -; R MECHANICAL POWERS. 72j5 2000 X 4 That is, P -= -- 163.26 lbs. 49 Example 2. In a combination of wheels and axles there are given the radii of three pinions, 4, 6 and 8 inches, and the radii of the corresponding wheels, 20, 30 and 40 inches. What weight will P = 100 lbs. sustain at the circumference of the axle or last pinion. ByformulaB, PABC =Wabc. P A B C 100 X 20 X 30 X 40 50 W = ~.-12500 lbs. Wabc 4X6X8 Of the Wedge. (Fig. IX.) 319i. The power of the wedge increases as its angle is acute. In tools for splitting wood, the < A C B = 30~, for cutting iron, 50~, and for brass, 60~. P: W:: A B: AC; or, P: W:: 2 sine A C B: 1. Of the Pulley. (See next Fig.) 319:. The pulley is either fixed or moveable. In afixedpulley (Fig. I.), the power is equal to the weight. In a single moveable pulley (Fig. II.), the rope is made to pass under the lower pulley and over the upper fixed one. Then we have P: W:: 1: 2. When the upper block or sheeve remains fixed, and a single rope is made to pass over several pulleys (Fig. IV.)-for example, n pulleys-then W P: W:: 1:n, and P n = W, and P =-, so that when n= 6, the n power will be one-sixth of the weight. When there are several pulleys, each hanging by its own cord, as in Fig. III., P:W:: 1:2n. Here n denotes the number of pulleys. Example. Let W = 1600 bs., n = 4 pulleys. Then P X 24== W; that is, P X 16 - 1600, and P = 100 lbs. Of the Screw. 319k. Let L D = distance between the threads, and r = radius of the Power from the centre of the screw. Then P: W:: d: 6.2832 r. P r X 6.2882 = W D. W Pr X 6.2832 Wd --- -—,andP=. d 6.2832 r Example. Given the distance, 70 inches, from the centre of the screw to a point on an iron bar at which he exerts a power of 200, the distance between the contiguous threads 2 inches, to find the weight which he can raise. Here r = 70, d = 2, and P = 200 lbs. W-200X 70 X 6.2832 43982.4 2- 43982.4 lbs. 72j6 MECHANICAL POWERS. VIRTUAL VELOCITY. 319m. In the Lever, P: W:: velocity of W: velocity of P. In the Inclined Plane, vel. P: vel. W:: distance drawn on the plane: the height raised in the same time. Let the weight W be moved from W to a, and raised from o to a; then vel. P.: vel. W:: W a: o a. (Fig. VIII.) In the Wheel and Axle, vel. P: vel. W:: radius of axle: rad. of wheel: W: P. In the single Moveable Pulley, vel. P: vel. W:: 2: 1:: W: P. In a system of Pulleys, vel. P: vel. W:: n: 1;: W: P. Here n = number of ropes. In the ARCHIMEDEAN Screw, vel. P: vel. W, as the radius of the power multiplied by 6.2832 is to the distance between two contiguous threads. Let R = radius of power, and d = distance between the threads; then vel. P: vel. W:: 6.2832 R: d:: W: P. OF FRICTION. 319n. Friction is the loss due to the resistance of one body to another moving on it. There are two kinds of friction-the sliding and the rolling. The sliding friction, as in the inclined plane and roads; the rolling, as in pulleys, and wheel and axle. Ezperiments on Friction have been made by Coulomb, Wood, Rennie, Vince, Morin, and others. Those of Morin, made for the French Government, are the most extensive, and are adopted by engineers. When no oily substance is interposed between the two bodies, the friction is in proportion to their perpendicular pressures, to a certain limit of that pressure. The friction of two bodies pressed with the same weight is nearly the same without regard to the surfaces in contact. Thus, oak rubbing on oak, without unguent, gave a coefficient of friction equal to 0.44 per cent.; and when the surfaces in contact were reduced as much as possible, the eoefficient was 0.41k. Coulomb has found that oak sliding on oak, without unguent, after a few minutes had a friction of 0.44, under a vertical pressure of 74 lbs.; and that by increasing the pressure from 74 to 2474 lbs., the coefficieni of friction remained the same. Friction is independent of the velocities of the bodies in motion, but if dependent on the unguents used, and the quantity supplied. Morin has found that hog's lard or olive oil kept continuously on wooc moving on wood, metal on metal, or wood on metal, have a coefficient o 0.07 to 0.08; and that tallow gave the same result, except in the case o metals on metals, in which case he found the coefficient 0.10. Different woods and metals sliding on one another have less friction Thus, iron on copper has less friction than iron on iron, oak on beach ha less than oak on oak, etc. The angle of friction is < B A C, in the annexed figure, where W represents the weight, kept on the inclined plane A C by its friction. Let G = centre of gravity; then the line I K represents the weight W, in direction of the line of gravity, which is perpendicular to A B; I L = the pressure perpendicular to A C, and I N = L K = the friction or weight sufficient to keep the weight' on the plane. The two triangles, A B C and I K L are similar to 0o 72j7 MECHANICAL POWERS. another;.'. KL:LI:: BC: AB:: the altitude to the base. Also, K L:KI:: BC: AC. In the first equation, we have the force of friction to the pressure of the weight W, as the height of the inclined plane is to its base. In the second equation, we have the force of friction to the weight of the body, as the height of the plane is to its length. Hence it appears that by increasing the height of B C from B to a certain point C, at which the body begins to slide, that the < of friction or resistance is = < B A C. That the Coefficient of Friction is the tangent of < B A C, and is found by dividing the height B C by the base A B. Angle of Repose is the same as the angle of friction, or the < B A C = the angle of resistance. 819o. Friction of Plane Surfaces having been somi in Contact. Disposition of State of the Sur- E. Angle of Surfa tthe Fibres. faces. i Repose. '3 the~~~~~~~~ Fibres Oak upon oak.................... Parallel........ do..................... do.................... do................... Oak upon elm.................... Elm upon oak.................... do................... Ash, fir or beach on oak.......... do........ Perpendicular.. End of one on flat of other... Parallel....... do......... Perpendicular,. Parallel....... Leather length Without unguent Rubbed with dry soap............ Without unguent do, do. do. do. With soap........ Without unguent do. do. 0.62 0.44 0.64 0.43 0.38 0.41 0.67 0.53 0.48 0.74 0.47 0.80 0.66 0.66 0.62 0.28 0.16 0.10 Tanned leather upon oak........ ways, sideways do. do. Black strap leather upon oak.... Parallel........ do. do. do. do. on rounded oak Perpendicular.. do. do. Hemp cord upon oak............ Parallel........ do. do. Iron upon oak.................... do......... Steeped in water Cast-iron upon oak............... do.... do. do. Copper upon oak................ do........ Without unguent Bl'k dress'd leather on iron pulley Flat............ do. do. Cast iron upon cast iron........ do............. do. do. Iron upon cast iron............. do............. do. do. Oak, elm, iron, cast iron and brass, sliding two and two, on do............. With tallow..... one another..................) do. do. do. do............. Hog's lard...... Common brick on common brick................................... Hard calcareous stone on the same, well dressed.................... Soft calcareous stone upon hard calcareous stone.................... do. do. do. on same, with fresh mortar of fine sand........ Smooth free stone on same.......................................... do. do. do. with fresh mortar........................ Hard polished calcareous stone on hard polished calcareous stone.... Well dressed granite on rough granite............................ Do., with fresh mortar....................................... 81~ 48 28 46 28 22 23 16 20 49 22 18 29 41 27 56 23 16 36 80 26 11 38 40 88 02 83 02 31 48 16 83 9 6 10 46 6 43 832 33 60 86 00 8 62 86 80 86 23 83 26 80 07 83 26 26 07 I 0.10 0.16 0.67 0.70 0.76 0.74 0.71 0.66 0.68 0.66 0.49 319p. Friction of Bodies in Motion, one upon another. S Disposition of State of the Sur. o Angle of Surfaes In Contac t. the Fibres. faes. d d Repose. Oak uponoak.................... Parallel........Without unguent 0.48 2 do................... do.........Rubbed with soap 0.16 9 06 Elm upon oak............. Parallel........ do. do. 0.4 28 17 do..................... Perpendicular.. do. do. 0.46 24 14 Iron upon oak....................Para.... Rubbed with dry soap. 0.21 11 62 do..................... do.........Withou unguent 0.49 26 07 Cat iron upon oak............... do.. Rubbed with soap 0.19 10 46 Iron upon elm.................... do........ Without unguent 0.26 14 08 Cast ron on elm................. do. do. 0.20 11 19 Tanned leather upon oak... L'thw'ys and do do. 0.6 29 16 sido. on cdewayst iron and bra........... 8 do. on cast iron and brass do. do. With oil.......... 0.16 8 82 72j8 MECHANICAL POWERS. 319q. Friction of Axles in motion on their bearings. Cast iron axles in same bearings, greased in the usual way with hog's lard, gives a coefficient of friction of 0.14, but if oiled continuously, it gives about 0.07. Wrought iron axles in cast iron bearings, gives as above,.07 and.06. Wrought iron axles in brass bearings, as above,.09 and.00. MOTIVE POWER. 319r. Nominal horsepower is that which is capable of raising 33,000 pounds one foot high in one minute. The English and American engineers have adopted this as their standard; but the French engineers have adopted 32,560 lbs. Experiments have proved that both are too high, and that the average power is 22,000 lbs. The following tables are compiled, and reduced to English measures, from Morin's Aide Memoire: Work done by Man and Horse moving horizontally. A man unloaded............................................ A laborer with a small two-wheel cart, going loaded and returning empty....................................... Do. with a wheelbarrow as above....................... Do. walking loaded on his back........................... Do. loaded on his back, but returning unloaded...... Do. carrying on a handbarrow as above............... A horse with a cart at a pace continually loaded...... Do. do. returning unloaded.............................. Do. with a carriage at a constant trot.................. Do. loaded on the back, going at a pace............... Do. do. at a trot........................................... 0 30 6 32.5 10 97.5 10 50 10 30 7 30 6.32.5 10 16.5 10 770 10 420 4.5 770 10 132 7 176 ~ Pr-e,y 0 " 12902 6617 3970 3970 4301 2183 101894 55579 101894 17467 23290 I1 I? 1 ~.., m 319s. Work done by Man in moving a body vertically. o 7 ' [ ' s ' j ' Man ascending an inclined plane...................... 8 9.76 1290 Do. raising weight with a cord and pulley, the cord descending empty.......................................... 6 3.60 476 Do. raising weight with his hands........................ 6 3.40 450 Do. raising a weight, and carrying it on his back to the top of an easy stairway, and returning empty.. 10 1.20 159 Do. shovelling earth to a mean height of 1.60 metres. 10 1.08 143 Hours W I Force in 319t. Action on Machines. per S ~ |. peods day to Uminute. A man acting on a wheel or drum at a point level with the axle................................................ 8 9 1191 Do. acting at a point below the axle at an < of 24~.. 8 8.40 1112 Do. drawing horizontally, or driving before him...... 8 7.20 753 Do. acting on a winch....................................... 8 6 794 Do. pushing and drawing alternately in vert. position 8 5.50 728 A horse harnessed to a carriage and going at a pace.. 10 63 8337 Do. harnessed as a riding horse, going at a pace...... 8 40.50 536 Do. do. going at a trot....... 4.5 60 7940 ROADS AND STREETS. 319u. Roman roads were made to connect distant cities with the Imperial Capital. In low and level grounds, they were elevated above the adjoining lands, and made as follows: 1st. The Statumen, or foundation-all soft matter was removed. 2d. The Ruderatio, composed of broken stones or earthenware, etc., set in cement. 8d. The Nucleus, being a bed of mortar. * 4th. The Summa Crusta, or outer coat, composed of bricks or stones. Near Rome, the upper coat was of granite; in other places, hard lava, so closely jointed, that it was supposed by Palladio that moulds were used for each stone or piece. The Curator Viarum, or superintendent of highways, was an officer of great influence, and generally conferred on men of consular dignity after Julius Ccesar, who held that office, assisted by his colleague, Thernus, a noble Roman. Victorius Marcellus, of the praetorian order, had been selected to this office by the Emperor Domitian. These are but a few instances of the many in which men of the highest position in society became Curator Viarum-or, as the Americans call him, commissioner of highways, or path master. The Appian Way, called also Queen of the Roman ways, was made by Censor Appius Cacus, about 311 years before the Christian era, and built then as far as Capua, 125 miles; but subsequently to Brundusium, about the year B. C. 249. " The Appian Way was of a sufficient width (18 to 22 feet) to allow two carriages to pass; was made of hard stone, squared, and made to fit closely. After 2000 years, but little signs of wear appear."-Eustace. Gravel roads, with small stones, were commonly used by the Romans. Porticos were built at convenient distances, to afford shelter to the traveler. Roman Military roads were 36 to 40 feet wide, of which the middle 16 feet were paved. At each side there was a raised path, 2 feet wide, which again separated two sideways, each 8 feet wide. The breadth of the Roman roads, as prescribed by the laws of the twelve tables, was but 8 feet; the width of the wheel tracks not above 3 feet. There were twenty-nine military roads made, equal in length to 48500 English miles. The Carthaginians, according to Isadore, were the first who paved their public ways. The Greeks, according to Strabo, neglected three objects to which the Romans paid especial attention: the cloacce, or common sewers, the aqueducts, and the public highways. The Greeks made the upper part of their roads with large, square blocks of stone, whilst the Romans mostly used irregular polygons. The French roads are from 30 to 60 feet wide, the middle 16 feet being paved; but once a vehicle leaves the 'pavement, it becomes a matter of much difficulty to extricate it from the soft surface of the sides. To obviate this difficulty, the system of using broken stones is now generally adopted, and has been used in France, under the direction of M. Turgos, a long time before McAdam introduced it into England. m3 72j10 ROADS AND STREETS. The German roads resemble those of France. The Belgium roads have their surfaces composed of thin brick tiles, which answer well for light work. Sweden has long been famous for her excellent roads of stone or gravel, on which there is not a single tollgate. Each landowner is obliged to keep in repair a certain part of the road, in proportion to his property, whose limit is marked by land marks on each side of the road. The English, Irish and Scotch roads are now generally made of broken stones, or macadamised; are 25 to 50 feet wide: well drained-having *the centre 12 inches higher than on the sides, in a road 40 feet wide, and in proportion of 3 inches in 10 feet wide; the stones broken so as to pass through an inch-and-half ring. For the purpose of keeping them in repair, there are depots, or heaps of broken stones, at intervals of 600 feet. When a small hole makes its appearance, a man loosens the stones around the spot to be repaired, and then fills it up with new material, which soon becomes as when originally made. Arthur Young states that it was not until 1660 that England took an interest in her roads. (See Encyclopadia Britannica, vol. xii, p. 528.) In his tour through the British Isles in 1779, he states that Ireland then had the best roads in Europe. This is not to be wondered at, when we consider that there, granite, limestone and gravel beds are abundant; that since the beginning of the reign of Charles I, the roads were under the charge of the grand jury. There, good roads must have existed at a very early date, as the stones of which the round towers are built are large, and, in some places, have been brought from a great distance. Many of the English and Irish highways were turnpike roads; that is, roads having tollgates. Since the introduction of railways, these have been falling off in revenue. In a parliamentary inquiry into turnpike trusts in Ireland, the unanimous testimony of all the witnesses examined were against them, and in favor of having them kept in repair by presentment. Presentment is where the grand jury receives proposals to keep road R, blank miles, from point A to point B, in repair, according to the specification of the county surveyor, during time T, at the rate of sum s per rod, subject to the approval of the county surveyor, who has the general supervision of all the public works, and are gentlemen of integrity and high scientific attainments. The work on hydraulics by Mr. Neville, county surveyor for Louth, and that on roads by my school-fellow, Edmond Leahy, county surveyor for Cork, are generally in the hands of every engineer. By the parliamentary report for 1839-40, England had 21962 miles of turnpike trusts. The tolls amounted to ~1,776,586; the expenditure for repairs and officers, ~1,780,349, leaving a deficiency of ~3,763. The same deficiency appears to take place on the Irish roads. In England, the parish roads equal 104772 miles, costing annually for highway rates ~1,168,207. The number of surveyors and deputy surveyors, or way-wardens, is 20000, or one way-warden to every 56 miles of road. It was then shown that the trusts had incurred debts to the enormous amount of ~8,577,132. Under the new system, one man keeping a horse is supposed to take charge of 40 miles of road. ROADS AND STREETS. 72Jll Making and Repairing Alacadamised Roads. 319-. The road bed should have a curved surface of about 1 foot rise for 40 feet wide, be a segment of a circle, and have at least 12 inches of stones on the centre, and 8 to 10 on the sides, both of which are to be on the same level. When the stones are well incorporated with one another, a layer of sand, 1 inch in thickness, is spread on top. The bed must be thoroughly drained, and the water made to flow freely in the adjoining ditches. The overseers should never allow any water to accumulate on the road, and every appearance of a rut or hole immediately checked. Where there is frost, it is liable to disintegrate the road material, unless it is built of very compact stuff. In boggy land, a soling of 12 to 18 inches of stiff clay must be laid under the broken stone. Where the bottomx is sandy, and stiff clay hard to be procured, rough pavements or concrete, from 6 to 12 inches thick, under the broken-stones, will be the best. In general, where the soil is well drained, broken stones will be sufficient. The road is never to have less than 8 inches on the centre and 4 on the sides. All large stones raked to the sides, and broken, so as to pass through a ring 14 inches in diameter. The surface always kept uniform. The English and Irish roads are generally 25 feet between the ditches, but in approaches to cities and towns, they are 40 to 50 feet. On the Irish roads, no house is allowed nearer than 30 feet of the centre of the road. To allow for shrinkage. Mr. Leahy, in his work on roads, p. 100, says: In bog stuff, add one-fourth of its intended height; if the road is of clay or earth, add one-twelfth. When the road passes through boggy land, the side ditches, or drains, must be dug to a depth of 4 feet below the surface of the road, and have parallel drains running along j^ the direction of the rotd, about 40 feet on each side. In this mannetoads have been made over the softest bogs in Ireland. On the Milwaukee and Mississippi Railroad, near Milwaukee, a part of the road passed over the Menomenee bottoms. After several weeks of filling, the company was about to relinquish that part of the route, for all the work done during the week would disappear during Sunday. The author being employed as city engineer in the neighborhood, saw the respective officers holding a consultation. He came up, and on being asked his opinion, replied: "Imitate nature; first lay on a layer of brushwood, 1 foot thick; then 2 feet of clay, and so on alternately." The plan was adopted, and has succeeded. Where the road is wet and springy, cross drains filled with stones are to be made, to connect with the side drains or ditches; and if made within 60 or 60 feet of one another, will be sufficient to drain it. Where the road runs along a sloping ground, catch-water drains should be run parallel with the road, so as to keep off the hill water. Retaining walls should have a batter or slope of 3 inches to each foot in height, and the back may be parallel to the same. The thickness, 2k feet for 10 feet in height, and in all other cases, the thickness shall be onefourth of the height. An offset of 8 inches should be left at front of the footing course, and the foundation cut into steps. Where such walls are along water courses, the foundation should be 15 inches below the bottom of the water, and paved along the side to a width of 18 inches or 2 feet. The filling behind is put in in layers, and rammed in. 72j12 ROADS AND STREETS. Parapet walls should be 20 inches thick and 3~ feet high, built of masonry laid in lime mortar, in courses of 12 or 14 inches, the top course or coping to be semicircular, and have a thorough bond at every 3 feet. Where drains are covered, dry masonry walls, covered with flags, are preferable. Where the width of the drain is not more than 30 inches, these drains will require flags 6 inches thick; those between 18 and 24 inches are to have flags 5 inches thick; and those from 8 to 18 inches, require flags 4 inches thick. Drainage. When the road runs along a hill, cut a drain parallel to the road, and 3 to 4 feet below the surface; then cut another of smaller dimensions near the road, and sunk below the road-bed. Again, at every 60 or 100 feet, sink cross drains, about 15 to 24 inches below the roadbed; fill with broken stones to within 6 inches of the top, which space of 6 inches is to be filled with small broken stones of the usual size in road making-these cross drains to communicate with a ditch or drain on the lower side of the road, to keep it dry. Drain holes, about 100 feet apart; 8 inches square, and about 2 inches under the water table of the drain; may be made of 4 flag stones, draining tiles, or pipes. Road Materials. Granite is the best. Sienite is granite, in which hornblende is mixed. This is very durable, and resists the action of the atmosphere. This stone has a greenish color when moistened. Sandstone, if impregnated with silica, is hard, and makes a good material. Some varieties are composed of pure silex, which makes an excellent material; but others are mixed with other substances, which make the stone porous, and unfit to be used by the action of frost, it easily disintegrates. ' r Limestone has a great affinity for wate hich it imbibes in large quantities. If frozen in this condition, it is easily crumbled under the wheels of carriages, and becomes mud. Hence the great necessity of keeping a road made with broken limestone thoroughly drained, in all places where frost makes its appearance. There is nothing more injurious to roads than frosts. Stones having fine granular appearance, and whose specific gravity is considerable, may be considered good road material. Experiments made by Mr. Walker, civil engineer, during seventeen months of 1830 and 1831, on the Commercial Road, near London, will show the quality of the following stones: (See Transactions Inst. Civil Engineers, Vol. 1.) Absolute wear Time in which Description of Stone. Where procured. in 1 inch would 17 months. wear down. Granite................. Dartmoor..................207 inches. 6.8 years. "................. Guernsey..................060 22.5 "................. Herm, near Guernsey...075 19. Blue Granite........ Peterhead..................131 10.8 Granite...'..... Heyton....................141 10. Red Granite........... Aberdeen................. 159 9. Blue Granite.......... "..................22 6.33 W hinstone.............. Budle..................... 082 17.33 ROADS AND STREETS. 72J18 COMPRESSION. Nbs. avoirdupois )bs. avoirdupois to crush a cube to crush a cube of 1l inches. of 1{ inches. Chalk..................... 1127 Cornish granite...................14302 Brick, pale red color............ 1265 Dundee sandstone.................14918 Red brick, mean............... 1817 Craigleith gritstone, with the Yellow-faced paviers............. 2254 strata....................... 15560 Fire brick........................ 3864 Devonshire red marble, variWhitby gritstone.................. 5328 egated............................16712 Derby " and friable Compact limestone...............17354 sandstone........................ 7070 Penryn granite...................17400 Do. from another quarry....... 9776 Peterhead " close grained...18636 White freestone, not stratified. 10264 Black compact Limerick limePortland stone....................10284 stone.............................19924 Humbic gritstone.............10371 Black Brabant marble..........20742 Craigleith white freestone..... 12346 Very hard freestone..............20254 Yorkshire paving, with strata.12856 White Italian veined marble...20783 Do. against the strata...........12856 Aberdeen granite, blue kind...24556 White statuary marble, not Valencia slate.....................26656 veined....................13632 Dartmoor granite.................27630 Brambyfall sandstone, near Heyton granite.................. 31360 Leeds, with strata............13632 Herm granite, near Guernsey.. 33600 A road made over well dried bogs or naked surface, on account of its elasticity, does not wear as fast as roads made over a hard surface. It has been found that on the road near Bridgewater, England, the part over a rocky bed wears 7, when that over a naked surface wears 5. The covering of broken stones is, in the words of McAdam, intended to keep the road-bed dry and even. Some of the material used on the roads near London are brought from the isle of Guernsey and Hudson Bay. Weight of vehicles, width of tiers, and velocity, have great influence on the wear of roads. In Ireland, two-wheeled wagons or carts are generally used-the weight 6 to 8 cwt., and load 22 to 25 cwt., making a gross load of about 30 cwt. In England, four-wheeled wagons are generally used, and weigh, with their load, from 5 to 6 tons; therefore, the pressure of these vehicles is as 1660 to 8320, on any given point. It is evident that when the vehicle is made to ascend a large stone, that in falling, it acquires a velocity which is highly injurious to the road, and that there should not be allowed any stone larger than 1~ inches square on the surface. Table of Uniform Draught. Description of Surface. Rate of Inclination. Ordinary broken stone surface............................. Level. Close, firm stone paving.................................................. 1 in 48.6 Timber paving.............................................................. 1 in 41.5 Timber trackway................................... 1 in 81.66 Cut stone trackway........................................................ 1 in 31.66 Iron tramway....;..................... 1 in 29.26 Iron railway................................................................. 1 in 28.6 Explanation. If a power of 90 lbs. will move one ton on a level, broken stone road, it will move the same weight on an iron railway having an inclined plane of 1 in 28j. 72J14 ROADS AND STREETS. FRICTION ON ROADS. The power required to move a wheel on a well made, level road, depends on the friction of the axles in their boxes, and to the resistance to rolling. When the axles are well made and oiled, the friction is taken at oneeighteenth of the pressure; but in ordinary cases, it is taken at one-twelfth, W W a Wa - and power - X =. Here power is that force which, if - 12 a 12 d 12 d applied at the tier, would just cause the wheel to move. a = diameter of the axis, and d - diameter of the wheel. The following is Sir John McNeill's formula, given in his evidence before a committee of the House of Lords, for the draught on common roads: W+w w WP + - + c V. Here W= weight of the wagon, w = 93 40 weight of the load, V = velocity in feet per second, and c = a constant quantity derived from experiments on level roads. Kind of Road. Value of c. For a timber surface............................................................. 2 " paved road..................................................................... 2 " a well made broken-stone road, in a dry state....................... 6 " I " " s " covered with dust................ 8 " " " " wet, and covered with mud..... 10 " gravel or flint road, when wet............................................ 13 "t " t" very wet, and covered with mud............... 32 Let W = 720, w 3000, paved road; let V = 4 feet. Here c = 2, and we have720 + 3000 3000 = - 93 - +2 X 4. 93 '40 P = 40 + 75 + 8 = 123 = draught, or the force necessary to overcome the combined friction of the axle in the box and the wheel in rolling on the surface. This force is one-thirtieth of the total load of weight and wagon. By McNeill's Improved Dynamometer, the following results have been obtained. Weight of wagon and load = 21 cwt. Ratio of Kind of Road. Force in fbs. Draught to the Load. Gravel road laid on earth.......................... 147 = 1-16th of the load. Broken stones......................................... 6 = 1-36th " " on a paved foundation........... 46 = 1-51st " Well-made pavement.............................. 33 = 1-71st " Best stone track ways............................. 12~= 1-179th " Best form of railroad............................... 8 = 1-280th " M. Poncelet gives the following value of draught or force to overcome friction: On a road of sand and gravel...........................1-16th of the total load. On a broken stone road, ordinary condition........1-26th " c" " in good condition...........1-67th t" On a good pavement, at a walk........................ 1-64th "t 6 " " at a trot......................... 1-42d " On a road made of oak planks............................1-98th ROADS AND STREETS. '12j15 Table showing the Lengths of Horizontal Lines Equtivalent to several Ascending and Descending Planes, the Length of the Plane being Unity. In calculating this table, Mr. Leahy has assumed that an ordinary horse works 8 hours per day, and draws a load of 3000 pounds, including the weight of the wagon, making the net load 1 ton. One-forse Cart. vtage CUa One in Ascend'g. Desc'nd'g Ascend'-rwjDe 5 8.32 3.27 10 4.16 1.65 2.85 15 2.90 1.06 2.23 20 2.08 0.83 1.93 25 1.66 0.70 1.74 90 1.55 0.74 1.62 35 1.45 0.77 1.53 40 1.40 0.79 1.46 45 1.35 0.81 1.41 50 1.31 0.83 1.37 55 1-. 29 0.84 1.34 60 1.26 0.85 1.31 65 1.24 0.86 1.29 70 1.22 0.87 1.72 75 1.68 80 1.1-9 -0.88 1. 64 85 1.60 90 1.17 0.89 1.57 95 1.54 100 1.15 0.90 1.51 110 1.45 120 1.43 130 1.39 140 1.36 150 1.10 0.92 1.34 160 1.32 170 1.30 180 1.28 190 1.27 200 1.07 0.93 1.26 210 1.24 220 1.23 230 1.22 240 1.21 250 1.20 260 1.20 270 1.19 280 1.18 290 1.18 300 1.17 350 1.15 400 1.13 460 1.11 500 1.10 550 1.09 600 _ _ _ _ _ _ 1.09 %cll. Stage Wagon. Al sc'nd'r Ascend'g. Desc'nd'g El 6.07 5 4.39 3 0.07 3.54 2 0.26 3.04 2 0.39 270 1 0.47 2.46 1 0.54 2.27. 1 0.59 2.13 1 0.63 2.02 1 0.66 1.93 0.07 f 0.69 1.85 0.15 0 0.71 1.78 0.22 0 0.27 1.27 0.73 0 0.32 1.25 0.75 0 0.36.23 0. 77 0 0.40 1.22 0.78 C 0.43 1.21 0.79 C 0.46 1.20 0.80 C 0.49 1.19 0.81 0.55 1.17 0.833 0.58 1.15 0.85 0.61 1.14 0.86 0.64 1.13 0.87 0.66 1.12 0.88 0.68 1.12 0.88 0.70 1.11 0.89 4 0.72 1.10 0.90 0.73 1.10 0.90 0.75 1.09 0.91 0.76 1.09 0.91 0.77 1.08 0.92 0.78 1.08 0.92 0.79 1.08 0.92 0.80 1.07 0.93 0.80 1.07 0.93 0.81 1.07 0.93 0.82 1.07 0.94 0.82 1.06 0.94 0.83 1 06 0.94 0.85 1.05 0.95 0.87 1.05 0.95 0.89 1.04 0.96 0.90 1.04 0.96 0.91 1.03 0. 9 7 0.92 1.03 0.97 rogle of I'vation 42 58 48 51 51 21 17 26 54 37 38 14 25 57 16 24 86 2 30 57 18,52 54 '49 7 4 45 51 442 58 4 40 27 4 38 12 4 86 11 34 23 VW11 s )28 39 26 27 124 33 122 55.421 29 1 20 13 19 6 D18 6 0 17 11 0 16 22 0 15 37 0 14 57 0 1419 0 13 45 0 13 13 0 12 44 0 12 17 0 11 51 0 11 28 0 949 0 836 0 7 38 0 653 0 616 0 5 44 Pressure of a load on an inclined plane is found by multiplying the weight of the load by the horizontal distance, and dividing the product by the length of the inclined plane. Corrollary. Hence appears that on an inclined plane, the pressure is less than the weight of the load. 72J16 ROADS AND STREETS. M. Morin's Experiments. Draught Ratio of Vehicle used. Routes passed over. Pressure in draught pounds. to load. Artillery ammunition wagon,. Broken stone, 13215 398.4 "e "l " in good order, 13541 352.6 8 a8.4 id" " " and dusty...... 10101 250.7 1 Wagon without springs...... 15716 306.3 1 " " "...... Solid gravel, 12037 245.9 48 " "...... very dry,... 981.4 205.5 47.7, " "..... l 7565 150.8 50.1 Wagon with springs............. Paved, in good 3528 86.6 1 t" " o"............ order, with wet - 7260 196.7 mud,......... 11018 299.9 The greatest inclination ought not to exceed 1 in 30, and need not be less than one in 100, for a horse will draw as well on a road with a rise of 1 in 100 as on a level road. Where the road curves or bends, it should be wider, as follows: When the two lines make an angle of deflection of 90~ to 1200, increase the road-bed one-fourth. Example. Let us suppose that we ascend a hill 1 mile long at the rate of 1 foot in 30, and that we descend 1 mile with an inclination of 1 in 40. Here we have for a one-horse cart or vehicle ascending = 1.66, descending = 0.70, sum = 2.36, mean = 1.18. That is, passing over the hill of 2 miles with the above rise and fall, is equivalent to hauling over 2.36 miles of a horizontal road. The inclined road is easily drained, and requires less material in construction and annual repair, and avoids curves. The engineer will be able to judge which is the most economical line from the above table. M. Morin's experiments show that1st. The traction is directly proportional to the load. The traction is inversely proportional to the diameter of the wheel. 2d. Upon harf roads, the resistance is independent of the width of the tire when it exceeds 3 to 4 inches. 3d. At a walking pace, the traction is the same, under the same circumstances, for carriages with and without springs. 4th. Upon hard macadamised and paved roads, the traction increases with the velocity, when above 21 miles per hour. 6th. Upon soft roads, the traction is independent of the velocity. 6th. Upon a pavement of hewn stones, the traction is three-fourths of that upon the best macadamised roads, at a pace but equal to it at a trot. 7th. The destruction of the road is greater as the diameter of the wheels is less, and is greater with carriages without than with springs. i TABLE C.-For Laying Out Curver. Chord A B =,- 200feet or links, orany multiple of either. (See Fig. A, Sec. 319z.) Radf au4 'D0F Rad~of I angLofDCF HGW cvedefiect'n D FEH WScurve. deflect'nDCFEHGW 700 8 12 48 7.18 1.79 0448 0112 1900 3 01 01 2.63 0.66 0.17.041 20 765901 6.98.747.437.109 20 256908.606.652.163.040 40 46 69.788.699.425.106 40 67 17.579.642.161 60 33 34.604.663.41S.103 60 66 28.653.638.160 80 21567.438.614.403.101 80 63 48.630.633.158 800 10 6.27-4.570.393.0698 2000 61 67.503.626.166.039 20 01 16.148.638.385.096 20 60 15.477.619.156 40 50 14 6.97.495.374.093 40 48 38.452.613.153.038 60 6 40 39.844.460.365.091 60 46567.429.607.152 50 31 30.701.426.367.089 80 45 20 -.405.601.150.037 950-0 22 46.570.3-94 -.348'.087 210-0 43 46.382.596.149 -20 14 25.436.364.341,e085 20 42 13.357.589.147 40 06 25.310.334.334.083 40 40 42.339.585.146.036, 60 6 58 45.222.307.327.082 60 39 12.316.679.146 80 51 24.142.279.320.080 80 37 45.296.574.143 1000 440.1.264.313.078 2200 369.275.1-42.036 20 37 S4 4.91.229.307.077 20 34564.253.658.141 40 31 04.817.205.301.075 40 33 31.232.653.139 60 24 48.727.183.296.074 60 32 10.213.549.138.034 80 18 46.640.160.292.073 80 30 50.194.644.137 -11-00 12567.556.140 -.2-85. 07 1 23 00 2930.174.542. 13 6~ 20 07 21.473.117.279.070 20 28 14.157.534.136 40 01567.396.099.276.069 40 26567.138.530.134.03S 60 4 56 44.319.080.270.068 60 25 42.119.526.132 80 51 41.247.062.265.066 80 24 29.102.521.131 1200 46 49 i174.044.261.065 2 O 23 17.084 717:1T3.03 20 42 06.105.027.257.064 20 22 06.067.513.129 40 37 32.0029.010.252.063 40 20 56.051.608.128 60 33 07 3.98 0994.248.062 60 19 44.033.505.127 80 28561.914.978.245.061 50 18'39.018.500.126.031 13-00 724-4 2.5.9-63.241.0-60 2 50 0 17 33.001.4-96.125 20 20 41.798.949.237.069 20 16 27 1.99.492.124 40 16 47.737.935.234.058 40 15 23.969.489.123.030 60 13 00.681.920.230.057 60 13 19.954.485.122 80 09 20.628.907.227.056 80 13 17.939.481.121 140-0 0-6546.6-74.894. 22 4.0656 2600 12 15 -.924.477.120 20 02 18.526.882.221.056 20 11 14.909.474.119 40 3 59 06.481.870.218.054 40 10 15.895.470.118.029 60 65539.429.857.214.063 60 9 16.880.466.117 80 52 27.382.846.212.062 80 8 16.865.463.117 160-0 49b2 0.337.8-34.*209 20 7 22 -.861 -.460. 11 6 -20 46 20.293.823.206.051 20 6 25.839.456.116 40 43 23.250.813.203.050 40 5 29.825.463.114 60 40 31.208.802.201.049 60 4 36.8 121.450.113.028 80 37 43.169.792.198 80 3 42.799.447.113 160-0 -35 00.128 ~.7 2.19.0-48 2-800 ~248.78j ~.443.1-12 -20 32 19.089.772.193 20 1 56.773.440.111 40 29 45.062.763.191.047 40 1 04.760.437.110 60 27 13.011.763.188 60 0 13.747.434.109.027 80 24 45 2.98.745.186.046 80 1 69 23.735.431'.109 17-00 - -2220.943.736T~.184 83.726.429.0 - 20 19 69.910.728.182.046 20 67 45.714.426.107 40 17 41.876.719.180 40 66657.703.423.106 60 16 26.843.711.178.044 60 66 10.692.420.106 80 13 14.812.703.176 80 65623.681.417.106.026 18 00 -I11065.777.6-94 1Y74.0-43 30F0 ~64 37.669.416.104 - 20 8569.749.687.172 20 63651.668.412.104 40 6566.719.680.170.042 40 63 07.647.409.103 60 4665.686.671.168 60 62 22.636.406.102 80 2567.662.666.1671.041 80 61 38.6261.4041.102 72j21 I TABLE C.-For Laying Out Curve*. Chord A B = 200feet or linka, or any multiple of either. (See Fig. A, Sec. 319z.) Rad.of Iang1.of Rad.of j angLof FE HG WS urve. deflect'n WS curve. deflect'n 3100 1 50 55 1.61.404.101.025 4300 1 19 57 1.16.291.073.018 20 5013.603.401.100 20 1936.157.289.072 40 49 30.593.398.099 40 1913.152.288.072 60 48 48.583.396.099 60 18651.146.287.072 80 48 07.573.398.098 80 18 30.141.285.071 3200 4727.5t6 $.391.0-98 4400 1808.136.284.071 20 46 47.553.388.097.024 20 17 47.131.283.071 40 46 07.543.886.097 40 17 26.126.282.071 60 4528.584.884.096 60 17 05.121.280.070 80 44 60.525.381.095 50 16 45.116.279.070 3300-i 4411 7.516.379.095 4500 TW54o 16.iTI 7 i3 - -8 20 43 34.506.377.094 2Q 16 04.106.277.069.017 40 42 67.497.374.094.023 40 16 44.102.276.069 60 4220.489.872.093 60 15 24.097.274.069 80 4148.480.370.093 80 15 04.092.273.068 3400 4108.471.368.092 4600 14444 7.0827 72.068 - 20 40 32.462.366.092 20 14 25.082.271.068 40 89 54.463.363.091 40 14 06.077.269.067 60 39 22.445.861.090 60 13 47.073.268.067 80 38 48.437.859.090 80 13 28.069.267.067 3500 3814.429.~6357.089.022 4700 1309.064 7266.067 20 37 41.421.355.089 20 12 51.069.265.066 40 37 08.413.353.088 40 12 32.054.264.066 60 3636.405.351.088 60 12 14.050.263.066 80 3603.397.349.087 80 1155.046.262.066 3600 850 3.38.347.087 4800 1138.042.261.065 T.016 20 34 59.381.345.086 20 11 20.038.260.065 40 34 27.374.344.086.021 40 11 02.034.259.065 60 33 57.366.342.086 60 10 44.030.258.065 50 3326.358.339.085 80 10 27.026.257.064 3700 3255.T51)T.838.5 4900 1010.022.2 56.064 20 3226.344.336.084 20 9563.018.255.064 40 8156.337.334.084 40 936.018.253.063 60 31 27.330.333.083 60 919.008.252.063 80 30 57.323.831.083 80 902.004.251.068 3800 8082 3.329.0821 5000 846 1.00.2506.063 - 20 30 00.309.327.082 20 8 29.996.249.062 40 29 82.302.326.082 40 8 13.992.248.062 60 29 04.295.324.081.020 60 7 66.988.247.062 80 2837.288.322.081 80 741.984.246.062 3900 28 09.2-82.321.080 6100 7 I7 6 i.981: T 45 T0h1 20 2743.276.319.080 20 709.977.244.061 40 2716.269.317.079 40 6586.973.248.061 60 26 49.262.316.079 60 6 38.969.242.061 80 26 23.256.314.079 80 6 22.965.241.060 4000 25 57.26..078.0190 500 6 07.96 2T7i.060 20 25 21.243.311.078 20 5 52.958.240.060 40 25 06.237.309.077 40 6 37.954.239.060 60 2441.231.308.077 60 622.950.238.059 80 24 16.225.306.077 80 5 07.947.237.059 4100 23 62.2271To 5.0T76 5300 462.94 4.23-6 ':U5 20 2327.214.304.076 20 437.940.235.059 40 2303.208.302.076 40 4 23.936.234.059 60 2239.202.801.076 60 409.938.233.068 80 22 14.196.299.075 80 3 64.929.232.058 4200 21 62.191 076 50 40 340.926.232.058 20 2128.185.296.074 20 326.928.231.058 40 21 05.179.295.074 40 3 12.919.230.058 60 2042.173.293.073 60 258.916.229.057 80 20-20.168.291.0781.018 80 2 44.912.228.057.014 '7.Iqo' TA-BLE (X-ForLaying Out Curves. Chord A B7=200 feet or link., or any multiple of either. (See Fig. A, See. 319x.)Rad~of I angLof D FEH WSRad~of I angl~ofDOF HG W curve. deflect'n DCFEH Scurve. cleflect'nDCFEHGWS 5500 1 2 31.909.227.057.014 6700 056119.746.187.047.012 20 2 17.905.226.057 20 51 10.744.186.047 40 2 03.902.226.057 40 51 00.742.186.047 60 1 50.899.225.056 60 50 52.740.185.046 80 1 37.896.224.056 80 50 42.788.185.046 5600 1l 24 -.93.2-23.056 6800 56083.736A184.046 20 1 10.89.222.056 20 50 25.733.183.046 40 0 57.86.222.056 40 50 16.731.183.046 60 0 44.83.221.055 60 50-07.728.182.046 80 0832.80.220.055 80 49568.726.182.046 5700 01 9 -.7 7.219.055 6900 49$0 ~.1-81.045.011 20 1 0 06.74.219.055 20 49 41.722.181.045 40 0 59 54.71.218.055 40 49 32.720.180.045 60 59 41.68.217.054 60 49 24.718.179.045 80 59 29.65.216.054 80 49 15.716.179.045 5800 59 1 6.2.216.054 7000 - 4907.714.1-79.045 20 59 04.59.215.054 20 48 58.712.178.045 40 58562.56.214.054 40 48560.710.178.045 60 58 40.53.218.058.012 60 48 42.708.177.044 80 58 28.50.213.053 80 48 33.706.277.044 5900 58 16.47.21 2.058 71-00 4 8~25.70L176.0~44 -20 58 04.844.211.053 20 48 17.702.175.044 40 57563.842.211.053 40 48 09.700.175.044 60 57 41.840.210.053 60 48 01.696.175.044 80 57 29.837.209.052 80 47562.694.174.044 6000 5)7 18.884.209.052 7200 47 45.6-92.1-74.044 20 56607.831.208.052 20 47 37.690.173.043 40 56655.829.207.052 40 47 29.688.173.043 60 56644.826.207.052 60 47 21.686.172.043 80 56 33.823.206.052 50 47 13.684.172.043 -671 00 5622.8-20.2-05. - _ _ _ _ - 20 56611.818.205.051 7300 47 06.682.171.043 40 65500.815.204.051 50 47 47.679.169.042 60 55 49.813.203.051 7400 46 28.676.169.042 80 65838.810.203.051 50 46 09.672.168.042__ U6200 527.8-07.202.051 7500 4551l.6-68.167.042 20 55 16.804.201.050 50 45 32.663.166.042 40 55 06.801.200.050.012 7600 45 14.658.165.041.010 60 54 55.799.200.050 50 44567.654.164.041 80 54 45.796.199.050 7700 44 39.650.163.041__ 6300 5434.794. 199 U.050 560 -4422 ~i.6 16 2.041 20 54 24.791.198.050 7800 44 05.642.160.040 40 54 14.788.197.049 60 43 48.638.160.040 60 54 03.786.197.049 7900 43 31.634.158.040 80 58 53.783.196.049 50 43 15.629.157.039 6400 5343.781.195.049 8000 04258a.624.157.089 -20 53883.779.195.049 50 42 42.621.155.039 40 58 23.777.194.049 8100 42 27.617.154.039 60 53 13.775.194.049 50 42 11.614.153.038 80 63 03.772.193.048 8200 41565.611.153.038__ 65a0-0 52 53.7-69.1-92.048 -50 41 40.608.152.038 20 52 44.767.192.048 8300 41 25.605.151.038.009 40 52 84.765.191.048 60 41 10.602.150.037 60 52 24.762.191.048 8400 40566.599.150.037 80 52 15.760.190.048 50 40 41.596.149.037 66-00 5- 2 03 ~.M.189.047 (' - 4027.693. 14 8.0~3 7 -20 51566.755.189.047 50 40 13.589.147.037 40 51 47.753.188.047 8600 39568.585.146.087 60 51 37.751.188.47 50 39 45.581.145.036 80 528.7481'.1871'.047 8700 39 31.577.144.086.009 I I TABLE C.-For Laying Out Curve8. ChordA B =200 feet or links, or any multiple of either. (See Fig. A, Sec. 319x.) Rad. of J angl.of curve. deflect'n DOC 0 / // FE HG __crve 8750 8800 8860 8900 9000 9100 9200 9300 9400 9600 9600 9700 9800 9900 10000 100 200 800 400 500 600 700 800 900 11000 100 200 300 400 600 600 700 800 900 12000 100 200 300 400 500 700 800 900 13000 100 200 300 400 500 700 800 900 14000 100' 200 300 400 500 083917 39 04 38851 38 37 38 12 37 47 37-22 36 58 36 35 36 11 85 49 35 26 35 05 34 44 34 23 34 02 33 42 33 23 33 03 32 44 32 26 32 08 31 50 31 33 31 15 30 58 30 42 30 25 30 09 29 54 29 38 129 28 29 08 28 53 28 40 28 25 28 11 27 57 27 43 27 30 2717 27 04 26 51 26 39 26 27.26 14 26 08 25 51 26 89 25 28 25 17 25 06 24 65 24 44 24833 24 28 24 13 24 02 23 62 28 48.573.5730.566.563.757.548.537.531.525.518.504.491.48.481.476.467.466.451.447.448.436.431.427.424.421.414.411.407.408.396.39C.390q.387.387.376.378.370.364.361.366.368.348.346.344.143.143.141.141.139.137.136.134.133.131~.1301.128.1271.1261.125.124.123.122.120i.119.118.117~.116.115.114.111.110.109.108.107.106.105.104.104,.103.102~.101.100.098.098 ~.0978.096.096~.095.094!.093.092 Ij91.090.090.089.089.088.087.87.086.036i.036.035.035.035.034.034.034.033.033.033.032.032.032.031.031.031.030.030.030.029.029.929.028.028.028.028.028.027.027.027.027.026.026.026.026.026.025.025.025.026.025.024.024.024.024.024.023.023.023.028.023.022.022.022.022.022.022.022.009.008.007 14600 14700 800 900 15000 200 300 400 500 700 800 90(1 16000 200 300 400 500 700 800 900 17000 -T00 200 300 400 500 600 700 800 900 18000 100 200 300 400 500 600 790 800 900 19000 100 200 300 400 500 700 800 900 20000 21000 21120 15840 10560 5280 Iangi~of deflect'n o / /1 0 23 33 28 23 23 14 23 04 22 55 22 46 22 37 22 28 22 19 22 12 22 02 21 54 21 46 21 37 21 30 21 21 21 13 21 05 205b8 20 50 20 43 20 35 20 28 20 21 20 13 2007 19 59 19562 19 45 19 39 19 32 19 26 19 19 19 12 19 06 0 19 00 18563 18 47 18 41 18 35 18 29 18 23 18 17 18 11 18 06 18 00 17 54 17 49 17 43 17 38 17 32 17 27 17 22 17 17 17 11 -162-1 16 16 21 42 82 33 1 5 07.342.340.338.336.334.332.330.328.326.324.322.320.31.316.314.312.310.30.306.304.302.300.298.296.294.292.290.288.286.284.282.281.280.27.278 M27.275.273.272.270.266.268.267.265.264.262.261.259.258.256.255.253.252.251.249.238.237.816.473.947.086.086.085.088.083.082.082.081.081.080.080.07.078.078.078.077.077.076.076.071.075.074.074.07L3.072.072.072.071.071.071.070.066.066..066.068.067.067.067.067.066.066.065.065.065.064.068.068.068.062.056.079.118.237 D C IF E H G.022.021.021.021.021.021.021.020.020.020.020.020.019.019.019.019.019.019.019.019.018.018.018.018.018.018.018.018.018.0i8.017.017.017.017.017.016.016.016.016.016.016.016.016.016.015.015.01 5.015.015.015.015.015.020.029.059.119 ws8 M00 I.004.006.005. 004.005.007.080 I I I CANALS. 320. In locating a canal, reference must be had to the kind of vessels to be used thereon, and the depth of water required; the traffic and resources of the surrounding country; the effect it may have in draining or overflowing certain lands; the feeders and reservoirs necessary to keep the summit level always supplied, allowing for evaporation and leakage through porous banks, etc. The canal to have as little inclination as possible, so as not to offer any resistance to the passage of boats. To be so located that its distance will be as short as possible between the cities and towns through or near which it is to pass. To have its cutting and filling as nearly equal as the nature of the case will allow. To hate sufficient slopes and berms as will prevent the banks from sliding. The bottom width ought to be twice the breadth of the largest boat which is to pass through it. The depth of water 18 inches greater than the draft or depth of water drawn by a boat. Tow-path. About 12 feet wide, being between 2 and 4 feet above the level of the water, and having its surface inclined towards the canal sufficiently to keep it dry. Vegetable soil, and all such as are likely to be washed in, are to be removed. Where there is no tow-path, a berm or bench, 2 feet wide, is left in each side, about 18 inches above the water. Feeders may ha;ve an inclination not more than 2 feet in a mile, to be capable of supplying four or five times the necessary quantity of water to feed the summit level. Reservoirs, or basins, may be made by excavation, or, in a hilly country, by damming the ravines. There are many instances of this on the Rideau Canal in Canada; also, on that built by the author, connecting the Chats and Chaudiere lakes, on the river Ottawa, in the same country. This necessarily requires that an Act of the Legislature should emp6wer them to enter on any land, and overflow it if necessary, and have commissioners to assess the benefit and damages. Draft is the depth of water required to float the boat. Lift is the additional quantity required to pass the boat from' one lock into another. A boat ascending to the summit has as many lifts as there are drafts. A boat descending from a summit to a lower level has one more lift than drafts. Let the annexed figure represent a canal, where there are two locks ascending and two descending; there are four lifts and three drafts. To Ascend from A to B of Lock 1. (See annexed figure.) Boat arrives at gate a; finds in it one prism of draft, and the other lock empty. Now, all these locks must be filled to enable the boat to arrive at the summit level B C. Let L = prism of lift, and D = prism of draft; then it is plain that to ascend from A to B requires two prisms of lift and one of draft, and putting n = 2, or the number of locks, the quantity required to pasa the boat = n L - (n - 1) D. n 72L CANALS. To Descend from C to D = 2 locks. In lock 3, one prism of lift will be taken, and one of draft. The prism of lift passes into lock 4, together with one of draft, thus using two prisms of draft and one of lift, which is sufficient to pass the boat from C to D = L + 2 D. Or, To ascend = n L + (n - 1) D. To descend = L + 2 D. Add these two equations. The whole quantity from A to D = (n + 1) L + (n + 1) D = (n + 1) * (L + D). Each additional boat passing in the same order requires two prisms of lift and two of draft; that is, the additional discharge = 2 (N - 1) (L + D). Here N = number of boats; therefore the whole discharge = (n + 1) (L + D) + (2 N -2) (L + D) = (2 N + n -1). (L + D). To this must be added the loss by evaporation and leakage. Evaporation may be taken at half an inch per day. From one-third to two-thirds of the rain-fall may be collected. The engineer will, when the channel is in slaty or porous soil, cover it with a layer of flat stones laid in hydraulic mortar, having previously covered it with fine sand. Locks to be one foot wider than the width of beam, 18 inches deeper than draft of boat, and to be of a sufficient length to allow the rudder to be shifted from side to side. Bottom to be an inverted arch where it is not rock. Where the bottom is not solid, drive piles, on which lay a sheeting of oak plank to receive the masonry. The channel to have recesses to receive the lock gates. The lock gates to make an angle of 646 44' with one another, being that which gives them the greatest power of resisting the pressure of the prism of water. Reservoirs are made in natural ravines which may be found above the summit level, or they are excavated at the necessary heights above the summit. Dams are made of solid earth or masonry. When of earth, remove the surface to the depth where a firm foundation can be had; then lay the earth in layers of eight or twelve inches; have it puddled and rammed, layer after layer, to the top. Slope next the water to be three or four base to one perpendicular (see sec. 147). Outside slope about two or two and a half base to one perpendicular. The face next the dam is faced with stone. For thickness of the top of the dam, see Embankments (sec. 319). To Set Out the Section of a Canal when the Surface is Level. 321. Let the bottom width A B = 30 feet, height of cutting on the centre stake H F = 20 feet = h, ratio of slopes 2 to 1 = r-that is, for 1 foot perpendicular there is to be 2 feet base, 20 X 2 = 40 = base for each slope = C G = E D, and 20 X 2 X 2 = 80 = total base for both slopes. Bottom width = 30; therefore, 80 + 30 = 110 = width of cutting at top = C D; and 110 + 30 - 2 X 20 =sectional area 1400. In general, S = (b + h r) h = sec'l area in ft. C = (b + h r) h L = cubic content. Here S -= transverse sectional area, C - content of the section, b = bot tom width, h - height, r = ratio or slope, and L length of section. CANALS. 72M To Set Out a Section when the Surface is an Inclined Plane, as in fig. 44. 321a. This case requires a cutting and an embankment. We will suppose the slopes to be the same in both. Let the surface of the land be R Q, the canal A B = bottom b = 30 feet. Height H G = 20, ratio of slopes of excavation and embankment == 1 base to 1 height-that is, ratio of slopes = r = 1~ to 1. At the centre G set up the level; set the leveling staff at N; found the height S N = 5 feet; measured G S = 20.61, and G N = 20; because the slopes being 1} to 1, the slope to 5 feet = 7~;.'. G F = 121, and G M = 27j feet; and the slope corresponding to H =- 20 X 1.5 35, which added to half the bottom, gives G C = 45. To Find G E and G Q. G M: G S:: G C: G E; that is, 27.5: 20.61:: 45: G E = 33.72 feet. Let the top of embankment P C = 20 feet; then G P - 65. GF:GS:: GP:GQ; that is, 12: 20.61:: 65: G Q = 107.17 feet. Having G E, G Q, G S and S N, we can find the perpendicular Q V. G S: S N:: G Q: QV. 20.61: 5:: 107.17: Q V = 26, which is perpendicular to the surface G V. 20.61: 5:: G E = 33.72: E F - 8.18 feet. G V2 = G Q2 - Q V2;.. we can find G V - 103.96; and by taking 65 from the value of G V, we find 103,96 - 65 - 38.96 = P V. To Find the Point R. We find, when the slope G Q continues to R, that by taking G s = 20.61, ns = 5, n t = 7, G t =12, and st is parellel toBR;.t. Gt: G:: GD: GR; butGD =15 + 20 X 1 =4 45,.. 12.: 20.61:: 45: G R = 74.19. To Find G d = H a, and Area of Cutting. We have G s; G n:: G R: G d; that is, 20.61: 20:: 74.19: G d = H a - 71.99. Gn: ns:: G d: R d; that is, 20: 5:: 71.99: R d = 17.9975. But H G = a d = 20; therefore R a = 37.998; and H a - H B = 7 1.99 -15 = B a = 56.99. Let us put 18 =17.9976. G H+R- a 20+- 38 Area of sec. H G R a 2 X H a- 2 X 71.99 =-2087.71 2 2 Deduct the A B R a= 56.99 X 19 1082.81 Area of the figure G H B R = 1004.90 HG Area G H A C = (G C + A H) X -- (45 + 15) X 10, 600 Area of the figure C G R B A = 1604.90 Deduct triangle G E C = 46-X half of E f = 45 X4.09, 184.06 Area of B A E G R = 1420.86 72N CANALS. Or thus: We have R a by calculation or from the level book, 38 nearly. Also, Eg=gf -Ef z=20- 8.18 -11 82, which multiplied by ratio of slope, gives A g = 17.73, and H g 33.72. But from above we have II a 71.99;.-. 71.99 + 32.73 a g = 104.72. 104.72 2 X(E g + R a) 52.36 X (11.82 + 38)= E g a R = 2608.58 11.82 X17T.73 DeductL E g A +A- s B1 a; i.e., + 56.99 X 19 1187 59 2 Area of the section R E A 13 - 1420.99 Nearly the same area as above. The difference is due to calling 17.9975 = 18. To Find the Embankment. We have Q V = 26, P V = 38.96, E f 8.18, P C = 20, G F -=32.72, and C F = GC - G F = 45 32.72- 12.28 G V =45 + 20 + 38.96 G C + C P + P V = 103.96 G S: G N:: G E: G f; that is, 20.61:20:: 33.72: G f= 33.72. This taken from GOC or 45 will give C F 12.28; f.. fV =12.28 + 20 + 38.96= 71.24 V + E f) = (26 + 8.18)== 17.09 The product - area of Q V F E 1217.4916 Deduct A C fE = 4.09 X 12.28 = E EfX C f= 50.22 Also deduct A Q V P = 38.96 X 13 506.48 Sum to be subtracted, 556.70 4.retq of section Q P C E 660.79 To Set Off the Boundary of a Canal or Railway. 821b. Let the width from the centre stump or stake G to boundary line = 100 feet, if the ground is an inclined plane, as fig. 44. We can say, as GN: G S:: Gf: GE; i. e., 20:20.61:: 100:G E=103.05. Otherwise, take a length of 20 or 30 feet, and, with the assistant, meas-* ure carefully, dropping a plumb-line and bob at the lower end, and thus continue to the end. This will be sufficiently accurate. CANALS. 720 To Find the Area of a Section of Excavation or Embankment such as A B D C. (See Fig. 46.) 322. Let r = ratio of slopes, D = greater and d = lesser depth, and b = bottom width. We have dr = A E, and D r -BF;.. (D + d) r + b E F. But E F X (D + d) = twice the area of C E F D; i. e., {(D + d) r + bj } (D + d) - double area of C E F D..(D2+2 ID d + d2) r+(D+ d) b = double area of C E F D. d2 r = 2 A AC E, and D2 r = 2 A B D F; these taken from the value of twice the area of C D F D, gives the required area of A C D B = 2 D d r. This divided by 2 will give the area of D4d ABCD==Ddr+ (D ) b. 2 b Rule. Multiply the heights and ratio together; to the product add the product of half the heights multiplied by the base. The sum will be the area of A B C D, when the slopes on both sides are equal. Example. Let bottom b = 30, d = 10, D = 20, ratio of base to perpendicular = r = 2, to find the area of the section. D d. r 10 X 20 X 2 = 400 D+d ( — ) X b = 15 X 30 450 Area of section A B D C - 850 322a Let the slopes of A C and B D be unequal; let the ratio of slope for A.C = r, and that for B D = R. Required area of A B D C b R-+r (D + d.) + -- (Dd.). Rule. Multiply the sum of the two heights by half the base, and note the product. Multiply the product of the heights by half the sum of the ratios, and add the product to the product above noticed. The sum of the two products will be the required area. Example. Let the heights and base be as in the last example; ratio of slope A C - 2, and that of slope B D = 3. b (D d.) = 15 X 30 450 R+r — d-. D d. = 2.5 X 200= 500 Area of A F D C 950 Let the Surface of the Side of a Hill Cut the Bottom of the Canal or Road Bed, as in Fig. 47. 322b. Here A B is the bottom of the canal or road, A C and B D its sides, having slopes of r. D E = the surface of the ground, G F = d lesser height below the bottom, and to the point where the slope A C produced will meet the surface of the ground. D H = D = greater height above the bottom. 72P CANALS. Through F, draw F K parallel to A H; then D K = D + d, and A H b + r D, and A G = d; therefore FK G H= b + rD- rd = b - (D - d) r, and by similar triangles. D K: KF:: D H: M H; that is, B D + r D - r d D D + d: b + r D-r d:: D M H = - D-+d But M H X D H = twice the area of A M D H, and twice the area of A BD H = B H X D H - R d X D = r D2; bD2 + rD3 -rdD2.'. twice area of A M D B - r D2 D+ d b D2 + r D3 - r d D2 - r D - r d D2 D + d D + d Dqd b D2 - 2 r d D2 D+d (b-2rd) D2 Double area --- that is, D-]d AreaofAMDB ((b-2 rd)D2) O (b- r d) d D Or = i( - which is that givet by Sir John McNeil in his valuable tables of earthwork. Rule. From half the base take the product of the ratio of slopes and height below the bed; multiply the difference by the square of the height above the bed of road or canal; divide this product by the sum of the two heights; the quotient will be the area of the section M D H. Example. Let base = 40, ratio of slopes 1~ to 1, height G F below the bed = 56, height D H above the bed = 20 feet, to find the area of the section M D B. (See figure 47.) Half the base = 20 r d=5.5X 1.5 = 825 11.75 D = 20 X 20= 400 4700 Divide 4700 by D + d =20 + 5.5 25.5 The quotient = area of M D B = 184.313 feet. To Find the Mean Height of a Given Section whose Area = A, Base = b, Ratio of Slopes = r. 323. Let x = required mean height; then mean width = b + r x; this multiplied by the mean height, gives b x + r x - A = given area. I CANALS. b A x2 + - x - Complete the square: r r b b2 A b2 Mean height = and by substituting the value of r 4 r2 r 4 r2 4 A r2 + 2 4 Ar + b - 4r3 4 r2 b V(4A r + b2) 2r 2r Mean height = x t=x4 A r + b2 -2, b and by substituting the value of 2r 2r A in sec. 322, ((4 D d r2 + (D+d) 2 b r+b2Ii1-b 2r Rule. To the square of the base, add four times the area multiplied by the ratio of the slopes; take the square root of the product; divide this root by twice the ratio, and from the quotient take the base divided by twice the ratio. The difference will be the required mean height. Example. Let us take the last example, where the base b = 40, ratio r = 1j, area = 184.313 square feet. 4 A r = 184.213 X 4 X 1.5 = 1105.878 b2 = 40 X 40 = 1600 2705.878 Square root of 2705.878 = 52.018 This root divided by 2 r = 3 gives = 17.339 b 40 From this take - = - 13.333 2r 3 Gives the mean height = 4.006, or = 4 feet nearly. 4 r = 6, to which add base 40, sum - 46 Approximate mean height, 4 184 Area nearly as above. It need not be observed that if we took the mean height = 4.009, we would find 184.313 nearly. Our object here is to show the method of applying the formula to those who have no knowledge of algebraic equations. Or by plotting the section on a large scale on cartridge paper, the area and mean depth can be' computed by measurement. The mean heights are those used in using McNeil's tables of earthwork, and also in finding the middle area, necessary for applying the prismoidal formula. Rule 2. To four times the product of the heights and ratio add the continual product of the sum of the two heights by twice the base multiplied by the ratio; to this sum add the square of the base; from the square root of this last sum subtract the base, and divide the difference by twice the ratio. The quotient will be the mean height. Example. D = 70, d = 30, b = 40, r = 1. 70 X 80 X 4 X (70 + 30) X 80 = 16400 Square of base = 1600 18000 The square root = 134.164, which, divided by 2, gives 47.082, the mean height. 72R CANAtS. Another Practical Method.. 324. Let A B '= la'ge = b, C D B A = required seetlon, whose area A, and mean height Q R is required; ratio of slopes perpendicular to base is as 1 to r. (See fig. 48.) We have P Q X 2 r A B =b; that is, b b P Q = -; this X by the base gives twice area of A AB P -; i2r 2r b2 therefore, area AA B P -=; consequently, 4r b2 area of A C P D =- + A, or putting area of A A B P = a, 4r we have area A C P D - A + a, and by Euclid VI, prop. 19, A A B P: AP C D:: P Q2 P R2; b2 that is, a: A + a:: --; P R2. 4 r2 (A + a) b2 P R2 = take' the square root,, 4 a r2 pRp_(A +a) b a 2 r PR =((A + ^. b) Q R = (( + -2 ) = mean height. a 2 r 2r Example. Let A B = b - 20, ratio = 2. Given area of the sectiob 1200, which is to be equal to the section A B C D, whose mean height is required. b2 The constant area of A A B P is always = - =50. 4r (A + a) (1200 + 50) (1250)i 5 5. a - -60 60 b 20 Multiply by - = 6. 2r 4 25, product. b 6. 2r Q R = mean height = 20. In this example and formula the slopes are the same on both sides' Let R = greater, and r. = lesser ratio; then Q R =(A+a). b b a R+r. R+r. When the Slopes are the Same on Both Sides. 325. Rule. To the given area above the base add the constant area below the base; divide the sum by the constant area of the A A B P; multiply the square root of this quotient by the base divided by twice the ratio of the slope; from this product take the base divided by the ratio of slope. The difference will be the required mean height = L R. CANALS. 72s When the Slopes are unequal. Rule. To the given area above the base, add the constant area of tile triangle A B P below the base, divide the sum by the constant area of A A B P. Multiply the square root of the quotient, by the base divided by the sum of the ratio of the slopes, from the product subtract the base divided by the sum of the ratios, the difference will be the required mean height = Q R. Example. Let ratio R - ratio of Q B to Q P = ratio to slope B D - 3, and r = lesser ratio of A Q to P Q - 2. 20 A B = b = 20, therefore P Q -- - 4. R + r Let area of A B D C = 960, and constant area of the triangle under the base = 40 = A A A B P. A +-a b b 9 60 - 40 t 20 20 a +' R+r R+r 40 ' 5 - Q QR- 5 X 4 - 4 1=;. 326. Menn height must not be found by adding the heights on each side of the centre stump or stake, and then take half of the sum *for a m7ean height. This method is commonly used, and is very erroneous, as will appear from the following example: Let the greater height D IH = 70, (see fig. 49,) the lesser C E -30, base 40, ratio of slopes I to 1. Correct Jfethod. 70 greater height i D 80 _ lesser = d 2) 100, mean height 50 -30 + 4 0 + 70 = e base E H 140 Sectional area of C D I E — 7000 deduct the two triangles C E A + 1) 13 H = 2-)00 Area 4100 Correct. Or, by sec. 3"22, we can find the area D d r7 = 0 X 30 1 X 100 D + d b = 50 x0 4 000 2 4100, required correct area. By the Erroneous or1' Conmon Method. 70 +- 30 100 sum of heights. 50 = mean height. Half slope =- 50 100 mean base. 50 = mean height. Area 5000 incorrect. Area 4100 correct. Difference 900 square feet. From this great difference appears that where the mean height is required, it has to be calculated by the formula in section 323, where (4A r + 1-) _- b x _ mean height -,r 2 n2 72T CANALS. Area found by the correct method = 4100 4 16400 - 4 A 1 -r 16400 4 A r 1600 — b2 Square root of 18000 = 134.164, and 134.164, divided by twice the ratio, gives 67.082, from which take the base, divided by twice the ratio, leaves required mean height = 47.082. By the common method 50 Difference, 2.918 feet. Or thus, by sec. 324: We find the mean height Q R, (fig. 49,) area of triangle A B P, having slopes 1 to I = 400, the perpendicular P Q = 20. And from above we have the area of the section A B D C = 4100 (A+ a) i (410 400 00 + 400) 4 /45 6,7082 000 ~ 400 2 2 b _2 — _ 20 b 67.8020 Less 2 r 2r == 20 Mean height Q R = 47.802 TO FIND THE CONTENT OF AN EXCAVATION OR EMBANKMENT. In general, the section to be measured is either a prism, cylinder, cone, pyramid, wedge, or a frustrum of a cone, pyramid, or wedge. The latter is called a prismoid. A Prism is a solid, contained by plane figures, of which two are opposite, equal, similar, and having their sides parallel. The opposite, equal and similar sides are the ends. The other sides are called the lateral sides. Those prisms having regular polygons for bases, are called regular prisms. Prismoid has its two ends parallel and dissimilar, and may be any figure. 327. Prism. Rule. Multiply the area of the base by the height of the section, the product = content, or S = A 1. Here A = area of the base, and 1 == the length of the section, and S = sectional area. 328. Cylinder. Rule. Square the diameter, multiply it by.7854, then by the height, the product = content == D2 X.7854. Iere D - diameter, solidity S = A 1. Here A - area of the base, and 1 = length. 329. Cone. Rule. Multiply the square of the diameter by.7854, and that product by one-third of the height, will give the content =S = D2 X 1 AA1.7854 X - Or, solidity = - where A and 1 are as above. 0 3 330. Frustrum of a Cone. Rule. To the areas of the two ends, add their mean proportional. Multiply their sum by one-third of the height or length, the product = content. Solidity = S = (A X a X VA a) 3 s = (D2 + d2 + D d) 0.2618 sD3 -d. t I D3 d2s S = (D-d- ) = ( -d) X.2618 c. Here t = 0.7854, D and d = diameters, 1 = length, as above. I CANALS. 72u Example. Let the greater diameter of a frustrum of a cone be '= D: 2, and the lesser =d 1, and the length 16, to find the content. Dimensions all in feet. A 4 X0.7854 = 3.1416 = 3.1416 a I X 0. 7854 0.7854 0.7854 Product 2.467-41264, square root = 1.57-08 5.4978 One-third the length, 5 Content or S 27.489 Or thus: (By sec. 330.) D-2+ d2 + Dd ==4~1~ 2 7 I = —length 15 105 0.785.9 = tabular number. 0. 2618 3 S2'7.489=content. Or thus: 1) d ~~1 t.7854 5.4978 15 3)824670 S 27.489 content. 331. Pyramid. Rule. Multiply the area of the base by one-third of the length or height, and the product will be the required content. Or, AlI solidity= S=332. Frustrum of a Pyramid. Rule. To the sum of the areas of both ends add their mean proportional, multiply this sum by one-third of their I__ __ height, the product will be the content, or S - (A +a~V /A a )8 Let the ends be regular polygons, whose sides are D and d, then, D= V 1 Here D = greater and d ==lesser side, t tabular area, corresponding to the given polygon, and 1 as above. Rule. From the cube of the greater side take the cube of the lesser, divide this difference by the difference of the sides, multiply the quotient by the tabular number corresponding to that polygon, and that product by the length or height. One-third of this product will be the required Content, the same as for the frustrum of a cone. Example. Let 3 and 2 respectively be the sides of a square frustrum of a pyramid, and length 15 feet. A +a +V/A a=9 +4 +6 19 One-third the length Solidity =S Or thus, by secs.*'btk 41' D3-d3 27-s 19 Ai D-d 3-2 1 Tabular number per Table One-third the length -~ otn S i 333. Wedge has a an edge. meeting in 72v CANAL.S. Rule~ To twice the length of the base add the length of the edge, multiply this sum by the breadth of the base, and the product by one-sixth of the height, the product will be the solid content, when the base has its sides parallel. S = —l2L+- l).bh. Here L = length of the rectangular base N A B, 1 length of the edge C D, b =-i breadth of base, B F and IH = height. Example. LetA B = 40 feet, B F = b 10, C D = 1 30, and let the height N C -50 feet - i, to find the content. 2 L X = 80 + 80 110 b h = 10 X 50 500 6)55(00o 9166i.;;66 cubic feet. Let C D, the edge, be parallel to the lengths A B and E F, and A B greater than E F, H G = perpendicular width. Rule 2. Add the three parallel edges together, multiply its one-third by half the height, multiplied by the perpendicular breadth, the product 1. h b. will be the required content. Or, S i (L + Lil - 1) X- Here L = greater length of base, Li lesser length, 1 length of the edge, h = perpendicular height, and b == perpendicular breadth. Let us apply this to the last example: L;-L — -l 40 -40 80 110 3., 3 h 5h0l) X 10 = 50 2 2 Therefore, content -= - 250 27 = 9196.666, as above. 3 1 3 Example 2. Let A B = 4, E F = 2.5, C D = 3, height = 12, and width H G = 3A, then by Rule 2. 4 + 3 - 3..5 X 12 X 3 * 5 = 66- cubic feet. Note. As Rule 2 answers for any form of a wedge, whose edge is parallel to the base, the opposite sides A B and E F parallel, without any reference to their being equal. I' I MSBIOID. 334. The prismoid is a frustrum of a wedge, its ends being parallel to one another, and therefore similar, or the ends are parallel and dissimilar. When the section is the frustrum of a wedge, it is made up of two wedges, one having the greater end for a base, and the other having the lesser, the content may be found by rule 2 for the wedge. The following rule, known as the prismoidal formula, will answer for a section whose ends are parallel to one another. It is the safest and most expeditious formula now used, and has been first introduced by Sir John MacNeil in calculating his valuable tables on earth work, octavo, pp. 2G68. T F. Baker, Esq., C.E., has also given a very concise formula, wbich, as many perhaps may prefer, I give in the next section. To Mir. Baker, of England, the world is indebted for his practical method of laying out curves. I pCC -- CANALS. I 'W PRVISIMOIDAL FORMULA. S = (A a- a 4 MI)l IHere A = area of greater end, a= area of 6 lesser end, MI = area of middle section, and L = length of section. all in feet. Rule. To the sum of the areas of the two ends, add four times the area of the middle section, multiply this sum by one-sixth of the length, the product will be the required content, or solidity. Here A = —area of C A B D, a =area of G E F H, and M = area of section through K L. ]Eample. Let the length L 400 feet. AMean height of section A B D C 50 Mean height of section G E F H = 20 Ratio of slopes -= 2 base to 1 perpendicular, and base = 30, 50 = mean height, by sec. 326. Height 20 50 2 2 20 Half base = 100 for slopes. 40 2)70 30 30 35 Mean br'dth, 130 Mean breadth, 70 2 Height, 50 Ieight, 20 70 6500 a 1400 80 A = 65l)0) 100 M = 14000:5 2190()0 350= M. 400 = length. 6)876(o00()0 Content in cubic feet = 9)1460000 3) (2222.22 541074.07 cubic yards. On comparing this with Sir John MacNeil's table, we find 540.72, difference only 2 yards, which is but very little in this large section. Baker's Method Modified. (See fig. 48.) Solidity S= r l (D- + D d + d2 3 B ) 8 1 4 r-~ Here D = greater depth from the vertex, whose slopes meet below the base, d = lesser depth, r = ratio of slopes, B = base, 1 = length of section, all in feet. The depths D and d are found by adding the perpendicular P Q to the mean height q R of section. (See fig. 48.) b P Q, 30 Because p -= P Q... 7.5 = P Q. 22 4 Consequently D = 50 + 7.5 = 57.5 d = 20 - 7.5 = 27.5 72x ^ D2 == 57.5 X 57.5 d2 = 27.5 X 27.5 Dd = 57.5 X 27.5 CANALS. 3 B2 3 X 30 X 20 2700 4 r2 16 16 D2 + D d +d2 3 B2 4 r2 r l= 2 X 400 = 3306.25 - 756.25 - 1581.25 5643.75 = 168.75 5475 800 81)4380000 r.A7A nTA7 IT-U. lu-. -o f..A *-..-.. 1 above by the Prismoidal formula. V,.v, u ut uuu 3The base or road beds are, in England, for single track 20, double track 30 feet wide. And in the United States, in embankments, single track 16, for double track 28 feet. Also in excavation, single track 24, double track 32 feet. In laying out the line, we endeavor to have the cutting and filling equal to one another, observing to allow 10 per cent for shrinkage; for it has been found that gravel and sand shrink 8 per cent, clay 10, loam 12, and surface soil 15. Where clay is put in water, it shrinks from 30 to 33 per cent. Rock, broken in large fragments, increases 40 per cent.; if broken into small fragments, increases 60 per cent. The following, Table a, is calculated from a modified form of Wm. Kelly's formula. Content in cubic yards = L {B. i (- - h) H h d 27 +( -+ -- )s Here L = length, B = base, H and h = greater and lesser heights, r = ratio of slope, d == difference of heights. Rule for using Table a. Multiply tabular number of half the height by the base, and call the result = A. 2. Multiply the tabular of either height by the other height, and call the result - B. 3. Multiply the tabular number of the difference of the heights by one-third of the difference, and call the result = C. Add results B and C together, multiply the sum by the ratio of the slopes, add the product to the result A, and multiply the sum by the length, the product will be the content in cubic yards. Example as in section 334. Where length = 400, base = 30, heights = 50 and 20, and ratio of slopes = 2. 50+20 2 - + 35, its tabular number, by 30 = 1.2963 X 30 = A 38.889. 50 X tabular 20 = 50 X 7.7407 = 39.0350 = B. 10 X tabular 30 = 10 X 1.1111 = 11.1110 = C. 48.1960 X 2 = 96.292 135.181 Length, 400 54072.505 yds. By Sir John MacNeil's Table XXIII = 54072 By his prismoidal formula = 54074.072 Here we find the ditffrence between table a and the prismoidal formula to be 1 in 36049. ' Sir John's tables are calculated only to feet and 2 decimals. William Kelly's (civil engineer, for rmany years connected with the Ordinance Survey of Ireland) to every three inches, and to three places of decimals. Table a is arranged similar to Mr. Kelly's Table I, but calculated to 4enths of a foot, and to four places of decimals. Tables b and c are the same as MacNeil's Tables LVIII and LIX, with our explanation and example. TABLE a.-For the Computation of Prismoids, for all Bases and Slopes. 100.0037 6. 0.2259 12.1 0.4481 18.1 0.6704 24.1 0.8926 30.1 1.1148 2.0074 2.2296 2[.4518 2.6741 2.8963 2.1185 3.0111 3.233 3 3.4555 3.6778 8.9000 3.1222 4.0148 4.2370 4.4592 4.6815 4.9037 4.1259 5.0185 5.2407 5.4629 5.6852 5.9074 5.1296 G.0222 6.2444 6.4666 6.6889 6.9111 6.1333 7.0259 7.2481 7.4703 7.6926 7.9148 7.1370 8.0296 8.2518 8.4740 8.6963 8.9185 8.1407 9.0333J 9.2555 9.4777 9.7000 9.9222 9.1444 1. 0.0370 7.0.25911 13.0.4814 19.0.7037 25.0.9259 31.0.1481 1.0407 1.2628 1.4851 1.7074 1.9296 1.1518 2.0444 2.27 65 2.4888 2.7111 2.9333 2.1555 3.0481 3.2802 3.4925 3.7148 3:9370 3.1592 4.0518 4.2839 4.4962 4.718.5 4.9407 4.1629 55.0555 5.2778 5.5000 5.7222 5.9444 5.1666 6.0592 6.2815 6.5037 6.7259 6.9481 6.1703 7.0629 7.2852 7.5074 7.7296 7.9518 7.1740 8.0666 8.2889 8.5111 8.7333 8.9555 8.1777I 9.0703 9.2926 9.5148 9.7370 9.9592 9.18141 2.0.0741 8.0.296 3114.0.5185 20.0.7407 26.0.9629 32.0.1851 1.0778 1.3000! 1.5222 1.7444 1.9666 1.1888 2.0815 2.3037 / 2.5259 2.7481 2.9703 21.19251 3.0852) 3.3074 o.5296 3.7518 83 9740 3.19621 4.0889 4.3111 4.5333 4.7555 4.-977 41.199991 5.0926 5.3148 5.5370 5.7592 5.9815 5.2037 6.0963 6.3185 6.5407 6.7629 6.9852 6.2074 7.1000 7..3222 7.5444 7.7666 7.9889 7.9111 80.1037 8 0.3259 8 0.5481 8 0.7703 8 0.9926 8 1.2148 9.1074 9.3296 9.55181 9.7740 9.9963 9.2185 3.0 1111 90.1111 333315.0.555521.0.7778 27.0 1.0000 33.0.2222 1.1148 1.3370 1.5592| 1.7815 1.0037 1.2259 2.1185 2.3407 2.5629 2.7852 2.0074 2.2296 3.1222 3.3444 3.5666 3.7889 3~.0111 3.2333 4.1259 4.3481 4.5703 4.7926 4.0148 4.2370 5.1296 5.3518 5.5741 5.7963 5.0185 5.2407 6.1333 6 555 6 3.5778 6.8000 6.0222 6.2444 7.1370 7.3592 7.5815 7.8037 7.0259 7'.2481 8.1407 8.3629 8.5852 8.8074 8.0296 8.2518 9.1444 9.3666 9.5889 9.8111 9.0333 9.2555 4.0.1481 10.0.3704 16.0.5926 22.0.8148 28.0.0370 34.0.2592 1.1518 1.3741 1.5963 1 1.8185 1.0407 1.2629 2.1555 2.1778 2. 60001 2.8222 2.0444 2.2666 3.1592 3.38151 3.60379 3.8259 3.0481 3.2703 4.1629 4.1629 3852 4.46074 4.829; 4.0518 4.2740 51667 5.1667 3889 5.6111 5.83333 5.0555 1.2778 6.1704 6.3926 6.6148 6.8370 6.0592 6.2815 7.1741 7.3963 7.6185 7.8407 7.0629 7.2852 8.1.78 8.4000 8.6222 8.8444 8.0666 8.2889 9.1815 9.4037 9.6359 9.8481 9.0703 9.2926 6.0.1852 11.0.4074 17.0.6296 23.0.8518 29.0.0741 35.0.2963 1.1889 1.4111 1.6333 1.8555 1.0778 1 _.3000 2.1926 2.4148 2.6370 2.8592 2.0815 2.3037 3.1963 3.4185 3.6407 3.8629 3.0852 3.3074 4.2000 4.42222 4.6444 4.8666 4.0889 4.3111 5.2037 5.4259 5.6481 5.8704 5.0926 6.3148 6.2074 6.4296 6.6518 6.8741 6.0963 6.3186 17.2111 7.4333 7.6555 7 1.8778 7.1000 7.3222 8.2148 8.4370 8.6592 8.8815 8.1037 8.3269 9.2185 9.4407 9.6629 9.8852 9.1074 9.3296 16.0 0.2222 12.0 0.4444 18.0 0.6667 24.0 0.8889 30.0 1.1111 36.0 1.3333 I I I TABLE a.-For the Comsputation of Prismoids, for all Bases and Slope. -! +6 36.1 1.3370 42.1 1.5509 48.1)1.781 5 54.1 2. 00:37 60.1 2.22591 66.1 2.4481; 2.3407 2.5633 2.7852 2.0071 2.22961 2 *45181~ 3.3444 3.5667 3.7 889 3.0114 3.2:333 3.4Sss 4.3481 4.5704 4.79296 4.0148 4.23710 4.4592 5.3518 5.5741 5.7903 5.0185 5.24071 5.4629j 6.3-555 6.5778 6.8000 6;.02 22 6.2444 6.46661 7.3592 7.5815 71.8037 7.0259 7.2481~ 7473 8.3629 8.58-52 8.8074 8.0296 8.2518 8.47-401 9.3666 9.5889 9. 8111 9.0333 9.2S5S-f 9.4777, 37.0.3704 43.0.5926 49.0;.8148 55.().0370 61.0.2592' 67.0.4815~; 1.3741. 1.596:3 1 1.8185 1.0407 1.26291 1.48521 2.3778 21.6000 21.8222 2.0444 2.2~-)6 66 2.4889. 3.3815 3!.60 37 3~.82-59 3.0481 3.2703 3.49261 4.3852 4'.6074 4.8296' 4.0518 4.2740 4.496 5.3889 5.6111 5i.8338 5.0556 5.78 5.5000. 6.3926 6.6148 6.8370 6.0593 6.2815 6.5087) 7.3963 7.6185 7..8407 7.0630 7.2852 7.5074, 8.4000 8.62 22 81 8444 8.0667 8.2886 8.5111 9.403 7 96 62 59~ 9j (.8481 9.0704 91.29-25 9.5148 38.0.4073 44.0.62)9 5 506f.8 5Th1, 56.0.0741 62.(). 2 96W3) 68.0.5185: 1.4110 if.8)3 2 1.8555 1.0778 1.3000 1.5222 2.4147 4-.6869 2.8592 2.0815 2,.3087 2.5259 3.41841 3.6406 3-.8629 3.085-2 3,.3074 3.52196 4.422 11 4:6443 4:8666 4:0889 4:3 I1 11 4 3.3:8 6.4296 6-.618 6.8741 6.09,-63 6.31851 6.,5407. 7.4333 71.6 5 55 7.877-8 7.1000 7.32221 7.5444 8 1.4370 8 1.6592 841.8815 8 2.1 037 8 2.38259 8 2.5481 9.4407 9.6(129 9'.8852.9.1074 9.3296 9d.5 518S 39.0.4444~ 45.0.6667 5t.01.88891 57.0.1111 63.0 38369.0.55 1 481 1.7104 1.8 926O 1.1148 1.3 3 7 1.5 2.451 2 6741 2:.8963" 2.1185 2.3407 2.56t:10 3.40555.6778 3!. 900( 3.1222 8.3444 3.5667. 4.592 4!.6815 4.9037 4.1259 4.3481 4.2-704. 5.4629 5.6852 5,.9074 5.1296 5.3518 5.5741 6.4666 Cf.6889 61.9 1I I1 6.1 833" 6.35-5,5 6.5778 7.4703 71.6926 7.9148 7.1370 7.25921 7.5815 8.4740 81.6 963 8' 918S5 8.1407 8. 36 291 8.5852' 9.4777 9.7000 9..92221 9.1444 9.03666 9.50809 40.0.1814 46.0.70:17 52.0'.9259 58.0.1481 64.0.37041 70.0.59-26. I.48-51 1.70)74 1 11.9296 1.1.518 1.137411 1.59613 2.4888 2.7111 2.9 333 2.155.5 2.3778~ 21.6000 3.4 9 25 3.7148 3.9370 3.1 5 92 3.3 811,f.o037 4.4962 4 4.785 1.9407 4. 1629 4.3852 4f 67 5.5000 5722 5.9444 5.1667 538819 5.11 6.5037 6..71259 61.9481 6.1704 6.3926f 6.6148. I 7.5074 7.7296) 7.9518 71.1741 7 3t,3~3.618 1 8.5111 8.73 33 8.955.5 8.1778 8.4000 8.62 9.5148 9.7370 9.9592 9.1815 9.4037 9 62 59 41.0.518.5 47.0. 741) 753.0.9629. 59.0.1851 65.0.4074 7-1.0.62)96 I ~5922 1.7444 1.9 (1 66 1.1888 1.4111 1. W 3. 2.5259 2.7481 2f.9703k 2.1 925 2.4148 2.6370 3.5296 '3 7518 3;.974O0 3. 1962 3.4185 3.41407'; 4.5333 4f 75-55 4;.9777 4.1999 4.4222 4.6444. 5.5370 5.7592 Sf1.9814 5.2037 5.4259.- 5.6481; 6.5407 6.7629 6;.98.51 6.2074 6).4296 6.A51 7.5444 7.7666 7i.9888 7.2111 7.4333 7.6555' 8 5481 8.776)3 81.95 7.18 7.7( 8.62 9.5518 9.7740 91.9962 9.118.5 9.5407 9.6629 42.0 1.5555 48.0 1.7778 54 0.2.000() 60.0,2.2222 66.0 2.4444 720- 2.6667 TABLE b.-For the co0 Ft1 2 3 4 5 0 2 8 18 32 50 1 6 14 26 42 62 2 14 24 38 56 78 3 26 38 54 74 98 4 42 56 74 96 122 65 t62 78 12 150 61 80 104 1 126 152 182 7 114 134 158 181i 218 i 81 146 1t68 194 224 258 i1 182 206' 2:34 266 302 101 222 248 278 312 350 l1I 266 294 326 362 402 121 3141 344! 378 416 458 13 3664 398 434 474 518 14 2 42 456 494 536 582 15 482) 518 5.58 602) G650 116i 546j 584; 626 672 722 17 6141 6541 698 746 798 18 686i 728; 774 824 8781 19 7602 8061 854 906 962 1 20 84888 938 992 105011 21 926: 97411026 1082 1142 1 22110141106411118 170 1238 1 23 11 i061158i1214 1274 1388 1 24 1202l125 ti13141137ti 1442 1 25 13021365811418 1482 1550 1 260 14061464 1526 1592 1662 1 271151415741138 170 1778 1 18!626; 1;881 1754 1824 1898 1 1291742,1806 1874, 944 20222 30 186219819281198 2072 21.01 2 31 1986 2054l2126 2202 22282) 2 32 2114i2184 2254 2336 2418 2 833 2246'2318;2394 2474 255812 34 2382 2456'i2534 2616 2702 2 35 2522 25 98 2678 2762 285t0 2 3626662744 282 29 12 3002 13 37 2814 2894 2978 i30)6i 3158l' 38 2966 3048 3134 3224:318:3 39 3122 320,;i3294:338 134821 3 40 3282 3368 3458 3552 3650 3' 41 3446 3534 3620 3722 18221 31 4213614 37374 98 3890 3998 4 4313786 387813974 -074 4178 4: 44 3962 4056 4154 4256 4362 4 454142 4238 43308 4442 4:550 4( 46 4326 4424 4526 4632 4742 41 47 4514 1614 4718 482(i 4938 5( 48 4706 4808 4914 5024 5138 15: 49 4902 5006 5114 5226 5342 5' 50 5102 5208 5318 3432 5550 5( pt1~ 2 83 4 5 -I _I, L.I-c nputation of 'rismoids or Earthwork. _ i__! 6 1 i 1C 1t 15 21 2' 34 39 5O 50 63 70 77 85 93 02 11 3( 4: I1;( 34 I( )2 lf! )4 2 J2, il 20(; 304 40; 512 622 730; 854 976 102 232 366 504 646 792 942 096; 254 416 58'2 752 926I 1()4 286. 172, 66'21 j62 356 )541 256: 462 3721 6 11 9 9 1 2 i4 i 4 4 1 5 I;, 8 149 10 11 12 13 14 15 16 18 19: 20. 21 24, 251 27: 281:30 31. 338;51 361 385 403 421 439 456 477 497 517 537 558 579 7 7 8 9 10 11 12 13 Ft 981 128 102 200 2421 2881 338 0 114 140 182 222' 2661 314 3601 1 [34 168 206(; 248 2941 344 398 2 158 194 234 278 3261 378 434 3 186 24 2664 t 312 302(; 41 4; 4 4 18 258 302 350 402 458 518 54 296 34; 342 392 446J 504. sG66 06; '94 338 3(86 438 494 554 618 7 3 384 434 488 546 608 674 83 8| 4841 480; 542 602 6(36 7'341 91 1381 488i 542 (00 16621 728; 7i81 10I ['94 54-( 602 662 726 794 8)0, lll1;54 608; 60 728J 794 864 938 12I;18 (074] 734: 78 801 938 1014113;86 744 806 872 94211(161094 14i 58 818 882 8 9501C2)2110981178 1 34 896 962 1032 1106 11841'266 1 6; 14 9781046 1118/11)4jl274!1358 1017 98101 0;4 1134 12(;811 286;13068 1454 18' 80 115 4 1226 1 04)21 8821 S8 4 16 015541 1 98 78 1 "48 1322 1400 1482 156811658 20 74 1346 1422 1502 1586 167411766 211] 74 144811526 16081 694,178418781 22)' 78155411384 1I 17181806;11898199(33 243 86 1664 174; 18 2 1922:2016!2114 241 9811774 1862 1950 2()042 2138 2238 25' 14 1189( 1982 2072 2166 22642860 2(;1 342(18 210021 198224 2:193:2498 27i 58 2144 22: 4 2328 2426'252)82634 281 34O 22742360 2462 256212666;2774 2911 18 2408'2502 '2600o 2702 22808 29181 01 54 2546 2642 2742 28461295430601 831 9 2068812780 288812991;3104 1218 32' 38 2834 29314 3:0'38 314;63258 331741 33' 36 2984 3080 3192 3202 341 1;0 -58S4 841 3813138/324213350134 623157813698 351 41 3296 3402 3512 3626 3744,3866 36! A4 13458 3566 3678 8 3794 3914 4038 371 181i3624:1 734:3848 39064 4088142141 38 36 3794139(16 4022 4142 42f614394 39! i8 396(8 4082 4200 4322 4448 4578 40 4 4146 426fi2 4382 4501 4634 4766 41 4 4328 4444; 4568 4694 4824 4958 42 )8 45141 4634 4758 4881;65018 5154 43 36l4701 1482(; 4952 5l 82 521. A153"54 441 '8 4898 5022 5150 5282 5418 5558 45 '4 5096 5222 53632 5486 56024 5766 46; '4 5298 5426 5558 4694 5834 5978 471 8 550)4 5(13;1 5768 51906 6048 6194 48 4615714 584(;, 98216122A626(f{6414 49 3815928 6062;20(i 6342 6488 6638 50 8 9 10 11 1 12 13 Ft1 7 2A* TABLE b.-For the computation of Prismoids or Earthwork. Ft 14 1 16 17 18 19 20 21 22 23 24 25 26 Ft1l 0 392 450 512 578 648 722 800 882 968 1058 1152 1250 1352 O)1 1 422 482 546 614 686l 762 842 926 10141106 1202 1302 1406!!3 456 518 584 654 728; 806 888 974 10)4 1158 1256 1358 1464 2,1 3 494 558 626 698 774 854 938102);1118 1214 1314 1418 81526 31i 4 5361 602 672) 746 824 906 992 1082 1176 1274 1376 1482 1592 4|1 5 582 650 722 798 878 962'1050I114212381338144215501662 51 iI Ii 6 632 702 776 854 9186 102 11121126 1304 14061512 16221 736 61 7 686 758 834 9124 9981086 16178 1 274 1374 14781 586 1698 1814 7 8 744 818 896 978 106411 54 1521811346 1448 1554 1664 1778 1896 8 91 806 882 962 1046 11341226 1 322 1422 159f; 16634 17461862 1982 19 101 872 3950 14032 11]2081302 1 402 11502 1 608 1718 183 2 1950 2072 105 I11 942 102 1106 1194 128l6 138211482 158 l1694 1806 1922 20422166 11ii 12 1016 1098 1184 127413 88 1466 158168174 1784 1898 201f6 21638 2264 12'| 13 1094 1178 1266 1358 1454 1554 216858 176 41878 2l 4 21114 22388 236 13 1141117,61262 1352 1446 11544 16-6; 1752 1862 1976 2094 2216 92342 2472 141j 157 122 135011442 1538 16381174211850 1962)2078219 28 212 2450 1582 151 16'1356 1442 1,36 163417436 842 1952 2066 2184 2306432 52|6 16 17 144615381 63411734 18038 1194620568i217412294 241812546 2678 2814 1, 118 1544 1C381 736 11838 1994 2054 271t 8 2286 2408 2534 32664 2798 2936 181 ' 21646 1742 1842 19462054 21 6fii282 2402 2526 2654 286:19322 1302 19 20 1752 18501 952120)5821682282824002 5282 1648 778 912 350 3592 250| 211186211962 2066 21714 2286 2402.2522I26t462774 )2#906 2)042) '81I821"326 21 221 1976,2078 2184 2294124082526';2648;i2774 29)04 30()38131 76|-1318 3464 22 } 2312094 219818306f241812.534 2654 2778i2906 f30388-3174 13814 458 13()606 28' 24l22162322 2432 254612664 '76 2)9123042 3176 3G314 3456 6t;l:02'1875')2 24i/ 25 23422450 562) 2678l2798L2922, 3'050 '3182338 1813458 3602 3 750:13'9)()02 25'; 26 2472 2582 2696 2814,2936:3062 31 92f3326 3464 3606 3752 3902 4056 261: 27 2606 2718 2834 295413078 3206 333383474 3614 37583906 40(58 4214 27' 28 2744 2858 2976 30983224 3354 3488F3626 3768 3914 40164 4218 4376 28 29 2886 3002 3122 3246 3374 3506 3642 3782 3926 4074 4226 4382 4542 2919 30!3032 3150 3272 3398 3528 3662 3800 39424088 4238 4392 4550 4712 30 31 3182 3302 3426 3,554 3686 3822 39624106 4254 4406 4562 1722 4886 311 3238336 3458 3584 371413848 3986 1128142744424145,78 4736 1898 5064 328 33 3494 3618 3746 3878 4014 4157 429814446 4.598 4754 4914 5078 5246 33 3413656 3782 3912 4046 4184 4326 4472:4622 4776 4934 5096 5262 5432 34 35 3822 3950 4082 4218 4358 45024650 4802 4958 5118 5282 5450 5622 351 36 3992 4122 4256 4394 4536 4 682 4832 1986 5144 5306 5472 5642 5816 306 3714166 4298 4434 4574 471814866 15018 5174 5334 549815666 5838 6014 37 38 4344 4478 4616 4758 4904 5054 520815366 5528 5698 5864 6038 6216 38 39 4526 4662 4802 4946 5094 5246 54025562 5726 5894 6061 6242 6422 391 40 4712 4850 4962 5138 5288 5442 5600 5762 5928 6098 6272 6450 6632 40 41 4902 5042 5186 3334 5486 5642 5802 5966 6134 6306 6482 6662 6846 41 42 5096 5238 5384 5534 5688 5846 6008 61 74 6344 6518 6696 6878 7064 42, 43 529415438 5586 5738 5894 60.54 621816386 6558 6734 6914 7098 7286 4A3 44 5496 5642 5792 594616104 6266 643216602 6776 6954 7136 7322 7512 44 45 570215850 6002161586l31816482 6650 6822 6998 7178 7362 7550 7742 45 46 5912 6062 621616374 6536 6702 6872 7046 7224 7406 7592 7782 7976 46 4716126 6278 6434 6594 8758 6926 7098 7274 7454 7638 7826 8018 8214 47 48 634416498 665616818 6984 7154 7328 7506 7688 7874 8064 8258 8456 48 49 6566167221688217046 21147386 756217742 79261811418306 8502 8702 49 50 6792 6960 7112 7278 7448 7622 7800 7982 8168 8358 8552 8750 8952 50 lFt 14 15 16 17 18 19 20 21 22 23 24 25 26 Ft 72I. * TABLE b.-For the computation of Prismoids or Earthwork. Ft 27 28 29 30 31 32 33 34 35 33 37 8 Ft /i_ rlj t j II I~~~. I~~ ill I II I rJ )11) 37 6 i.01458 1568 1682 1800 1922'2048 3178 2312 2450 2592 2738 2888 0 1 1514 1626 1742 1862 198612114 2246 2 382 2522 2666 2814 2966 1 211574 16881 8(06 1(928 (205412184 2318 2456 2598 1 44 28941 3048 21i 3 1638 1754 1874 19 [982'12;62258 2394 25:34 2678 8"L'; '!2978I 3134 3 4 1706 1824 1946 2072 I '336 2474 2 2912 3066,; 4224 4 5177818982022215022 8224182558 2702 2850 3002 1. 85 3318 5 1 6 1854 1976 2162 2232 2366 25 04 646 2792 2942 3(09C '3254; 3416 6 7 1934 2058 2186 231L8 2454i2594 2738 2886i 038 3194' 3354' 3518 7 8 2018 2144 2274 2408 2546 2688 2834O 2984 3138 3 '96; 34581 3624 8 9 2106 2234 2366 25022642'2786 2934 3086 3242 340 2 3566 3734 9 10 '2198 2-328 2462 2600 2742!2 888303831 3192 3 51 3512 3678 4 384810 110 2294 '426i 25621 27 02284612994 3146 33(21 3462 3626 3'94 396611 i; 12!2394 2528 t2666; 280'8 2954i3104:3258 3416 3578 37441 391. 4088 12 13 j2498 2634 2774J2918 (3066)j3218 3374, 3534 3368 38661 40381 4214 13 | 1412606 2744 2886 032 3182i3333494 3561 3822 39921 41661 4344 14 15)2718 2858.3002 3150 3302)3458;3618 3782 3950 ()412 2 4298 447815 l16 283429761 31 223372 142613584 3:746, 912 4082 4256! 4434 4616161 i 171'954 3098 324 3 3243983 437143878 2 4046! 4218 4392 4574 475817 18'3078 3223374 34528 3686 3848 40144184 4358 4536 4718 4904118 193206 3354 3550613062 3822 398614154 4326 4502 46821 48661 5054 19,12033383488 364238003:96294128 4298 4472 4650 4832! 50181 520820! '2:1;347413626 3782'39424106 42741441 4622 4802 4986 5174 536621 j22 3614 3768.3926 4088 4254|4424 4598 47761 4958 5144 5334 5528 22 1231375813914 1074 42381440614578 47541 49341 5118 5306 54981 5694123 124'3906 4064 4226 4392 4562'4736 4914 5096 5282 5472 5666 5864'24 254058 4281438214550 47224898 5078 5262 0450 5642 5838 6038125 2614214 4376 4542 47124886i5064 5246 5432 56221 5816 6014 621626 274374 4538 4706 4878|50545234 5418 5606 5798 5994 6194! 6398127 i284538 4704,4874 5048 522'615408 5594 5784 5973 6176 63781 658428 1'2914706 874i5046 5222 540215586:5774 5966 6162 6362 65661 6774 29, 30i4878 5048i5-221 5400 5582 5768 5958 6152 6350 6552 6758 696830 3150()54 5226 5402 5582 5766954 6146 6342 6542 6746 6954 7166 31 3215234 5408t5586 5768 5954 6144 6338 6536 6738 6944 71541 736832 33 5418 5594 5774 5958i6146 6338 6534 6734 6938 7146 735 7757433 34 5606 57841590666152 63426536 6734 (6936 7142 7352 7566 7784134 3855798g5978g6162;63506542 6738[6938 7142 350 75621 7778 799835 36 5994 6176 6362 6552 6746 6944 7146 7354 7562 7776 7)(41 8216 360 37 619416378 6566i675816954 7154173,58 7566 7778 7994 8214i 8438371 38J6398t6584167741696815166736875747 7784 79988 8216 8438 866438 391;660616794 6986 7182 7382 7586 7794 8006 8222 8442 8666 88941391 401681816008 720217400 76021780818018 8232 8450 8672 8898 9128140 4117034 7226 7422 7622 782680)3418246! 8462 8682 89061 9134i 936641 42725417448|7646}7848i8054826484781 8696 8918 8144 9374 9608142 43747817674 7874]8078]8286J849818714 8934 9158 9386 9618 9854!43 441770617904 8106[8312185228736 8954 9176 9402 9632 98661010444 45 79381713818342 855018762 8978 9198 9422 9650 9882 10118160358 45 461817418376,8582187921900619224 9446 9672 99021 013611037411061646 4718414186188826 903819254947419698 9926 10158 10394 10634110878 47 4818658188691907419288 9506 9738 9954 10184 10418110656110898111144148 49 8906 9114 9326( 9542 9762 998610214 10446 10682 10922 1116611414149 501915819368 958298001 0022 10248 10478 10712 10950 11192 11438111688 50!Ft27 28 29 30 31 32 33 34 35 6 37 18 Ft| _................................... 72* TABLE b.-.For the computation of Prismoids or Earthwork. 'Ft 39 40 41 42 43 44 45 46 47 48 |Ft..3042 321)0 3362 3528 3698 3872 4050 4232 4418 4608 0!1 3122 32822,3446. 36i14.3786 30962 4142 4326 4514 4706(ti! 321)6 8368 3534 /3704 3878 4056; 4238 4424 4614 4808 8 3,29!4 3458 3626 7. 08 3974 4151 - 4s.1526 4 7 4 9.141 3 4I 3386:i:552, 83722 i,896(. 4)74 4 46 44. 4632 4826 50214 4 5 8482 36503 3 822 83998 4178 14362 4550 4742 4938 5138 5il i 3582 352 3926 4104 42861i 4479 46(62 4856 4054 5;256 6i 1.7686( 838 5 4031 4214 43198 4586i 4778 49!4 5174 5 5378! 7I 8 8 794 t968 4146 4328 4-14 4704 4898 5096 529 8 55041 8i t 1 39061 44'i8" 42C62 4446 4:634 4826 5022 5222 5426; 56( 3;, 1( 4022 4200 4382 4568 47581 4952 5150 5835 58 58768 10 1I 41423 4n4506 4 694 483861 40C)82 5282 5486( 5694 50906.11 ' 12 4266i 4448 46-34 4824 5018 5216 51 418 t524 5824 84 6048 11 13 4394 4578 4766 4958 5154 5:354 5558 57 66 5978 6194.11 14 4 52 6 4712 490)2 5l96 5'2941 5496 5702 5912)l 6126 6:44 141. 1i5 4662 4850 5042 52)38 5483 56(;42 5850 6062 6278 6498: 151 ' 1i 4802 4992 5186 5384 5586 579 2 6002 6216 6434 6656:1l I 49461 5138 53- 4 5738 546 6158 6374 (65)94 681 817 ] i18 )094 '5288 54861 5688 5894 6104 6318 65 6 (1758 6984 18!| I 5 5 46 44) 56- 546 6054 6266 672 6926 7 1 9 1 20 5402 5600 5802 6(008 6218 6432 6650 6872 7098 7328 20j 5!62 0..16162 55 9666174,6386 6. 02 682 70(46( 7274 7506I21 i2 572 7 6 5! 923 48 i 3 4 344 G65598 6776 6998 2241 7454 76',8822! 3 58941 60()98 6;:3i06 6518 6784 6954 7178 7406- 76)388 78741 23 24 6091 6272 6482 66 6691 4 71136 7')2 7592 7826t 8064' 24 251 6242 6450 6662 6878 7098 73282 7 550 77821 8018 82582.5 i 6402 6632i 63846 7064 7286 7512 7742 7976 8214 8456 2(6 27 6(606; 6818 70)134 7254 74781 7706 7938S 8174 8414 86;58:27 'i (6794 708 7226; 7448 7674 7904 8138 8376 8618 886418 i 6986 721'92 74222 7646 7874 8106 8342 8582" 8826 90741291 301 71821 7400 7622 7848 8078 8312 8550 87921 9038 9288R30,1 73.82 ',02 782 8054 8286 8522 8762 (90061 9254 9506.31 i3'2 7 -586 7808 80)34 82)i4 8498 8736 8978 9224 9474 9728 '>2 37I 7794-1 8018 8246 8478 8714 8954 9198 9446 9698 995438i!, 34 8006 8 2 8462 86 8!96 8134 9176 9422 9672 992611)1843,14 35 8222' 81950 8682 8918 9158 i 9402 9650 9902101581 1041835,; ( 36 84-128 8672 8906 9144 9386 96 32 9882 10183610394 1065)6 36 3 86;t6 18898 9134 9374 9618 9866 10118 10374 10634 108098 37 138 8894 91128 983 6 69608 9854 10104 10358 106161087811144l381 39 9126 962 (; 9602. 846 00941 0346 100()2 11)8(62111126111394!39! 4(0 9362 9 600 9842 100(88 10338 10592 10850( 1111211 1378 11648l 40h 41 9602) 9842 10086 10.~34 105i86 10842 11102 111366l11634 11906 41[ 42 9846' 11 )088 1(03.4 10584 10838 i11096 11358 116(241118841 2168 42i 43110094 11)0338 10586 10 8 8 11094 11254 l1618 11886112158 12 I44 431 4410S146 110592 010084 11096 1 185411616 11882 12152142612426 127041441 451106012 108501 11102 S 1158ll 11882 121 12422126981 297845i 46108662 11112 11366 11624 1188 52 12422 12269612974113256461 4711126 11378 11 03 1181)4 11']8 1142ti 12698 12974 13254112538847 481 184 Il (;48 11906 121(8 12434 |12704 12978 13256 13538 13824 48: 490.1C1166 11922 12182 12446 12714112986 13262 2354211382t614114 49 151i11942 12200 12462 11 2728 1299813272 13555 1383211411 1440850 Ft 89 40 41 42 43 44 45 46 | 47 48 Ft;1 721)* .....~.__..__-.. - "z. _- _- 7:. - 7_ --. " - TABLn. c.-For calculati Ft 1 2 3 4 5 6 7 8 9 10 0 3 (-1 12 1 5 18 21 24 271 80 1 6 12 15. 18 21 21 2.7 3,)' 33 2 9) 1 2 1 181; 2 1 24 27 1 -08 88 3o 18 12 1 1 18 2 41 ' 27 3 80 ' 8 6 3 9 4 15 18 241 27 31( 3t; 39f 42 1 21 27 32 3 3 3 9; 88 4 2 42, 48 51 ) 27 0 3 36; 42 48 1 8 514 j: ' 91 'I3 3 3 4 42 1 48! 45 8 5 54 157 310;13 I 3), 3 9 42 451 48 51 54 57i GO 11 308 394 4 5 48; 51 54 57 60 03 6 13 '2 15 48 S1 54 57 60 l t6; 6 0, G 14 45 48) 51 51 57; 60 03 00 9; 72 11 5 48 51 4i 5 7] 0 6 601 69 72 75( 1 51 54, 571 04 63 I66 69 72 75 78i 17 54 571 60f( G6' G( 9'il 72 75 7 81i 39 G0 (31 66( 6;1 79 75 7 8 81 84, 87 1I 683 66 619 72 75' 78 81 841 87 90!21 6(i0 69 72 75 78 81, 84 90 93 22 9(;: 712,5 78 81 84 847 90( 93 9 21'4 2 75 78 81 8 84 8 9I 951 9610 [i 24 75 78 81 84 87' 90 9'1 96 99 102 ii25 78 81 84 877:90 98' 9 99,102 105 2.81 84 87 90 9 96 9 9.102,105108 27 84 87 90 9S 3 9 99 1102 1305, 0l111 i128 87 90 9 96 99 102|.105 108 111 114 291 901 9 961 99102 0108111! 1170 30 93 96 99 10210510 1 1 1117120 '81 96 99102105,108! 1114,117 120 121 12 99 102105 1 1 1 141 14 1 Iil7'8 1 216 38102 1)5!108 111l11 4l117 120 123!126129 84 1 051ll 15 1111 14 117120 12 1(26 191 32 3 8 108 11I 114 117 120 12 11 126 12 135 '36i111 114117120123126129132135.l138 37118 4 7 017 18120 312.612 1 832 5188 141 38 117 13201123:112i 3 2 i17 18 138 14 14 144 39 120 1120316 129 132 15 1) 8 1 41 144 1 47 40 123 126129 1215 138 141 144 147 150 41 126 122(l11235138141 144 147 150158 42 129 1321851 1 1141 144 147 150 15 156 43 12. 13, 1 l8 1411144 147 150 158 156 159 441.35 188 141 144147 150 15156 1,59162 451138 141 144 147 150153 156 159 162 1165 46 141 144 147 150 153 156 159 162 165 168 47 144 147 1501531156 159 1 62 165! 168H171 48 147 150 153 156 159 162 165 168 171 174 49 150 15.81156 159 162 15168 171 174 177 o0 153 156 159 162 165 168 171 174 177 180 Ft. 1 2 3 4 6 6 7 8 9 10 ig P'rismoidcs.! 11 12 13 14 15 16 17 38 89 42 45 48S 1)1 54 4;8 (69 72 75 7'81 84 87 904 96 991 1102 15 108 111 114 117 123 121) 1 32 1385 188 3 1,(; 42 45 54 *14 57 60 (;3 t),. 66 69 72 75 78 81 84 87 940 93 9ti 99 102 105 10)8 111:191 42 45 48 51 54 74 11(4 6C);09 72 78 81 84 87 9( 941) 98 99 102 105 108 111 114 42 45 48 51 54 57 60 63 66i 9t; 72 75 78 81 84 87 90 93 96 99 102 (3.} 10. 108 111 114 117 45 4< 51 54 57 60 (;1 9;I 72 75 81 84 87 90 93 99 102 10(5 1(8 111 114 117 120 123 124; 12149 132 1 '0; 185 188 141 144 147 150 153 150 159 162 165 168 171 174 177 180 183 186 199 192 195 l4 51 54 57 72 75 78 81 84 87 98 93 99( 12 1 (), 105 108 111 114 117 120 123 126 129 132 185 138 141 144 147 150 15:3 1:59 162 195 168 171 174 177 180 183 186 189 192 195 198 51 54 57 611 72 7I( 78 81 84 87 90 93 96 99 102 1()5 108 111 114 117 120 123 126 1 S 138 141 144 147 150t 158 156 159 1(i2 118 171 174 177 180 188 186 189 192 195 198 201 Ft. 5i' 4 9 6 1 5 12 14 1 I I 8li 1 9 20 1 211 22 23 14 15 i '0) II 80 82 I 31 I 83 I 34 ji 36! 114 117 12(4 12. I 2( 121 132t 1138 I'll8 1171 12;' 123 126 129 135 138 1 88 141 144 12(! 128 126 132 13,5 1.88 141 144 1471 141 144 147 15C 153 154 1( 6 16. 168 171 174 177 18( 188 144 1 47 165 115 154C 16i 1(;5 1(6i 171 174 177 188 118C 15C 1 54 15:~ 15C 15 6 162 168 174 177 18C 18: 18C 189 150 153 156 159 162 165 1418 171 174 177 180 183 186 189 192 36 87i 388 39 40 41 42 48 44 45 46 47 48 49 50 I 11 12 | 13 1 14 I 15 I 16 1 17 Ft. T2 9;,* 1; TABLE c.-For calculating Prismoids. Ft i 18 19 20 21 22 23 I 24 1 26 I 27 28 29 30 31 32 33 34 Ft. | 5-4 57 6( Ci (6 91 72 75 8 8 81 84 87 9 96f 99 102 0 1 1 57 601 631 66 69 72! 75 78 818 84 87 90) 93) 96 99102 105 1! i 2 60i 63 66i 6 (9 72 75 78 81 841 87 90 )3 961 9 9102 105 108 2| 3 8 63 66 9,i 721 75 78! 81' 84| 87 9) 93 96 9 99102 105 108 111 3!4 66 6(9 72' 75 781 81 84' 87 90 93 96 99102 105 108 11] 114 4 5 69 672 75 78 81 84 8 9 93 9 93 96 991021105108111 114117 5! 6 72 75| 78| 81 84 871 90 9 3 I96' 99102;1051081111 14117120 6 7I 751 78 81 84! 87 90i 93 6 9(( 99102 5108111 11411720 13 7 i| |8 8 78i 81 879 89 3 9 60 9 6 9912 8 105 108111114 11712 123 126 81 I 819 84! 887 90 93 0 9 )6, 99)10210510811 114n'121712 123126 129 9o i 11 84 879 90 3 )96 99102 1021(0 111 114 117 120 123'126 129 132 10 llj 87 0 938 963 99l' 02l01008 ll 11114 111/ 2123 12619 132 135 11 I 12 90i 93 96. J 99. 02) 1 l051 ()0811 1 1417 12 123 1 26 129 132 135 13812 il 13 91; 993 3021 05 108> l 1114117120123126il29132 135l38 141 13 114 961 9902 l05 1 8 111 11117 1 2) 23126l 129!1321351S84 144 14 15 99)102105!10811 11141.17 121.)l23126129 132 135 138;141 144 147 15 ' 16 102105108 111114 11712012 6111329 135138 141 144 147 150 16 17105O1058|4 11 14117 121213. 12)0 11261I29 3 135.:1; 1388141 914 4147l 1503 131l i 181081111141171i I23I 6 1 126129l 13 1418 144 147 153 156 16 8 i 9l 1114l117120')l.3;1' 2) 1291 132i53 138 1141 14411471153ll6 159 19 ' 'i 20 114117 120 1231126l 12132135 1381 144 147 150 153561501 162 20 1i21 117171121 121i 35' 138"1- l: 144.147150' 14114 4 1 56159l162 165 21 I 22 120 1226 126129 132 135l-18 141 144; 1477 150153 156 19,.162 16f5 16822 23 12311269129,1132il35 183841ll44l147t 1503 15 155 j1621165 168 171 213 I 24126 129132l3 38141 144147 15(01531156 159 1621651168 271 17424 i 25 129l132 135 138141 144 147 1441471 53 156 159 162116 168!171 174 177 25 il I I I -- ~,: t _ I I 2613213 5138 14l 144 74 m 150 56159162 165168 171 174177 180 26 i 271235l1381141 14 147 15(1315 615 15 215681 416 41 4 1 7801183 27 28 138 141 144 147 15115 153l51516211il611 68 171 174 177 180 183 1186 28 i 2941 14 144l147ll 153 156(113 62! 65 168l7 1 741177!1 186 16 1892) i 30 144 147 150 156 15315l159l16165 165181 '171771580 183186189192 30 I j 3111471150153 156159162 )165t! 1174l177 18o1)18 186l189192 195 31 32 1501153156 159 1616 1 168171 174177 18!) 183181892192 195 198 32 33 153 1561159 162 165 1681171174 17718()180 186 189192 1951981201 33 35 159 162 165 1 68 171 174 177 180 1831186 189 12195 198101 204120735 136 162165 1 68 171 174 7 17 7180183 186 189192 195 1981201 204 207 210 36 137 165 168171 174 177 180 180118 1891192 195 198 201 2(04207201 3 37 38 168 171 174 171180 1831186 189 192 195 1981201 1042071210213 216 38 39 171 174 177 180 183 186 189 192!3951198 201 204i207 210I213 216 219 39 ' 401174 177 180 183 186 189 192 195 198 201 204 207 210 1213 )16 219 222 40 41117711801831861861892 19 5198 201 204207 210 213 l6 219 222122541 42 180 183 186 189 192 195198 201 204 207 21)10) 132612199221 251222228 42 43 183 186j189 192 195 198201()204 207 210 213 2161219 222 225 228 21 43 44186 189 192 195 198120112427210 213 216219222 225228 231 234 44 i45 189 192195198 201 204,207 210 213 216 219 )222122 228 231 234 237 45 46 192 195198 201 204 207 210 213 216219 222225 228231 234 2.37 240 46 47 195 198 201 204 207 210 213 211 2191222 225 228 231 234 237 240 243 47 481198 201204 207 210213i 216 219 222 225 228 231 234 237 2401243 246 48 49 201 204 207 210 213 216 219 222 22, 228 231 234 237 240 2483246 249 49 5012042007210 213 216219 2222 22l 228 231 234 237 240 243 246 24925250 Ft. '18 19 20 21 22 23 24 2 26 27 28 29 30 31 32 33 34 Ft. TABLE c.-For calculating Prismoids. Ft. 35 36 37 38 39 40 41 42 43 44 4546 47 48 4950 Ft. | I0 1051081m11 114111712( 11231" 12)'1I2132 5 138 141 1441 j1 5 O 111114 11712, 12311261129132 135i138i141144114715T1h3 1 I 2 I 1 ( -I) 1531 2 -, 1 4 156; 2 " 1171123 126'12!1.1 3211 351381 41 414 II 1) l53 l5f5 4 9 I 4 5 120 12 31 126 12932 135138 141 144 147 115 153 615ll 12' 165 5 4i l! 123126129 1321135 138 41 144165 168 b 7 126 129132 135138 141144 147 150 153 156 159 165 165 16811 1 8129132 135 138 141 144 147 150 1 531561(;' 59 162 ( 6.2 5 7 1 7 8 1 I 9132135 138141 144 147 1 5 15 3 156; 5 15 62,165 168 171 174! 177 9 1 10135 138141 144 147 1 50)l53156159 162|5 1 6 7 117417780 17 0 180 | 11 138141 144 147 15(1 I 15156 159162 165 1 68 171 7417 1 80 183 11 12141 144 147150 I I156 1962 1651168 171 174 177|18(I183!186 12 |131441471150(153 156 59|162 165 168 171174 177 1811831 86 89 13 I! 14 147 1501531156 159 1'1621165 168 171 174 1 77 181 183 861889 192) 14 | 15 0 153 156315(9) 162 165 168 171 1'74 177 180 183 1 18 11819 2 195 15 162 1 68171 174 1 77 1808 189 1 92 195 98 16 7 1756159 1621165 168 17l1l74 177 180|183 186 189192 1 95198201 2 19 18151)1 62 1 65168 1 7 1 1; 871 1 77 180 18 18( 1 89 1 92 1 5I 98'201 1042 I 1) 1962 165 168 171 174 177 18(18 1886I 181192 19 8 018 5 11982)14 207 13 20165 168 171 141 80 187 1 8 18 9295 18 21 204 2072 102 0 1: 21 1681 171 74177 180 183; 18(;!118 I 1; 1 1 207 10213821 54 i22171 144l77118018318i9 19 2195;198 201 2104 2017 210213 21622 11 237 17177 18018| 18318192 195! 0 1 ' 204 2.71 213 216 19 23 i 24 177 180 18318618911 929511820 )4207 212 1321 21 922224 i 2518018318561589192 195 198 201 204207 21 21( 216 21(922 22525 I 26 183186 189,192 1(5 198 201 )204 2(7|210 213 216)219,222225 228 26 27 186 1891192 1)95 198 201 204 207 21i213 216 211)'292 55 228'c231 27 28189 192 195 19820)1 204 207 021321 9222225 228 23123428 29 192195 198201 204 2(107 210(1 21321 1 219 222 225 228 231 134237 29 30 1951982011 204207 211321 6219 222 2252282312342374030 31 198201 204207 21021216219 222225228231 23423724024331 32 201 204 207 210 213216 219 222 225 128:231 234 237 240 2431246 32 33 204 207 21021 33216 219 222225 228 231 234 237 240 243 2461249 33 34 207 210 213 216 219 222 225 228)231 234237 24(0243 246 2491252 34 35 210 213 216 219 222 225 228 231 234 237:240243 246 246 9 252 255 35 36 213 216219 2'25225 8 231 234237 240'243 246 249 252 255 258 36 37 217 219 222 225 228 231 234 237 240 243.246 249 252 255 258 261 37 38 219 222 225 228 231 234 237 24)0 243 246 249 252 255 258 261 264 38 39 222 225 228 231 234 237 24(0 243 246 2491252 255 258 261 264 267 39 40 225228 231 234 237 240 243 246 249 252 255 258 261 264 267 270 40 41 228 231 234 237 240 243 246 249 252 2551258 261 264 267 270 273 41 42 231 234 237 240 243 246 249 252 255 2581261 264 267 2710 2 73 276 42 43 234 237 240 243 246 299 252 255 258 261 264 267 270 273 276 279 43 44 237 240o243 246 249 252 255 258 261 2641267 7273 273276 279 282 44 45 240 243 246 249 252 255 258 261 264 267 270 273 276 279 282 285 45 46 243 246249 252 255 258 261 264 267 270 273 276 279 282 285 288 46 47 246 249 252 255 258 261 264 267 270 273 276 279 282 285 288 291 47 48 249 252 255 258 261 26426 270 27073 2761'279 282 285 288 291 294 48 49 252 255 258 261 264 267 270 273 276 279282 285 288 291 294 297 49 50 255 258 261 264 267 270 273 276 279 2821285 288 291 294 297 300 50 I 1 1 111l'1 -:,~ - -.,; -,1 t 385 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 JFt. - -..!._ '..1:0. 4 - 0____......._ 72n* 7211* ~~COMPUTATION OF EAiRTHiWORK. Application. In using either of the foregoing tables, a,, b and c, we must use the imean heighits of the end sections, as Q0 in the annexed figure. D Q is tile centre of the road bed. i is tile centre stump. C E d ~-lesber height. D 1II- D '=gieiter height. 1 is where the slopes mneet on the other side of tile road bed. We find thle end area, of tile section by the formula in sec. 322, where A -= area = D d r +-j- b. And the mean height, x, (from forinula ia 323.) jY(4 A r ~b 2) -1). 2r The following tabular form will show how to find the contents of any section or number of sections fromt Tables b and c. Byi Tables b and c. The an- 11 II IIV v vi nexed table shows our method. __ ____ ____ of usingf Sir John 'McNeil's E'nd Mean 'Iu From From Sum. tables 58 anld 59: which we Are's Htig. ini ft. Table b. Tabte c. use as tabe 6 n.O -4100) 47.08 5 9 78. 180. site 47 and under 13 in table72135 10 178.24 6, we find 5.978 which we put 72 35 2 79.28 0.24 in column IV. 7.2 16 Find thle vertical difference 6007 5. 2 18l.8ti 1.39. between 47 and 13, and 48 and r- 1 b=40 613.349 13 to be 216, which multiplied a ~ 6075 7274.4 (.12 by the decimal.08, givesl17.28, AIhL n 8 82.40451 which put in col. IV. Find B d 1 n1 t; 12 the horizontal difference be- 0'd I v 9888.53 -tween 47 and 13, and 47 and 14 to be 148, s a content. which multiplied hy 0.54 gives 79.92, which r h is also put in col. IV. In like manner we take. A rS + bQ from table c, tabular numbers similar to those L in col. IV and put them in aol. V. 'Now add rL — ~ the results in col. lV and V, multiply thle (r.72 sum. in col. IV by the base 6, and that in aol. 6-12 V by the ratio of the slopes, add the two pro- Wducts together, cut off three figures to die Contents in Cubic Yards. right for decimals, multiply tue result by the constant multiplier 6.1728, the product will be the content in cubic Yards. When there are several sections having the satme length, base, and ratio of slopes, as A, B, C, etc., put their end areas in col. I. Their mean heights in col. II, their lengths in col. Ill, their ftabular numbers froni tables b and c, in col. IV and V as above, where 8 arid Q are the sums of columins IV and V. r S is the pro. duct of col. IV X by thre ratio of the slopes and b Q =co]. V X by the base. From their sum, cut off 3 places to the right and proceed as in the above example. 72'*9 SPHERICAL TRIGONOMETRY. 346. A Spherical Triangle is formed by the intersection of three great circles on the surface of a sphere, the planes of each circle passing through the centre of the sphere. 346. A Spherical Angle is that formed by the intersection of the planes of the great circles, and is the measure of the angles formed by the great circles. 347. The sides and angles of a spherical triangle have no affinity to those of a plane triangle, for in a spherical triangle, the sides and angles are of the same species, each being measured on the arc of a great circle. 348. As in plane trigonometry, we have isoceles equilateral obliqueangled and right-angled triangles. 349. A right-angled triangle is formed by the intersection of three great circles, two of which intersect one another at right angles, that is one great circle must pass through the centre of the sphere and the pole of another of the three circles. Let the side of the triangle be produced to meet as at D in the annexed figure, the arc B A D and B C D are semi-circles, therefore, the side A D is the supplement of A B, and C D is the supplement of B C and the A A D C is the supplementary or polar triangle to ABC. 350. Any two sides of a i is greater than the third. Any side is less than the sum of the other two sides, but greater than their difference. 3651. If tangents be drawn from the point B to the arcs B A and B C the angle thus formed will be the measure of the spherical angle A B C. 352. The greater angle is subtended by the greater side. A right-angled A has one angle of 90~. A quadrantal A has one side of 900. An oblique-angled A has no side or angle = 90~. The three sides of a spherical A are together less than 860~ The three angles are together greater than two, and less than six right-angles. 853. The angles of one triangle if taken from 1800 will give the sides of a new supplementary or polar triangle. If the sides of a A be taken from 1800, it gives the angles of a polar. 364. If the sum of any two sides be either equal, greater or less thani 1800, the sum of the opposite angles will be equal, greater or less than 1800~. 865. A right-angled spherical A may have either, One right angle and two acute angles. One right angle and two obtuse angles. One obtuse angle and two right angles. One acute angle and two right angles. Three right angles. P 72H*10 SPHERICAL TRIGONOMETRY. 356. If one of the sides of the A be 900, one of the other sides will be 90~, and then each side will be equal to its opposite <. And if any two of its sides are each = to 90~, then the third side is = to 90~. 357. If two of the angles are each 90~, the opposite sides are each equal to 90~. 358. If the two legs of a right-angled A be both acute or both obtuse, the hypothenuse will be less than a quadrant. If one be acute and the other obtuse, that is when they are of different species, the hypothenuse is greater than a quadrant. 359. In any right angled spherical A each of the oblique angles is of the same species as its opposite side, and the sides containing the right angle are of the same species as their opposite angles. 360. If the hypothenuse be less than 90~, the legs are of the same species as their adjacent angles, but if the hypothenuse be greater, then the legs and adjacent angles are of different species. 361. In any spherical A the sines of the angles are to one another as the sines of their opposite sides. 862. SOLUTION OF RIGHT-ANGLED SPHERICAL TRIANGLES. Sin. a = sin.. sin. A, Equat. A. tan. a = tan. c. cos. B tan. A. sin. B, Equation B. tan. a, Sin. b - sin. c. sin. B- tan. tan. A. Equation C. tan. b = tan. b. cos. A = tan. B. sin. A, Equation D. Cos. A _ cos. a. sin. B, Equation E. Cos'. = cos. b. sin. A, Equation F. cos. A. Sin. B cs Equation G. COS. a. Cos. o = cos. a. cos. b, Equation IH. Cos. c = cot. A. cot. B, Equation I. sin. a. Sin c - -.- * ere c = hypothenuse. Equation K. sin. A. 863. NAPIER'S RULES FOR THE CIRCULAR PARTS. Lord Napier has given the following simple rules for solving rightangled spherical triangles. The sine of the middle part product of the adjacent parts. The sine of the middle part = product of the cosines of the opposite parts. In applying Napier's analogies, we take the complements of the hypothenuse and of the other angles, and reject the right angle. We will arrange Napier's rules as follows, where co. = complement of the angles or hypothenuse. Is equal to the product of the Is equal to the product of the Sine of the middle part, tangents of the adjacent cosines of the opposite parts. _part_ Sine comp. A. tan. co. c. tan. b. Cos. co. B.. cos. a., Sin. comp. c. tan. co, A.. tan. co. B. Cos. b.. cos. a. Sin. conp. B. tan. comp. c.. tan. a. Cos. b.. cos. A. gin. a. tan. comp. B.. tan. b. Cos. comp. A. cos. coml. Sin. b. tan. co. A.. tan. a. Cos. com... c. com n e. co.... c..o._ / r SPfIERIOAL TRIGONOMETRY. 7a1 72011 It is easy to remember that adjacent requires tangent, and opposite requires cosine, from the letter a being found in the first syllable of adjacent and tangent, and o being in the first syllable of opposite and cosine. Example 1. Given the < A X 230' 28'1 and c = 1450 to find the sides a and b, and the angle B. Comp. c comp. 180 - 145 35 and 550 = comp. Comp. A =900 - 230 28' - 660 32'. Sin, a cos. 550 X cos. 660 32'1 = 0.57358 X 0.239822'and a == 130 12'1 13"1. - natural sine of 0.229841. Having a and comp. of c, we find B = 500 81' and b =- 240 24'. Example 2. Given b - 460 18' 23"/. A -- 340 27'- 29"1 to find < B. Answer, B - 660 59'1 25"/. Example 3. Given a = 480 24' 16"/, and b= 59'0 38'1 27"1. We find o = 7901 23'1 42"/. Eaple 4. Given a = 1160 30' 43"/ and b= 290 41'1 32"1. We fin A = 1030 52,' 48" Example 5. Given b -- 291 12'1 50"., and < B - 370 26' 21"'. We Ab460 55' 2"1. or a -= 1330 4/ 58". We can use either natural or logarithmetio numbers. QUADRANTAL SPHERICAL TRIANGLES. Let A D-=900, produce D B to C making D C = A D = 900; therefore the arc A C is the measure of the angle A D B. If the < D A B is less than 900, then D B is less than 900. But if the < D A B is greater than 900, then the side ID B is greater than 900. Example. Let the < ID - 420 12,' - Arc A C in the triangle A B C, and let the < ID A B -540 43', then 900 -640 13'= 350 17' < B A C < A in the B A C. By Napier's analogies, sin. comp. A X radius =tan. b X tan. comp. c. Rad. cos. A ie., rad. cos. A =tan. b.cot. c, and cot.c _____ tan. b Rad. cos. 540 43V ------ =48o0/09-//= c. And Sin. comp. B = cos. B tan. 420 12' Cos. h. cos. A = cos. b. sin. A, and having b and A in the above, we have cos. B = cos. 420 12'1 X sin. 480 0,' 9"1 - 640 39/ 655"/ B. Again, sin. comp. B tan a. tan. comp. c i. e. cos. B =- tan. a. cot. C, cos. B cos. 640 89' 655" Tan. a == - - ~ 0' = 250 25'1 20"1 = value of a. 900 -250 25' 20"' = 640 34'1 40"/ - side D B.-YFoung'a8.:Wgonomet?.y 365. OBLIQUE-ANGLED SPHERICAL TRIANGLES. Oblique-angled triangles are divided into'six cases by Thomson aild other mathematicians. -. - 1 " 1 j,. I -Amiga, 72n*12 72u*12 ~.SPHERICAL TRIGONOMETRY. I. When the three s-ides are given, to find the angles. II. When the three angles are given, to find the sides. III. When the two sides and their contained angle are given. IV. When one side and the adjacent angles are given. V. When two angles and a side opposite to one of them. VI. When two sides and an angle opposite to one of them. The following formulas may be solved by logarithms or natural numbers. 366. The following is the fundamental formula, and is applicable to all spherical triangles. Puissant in his Geodesie, vol. I,-p. 58, says: "Ii1 sverait aise de prouver que l'equation est le fonden~ent unique de toute la Trigonometrie spherique." Cos. a = cos. b. cos. c + sin. b. sin. o. cos. A. Cos. b = cos. a. cos. c + sin, a. sin. c. cos. B. Cos. e = cos. a. cos. b + sin, a. sin. b.cos. C. From these we can find the following equations: Co.A=Cos. a - cos. b.- cos. a Cos. A = sin. b. sinec cos. b - cos. a. cos. o' Cos. = ~~sin, a. sin. C cos. e - cos. a. cos. b Equation A. Equati Cos. C= Equat! sin, a. sin. b If we have a, b and A given, then side a: sine of K A: B ide b to the sine of K B. The following formulas are applicable to natural numbers and logarithms. The symbol J = square root. 367. CASE I. Having the three sides given, let is = half the sum of the sides. sin. (s -b) sin (s -c) Sine A =(.-) Equation A. sin. (s -a) sin. (s -c) Sin. J B sin. a.sine ) sin. (s -a) sin. (s -b) SinekJC ( sin. a.sin.)b sin. s-,sin. (s -a) sin. s sin. (s -b) Cos. J s in. s - sin. (s(sin, (s - bin. sin (s - c TanAA=( sin.sa sin.(s-)) sin. (s -ab). sin. (s - c) Tan. AB ( s~in.sa -sin. (a-b a)-) sin. (s -a).sin. (s -b) Tan.~(J=( sin.is sin. (Bs-c) Equation B. Equation C. Equation D. Equation E. Equation F. Equation G. Equation H. Equation J. ( SPHERICAL TRIGONOMETRY. 7u1 72018 368. CASE IL. Having the three angles gaven, to find the sides. -Cos. s. cos. (s - A) Sine C~ sin. B -sin. C. Sine ~b (Cos.S Cos. (S -B) Sine b ~~sin. A.- sin. C. Sine C - Cos. S * Cos. (S - C) Sine~~c( sin. A.sin. B Cos. (S -B). cos. (S -C) Cos. ~a ( in. B -sin. C Cos. 005os (S -A).cos. (S -C) sin. A sin.C Co.0 cos. (S -A).cos. (S -B) Cos~~c=( sin. A Sin. B Tan. a Cs.S cos. (S -A)) Tan. b =(Cos. S. Cos. (S - B) ( Cos. (S - A)05o. (5 - C) Equation A. Equation B. Equation C. Equation D. Equation E. Equation.F. Equation G. Equation H. Equation I. 369. CASE Il. When two sides and tha, angle contained by them are given to find the remaining parts. Let us Suppose the two sides a and b and the contained < C. By Napier's analogies, Cos. j(a + b): cos. j (a *b): cot. jC: tan. (A + B) Equat. 3..Sin. j(a + b): sin. (a b): cot. C: tan. (A ow B) Equat. K. Tan, of half the sum of the unknown angles Cos. j (a.~b).- cot. j C 008. ~~~ (a ~ b.) ~~~Equation L. Tan, of half the difference of same = sin. J (a.-~ b). cot. J.C sin. J (a + b) Equation M. signifies the difference between a and b. Having determined half the sum and half the difference of the angles", we find the angles A and B. Then the side c may be found from (Equation F.) sin. B: sine b: sine C: sine c, from which C is found. 370. Napier's analogies for finding the Side from the angle. Cos. (A + B): cos. (A,QB): tan. J c: tan. J (a + b) Equation N. or sin. (A + B): sin. (A B): tan. J c: thn (a - b) Equation 0. or tn. C 005o. (A + B). tan. j (a + b) Equatiois P. ol' tan. jc=cos.( B) or tn. C sin. (A + B).tan. J (a - b) Equation Q (Sin. A.-. B) The value may be found from the general equation. 72H*14 * 72a*14 ~~SPHERICAL TRIGONOMETRY. 871. CASE IV. When one side and the adjacent an~gles are given. Given A and B and the adjacent side c. 00s. 4 (A + B): cos. (A oz- B):tan. 4 c:tan. 4 (a + b) sin. 4 (A + 14): sin. A ( B):B) tan. 4 c, From these we have the sides a and b. tan. 4 (a + b) - cos. (A ~wB).tan. c. cos. J (A + B) tan. (a.b)_sin. 4 (A B.). tan. J c tan.J (a- b)= ~~ sin. 4 (A + B):tan. 4 (a - b) And to find < C, we have cot. 40 cos. 4I (a ~ b).tan. 4 (A 4 — B) cos. 4 (a,zb) cot. 40C = sin. 4 (a + b) tan. 4 (A -B) sin. 4 (a b) Equation R. Equation 8.. Equation T. Equation U. 872. CASE V. When two sides and an angle opposite to one of them are given, as, a, b and the angle A. sin. b. sin. A Sin.a:sin. b;sin. A:sin. B sina.-. wehave B. To find C and c, as we have now a, b and A and B. We have from (Eq. T) cot 4 C - COS. 4 (a ~ b). tan. 4 (A + B)(V ICOS. J(a -wb) and from (R) we have the gblue of c, for cos. 4 (A + B). tan. 4 (a ~ b)* W aigteage tan. 4 e =.W Haigtenls cos. 4 (A.;, B) A, B and C, and the sides a and b, we can find c, because sin. B: sin. C sin. b: sin. c. NOTE. As the value determined by pwoportion admits sometimes of S double value, because two arcs have the same sine. It is therefore better to use Napier's analogies. 837. CASE VI. When two angles A and B and the side a opposite to one of them are given to find the other parts. Sin. A: sin. B sin. a:sin. b..we have side b. By Eq. (V) we find the < C. By Eq.. (W) we find c, which may be found by proportion. NOTE. If cosine A is less than cosine B, B and b will be of the same species, (i. e.,) each must be more or less than 900 in the above proportion. If cos. B is less than cos. A, then b may have two values. 874. Examples with their answers for each case. CAsED I. Ex. 1. Given c - 790 17' 14"1 b - 580 and a- 1100 to find A. Answer. A - 1210 54' 56"/. Ex. 2. Given a =- 1000, b - 370 18', and c -620 46'. Answer. A 1760 15' 46"/. Ex. 3. Given a -610 32' 12"f, b =880 19' 42" e 280 27' 46"/ to find A. Answer. Aw- 200 89' 48"1. Ex. 4. Given a 460, b 720, and c -680. Answer. A- 480 58'1 B- 860 48', C- 760 28'. SPHEXUICAL ASTRONOMY. 72nu*1 6 CASEm II. Ex. 1. Given A 900, B.= 950 6', C- 710 86', to find the sides. Answer. a = 910 42', b - 950 22' 30"', c - 710 31' 80"1. Ex 2. A T —890, B-S 0, C-=:880. Answer. a = 530 10', b =_ 40, c __ 530 8'. Ex. 3. A =- 1030 59/' 57"/, B -= 460 18' 7"-1 C -: 360 7/ 52"/. Answer. a = 420 8,'48"/. CASE III. EX. 1. Given a == 380 30,' b -= 700, and C == 310 34' 26".1 Answer. B = 130 3' 11", A=-300 28'11"./ Ex. 2. Given a = 780 41-' b -= 1530 30', C n- 1400 22'. Answer. A = 1330 15,', B = 1600 39k, c - 1200 50Q/ Ex. 3. Given a - 13Y c __- 901 B -= 1760 to find other parts. Answer. A = 20 24'1 C- 10 40'1. CASE IV. Ex. 1. Given a -= 710 45't B -- 1040 5', C --- 820 18,' to find etc. Answer. A = 700 81', b -= 1020 17', c -= 860 41'. Ex. 2. A T- 300 28-' 11",f B = 1300 3~/ II/ c = 400 to find etc. Answer. a = 380 30'1 b - 700, C - 310 34,' 26"/. Ex. 3. Given B - 1250 37', C = 980 44/, a __ 450 64,' to find etc. Answer. A == 610 56,', b = 1380 34,, c-=1260 26'. CASE V. Ex. 1. a = 1360 25', c -= 1250 40', C - 104Y0 to find etc. Answer. A = 1230 19', B =- 620 6', b - 460 48'. Ex. 2. Given a = 840 14-' 29"', b - 440 13' 46"/ A = 1300 5' 22"/ to Answer. B == 320 26' 7"/, C = 360 45-1 28"/, c = 610 6' 12"/. Ex. S. Given a = — 6401 c -= 220, C = 120 to find etc. Answer. b 730 16'1 B -- 1470 53', A - 260 41', or b - 330 32', B _ — 1710 51'1 A - 1530 19' -Peirce's Trigonometry. CASE VI. Ex. 1. Given A = 1030 16'9 B -= 760 44', b =_ 300 7' to find etc. Answer. a 1490 53'1 c L- 1640 50'7 C - 1490 30,'.-Thomson. Er. 2. Given A -10401 C - 950, a -= 1380 to find etc. Answer. b == 170 21'1 c 13601 36', B = 260 37', or b -= 1710 37/, c -: 430 24', B = — 1670 47' -Peirce. Er. 3. Given A t- 170 46' J16V' B - 1510 43-,' 52"1., a -= 370 48'1 to find etc. Answer. b 1800, c = 740 30'.-Young's Trigonometry. SPHERICAL ASTRONOMY 376. Meridians, are great circles passing through the celestial poles and the place of the observer, and are perpendicular to the equinoctial. They are called hour lines, and circles of right ascension. Altitude of a Celestial Object, is its height above the horizon, measured on the meridian or vertical circle. Zenith Distance, is the complement of the altitude, or the altitude taken from 9900 Azimuth or Vertical Circles, pass through the zenith and nadir, and cut the horizon at right angles. the uthor Bearing of a celestial object, is the arc intercepted between teNorth and South points and a circle of altitude passing through the, 72aH16 SPHERIOAL ASTRONOMY. place of the body, and is the same as the angle formed at the zenith by the intersection of the celestial meridian and circle of altitude. Greatst Azimuth or Elongation of a celestial object, is that at which during a short time the azimuth or bearing appears to be stationary, and at which point the object moves rapidly in altitude, but appears stationary in azimuth. When the celestial object is at this point, it is the most favorable situation for determining the true time, and variation of the compass, and consequently the astronomical bearing of any line in surveying. See Table XXII. Parallax, is the difference of the angles as taken from the surface and centre of the earth. It increases from the horizon to the zenith, and is to be always added to the observed altitude. (See Table XVIII.) Dip, is the correction made for the height of the eye above the horizon when on water, and is always to be subtracted. When on land using an artificial horizon, half the observed altitude will be used. (See Table XVI.) Refraction in altitude, is the difference between the apparent and true altitude, and is always to be subtracted. (See Table XVII.) As the greatesteffect of refraction is near the horizon, altitudes less than 26~ ought to be avoided as much as possible. Prime Vertical, is the azimuth circle cutting the East and West points. Elevation of the Pole, is an arc of the meridian intercepted between the elevated pole and the horizon. Declination, is that portion of its meridian between the equinoctial and centre of the object, and is either North or South as the celestial object is North or South of the equinoctial. Polar distance, is the declination taken from 90~. Right Ascension is the arc of the equinoctial between its meridian and the vernal equinox, and is reckoned eastward. Latitude of a celestial object is an are of celestial longitude between the object and the ecliptic, and is North or South latitude according as the object is situated with respect to the ecliptic between the first points of Aries and a circle of longitude passing through that point. Mean Time, is that shown by a clock or chronometer. The mean day is 24 hours long. Apparent Solar Days, are sometimes more or less than 24 hours. Equation of Time, is the correction for changing mean time into apparent time and visa versa, and is given in the nautical almanacs each year. Sidereal Time. A sidereal day is the interval between two successive transits of the same star over the meridian, and is always of the same length; for all the fixed stars make their revolutions in equal time. The sidereal is shorter than the mean solar day by 3/ 66i/t. This difference is owing to the sun's annual motion from West to East, by which he leaves the star as if it were behind him. The star culminates 3/ 56.5554" earlier every day than the time shown by the clock. Civil Time, begins at midnight and runs to 12 or noon, and then from noon again 12 hours to midnight. Astronomical or Solar Day, is the time between two successive transits of the sun's centre over the same meridian. It begins at noon and is..X.:.*::.. SPHERICAL ASTRONOMY. 72H*17 reckoned on 24 hours to the next noon, without regarding the civil time. This is always known as apparent time. Nautical or Sea Day, begins 12 hours earlier than the astronomical. Example. Civil time, April 8th, 12h. = Ast. 8d. Oh. Example. Civil time, April 9th, 1Oh. = Ast. 8d. 22h. If the civil time be after noon of the given day, it agrees with the astronomical; but when the time is before noon, add 12 hours to the civil time, and put the date one day back for the astronomical. The nautical or sea day is the same as the civil time, the noon of each is the beginning of the astronomical day. 876. To find at what time a heavenly body will culminate, or pass the meridian of a given place. (See 264E, p. 69.) From the Nautical Almanac take the star's right ascension, also the R. A. of the mean sun, or sidereal time. From the star's R. A., increased by 24 if necessary, subtract the sidereal time above taken, the difference will be the approximate sidereal time of transit at the station. Apply the correction for the longitude in time to the approximate, by adding for E. longitude, and subtracting for W. longitude, the sum or difference will be the Greenwich date or time of transit. The correction is 0.6571s. for each degree. Ex. At what time did a Scorpie (Anteres) pass the meridian of Copenhagen, in longitude 12~ 35' E. of Greenwich, on the 20th August, 1846? Star's R. A. 16 20 02 Sun's R. A. from sid. col. 9 53 45.5 Sidereal interval, at station, = 6 26 16.5 Cor. for long. = 12~ 35/ X 0.6571s. = + 8.27 (Here 3m. 56.55s. divided by 360~ = 0.6571s.) 6 26 24.77 This reduced to mean time, = 6 25 21.46 The correction for long. is added in east and subtracted in west long. NOTE. The sidereal columns of the Nautical Almanac, are found by adding or subtracting the equation of time, to or from the sun's R. A. at mean noon. What we have given in sec. 264E, will be sufficiently near for taking a meridian altitude. 377. LATITUDE BY OBSERVATION OF THE SUN. RULE. Correct the sun's altitude of the limb for index error. Subtract the dip of the horizon. The difference - apparent altitude. From the apparent altitude, take the refraction corresponding to the altitude; the difference = true altitude of the observed limb. To this altitude, add or subtract the sun's semi-diameter, taken from p. 2 of the Nautical Almanac, the sum or difference = true altitude of the sun's centre. Add the sun's semi-diameter when the lower limb is observed, and subtract for the upper. From 90, subtract the true altitude, the difference will be the zenith distance, which is north, if the zenith of the observer is north of the sun, and soath, if his senith is south of the sun. From the Nautical Almanac, take the sun's declination, which correct for the longitude of the observer; then if the corrected declination and the zenith distance be of the same name, that is, both north or south, their sum will be the latitude but if one is north and the other south, their difference will be the latitude. p2 72H*18 SPHERICAL ASTRONOMY. Example. From Norie's Epitome of Navigation, August 30, 1851, in long. 129~ W., the meridian altitude of the sun's lower limb was 57~ 18' 30/, the observer's zenith north of the sun. Height of the eye above the horizon, 18 feet. Require the latitude. 0o // Observed altitude, 57 18 30 Dip of the horizon, correction from Table XVI, - 4 08 Apparent altitude of sun's lower limb = 57 14 22 Correction from Tables XVII and XVIII for refraction and parallax, - 32 True altitude of the sun's lower limb = Sun's semi-diameter from N. A. for the given day + True altitude of sun's centre - Zenith distance = 90 - alt. Declination on 30th August, is N Declination on 31st August, is N 57 13 50 15 52 57 29 42 32 30 18 N.. 9 08 30 8 46 58 0 21 32 Decrease in 24 hours, 360~: 21/ 32:: 129: 7 43//. 0 / // Declination, 30th August, 1851, = N. 9 08 30 Correction for W. longitude 129~ - 7 43 Correct declination at station = 9 00 47 N. From above, the zenith distance 32 30 18 N. North latitude - 41 31 05 Norie gives 41~ 30' 53//, because he does not use the table of declination in the N. A., but one which he considers approximately near. As the Nautical Almanacs are within the reach of every one, and the expense is not more than one dollar, it is presumed that each of our readers will have one for every year. Example 2. On the 17th November, 1848, in longitude 80~ E., meridian altitude of sun's lower limb was 50~ 6' south of the observer, (that is, south of his zenith) the eye being 17 feet above the level of the horizon. Required the latitude. Answer, 20~ 32/ 58t. NOTE. On land we have no correction for dip. 378. To find the latitude when the celestial object is off the meridian, by having the hour angle between the place of the object and meridian, the altitude and declination or polar distance. Let S - place of the star. P the elevated pole. Z - the zenith. Here P S p codeclination -.polar distance. Z S -- z -- zenith distance and P Z is the colatitude = P, and the hour angle, Z P S -= h. By case VI, we have p, z, and the hour angle Z P S = h, to find P Z. Let fall the perpendicular S M. Let it fall within the A S P Z, then we have SPHERICAL ASTRONOMY. 72H*19 Tan. P M = cos. h X cotan. declination = cos. h. tan. pol. dist. Cos. Z M = cos. P M X sin. alt. X cosecant of declination. Colatitude = P M + Z M when the perp. falls within A P S Z. Colatitude - P M - Z M when the perp. falls without the same. It is to be observed that there may be an ambiguity whether the point M would fall inside or out of the A P S Z. This can only happen when the object is near the prime vertical, that is due E. orW. As the observation should be made near the meridian, the approximate latitude will show whether M is between the pole, P and zenith, Z or not. Having the two sidesp and z, and the < h = < S P Z, we find P Z the colat. by sec. 372. 379. Latitude from a double altitude of the sun, and the elapsed time. The altitudes ought to be as near the meridian as possible, and the elapsed time not more than two hours. When not more than this time, we may safely take the mean of the sun's polar distance at the two altitudes. Let S and Si be the position of the object at the time of observations. Z S and Z S zenith distances. P S and P Sf, the polar distances. Angle S P S = elapsed time. To find the colatitude = - P Z. Various rules are published for the solution of this problem, but we will follow the immortal Delambre. Delambre, who has calculated more spherical triangles than any other man, found, after investigating the many formulas, that the direct method of resolving the triangle was the best and most accurate method. We now have the following: P S and P St = polar distances. Z S and Z S/ - colatitudes. To find colat. P Z. Hour angle = S P S'. Half of P S + P S = mean polar distance p. One-half the elapsed time in space - h. Draw the perpendicular P M, then we have Log. sin. S M = log. sin. mean polar distance + log. sin. one-half hour angle in space, and having S M - St M, we have the base, S M S/. Consequently, in the A S Z S', we have the three sides given to find the angles, and also the three sides of the triangle P S S'. By sec. 867, we find the angles P S S/ and Z S SI.'. the < P S Z is found, and the sides P S and Z S is found by observation, then we have in the triangle P S Z the two sides P S, S Z and the angle P S Z, to find the colat. P Z, which can be found by sec. 369. 380. To find the latitude by a meridian altitude of Polaris, or any other circumpolar star. Take the altitude of the object above and below the pole, where great accuracy is required. Let their apparent zenith distances be z and z' respectively, and also, r and rt, the refractions due to the altitudes, then Colatitude - correct zenith distance _= (z + z' + r + r'.) Let A and At be the correct altitudes, then we have Colatitude == (180 - (A + At) + (r + r'.) NOTE. Here we do not require to know the declination of the object. 72Ht20 SPHERICAL ASTRONOMY. By this method, we observe several stars, from a mean of which the latitude may be found with great accuracy. The instrument is to be placed in the plane of the meridian as near as possible. The altitude will be the least below the pole, and greatest above it, at the time of its meridian transit or passage. 381. To find the latitude by a meridian altitude of a star above the pole. Correct the altitude as above for the sun. From this, take the polar distance, the difference = the required latitude. Let A and A -= corrected altitudes above and below the pole. p = polar distance of the object. Then Latitude = A -p when * is above the pole. Latitude = A + p when * is below the pole. 382. To find the latitude by the pole star, at any time of the day. The following formula is given in the British Nautical Almanacs since 1840, and is the same in Schumacher's Ephemeris: L =a -p * cos. h + j sin. 1//(p sin. h)2 tan. a. - sin. 2 1 /(p cos. h) (p sin. h) 2. If we reject the fourth term, it will never cause an error more than half a second. Then we have L = a -p * cos. h + i sin. 1/ (p sin. h)2. tan. a. Here L = latitude, a = true altitude of the star. p = apparent polar distance, expressed in seconds. h = star's hour angle = S - r. S = sidereal time of observation. r = right ascension of the star. p is plus when the * is W. of the meridian, and negative when E. Example. In 1853, Jan. 21, in longitude 80~ W., about 2 hours after the upper transit of Polaris, its altitude, cleared of index error, refraction and parallax, was observed = 40 10'. Star's declination - 88~ 31'47/. Mean time of observation by chronometer = 7h. Om. 32.40s. To find the latitude. hm s 1853, Jan. 21, Polaris' R. A., 1 5 36.79 Sidereal time, mean noon, Greenwich, 20 3 2.73 Sid. interval from mean noon at Greenwich = 5 2 34.06 Cor. 80~ X 0.6571, to be subtracted in W. long. 52.57 Sidereal interval of meridian passage at station, 5 1 41.49 Mean time of observation, 7h. Om. 32.40s. which, reduced to sidereal time by Table XXXI, = 7 1 41.49 Hour angle h in arc = 30~ - in time, 2 0 00 p = 5292.6/, its log. 3.7236691 h = 30~ its log. cosine, 9.9375306 Log. of p cos. h = 3.6611997 = 4583.5 = first correction. 4583.5" = 1~ 16' 23.5// = negative = - 10 16t 23.5// = first cor. To find the second correction. Log. sin. h = 300 = 9.6989700 4 Polar dis. p = 5292.6, log = 3.7236691 - 3.4226291 SPHERICAL ASTRONOMY. 72H*21 (p sin. h)2 = 3.4226291 X 2 = 6.8452782 i sin. 1" = 4.3845449 tan. of alt. 400 10 -= 9.9263778 i sin. 1", (p * sin. h) 2. tan a = 1.1562009 -= 14.31" -= second cor. o / // Altitude, 40 10 00 First correction - 1 16 23.50 38 53 36.50 Second correction + 0 0 14.31 38 53 50.81 = required latitude. NOTE. Here we rejected the fourth term as of no consequence. The longitude may be assumed approximately near; for an error of one degree in longitude, makes but an error of 0.63s. in the hour angle. 383. To find the variation of the compass by an azimuth of a star. At sec. 264c and 264H, we have shown how to find the azimuth, when the star was at its greatest elongation. To find the azimuth at any other time, we take the altitude, and know the polar distance of the star and the colatitude of the place; that is, we have the Polar distance, P S Colatitude, P Z Zenith distance, Z S To find the Azimuth angle P Z S. We find the required angle P Z S by sec. 367. By Table XXIII, we can find the azimuth from the greatest elongation of certain circumpolar stars. 884. To find at what time Polaris or any other star will be at its greatest eastern or western elongation or azimuth. Its true altitude and greatest azimuth at that time. Also to determine the error of the chronometer or watch. In the following example, let P = polar distance, L _ latitude, R. A. = right ascension, and G. A. = greatest azimuth. Given the latitude of observatory house in Chicago = 41~ 50/ 30/ N. longitude, 87~ 34/ 7// W. on the 1st December, 1866, to find the above. Polaris, polar distance - 1~ 24 4//. NOTE. In determining the greatest azimuth, we select a star whose polar distance does not exceed 16~, and for determining the true mean time, we take a star whose polar distance will be greater than 16~ or about 20 to 30~, and which can be used early in the night. Calculating the altitude and time of the star's greatest azimuth, is claimed by us as new, simple and infallibly true, and can be found by any ordinary surveying instrument whose vertical arc reads to minutes. It is generally believed by surveyors, that when Polaris, Alioth in Ursa Majoris, or Gamma in Cassiopeae, are in the same plane or vertical line, Polaris is then on the meridian. 72H*22 SPHERICAL ASTRONOMY. It is to be much regretted that the above two last named stars so much used by surveyors, have not found place in the British or American Ephemeris. However, we have calculated the R. A. and declination of them till 1940. See Table XXV. NOTE. We will send a copy of this part of our work to the respective Nautical Almanac offices above named, urging the necessity of giving the right ascension and declination of these two stars. With what success, our readers will hereafter see. Time from Merid. Passage. Altitude at G. A. Greatest Azimuth. Tan. p 8.388437 Radius, 10.000000 Radius = 10.000000 Tan. L + 9.951023 Sine L + 9.824174 Sine p = + 8.388307 18.339460 19.824174 18.388307 Less 10. Cos. p - 9.999870 Cos L - 9.872151 Cosine - 8.339460 Sine = 9.824304 Sine = 8.516156 88~ 44/ 53" True alt. 41~ 51/ 25" 1~ 52/ 51" Sid. 5h. 54m. 59.53s. Cor. tab. XII + 1 8 -Greatest azimuth. Appt. alt. 41~ 52' 33" Polaris R. A. = lh. 10m. 54.30s. Sun's R. A. = sid. column, 16 41 25.04 8 29 29.26 Cor. for 87~ 34' 7/" at 0.6571s. for each deg. - 57.54 Upper transit in sidereal time = 8 28 31.72 Time from meridian passage to G. E. A. = 5 54 59.53 This would be in day time, for G. E. A., 2 33 32.19 This is after midnight, for G. W. A., ' 14 23 21.25 Or, December 2d, 2 23 21.25 Which, if reduced to mean time, gives 2 22 57.70 385. To find the azimuth or bearing of Polaris from the meridian, when Polaris and Alioth (Epsilon in Ursa Majoris) are on the same vertical line. Example. The latitude of observatory house in Chicago, (corner of 26th and Halsted streets,) is 41~ 50' 30//. Required the azimuth of Polaris when vertical with Alioth, on the first day of January, 1867. Right Ascension. Ann. variation. N. P. D. Ann. variation. Polaris, lh. 10m. 17s. + 19.664s. 1 1~ 23/ 59"/ 19.12/ Alioth, 12h. 48m. 10s. I 33 19' 05" - 19.67 Gamma, Oh. 48m. 42s. + 3.561s. 300 0' 15/ - 19.613/ Latitude, 41~ 50' 30/.-. colatitude = 48~ 9/ 30/. Polaris N. P. D. 1~ 24/ and colat. less polar distance = Z. Altitude above the pole = 43~ 14/ 29" 48~ 9/ 30// - 1 24/ - 46~ 45' 30/, zenith dist. of Polaris. To find Alioth's zenith distance. Latitude, 41~ 50/ 30/ Alioth below the pole, 33~ 19/ 05" = polar distance. Alioth's altitude, 8~ 31' 25/ under transit. Alioth's zenith distance, 81~ 28' 356 Polaris' upper transit, 1st January, 1867, lh. 10m. 17s. Alioth's upper transit, 12h. 48m. 10s. Under at Oh. 48m. 10s. Hour angle in space = 6~ 31/ 45//, in time - 22m, 07s. SPHERICAL ASTRONOMY. 72H*23 Here we find that Alioth passes the meridian below the pole 22m, 7s, earlier than Polaris will pass above it, consequently, they will be vertical E. of the meridian. As Polaris moves about half a minute of a degree in one minute of time, it is evident that we may take the zenith distances of both stars the same as if taken on the meridian without any sensible error. We have in the A P Z S, fig. in sec. 383, the sides P S =polar distance. Z S = zenith distance. And the hour angle S P Z, in space, to find the azimuth angle S Z P. By sec. 372, sin. <SPZ.sin. PS sin. hXsin. p we have sin. < S Z P = ---— _ sin. Z S sin. z sin. 5~0 31/ 45// X sin. 10 24/ sin. < S Z P - sin. 46~ 45/ 30// 0 11 That is, the azimuth of Polaris is 11/ E. of the meridian, when Alioth is on it below the pole. Alioth is going E. and Polaris going W., therefore, they meet E. of the meridian. Their motions are Asine polar distance of Polaris sine polar distance of Alioth. sine of its zenith distance sine of its zenith distance. sine 1~ 24/' sine 330 19/ 05// ~ *.0244..5468 sine 460 45/ 30/ sine 810 28' 35//..7285..9889 Or as 0.0244 X 0.9899: 0.5468 X 0.7285. Or 1: 16. And 17: 11:: 1: Polaris' space moved west= 39// nearly. Therefore, 11/ - 39/ = N. 10/ 21/ E. = required azimuth. 386. To find the azimuth of Polaris when on the same vertical plane with y in Ursa Majoris, in Chicago, on the 1st Jan., 1867: Lat. 41~ 50/ 30//. R. A. of Polaris at upper transit, Ih, 10m, 17s. R. A. of y Urs. Maj. at upper transit, llh, 46m, 49s.,, *," "( under transit, 23h, 46m, 49s. Hour angle in space, 20~ 52'=in sidereal time to, lh, 23m, 28s. Polaris' polar dist. above the pole =1~ 24/.. its alt. =430 14' 30//, and the altitude taken from 90~, gives the zenith dist. =46~ 45' 30". Gamma's polar distance, from Nautical Almanac, 35~ 34/ below the pole.'. its altitude = 41~ 50/ 30" - 35~ 34 -= 6~ 16' 30/, and its zenith distance, 83~ 43/ 30/. In the A s P Z, we have the hour < S P Z = h, equal to 200 52', P S = 1~ 24', and Z P = 430 14' 30//. By sec. 372, sin. 20~ 52' X sin. 10 24/ sin. < S Z P= By using Table A, sin. 46~ 45/ 30"/ we have sin. S Z P =.35619 X.02443 -- =.01195 = 41/ 72837 Angular motion of Polaris is to the angular motion of y nearly sin. polar dist. of Polaris * sin. polar dist. of y sin. of its zenith dist.. sin. of its zenith dist. sin. p * sin. P * * sin. PX sin. z ~ sin. z * sin. Z * * sin. pX sin. 1 By TableA, sin. P= sin. 35~ 34/ -.817 sin. z - sin. 460 45/ 30/ =.7284. Their product =.42371028 = B. 72n'24 SPHERICAL ASTRONOMY. Sin. p X sin. Z = sin. 1~ 24'X sin. 83~ 43' 30"t =.0244 X. 294 =.02428342 = C, divided into B, gives the value of the 4th number =-27. As y moves E. 27' and Polaris moves W. 1/ in the same time, making a total distance of 28'.-. 28: 41':: 1: 1' 28"/, which, taken from the above 41', leaves the azimuth of Polaris N. 39' 32/ E. of the meridian. Table XXIII gives the greatest azimuths of certain stars near the North and South Poles; by which the true bearing of a line and variation of the compass can be found several times during the night. There are several bright stars near the North Pole. The nearest one to the South Pole is P Hydri, which is now about 12~ from it. This circumstance led us to ask frequently why there should not be the same means given those south of the Equator as to those north of it. It was on the night of the 18th January, 1867, as we revelled in a pleasant starry dream, that we heard the words-God has given the Cross to man the emblem of and guide to salvation. He has also made the Southern Cross a guide in Surveying and Navigation. Not a moment was lost in seeing if this was so. We found from our British Association's Catalogue of Stars, that when a' (a star of the first magnitude) in the foot of the Southern Cross was vertical with /3 (a bright star) in the tail of the Serpent, that then, in lat. 12~, they were within 1/ 12" of the true meridian, and that their annual variations are so small as to require about 50 years to make a change of half a minute in the azimuth or bearing of any line. We rejoice at the valuable discovery, but struck with awe at the forethought of the Great Creator in ordaining such an infallible guide, and brought once more to mind the expression of Capt. King, of the Royal Engineers, who, after taking the time according to our new method, in 1846, near Ottawa, Canada, and seeing the perfect work of the heavens, said —" Who dares say there is no God?" Our readers will perceive that Tables XXIII, XXVI, XXVII and XXVIII are original, and the result of much time and labor. Table XXVI gives the azimuth of a/ Crucis when vertical with / Hydra in the southern hemisphere until the year 2150. Table XXVII gives the azimuth of Polaris when vertical with Alioth in Ursa Majoris until the year 1940. Table XXVIII, when Polaris is vertical with y in Cassiopeae till 1940. 387. TO DETERMINE THE TRUE TIME. The true time may be obtained by a meridian passage of the sun or star. When the telescope is in the plane of the meridian, as in observatories, we find the meridian transit of both limbs of the sun, the mean of which will be the apparent noon, which reduce to mean time by adding or subtracting the equation of time. If we observe the meridian passage of a star, we compare it with the calculated time of transit, and thereby find the error of the chronometer or watch. 388. By equal altitudes of a star, the mean of both will be the apparent time of transit, which, compared with the calculated time of transit, will give the error of the watch, if any. 389. By equal altitudes of the sun, taken between 9 A. M. and 3 P. M. In this method we will use Baily's Formula, and that part of his Table XVI, from 2 to 8 hours elapsed time between the observations. c *: —;-I ~Ili.1, — L ~.: i i~' L;~I..fr. %~:l~l~-;;prr-; ~, i' k~ ( ~.. SPHRABICAL ASTIONONY.9 72H*'25` X-=- A tan. L + B S tan. D. Here T = time in hours, L = latitude of place, minus when south. D = dec. at noon, also minus when south. 6 = double variation of dec. in seconds, deduced from the noon of the preceding day to that of the following. Minus when the sun is going S. X = correction in seconds. A is minus if the time for noon is required, and plus when midnight is required. The values of A and B for time T, may be found from Table XXVIIIA, which is part of Baily's Table XVI, and agrees with Col. Frome's Table XIV, in his Trigonometrical Surveying, and also with Capt. Lee's Table of Equal Altitudes. We give the values of A and B but for 6 hours of elapsed time or interval, for before or after this time, (that is, before 9 A. M. or after 3 p. M.) it will be better to take an altitude when the sun is on or near the prime vertical, which time and altitude may be found from Tables XXI and XXII of this work. 390. To determine the time at Tasche in lat. 45~ 48/ north, on the 9th of August, 1844, by equal altitudes of the sun. Chronometer Time. A. Chronometr Ti. Elap. time T. Value of X. A. M. P. M. 0o hm hms h m s Alt. U. L. 78 50 1 28 23 8 03 16.5 0 6 33 10.63 " 79 19.30 1 29 52.8 8 01 46.5 <" 85 36.00 1 49 33 7 42 18 5 48 10.1 " 87 02.10 1 53 53.5 7 37 46.2 Here the sun is going south, therefore D is minus. The lat. is north,... L is plus. Also * is minus. We want the time of noon,.. the value of A is minus, and A X - 6 X + L, will be positive or plus, and also, B X - 6 X - D, will be plus in the following calculation, where we find 6 - 2094"-tfrom the Nautical Almanac: T = 6h. 3m. its log. A - 7.7793, and log. B == - 7.5951. - = 2094", its log. -= 3.3210, log. 6 - 3.310. L = 45~ 48' log. tan. _ + 0.0121, log. tan. D = - 9.4433. First correction + 12.95s. = 1.1124. 2.32s. - 0.3654. Second correction 2.32 X - 10.63 Time A. M. = t — h. 28m. 23.0s. Time P. M. = t 8 03 16.5 t 4t- _ 9 31 39.5 t + t' -- = 4 45 49.75 2 X =mi_ + 10.63, i' I. I- 4 46 00.38 chron 05 09.09 equat 4h. 40m. 51.29s. chroi ap p3 ometer time of app't noon.: time from Naut. Almanac. tom. fast of mean time, at ~ < p't noon, August 9, 1844.:-! -.... ;gp^^.^,... 72i*26 SPHERICAL ASTRONOMY. Correct this for the daily rate of loss or gain by the chronometer, the result will be the true mean time of chronometer at apparent noon. This time converted into space, will give the long. W. of the meridian, whose mean time the chronometer is supposed to keep. The above is one of Col. J. D. Graham's observations, as given by Captain Lee, U. S T. E. in his Tables and Formulas. Time by Equal Altitudes, (See sec. 388.) We set the instrument to a given altitude to the nearest minute in advance of the star, and wait till it comes to that altitude. Example from Young's Nautical Astronomy. Observations made on the star Arcturus, Nov. 29, 1858, in longitude 98~ 80/ E. to find the time: Altitudes E. and W. of the Meridian. o! 43 10 43 30 43 50 Times shown by Chronometer. h. m. s. 1. 55 47 1 { 18 11 55 11 57 57 1 { 18 945 5 f 12 0 7 1 18 73 { Sum of Times. h. m. s. 30 7 42 30 7 42 30 7 42 From the sum of the times, we get the chronometer time of the star's meridian passage, or transit, equal to 15h. 3m, 61s. Arcturus, R. A. Nov. 29, R. A. of mean sun, sid. col., Mean time of transit at station, Long. 98~ 30' E. in time, Mean time at Greenwich, Cor. for 151 hours, Mean time at Greenwich, Mean time by chronometer, nErrnr on,nA.q.n ftimP h. m. s. 14 9 13 16 20 48 Diff. for lh. = - 10.76s. 21 48 25 nearly. 15} hours. 6 24 00 subtract. 164.09 15 14 25 nearly. or 2m. 44s. - 2 44 subtract, because R. A. is increasing. 15 11 41 15 3 51 7 F0 ot fta.tonnn h. m. s. Mean time of transit at place, 21 48 25 nearly. Cor. for increase in R. A., - 2 44 21 45 41 Mean time as shown by chrcnometer, 15 3 51 Error of chronometer on mean time, 6 41 50 at station. By sec. 388. Set the altitude to a given minute in advance, and wait till the star comes to this, and note the mean time. Time before Midnight. Altitudes of Star. Time after Midnight..;:rh. m s h.., s. '..i. 9 50 10 50 0 2 7 40 9 500 20 10 2 7 30 9 50 21 50 20 7 19 9 50 20.3 2 7 29.7 Mean. X:~': 14 7 29.7 4 12 i! ~;: - 2) 23 67 60.0 14 7 29.7 11 58 65 Mean time by clock at station. |^ i~pat:R''I ':'CA ASTRONM.: 2' 7 $::: * ': ~l...:: ' " ": D.,: SPHEBICAL ASTRONOMY.72*27 i 390.* True time by a Horizontal Dial. This dial is made on slate or brass, well fastened on the top of a post or column, and the face engraved like a clock. (See fig. 49.) It may be set by finding the true mean time and reducing it to the apparent, by means of the equation of time, found in all almanacs. Having the correct apparent noon by clock, set the dial. Otherwise. Near the dial make a board fast to some horizontal surface, on which paste some paper, and draw thereon several cocentric circles. Perpendicular to this, at the common centre, erect a piece of fine steel wire, and watch where the end of its shadow falls on the circles between the hours of 9 and 3. Find the termini on two points of the same or more circles; bisect the spaces between them, through which, and the centre of the circles, draw a line, which will be the 12 o'clock hour line, from which, at any future time, we may find the apparent, and hence the true mean time. A brass plate may be fastened to an upper window sill, in which set a perpendicular wire as gnomon, and draw the meridian. Calculation. We have the latitude, hour angle and radius to find the hour arc from the meridian. Rule. Rad.: sin. lat.:: tan. hour angle: tan. of the hour arc from the meridian. Example. Lat. 41~. Hour angle between 10 and 12 = 2 hours = 30~. As 1:.65606::.57735: tan. hour are =.37878, whose arc is = 20~ 44' 55". In like manner we calculate the arc from 12 to each of the hours, 1, 3 and 5, which are the same on both sides. The morning and evening hours are found by drawing lines (see fig. 49) from 3, 4 and 5 through the centre or angle of the style at c. These will give the morning hours. For the evening hours, draw the lines through 7, 8, 9, and centre d, at the angle of the style. The half and quarter hours are calculated in like manner. The slant of the gnomon, d f, must point to the elevated pole, and the plate or dial be set horizontal for the lat. for which it is made. The < of the gnomon is equal the latitude. A horizontal dial made for one latitude may be made to answer for any other, by having the line df point to the elevated pole. Example. One made for lat. 41~ may be used in lat. 50~, by elevating the north end of the dial plate 9~, and vice versa. The following table shows the hour arcs at four places: LAT. 41~. LAT. 49~ LAT. 540 36'. LAT. 550 52'. BELFAST, IRELAND GLASGOW,SCOTL'D. lh.= 9058/ 11~ 26/ 12~ 19' 12~ 30/ 2 20 45 23 33 25 12 25 32J 3 33 16 37 03 39 11 39 37j 4 48 39 52 35 54 41 55 06J 5 67 47 70 27 71 48 72 04 6 90 00 90 00 90 00 90 00 To set off these hour arcs, we may, from c, set off on line c n the chord of 60~ and describe a quadrant, in which set off from the line c n the hour arcs above calculated. In our early days we made many dials by the following simple method: We draw the lines, c n and g h, so that c g will be 5 inches, and described the quadrants, c, g, k, We have, by using a scale of 20 parts to the inch, a radius c k = 100. As the chord of an arc is twice the sine of that arc, we find the sines of half the above hour arcs in Table A; double it; set the decimal mark two places ahead; those to the left will be divisions on the scale to be set off from k in the arc k g. ExampleLet half of the hour arc 4~ 59/, twice its sine =.17374, which give 17.4 parts for the chord to be set off.,, i ..r t;! t;,~:,i i, ~:~,:?i -? 1. ~~: I 1 ii t X, -...'. B 7'/' D. itll a _ f 'I In ' He ''9+;''St'~~~~~~~~~c,: s 72H*28 SPHERICAL ASTRONOMY. ->: ~ 391. By our new method, we select one of the bright circumpolar stars given in the N. A., whose polar distance is between 15 and 30 degrees. (See our Time Stars in Table XXIV.) By sec. 264c, we find the sidereal time of its meridian passage = T. By sec. 264b, we find its hour angle from ditto = t. By sec. 264f, we have its true altitude A, when at its greatest azimuth or elongation from the meridian. Example. Star, S, on a given day, in latitude, L, passed the meridian at time, T, and took time, t, to come to its greatest azimuth, east or west. We now reduce the sidereal time to mean time. Greatest eastern azimuth was at time T - t. Mean time. Greatest western ditto, T + t. Ditto. True altitude of its greatest azimuth == A. Let r = refraction and i index error, then App. alt. = A - r ~ i. We now set the instrument a few minutes before the calculated sidereal time reduced to mean time, and elevate the telescope to the alt. = A - r - i, and observe when the star comes to the cross hairs at time T'. The difference between mean time, T - t and T' gives the error of time as shown by the watch or chronometer. This method is extremely accurate, because the star changes its altitude rapidly when near its greatest elongation. As we may take several stars on the same night, we can have one observation to check another. Now having the true time at station and an approximate longitude, we can find a new longitude, and with it as a basis, find a second, and so on to any desired degree of accuracy. 392. To find the difference of Longitude. 1. By rockets sent up at both stations, the observers having previously compared their chronometers and noted the time of breaking. 2. As the last, but instead of rockets, flashes of gunpowder on a metal plate is used. This signal can be seen under favorable circumstances, a distance of forty miles..; * ~3. By the electric telegraph. 4. By the Heliostat. En;' E5. By the Drummond light. F- '~ 6. -By moon culminating stars. 7. By lunar observations.!~'\, ~ In 7, we require the altitudes of the moon and star, and the angular distance between the moon's bright limb and the star at the same time, 2?M - '*" thus requiring three observers. If one has to do it alone, he takes the altitudes first, then the lunar distance, note the times, and repeat the: ' observations in reverse order, and find the mean reduced altitude, also: the mean lunar distance. 8. By occultation or eclipse of certain stars by the moon. 8 i 393. By the Electric Telegraph. The following example and method used by the late Col. Graham is so K% e. very plain, that we can add nothing to it. No man was more devoted to ~::.;the application of astronomy to Geodesey than he:. -, X. |',7 W *,. ' ',S SPHERICAL ASTRONOMY. 72H*29 LONGITUDE OF CHICAGO AND QUEBEC. The following interesting letter of Col. Graham, Superintendent of U. S. Works on the Northern Lakes, is in reference to the observations made by him, in conjunction with Lieut. Ashe, R. N., in charge of the observatory at Quebec, to ascertain the difference of longitude between this city and Quebec: CHICAGO, June 5, 1857. To the Editor of the Chicago Times: A desire having been expressed by some of the citizens of Chicago for the publication of the results of the observations made conjointly by Lieut. E. D. Ashe, Royal Navy, and myself, on the night of the 15th of May, ult., for ascertaining by telegraphic signals the differenbe of longitude between Chicago and Quebec, I herewith offer them for your columns, in case you should think them of sufficient interest to be announced. All the observations at Quebec were made under the direction of Lieut. Ashe, who has charge of the British observatory there, while those at this place were made under my direction. The electric current was transmitted via Toledo, Cleveland, Buffalo, Toronto and Montreal, a distance, measured along the wires, of 1,210 miles, by one entire connection between the two extreme stations, and without any intermediate repetition; and yet all the signals made at the end of this long line were distinctly heard at the other, thus making the telegraphic comparisons of the local time at the two stations perfectly satisfactory. This " local time" was determined (also on the night of the 15th ultimo) by observations of the meridian transits of stars, by the use of transit instruments and good clocks or chronometers at the two stations. The point of observation for the "time" at Quebec was the citadel, and at Chicago the Catholic church on Wolcott street, near the corner of Huron. The following is the result: 1. CHICAGO SIGNALS RECORDED AT BOTH STATIONS. ELECTRIC FLUID TRANSMITTED FROM WEST TO EAST. Correct Chicago Correct Quebec Difference of longitude. sidereal time sidereal time Electric fluid transmitted of signals. of signals. from west to east. h. m. s. h. m. s. h. m. s. 16 11 13.19 16 16 54.83 1 05 41.64 15 42 18.28 16 47 59.83 1 05 41.55 Mean; electric fluid transmitted from west to east, 1 05 41.595 2. QUEBEC SIGNALS RECORDED AT BOTH STATIONS-ELECTRIC FLUID TRANSMITTED FROM EAST TO WEST. Correct Quebec Correct Chicago Difference of longitude. sidereal time sidereal time Electric fluid transmitted of signals. of signals. from east to west. h. m. s. h. m. s. h. m. s. 16 24 15.83 15 18 34.40 105 41.43 16 54 45.83 15 49 04.39 1 05 41.41 Mean; electric fluid transmitted from east to west. 1 05 41.435 Mean; electric fluid transmitted from west to east, as above, 1 05 41.595 RESULT-Chicago west, in longitude from Quebec, 1 05 41.515 Difference between results of electric fluid transmitted east and west = 0.16 and half diff. = 0.08. From which it would appear that the electric fluid was transmitted along the wires between Chicago and Quebec in 8-lOOths of a second of time. At this rate it would be only 1i seconds of time in being transmitted around the circumference of the earth. I will now proceed to a deduction of the longitude of Chicago, west of the meridian of Greenwich, by combining the above result with a determination of the longitude of Quebec made by myself in the year 1842, while serving as commissioner and chief astronomer on the part of the United States for determining our northwestern boundary, which will be found published at pages 368-369 of the American Almanac for the year 1848. That determination gave for the longitude of the centre of the citadel of Quebec west of Greenwich::i 1. ; '':+r ~.~~ ic';. ~:? II, i -Icl I, I:: 1,.1,~ 41 5, -~~~~~~~~~~~~~I 72U*830 S PRRICAL ASTRONOMY. h. m. s. 4 44 49.65 Difference of longitude between the same point and the Catholic Church on Wolcott street, near the intersection of Huron street, Chicago, by the above described operations, 1 05 41.51 Longitude west of Greenwich of the Catholic Church on Wolcott street, street, near Huron street, Chicago, Illinois, 6 50 31.16 That is to say, five hours, fifty minutes, thirty-one and sixteen-hundredth seconds of time, or in arc, 87deg. 37min. 47 4-lOsec. J. D. GRAHAM, Major Topographical Engineers, Brevet Lieut. Col. U. S. Army. By the Heliostat. This instrument consists of a mirror, pole, Jacob staff or rod, and a brass ring with cross wires. The brass ring used in our Heliostat, is i of an inch thick and 3~ inches diameter. In this is fixed a steel point 2 inches long. There are 4 holes in the ring for to receive cross wires or silk threads made fast by wax. The flag-staff is bored at every 6 inches on both sides to receive the ring, which ought to be at a sufficient distance from the side of the pole so as not to obstruct the direction of the reflected rays of the sun. The pole and ring are set in direction of station B, about 30 to 40 feet in advance of the mirror placed over station A, and the centre of the ring in direction of B, as near as possible. The ring can be raised or lowered to get an approximate direction to B. It will be well to remove the rings from side to side, till the observer at B sees the flash given at A, when B sends a return flash to A. The mirror is of the best looking-glass material, 3U inches in diameter, set in bronzed brass frame or ring, 4~ inches outer diameter, 34 inches inner diameter, and three-tenths of an inch thick. This is set into a semicircular ring, four-tenths of an inch thick, leaving a space between it and the mirror of two-tenths of an inch; both are connected by two screws, one of which is a clamping screw. Both rings are attached to a circular piece of the same dimensions as the outer piece, 1~ inches long; and to this is permanently fixed a cylindrical piece, i inch in diameter and 1~ inches long, into which there is a groove to receive the clamping screw from the tube or socket. The socket or tube, is 8 inches long, and ~ inch inner diameter, having two clamping screws, one to clamp the whole to the rod or Jacob staff, and the other to allow of the mirror being turned in any direction. By these three clamping screws, the mirror is raised to any required height, and turned in any direction. The back of the mirror is lined with brass, in the centre of which there is a small hole, opposite to which the silvering is removed. The observer at A sets the centre of the mirror over station A, looks through the hole and through the centre of the cross, and elevates one or both, till he gets an approximate direction of the line, A, B. Our Heliostat, with pouch, weighs but 34 pounds. A mirror of 4 inches will be seen at a distance of 40 miles. One of 8 to 10 inches will be seen at a distance of 100 miles. We use a mirror of 4 inches diameter, fitted up in a superior style by Mr. B. Kratzenstein, mathematical instrument maker, Chicago. Like all his work, it reflects credit on him. We have found it of great use in large surveys, such as running long lines on the prairies, where K27i; it is often required to run a line to a given point, call back our flagman, I. II S" i Vk~ ~r: ct::?: i.I,:':S-~ ",..;~~. _21 v; k SPrltAICAL ASTRONOMY. ' 72*3S1 or make him move right or left. We are indebted to Mr. James Reddy, now of Chicago, formerly civilian on the Ordnance Surveys of Ireland, England and Scotland, for many hints respecting the construction and application of the Heliostat. Example. Let A be the east and B the west station. Observer A shuts off the reflection at 2h. P. M.-2h. lm.-2h. 2m., etc., which B observes to agree with his local time lh.-lh. lm.-lh. 2m., etc., showing a difference in time of lh. or 15 degrees of longitude. The Drummond Light. This light was invented by Captain Drummond, of the Royal Engineers, when employed on the Irish Ordnance Survey. It is made by placing a ball of lime, about a quarter of an inch in diameter, in the focus of a parabolic reflector. On this ball a stream of oxy-hydrogen gas is made to burn, raising the lime to an intense heat, and giving out a brilliant light. This has been used in Ireland, where a station in the barony of Ennishowen was made visible in hazy weather, at the distance of 67 miles. Also, on the 31st December, 1843, at half-past 3 P. M., a light was exhibited on the top of Slieve Donard, in the County Down, which was seen from the top of Snowdown, in Wales, a distance of 108 miles. On other mountains, it has been seen at distances up to 112 miles. As the apparatus is both burdensome and expensive, and the manipulation dangerous, unless in the hands of an experienced chemist, we must refer our readers to some laboratory in one of the medical colleges. The Heliostat is so simple and so easily managed, that it supersedes the Drummond light in sunny weather. (See Trigonometrical Surveying.) To find the Longitude by Moon Culminating Stars. 394. We set the instrument in the plane of the meridian by Polaris ' at its upper or lower transit, or its greatest eastern or western elongation, or azimuth. If we cannot use Polaris, take one of the stars in Ursa Minoris at its greatest azimuth, as calculated in Table XXIII. When the instrument is thus set, let there be a permanent mark made at a distance from the station, so as to check the instrument during the time of making the observations. If the instrument be within a few minutes of the meridian, it will be sufficiently correct for our purpose; but by the above, it can be exactly placed in the meridian. Moon culminating stars are those which differ but little in declination from the moon, and appear generally in the field of view of the telescope along with the moon. We observe the time of meridian passage of the moon's bright limb and one of the moon culminating stars, selected from the Nautical Almanac for the given time. Let L = longitude of Greenwich or any other principal meridian. 1, longitude of the station. A, the observed difference of R. A. between the moon's bright limb, and star at L, from Nautical Almanac. a, observed difference R. A. between the same at the station. d, difference of longitude. h, mean hourly difference in the moon's R. A. in passing from L to 1. A-a,. Then we have d= — i ' 0 7., .; ~ _...,2a.82 SPR A 'AS. BiCAL ASTOO The following example and solution is from Colonel Frome's Trigonometrical Surveying, p. 238. Londoh, 1862. At Chatham, March 9, 1838, the transit of a Leonis was observed by chronometer at 10h. 20m. 7s.; the daily gaining rate of chronometer being 1.5s. to find the longitude. Eastern Meridian, Chatham. Observed transits. '~,~~~~~~~~~~~~- -. h. m. s. a Leonis, 10 52.46 Moon's bright limb, 11 20 7.5 I I~ On account of rate of chronometer, As 24h: 1.5s.: lh.: 0.03s. Equivalent in sidereal time, 0 27 21.5 - 0 0 0.03 0 27 21.47 -a, 0 27 25.96 Western Meridian, Greenwich. Apparent right ascension. i Ii '; h. m. s. a Leonis, 9 69 46.18 Moon's bright limb, 10 27 16.76 A, 0 27 30.58 Observed transits, a, 0 27 25.96 Difference of sidereal time between the intervals==A-a= 0 0 4.62 Due to change in time of moon's semidiameter passing the meridian, (N. A., Table of Moon's Culminating Stars,) + 0 0 0.01 Difference in moon's right ascension, 0 0 4.63 Variation of moon's right ascension in 1 hour of terrestrial longitude is, by the Nautical Almanac, 112.77 seconds. Therefore, As 112.77: lh.: 4.63s.:: 147.80=2m. 27.8s., the difference of longitude. When the difference of longitude is considerable, instead of using the figures given in the list of moon culminating stars for the variation of the moon's right ascension in one hour of longitude, the right ascension of her centre at the time of observation should be found by adding to or subtracting from the right ascension of her bright limb at the time of Greenwich transit, the observed change of interval, and the sidereal time in which her semidiameter passes the meridian. The Greenwich mean time corresponding to such R. A., being then taken from the N. A.:::v and converted into sidereal time, will give, by its difference from the observed R. A., the difference of longitude required. From above: h. m. s.:;I - Moon's R. A. at Greenwich transit, 10 27 16.76 Sidereal time of semidiameter passing the meridian J 0 1 2.26 Moon's R. A. at Greenwich transit, 10 28 19.02!i:.; Observed difference, 0 0 4.62 I, Moon's R. A. at the time, and sid. time at station, 10 28 14.40 Greenwich mean time, corresponding to the above R. A., taken from Nautical Almanac, (Table, Moon's R. A. and Dec.,) llh. 17m. 0.5s., or sidereal time, Difference of longitude, - 10 25 46.5 0 2 27.9 SPHERICAL ASTRONOMY. 72H*33' Longitude by Lunar Distances. —Young's Aelthod. 395. In this method we take the altitudes of the moon and sun, or one of the following bright stars, and the distance between their centres. In the Northern Hemisphere we have a Arietes, a Tauri (Aldebaran,) fl Geminorum (Pollux,) a Leonis (Regulus,) a Virginis (Spica,) a Scorpii (Anteres,) a Aquilae (Aflair,) a Piscis Australis (Fomalhaut,) and a Pegasi (Markab.) We observe the moon's bright limb, and add the semidiameter of the moon, sun, or planet, and thereby find the apparent distance between their centres. This has to be corrected so as to find the true altitude and distance of the centres. The following formula by Professor Young, formerly of Belfast, Ireland, appears to us to be easily applied, by either using the tables of logarithms, or natural sines and cosines, given in Table A. Let a, a', and d represent the apparent altitudes and distance of the moon and star. A, A', and D the true altitudes and distance. D is the required lunar distance and w = symbol for difference, cos. (A+A') + cos. AmA' D = cos. d+cos. (a+as..(a+ ) - - cos. (A+A') ( cos. (a + a') + cos. a ma' Example from Young's Nautical Astronomy:Let the apparent altitude of the moon's centre, 24~ 29' 44" a' The true altitude, 25~ 17'45"= A The apparent altitude of the star = a', 45~ 9' 12"= a' Its true altitude, 45~ 8' 15" A' The apparent distance of the star and centre of the moon, 63~ 35' 14"= d Here we have, Cos. d = cos. 63~ 35' 14", nat. cos. 444835 Cos. (a + a') = cos. 69~ 38' 56" " it 347772 Cos. d + cos. (a+ a') = sum,.792607= S Cos. (A m A') = cos. 19~ 50' 30" = nat. cos. 940634 Cos. (A + A') = cos. 70~ 26' 0" = nat. cos. 334903 Cos. (A + A') + cos. (A mA',) sum, 1275537=S' and S multiplied by S'= 127537 x 792607= P Cos. (a + a') = from above, 347772 Cos. (a cn a') = cos. 20 29' 28" = 935704 Cos. (a + a') + cos. (a c a') = 1283476 = S". Divide P by S", and it will give.45280, which is the nat. cos. of 63~ 4' 45" = D 396. Example. September 2, 1858, at 4h. 50m. 11s., as shown by the chronometer, in Lat. 21~ 30' N., the following lunar observations were taken:Height of the eye above the horizon, 24 feet. Alt. Sun's L.L. Obs. Alt. Moon's L.L. Dist. of Near Limbs. 58~ 40' 30" 32~ 52' 20" 65~ 32' 10" Indexcor. + 2 10 + 3 40 - 1 10 Sun's noon, Dec., at Greenich, 7~ 56' 46" 5 N. Diff. for 1 hour, = -54" 96 Cor. for 4h. 50m., - 4 26 5 Dec. 7 52 21 For 5 hours = 27480 90 For 10 m. = 916 Polar dist. 82 7 39 60 ) 26 5 64 - 4' 26" _ __ 72H*34 REQUIRED THE LONGITUDE. Sun's semidiam. 15' 53", 8 Equa. of time, 25s. 35 "Cor. for 4h. 50m., 3 85 Corrected eq. of time, 29 2 Sub. Moon's Hor. Parallax, 59' 35" 1 Cor. for 5 hours, 2" Moon's semidiam. Diff. for lh., 16' 17" + 0" 796 5 For 5 hours, 3980 For 10 m., 133 + 3 847 Diff. for 12h., 5" 7 Diff. for 5h., = 2" Hor. Parallax corrected, 59 37 Minutes and seconds may be easily obtained, but there is a table for furnishing this difference in the Nautical Almanac, p. 520. The difference between the moon's R. A. at 23h., and at the following noon is by (Naut. Alm.) + 2m. 5s., the proportional part of which, for 7m. 42s., is + 16s. Also, the difference between the two declinations is - 8' 1", the proportional part of which is 7m. 42s., is 1'2". 1. For the App2arent and True Altitudes. SUN. Obs. Alt. L.L. 58~ Dip - 4'49" -4'49" + Semidiam. + 15 54 Apparent Alt., 58 Refrac.-less parallax, True Alt., 58 2. For Sun's Alt., 58~ 53' 15" Lat., 21 30 0 Corn Pol. dist., 82 7 39 2 ) 162 30 54 % sum, = 81 15 27 c( Y2 sum-alt. 22 22 12 si Y~ hour angle 14~ 30' 31 i" Hour angle, 29 1 3 Equa. of time, Mean time at ship, 42' 40" 11 5 3 53 45 - 30 53 15 MOON. Obs. Alt. L.L., 32~ 56' 0" DIip, - 4 49 Semidiam., +16 17 + 11 37 Augment. n + 9 Apparent Alt., 33 7 37 Cor. for Alt., + 48 26 True Alt., 35 56 3 the Mean Timie at Ship. Tab. Parts ipliment of cosine, 0.0312 32 diff. for secants... " 0. 041 24 29- 1131 3sine, 9.182196 ne, 9.580392 18.798034 320 1369 - 36962 511 + 6132 31962 2) 18.797714 sine, 9.398857 lh. 56m. 4s., apparent time at ship. 29 lh. 55m. 35s. 3. For the True Distance, the G. Time, and the Longitude. Obs. dist. 65~ 01' 0" ( Appt. dist. 66~ 3' 20" nat. cos. 403850 = Y Sun's semi, + 15 54 Apt. alt. 8 53 45 Moon's+Augm. + 16 26 Appt. alt. 33 7 37 Sum, 92 1 22 nal. cos. -035297 = x Multiplier = y - x = 370553 REQUIRED THE LONGITUDE. 72i*35; True Alt. 580 53' 15" Diff. 250 40' 18" nat. cos. 900556 + = W 33 56 3 - x = 865259 = Divisor.,,. Sum, 92 49 18 nat. cos. Diff. 24 57 12 nat. cos. Multiplier, 370553, inverted = NOTE. -This rapid method is done by throwing off a figure in each line as we proceed. Divisor, 865259 NOTE.-The division is abridged by rejecting a figure each time, in the divisor. True distance, 65~ 23' 27" Dist. at 3h. (Naut. A.) 66 24 23 1 0 56 Interval of time, lh. 49m. 18s. + 1 - 049228= v 906652 857424 Multiplicandf. 355073 Multiplier. 2672272 600197 4287 429 26 3177211 i 367198= Quoti 2595777 7 + 049228 = v 581434 416426 519155 62279 nat cos. 65~ 23' 27". 60568 1711 865 846 779 67 69 Proportional Log. of diff. 2537 4704 P L = 2167 ient. Mean time at Green., 3h. + 1 49 19 1 55 35 Long. W. in time, 2 53 44 Long. = 43~ 26' W. And the error of the chronometer is 52s. fast on Greenwich mean time. A base line is selected as level as can be found, and as long as possible, this is lined, leveled, and measured with rods of Norway pine, with platt inum plates and points to serve as indices to connect the rods. They are daily examined by a standard measure, reference being had to the change of temperature. (See p. 165.) At each extremity stones are buried, and at the trig. points are put discs of copper or brass, with a centre poinin them. From these extreme points angles are taken to points selected on high places, thus dividing the country into large triangles, and their sides calculated. These are again subdivided into smaller triangles, whose sides may range from one mile to two miles. These lines are chained, horizontally, by the chain and plumb-line; or, as on the ordnance survey of Ireland, the lines of Slopes are measured, and the angles of elevation and depression taken. Spires of churches, angles of towers and of public buildings are observed. 72ni*36 TRIGONOMETRICAL SURVEYING. On the main lines of the triangles, the heights of places are calculated from the field book, and marked on the lines. When inaccessible points are observed from other points, we must take a station near the inaccessible one, and reduce it to the centre by (sec. 244.) On the second or third pages of the field book, we sketch a diagram of the main triangle, and all chain lines, with their numbers written on the respective lines, in the direction in which the lines were run. The main triangle may be subdivided in any manner that the locality will allow. See Fig. 64 is the best. Here we have three check-lines, D F, D E, and F E, on the main triangle, and having the angles at A, B, and C, with the distances, A D, D C, C E, B E, B F, and F D, we can calculate F 1), D E, and F E, insuring perfect accuracy. We chain as stated in Section 211. In keeping our field book we prefer the ordnance system of beginning at the bottom, and enter toward the top the offsets and inlets, stating at what line and distance we began, and on what; we note every fence and object that we pass over or near; leave a mark at every 10 chains, or 500 feet, and a small peg, numbered as in the field book. 398. See the diagram (figure 65). I-ere we began 114 feet f.rther on line 1 than where we met our picket and peg at 3500 feet, and closed on line 3 at 870, where we had a peg and a long Isoceles' triangle dug out of the ground. We write the bearings of lines as on line 3, and also take the angles, and mark them as above. When there are [Woods. Poles are fastened to trees, and made to project over the tops of all the surrounding ones. The position of these are observed or Trizgged. The roads, walks, lakes, etc., in these woods can be surveyed by traversing, closing, from time to time, on the principal stations or Trig. points, but we require one line running to one of the forest poles, on which to begin our traverse, and continue, closing occasionally on the main lines and Trig. points. 399. Traverse Surveying. See Sees. 216, 217, 255. The bearing of the most westerly station is taken. At Sec. 216 is given a good example where we begin at the W. line of the estate, making its bearing 0, and the land is kept on the right. There we began with zero and closed with 180, showing the work to close on the assumed bearing. 400. To Protract these Ang-les at Sec. 216. Draw the line A B through the sheet; let A be S, and B, N. On this lay of other lines parallel to AB, according to the number of bearings, size of protractor and scale. We lay down A B, then from B set off four, five, or more angles, IL, K, I, and H. Lay the parallel ruler from A to L, draw a line and mark the distance A L of the second line on it. Lay the ruler from A to K, move one edge to pass through L, draw a line, mark the third line L K on it. Lay the ruler on A I, move the other edge to pass through K, draw the line K I, equal to the fourth line. Lay the ruler on A to H, make the other edge pass through I, and mark the fifth line, I H. Now, we suppose that we are getting too far from our first meridian, A B. We now remove the protractor to the next meridian, and select a point opposite H, and then lay off the bearings, G, F, E, D, etc. Now, from this new station, which we will call X, we lay the parallel ruler to F and make the other edge pass through H1, and set off the sixth line H G. Lay the parallel ruler from X to F, and move the other edge through G, and mark the seventh line, G F, and so proceed. TRIGONOMETRICAL SURVEYIN'lG. 721'*37 l We have used a heavy circular protractor made by 1Troughton & Simms, of London, it is 12 inches diameter, with an arm of 10 inches, this, with a parallel ruler 4 feet long, enabled us to lay down lines and angles with facility and extreme accuracy. 401. By a table of tangents we lay off on one of the lines, A B, the distance, 20 inclhes, on a scale of '0 parts to the inch. Then find the nat. tangent to the required angle, and multiply it by 400 divisions of the scale, it will give the perp., B1 C, at the end of the base. Join A and C, and on A C lay off the given distance, and so proceed. By this means we can, without a protractor, lay off any required angle. REGISTE'RED SIEET FOR COMPUTATION. Triangles Contents Plans and Plats. and Traperiums. 1st side. 2d side. 3d side in Chains. a. d _raeis_ _n Chains. 'lat 1 Triangle A C B, 4454 llks 3398 4250 679.5032 " A F D, 2234 176G6i 16;84 143.0516 Division K On line D if, 22i 10 98 0.0490 of 90 400 3.2000 Thos. Linskey's Additives,70 50 900 5.4000 Farm. 50 00 1.5000 Total Additives, 158.2006 1) F, 20 140 1400 Div. K, Negatives, D F, 20 100 260 9600 100 80 500 4.5000 80 500 2.0000 7.6000 150.6006 Area, 15.06006 Acres. There is always a content plat or plan made, which is lettered and numbered, and the Register Sheet made to correspond with it. 403. Computation by Scale. Where the plats or maps for content are drawn on a large scale, of 2 or 3 chains to the inch, we double up the sheet by bringing the edges together. Draw a line about an inch from the margin; on this line mark off every inch, and dot through; now open the sheet and draw corresponding lines through these dots; make a small circle around every fifth one, and number them in pencil mark. Lines are now drawn through the part to be computed. Where every pair of lines meet the boundaries, the outlines are then equated with a piece of thin glass having a perpendicular line cut on it, or, better, with a piece of transparent horn. When all the outlines of the figure are thus equated, we measure the length in chains, which, multiplied by the chains to one inch, will give the content in square chains. This gives an excellent check on the contents found by triangulation or traversing. It will be very convenient to have a strip of long drawing paper, on the edge of which a scale of inches is made. We apply zero to the left-hand side of the first parallel, and make a mark, a, at the other end; then bring mark a to the left side of the second parallelogram, and make a mark, b, at the other end, and so continue to the end. Then apply the required scale to the fractional part, to find the total distance. The English surveyors compute by triangulation on paper, and sometimes by parallels having a long scale, with a movable vernier and cross-hairs, to 72nI*38 DIVISION OF I,AND. equate the boundaries. We (1o not wish to be understood as favoring computation from paper. The Irish surveyors always draw the parallel lines on the content plat or map, and mark the scale at three or four places, to test the expansion or contraction of the sheet during the construction or calculation. We prefer, when possible, 3 chains, or 200 feet, to an inch for estates in the country, and 40 feet for city property. 403a. Division of Land. When the area A is to I:)e cut off from a rectangular tract, the sides of which are a and b. Then corresponding sides of the tract, A A A ) S = \- and - respectively, the required side, S. a b 404. When the area A, = triangle A l) i, is to be cut off from the triangle A C 13, by a line parallel to one of its sides. (Fig. 66.) Then triangle A B C: triangle A E:: A 2 A D 2. 405. From a,givez point, )], inz the tri.ngle, A. C, to draw a linc, dividizngz it inZo two jparts, as A antzd B. (See Fig. 66.) We find the angle A B C. By (Sec. 29,) A D x A E x,; sin. A = area B (i. e.) A I) x A E, sin. A - 2B3 2B ) A E = A D. Sin. A NOTE.-We prefer this to any other complicated formula, in cutting off a given area from a quadrilateral or triangular field. 406. When the area B or A is to be cut off by the line D E, (Fig. 66,) making a given angle, C, with the line A BI, let area =S. Let the angle at A = b, that at D = c, and that at E = d, and AD, the required side. Sin. c.x AD = x, and AE = Sin. d Sin. b. x D E = - but A D x DE x sin. c = Area = B Sin. d Sin. b. x -. Sin. c. x= 2B Sin. d x 2. Sin. c. Sin. b = 2 B Sin. d A 2 B, Sin. d t A D-= x = - ~ ------ I Sin. c, Sin. b From the value of x we find A E and I) E from above. Having A D and A E from these formulas, let us assume A = 10 chains, and having found the value of A E by substituting 10 chains for x. Multiply the numerical value of A E by 10 chains, and again by,'2 the natural sine of the angle D A B, let its area = s, L, Then s: S:: A D 2: the required A E 2, s: S::100: A D 2. As s, S, and 100 are given, we have AD — = 100S } t s DIVISION OF LAND. 72H*39 This useful problem was proposed to us in Dublin, at our examination for Certified Land Surveyor, September, 1835, by W. Longfield, Esq., Civil Engineer and Surveyor. NOTE.-When the given area is to be cut off by the shortest line, D E, in the triangle A D E, (Fig. 66.) then A D = D E. 407. eWhen the area B is to be cut off by the line D S, starting fromt the point D. (Fig. 66.) 2B 2B AD = AE -E= A E Sin. A A D Sin. A 408. From the quadrilateral, (Fig. 67,) A B C D, to cut off the area A by the line F E, parallel to the side B C. Produce the lines 13 A and C 1) to meet at G. Take the angles at B, C, D and A, andt, as a check, take the angle G(. Measure G D and G A. We have the area of the quadrilateral = A + 13, and of the triangle G 1) A = C, and the line C 13 is given. By Sec. 404 we find the line A F or G E. For triangle G C 13: triangle F E:: G B 2: G F2 or::GC 2:GE 2 By taking the square roots we find G F and G E. 409. To divide any quadrilateral fig'ure into anzy nnmber of equal parts, i' lines dividing one of' te sidtes into equal Jarts. Let A B C I) be the required figure, (see Fig. 70,) Nwhose angles, sides, and areas are given, produce the the sides C D and B A to meet in E. As the angles at A and 11 are given, we find the angle E, and consequently the sides A E andl 1), and area B of the triangle A E D. We have the distances E A, l F, and E G, and areas 1 + A == triangle E F K, and B + 2 A = triangle E G II: and ly Sec. 29. F E. 5/ x s 13 +2 A E K - =- - and E H — = B + A GE. sin. E 410. If, in the last problem, it were required to have the sides B A and C D proportionally divided so as to give equal areas, Let B A = a, C D = n a, A E-= b, D E = c, and Y sin. E = S, and x = A F, then we have, by Sec. A (b + x) (c + n x) - from which we have s A b c + (b n + c) x + n x 2 - s n c A - bcs bn+ c X 2 + = ----- put = 2 m, and complete I n s n the square, and find the square root. A - bcs + m x - 2_: -xr 1 2 - -- /tA - bcs + m 2 x= -m + / ---- = AF and n x AF = KD. s In like manner we find the points G and H. 71H*40 CONTOURING. 411. Contouring. (Fig. 70a.) Three points forming the vertixes of a triangle, A B C, whose altitudes above the sea, or datum line, are given. Iines are chained from A to B, B to C, and C to A, and stations marked at given distances, and contour points made at every change of altitude equal to 10, 20, or 30 feet. Lines are chained down the side of the hill, and connected with checklines. The level of station a is carried around the hill, showing where the contour line intersects each chain line, to the place of beginning. Begin again at the next station, b, below, and proceed as in the above, and so to the lowest station. The contour lines will be the same as if water raised to different heights around the hill, leaving flood-line marks on the hill. The plotting is similar to triangular surveying. The shading of the hill requires practice. Final Examination. When a plan is ready for final examination, tracings are taken, of such size as to cover a sheet of letter paper, or white card-board of that size, made to fit an ordinary portfolio. In the field, the examiner puts himself in the direction of two objects, such as fences or houses, and paces the distance to the nearest fixed corner, and, by applying his scale, he can find if it is correct; by these means he will detect all omissions and errors. He will be able to put on the topography of the survey. He generally finds pacing near enough to discover errors, but where errors occur, he chains the required distances. 412. In plotting in detail we use two scales, one flat, 12 inches long, but having the same scale on both sides, such as one chain to an inch, or three chains to an inch. The other scale is 2 inches long, for plotting the offsets graduated on both sides of the index in the middle, ends not beveled. If the index is one inch from each end, we draw a line parallel to the chain line, one inch distant. If the index is two inches, we draw it two inches from the line. On each end of the small scale we have, at two chains' distance, lines marked on it to check the reading on the large scale. At each end of the chain line, perpendiculars are drawn to find the point of beginning. The large scale in position, the small one slides along its edge to the respective distances where the offset can be set off on either side of the chain line. 413. Finishing the Plans or Matp. Indian ink, made fresh, to which add a little Prussian blue, expose to the sun or heat for a short time, to increase its blackness. 1 and 2. FORESTS AND WooDs.-7azunnejonquille, composed of gum gamboge, 8 parts; Prussian blue, 3 parts; water, 8 parts. The woods have not the trees sketched as heavily as forests. 3. BRAMBLES, BRIA-RS, BRUSsIWOOD.-Same as No. 1, but lighter, by adding 4 parts of water. 4. TURF-PIT. —The water pits by Prussian blue, and the bog by sepia and blue. 5. MEAIDOWS OR PRAIRIES.-Prussian blue, 6 parts; gamboge, 2 parts; and water, 8 parts. 6. SWAMP.-In addition to dashes of water, we pass a light tint of Prussian blue. 7. CULTIVATED LAND.-Sepia,. 6 parts; carmine, 1 part; gamboge, Y part. 8. CULTIVATED LAND, BUT WET.-Same as above, except that dashes of water are marked with blue. I EVE I I.ING. 72JII41 9. 'REES.-Same as 1 and 2; sketched on, and shaded with sepia. 10. HEATII, FURZE.-Une teinte panachee, nearly green, and light carmine. Teinte panachee is where two colors are taken in two brushes, andi lai(l on carefully, coupled together. 11. MARSII.-The blue of water, with horizontal spots of grass green, or to No. 5 add 2 parts of water. 12. PASTURES.-To No. 5 add 4 parts of water. 13. VINEYARi)s.-Carmine and Prussian blue in equal parts. 14. ORCIIARDS. —Prussian 1lue and gamboge in ecqual parts. 1. UNCULTIVATE.1) LANI), FILl;:I) WITiI WEcEDs.-Same as No. 3. 1(6. FIE'LS O)R ENCLIOSUREs..-W\alled in are traced in carmine, and if boarded, in sepia. IHedges, same as for forests, to which is added 2 parts of green meadow. 17. HIABITATIONS. —A fine, pale tint of carnilne, light, for massive buildings, and heavier for house of less importance. 18. VEGI rETAB.I (;:ARDE)NS.-Each ridge or square receives a different color of carmine, sepia, galiboge —the color for woods and meadows. 19. PI)LE.ASURE GARDENS, FLO\WER (GA.\R)ENS. -Are colored with meadow color, and wood color for massive trees; the alley, or walks, are white, or gamboge with a small point of carmine. 20. The colors used are, generally, Indian Ink, Carmine, (Gamboge, Prussian Blue, Sepia, 5Minum, Vermillion, lEmerald (;reen, (..obalt Blue, Indian Yellow. 414.,ec i'//'.,. ITHE ENGLISIt AND IRt ISit ] )i(ARi)S ) \OtIKS M ETl"l)lS. DISTANtCES.., I \ _ |j S E i | ^ t - U - II S. 10.00 2.44 97.03 94 59 90.60: 99 Bencl Mark. 94.59,. 0O 10.50 8.s4 97 0. 88. 19 at Station, 900 ft.. 11.00 2 83 97.03 94 20 90.50:I 70 174 11.50 0.74 94 94 aIItk of ('reekI 12 00 2.1S s.30 9494 92.76 2.3i; I -Middle of (reek. 13 00: '.3 94 94 8 9.59 14,0( (.77 9; 36 15.00;3.57 93(;6 92 79! 10 1( 2.;9 B.M., Peg anl Stake 15.00 120 6.32 96.3(;.9004 in.Metaduw. 15 00 13; S.27 9(6.36 SS 09 15.70 13; 2 3 9!}I 93 73 This method of keeping a fiel(l-blook wa usted by the English and Irish lBoardl of Works. Size of blooks S l )I ('; itches. Many Enginieers there keplt their bookl; thus: irledl firom left to right, IBack Sights, Fore Saights, Rise, 'all, Reced 1.evcl, D)istance, I'ermanent Reduced,evels, and Remtarks. Book, 7. ' by.5 inches. 414e(. 'Colonel l Irnm, Royal nl. i, Ioy i:n Enineerl, in iis Treatis e (c Surveying, gives, from left to riglit. istances, I. S., I. S., + -, Rise, 'all, Remarks. 'l1he colutlmns Risie anl F all show( the elevation at any station ab>ov e (ia/l//u, that a-sIIined at tle begininnin. Sir John \IcNeill's plian f sfhowitg the route for the road, and a profile of the cuttinlg aln filling onII the same: the line is not less than a scale of 4 inches to 1 mile, and the vertical sections not less than 100 leet to an inch. p5: 415. Ou lt'. /,~mod. Height IZ Dist. of ElevaLeft Centre Right. Bench. B.S. Collin- F. tion. Grade. Cut. Fill. REMARK S. ation. 00 50.0 10.0 60.00 4.00 56.00 60.00. 00 e0 nch Mark, nail in root of ash tree at the 100 4.50 55.50 60.30 4.80 S.-W. corner of lThos. King's garden. 200 9.00 51.00 60.60.0 300 1 1. 50 48.50 60. 90 11.40 No 11r,. — iAt t697 came to bank of Flaskagh river, 2 feet above level of water; dlepth, 400 48.50 8.00 56.50 0.10 56.40 61.20 4.80 S feet, width, 67 feet. (eIre make a 500 0.20 5.0 16.30 61.0 5.20 sketch showing depth of water for every 600 0.30 56.20 61.80 5.0 10 feet.) 600 30 1.10 55.40 61.80 6.40 600 90 2.40 54. 10 61.80 7. 70 40 600 0.40 56.10 61.80 5.70O 80 600 0.70 55.80 61.80 6.00 697 30.90 25.60 62.10 36. 530 I3. 'M. at elevation 38.50, opposite (listance, 764 22.40 34.10 62.20 28.10 8850 feet, on the S.-W. corner of John 800 20.10 36.40 62.40 26.00 MtcCalc's residence. 850 18.00 38.50 900 38.50 6.50 45.00 5.40 39.60 62.70 2:3.10 1175 38.50 7.10 37.90 63.22 25.32 B.M., 3S.00, door-step of Mr. Jas. Roger's _ 1175 170 38.50 7.00 38.00_____1 school-house. B. M. + Back sights = 50.0 + 10. + 8. + 6.50 = 74.50 F. sights at turning points 11.50 + 18.00 + 7.00 36.50 Proof, 38. 00 LEVEILLING.72*4 72ii*43 416. Lec'elli;<,-~j P' ]Jrm ',r Obsei-,catkois. BAkROMETRICAL TMEASUREMNE'NT OF HEIGHTS. - BAILI. TAELE, A. 'lIERMMETRSIN OPEN AIRc. A 1t/ A s/ A+ /s-/+ A -i/ A 1 4.74914 87 4. 76 742 78i 4.7 S4 9 7 109 4.S01S3 1.45 4.81807 236 8 79 -4 544 110 22~9 6 851.~4.75017 'i9 842 75 i92 1 275 7 895 4 069W 40 891 76 640 2 'P21 8 939 s 120 41 941 7 7 688s 3 367 9) 983 ~ 1 72 42 990 78 735 4 412 1)50 4.8202' 7 23 48 4.77039 79 78 31. 458 1 oil i 274 44 089.- 80 830' 6 504 2 IL1 9 864,5 138 8 1 878 ))00 a 159 10: 3-77 46 18 7 82 9~ 2 8I 595 4 2 0 11 428 47 236 883 9 641. 5 4 12 479 48 2 83 84 4 79 1 9 120 687 6 291 18 531 49 334 85 066 1 32 335 14 582 50:383 86 1 IL 2 7 7 7 S 1.) 15 633 5 1 43-2 8 7 I1(iO 3 822 j9 423 16 684 52 481 88 207 4 87160 466 17 73553 530 89 254 5 912 1 510 19 837 55 628 91 348 74.81002 3 596 2-0 888 56 I 67 7 92 895 8 047 4 60 2 -938 57 726 93 442 9 092 5 683 22 I 989 58 774 94 488 130 137 6 727 28-' 4.76039 5 9 823 95 535 1 182 7 770 24 090 60 871 96)( 582 2 22'7 8 813 25l 140 61 919 97 629 3 272 9 857 26 190 62 968 98 -~675 4 317 1 70 900 2 7 241 63 4.7J8016 99 722 5:362 1 943 28 2)91 64 065 100 768 6 407 2 986 29 342 65 113 101 814 7 452 3 4.83030 30 392 66 161 102 860 8 496 4 073 31 442 67 209 103 97 9 541 5 116 32 492 68 257 104 953 140 585 6 159 33 542 69 305 105 999 1 630 7 201 34 592 70 352 106 4.80045 2 675 8 244 35 642 71 400 107 091 3 719 9 287 36 4.76692 72 4.78449 108 4.80137 144 763 180 329 N7 o rE~. t= temperature of the air at the lower station; t' — that at the upper station; A — correction for temperature, dependent on t ~ tC. And for Tab~le 1B.:r temperature of mnercury at the lower station; r' - that at the upper station; 11 — correction clue to the~ mercury dePendent on r - r'; C correction for the latitude of the place; 1) latitude.; R — height of barometer at lower station; R' - height of barometer at upper station. For Table B3. see next page. '7211*44 LEVELI.ING. BAROMETRICAL MEASUREMENT OF IHEIGIHTS. TA:BLE B. 417. ATTACED THERMOME'TERS. r - I9 0 1 2, 4 10 6 7 8 9 10 1i 12 13 14 15 16 17 s1 19 B 0.00000 04 09 13 17 I....).. 22 26 30 35 39 43 48 52 56 0.00061 65. 69 74 78 0.00083 r1 t1 21 23 24 26 '27 28 29 30 31 32 33 34 36 '37 S, 38 39 B 0.00087; 91 96 100 104 0. 0010'9 13 17 22 26 30 35 39 43 48 52 56; 1 65001 0. 00169 40 41 42 43 44 46 47 48 49 50 51 52 53 54., 56 57 58 59 78 82 87 0.00200 04 08 13 17 21 26 30 34.39 43 47 52 0.00256; Lat. I t -20 -2 5 30 35 40 45 i50 -6,60 65 70 75 80 85 90 I C 0.00117 115 110 100 090 07.S 058 040 020 0.00000 9. 99980 62 42 25 10 9. 99900 890 85 9. 499883 418. Extamiple fJomt/ Coloel Froime's ' R IONA M(; t.I.'lli(, SURVEYING. SURVE INC;. p. 11. I I 0. - R ~ elllRemarks. Stations. A 1) F Bar. 3. High Water Mark 61 58I - 30.405 i.004 30.409 l'arade, Brompton Iarracks,.. 60~ 57 30.276.002i 30.278 1 16.6( t + t'. 58 + 57 - 115. 1From Table A -= 4.80458 r- -r': --- 61 - - 60 = 1. Lat. 51' 24' Log. of R -l Iog. 30.409 Log. of R' - l,og. 30.278 + 1 00004 l og. 1) -- 3.26245 A =- 4.80458 1. — 0.00004 - n 9. 99974 -- n 1.48300 = —p 1.48117 -- 1) --- 0.00183:-P - C =- 9.99974 2.06677 --- 116.;6: — altitude in feet, which was fountd by the spirit level to be 115 feet. These Tables are from the Smlithsonian Meteoroloical and Physical l'al)les, piublished in W\ashinlt,toll, 18,S. In 1844, in Ottawua, Canada, Mr:s. Icl)erImott, in my absence, kept a rcord of numerous observations of the state of thermometer and mountailn baromeler, for Sir William Logan, lrovincial (;eologist, then making a tour of the valley of the River Ottawa and( its tributaries. (See his (eolgical Repoits.) The observations were made at the hours of 7, 9, noon, 3, and( 6, to be used for the lower Station, at Montreal. Ll NG. 72n*45 41? To find tie A41lutite of one Stitdiou zi (lor' (11o0hel-, fr-ol thL' Tein;JL'ratnre of Ihe Roiling, of' [Voter. Thi- ethod i.- not so relialble as that by barometrical olbseirvations, although Colonel Sykes, in Australia, has~- found altitudes albove the se-a agTree Withi those found by trianigulation closer than he had anticipated. There are very valuable tables in the Smiths;onian Institute's Meteorologrical andl Phvsical T1ables-iablels XXIX, XXX, and XXVI -for finding- the altitudes by this method. Ta ke any tin pot and lay a piece of board a'cross the top, heaving groove to receiv~e the thermometer, and a button or slide to keep it steady, at about two inichesi from the bottom. Take several olbservatlons, carefully noting them, and at the same, time the temlperatinre of the surrounding air. Use Falhrenlheit':s thermomoter'. TABLE A T IN t. to 86 ~ 87 88. 89 94 96 97 98 99 200 91 93 94 96 97 98 99 100 11 12 13 24 17 048.423.809) 18.195.592.996 19.407.825 20.2501.685 21.126.57 6 22.033.498.971 23.450.943 24.442.949 25.465.990 26. 523 27.066 27.618 28. 180 28. 751 29. 331 29. 922 30. 522 31. 194.00 14. 548 13.97 7.408 12.843.280 11.719.161 10. 606 10.053 9.5020 8.953 8.407 7.864 7. 324 6.786 6.250 5.716 5.185 4.657 4.131 3.607 3.085 2.566 2.049 1.534 1.021.509 0.507 1.013 E t. 420 33 7 8 9 50 3 4 455 6 7 8 9 60 61..4 1.00 12 1.01 21 2 5 2 7 29 231 35 37 429 50 52) 544 56 58 1.06 V2 3Z. 7 0 71q 2.) 3 4 75 6) 7j 8 80 3 4 85 6 7 8 9 90 91 1.062 64 66 691 71 73 75 81 1.083 8 5 87 89 91 94 96 98 1.100 102) 104 106 108 110 112 114 116 117 121 123 i I 0) C C 0 0 -C p H - CO C b ' 0 C C 5) o C C o a, H 5) 00 C Hc 0r H H a, C Oh 0 5) Exrample.-Boiling point, upper station, 2_09', lower, 2020; temperature of the air at upper station, 7'2', lower, 84', mean temperature, 78'. From Table A, 2090. Alt., 1534 ft. 202. 115185 Approximate height, 3651 Mean temperature, 78'. Multiplier from Table B, 1096 Product, 4001 ft. Where the degrees are taken to tenths, then we interpolate. 72ni*46 I)IVISION OF LANI). 419a.-Confinuled front Sec. 410. Zliring, o;;e siZde, A B, and I/e a(t'acent angles, —o fintd tie area —let the triangle A B C (Fig. 68,) be the triangle; the side A B s, and the angles'A and B are given, also the angle C. S. Sin. A S. Sin. 13 Sin. C: S:: sin. A: I C ----, and( A C ---- Sin. C Sin. C S. Sin. A S2. Sin. A. Sin. B By Sec. 29. S. — --. Sin. 1B ---- area. 2 Sin. C 2 Sin. C 420. From a point, P', wilhiin a iven figiure, to drawc a lizt cuit/,'t; o anl, pa25rt of it by the lill F G. —Let the figure I G B1 A 1 - the required area. (See Fig. 69.) Let the A B C 1) E F the tract be plotted on a scale of ten feet to an inch, from which we can find the position of the required line very nearly, with reference to the points B and E'. Run the assumed line, A S, throughi P, finding the distances A P -- in and P' S == n, also the angles I' T A, P S G, an(t that the tract A S B3 A T is too great, by the area d. IIence the true line, T P (, must be such that the triangle 1 S ( - A T = d. Assume the angle S ' G - ', then we find the angles T and (C, and by Sec. 409 we find the areas of the triangles 1P S ( and P A F. If the difference is not -- d, agai!, calculate the sides P G and P T. 420a. From t ic lr;anle /A C /o cult ofi/ a 'gi;'et a-rea (say onl-tiyird,) Iy a line drawntz t/hrozhe the g'itz tpoit, 9. (Fig.;9a.) Through D draw th- line I) (; Iarallel to A C. Now all the angles at A, B, and C are given, and the line ) G is given to find the point I or I-, through which, and the given point D, the line I D H will cut off the triangle A 1- I == to one-third the area of the triangle A 13 C. (Fig. 69a.) Make A F one-third of A C, then the triangle A B IF= one-third of the triangle A B1 C, which is to be to triangle A I H. The triangle A H I -A II x A I x 2 Nat. Sin. angle A. The triangle A B F -- A 3 x A F x ' Nat. Sin. A. A B x A F A II x A I = A B x A F, and A I - -- and as the triangles A II I-I G D and II A I are similar. A 1, x A F TI G: G ):: II A: A: A I II: -- II A II CG: G D: I A2: A 13 x A F, and by Euclid, 6-16, ( I) x I-I A2 H G x A I x A F = (II A - A (). A F. A 1 = II A. A F. A B - A G. A F. A B AB.A. A BA A B. AF and -I A2 - --. I A - - -. A;. Let P -- I) I) (; ) Now we have I' and A G given, to find A 11 or A I, A' H2 P x H A - P x A G H A2 = P x II A- - P x AG. Complete the square II A2 - P x II A + --- -- - P x A G. 4 4 If A -— P - - A G x IP Whence 2 (4 h A 11 =2 P + ( 12 - A G x I') 2,, when I) is inside the triangle. A H = J P + ( I'P 2 -- A G x P)) 14, when d/ is outside. ADDITIONAL. -1 2 i i 447 421. Throug!i the point D to draw the line G D E so that the triangle B G iE will be the least lpossib~le. Through I) draw H- D I parallel to B C, make 1 111=1 H G, and draw G D Ti, which is the required line. Fig. 69a. Geadedlical.7Uriispi-m(IcelC, J. 72, P. Chiief justice Caton's opinion adds the following in support cf!>iablishied lines and moainments: Dreer z.'. Carskaddan, 4S P'enn. State, 28. Bartlett v. Hubert, 21 Texas, S. Thomnas -7. P~atten, 13 Maine, 329. After B'ailey v. Chamiblin, 2-0 Indiana, 313, add -Jones c'. ]TRamble, 1 9 W\isconsin, 429. Francoise v. Mlaloney, Illinois, April Term, 1871. \Vithbamn v. Cutts, 4 Greanleaf R., IMaine, 9. 309Me. After E'nglish R'eports, 42, p. 307, add Knowlton S.nSmith, 36 Missouri, 620. Jorda-n v. D)eaton, 23 Arkansas, 704. United States Digest, Vol. 27-where an owner points out a b1oundJary, and allows improvemrents to be made according to it, cannot be altered wvhen found incorrect by a survey,. Far ayin OltGr's Lxample after l). 72. Let radius 2000 fe-et; chord, 200; thenr tangential angle -= 2' 51' 57"; versed sine at theIi middle, 2,503 feet. If the ground does not admit of lavin, off long chord of 00 feet, maV _ __ 200 half feet =100, then for radius 4000 find the versed sine 1,231 and the tang. angle == %' 2557". If we use the chord of 200 feet, half feet, or links, then wve are to take the ordinates in Table C as feet, half feet, or links. CJanals. The Illinois.- and Michig~an locks are 128 feet longl, iS feet wvide, and 6 feet deep, bottom 36, surface 60, tow-path 15), berm. 7, tow-path. nbove water, 3 feet. The New York CJane/s.-Erie Canal,:363 mniles long, when first built, 40 feet at top, 28 at bottom, 4 feet deep, 84 locks, each 90xl15, lockag'e 6SS, 8 large feeders, 18 acqueducts. The acqueduct across the Mo1hawk. is 1188 feet in length. The Pennsylvania Canal-top 40, bottom 28, (1e1th 4,!()locks 0xI5, and some, 90x17. The Ohio and Erie Canal-40 feet at top, 4 feet deep. Rideau Canal, in Canada-129 '2 miles long, 53 locks, each 134x33. \Velland Canal, in Canada-locks, large enough to admit large vessels. It is nuw in progress of widening and deepening, so as to admit of the largest vessels that may sail on the lakes,:, and to correspond with the canals and lakes at Lachine, and on the River St. La~vwrence. 72i-i *48 C 0 R R E' C II ONS. CORRECTIONS. Page 43, example 2, read the polyg~on a h. C d e f 'g h, Fig(-3. 38. Page 72B53, soda. No 0 read soda No 0. 72B55, 4th line, read feispathic. 72B111, after the 8th line ins;ert Sir Williamn B'land mak-es it as 17 to 13, egg-shaped. 72s, hegin at 8th linie from 1)ottomn andl put mean lbase ==50 ~ 40: 90 50 4500 4100 1)ifference, square feet, 400 72'r. in 4th equation from hottomi readl sol1(llty s ~(A x at + 3'a -(d '3 1.) -( 72w)N, in 3(1 equ~ation from the bottomi read Because - 72H5, at 16th line from bottomi, for r S - b A, read r S ~ b Q. 72ui*10, at 14th fromt bottomn, for 1)rodlLct of the adjacent parts-, read1( product of tan of adjacent p~arts. 7211*24, Sec. 388, for apparent, read mean. 7211*30, by the Heliostat, insert after Heliostat Fig. 11. 72R5, under 82', opposite 48, for 2921 put 9921. 104, undler 2, opposite 12, make it 1.9300, and opposite 13 make it 1.9199. 110, under 2, opposite 12, p~ut 1.8999. 113, uinder 9 put 2.-9722. 264, after the words Froin t 1/ aboz'e we /hare insert Ri 'Y 2 0 0.00000647~ 0.000 ~ in metres in terms of its radius. Di ) '~~2 V ) ~~0.00000648 in terms of English feet. 0.000309 + 1 VT 0.00000162 2 0.00007726 + ~in terms of its hydraulic mean depthi. O-OW077-06 r 1 rt n1A, n;r I R I a vy1 I I(, "m 0 - ki, RI* _0 PI ro-) W -j a0 cD,5 — r, CP~ -1 00.~ Page Z._ ~I r- --- I M~~~~~~ Cli b 1 r F <-1 i< -P \ I "rn bi JOIr N 0 (i (@d)~~~~~~~~~~~~~~~~~~~~e T s"00 d co C LL~~~~~~~~~~c N iic Cto LL~~~~~~1 /^\^ \ \0. / ^ ^\ \ ^ —/ 4 U' "1* 1* H \0 IL; I \ \\ I! <D oo~ ~ ~~~~~~~//^ N d~~~~~~~~~~~~~~~~C ric"c / Ir/ ^ ii/ / A/ I I /;jl tZ \ ///n \ iJ~~~1 H! "* J / i < > a a *. \1L, Cb O-u d^ l. j i ^~ ^~~~~~~~ i^ i~~~~~~~~~~~ic~~~~~~~~~L P &Le 5. o E 5~o Fie, o D C. 0 F i.6. N f E -A -- -- I q EA + r Pa 5.e 6. 0 I r Fi. 61 6 Sprinwell @ 74 1I27S Irl a ~_ _~~~t ~.._. ~ ~ ~ ~ - '~ -, —_,_.m E-r —"R ' — R --- - __ —eE K 6 FT- D EI P _ 70 1004 *.-.97o V ^^ Ilr: i i d ~I ~ ' i / i I i: r ~ I: 1 ~i i I I $a07 480 42.o I o. 97 THoS LY N KEY \5 L 4o JAS. RoCjE RS is. SCH-OOL HouSE, 12 \, '2 5 It 4:1A - 4 J1 1,797i it A ^W7\ / = dl LLK.PM- 1 - W6.; -4 -0, 14 2 fl- r.1 0 N S o o ~o '. -- o o o - ',. C. / 2 \ Fi. 64 D L, N 4. t L ^A B i i i I ^r F Pa6e 7. F.B.^ ^< A \ Fi9.67 'A C^B X —AB,^^\^\. \ 66 /. --- —r-/ c / /B \ A, Fi.70. Pa.&e 8. 1 ii ii i' 'i Ii II ji ii 1 i j r 1 i I EA E I!. t&. -- P. L. < 3. Fi;6 70.1 P. 72. B.:l P. I, 2,, _ ZS _L ____2; r.2 -i 2~, '.. — I I I'/, 30 - -27 3 — I Pi,. 74., 40 -I3.30. $-o ---— 33. 3 _ /0I s o I so i. I 1 7.6 1?I ^.0 7 to 1. 78 Pate 9. Fi80o 3a oi Jo 4tA bys4Ov5C &~~ zay<3A04i Wea~cA I ^ JL tI htCs SCkeV =- - *h< Aim ' * G\^U~ O^pVWAD*<^~ l-OtA^ O^V<A^ 1 --- --- ^~u 65A3 NtJ^'^" ^~v^~ 83. F DI Fi,. 83 a. I Ra - k I 80 -- ~-r — ~~ --- —--—. ---- -— ~I --- —---- ~ ~ -I ~' II II ll I I I I I ll~~~~~ll _-l I I Page 11. SYDENHAM ENI-AN D 11111011 - - - - I i Ii j i i i I / j / i i i i/: i i I i;: 1 I i; ~ i I I 1 j j: I i i j I i; ~ i I i j I I i i ~ '; 1:j j I I j / i i ii ij i Pa.e iZ. s 1 TUNNE 1. FOR oNE. TrtACK - 83 I Fi6. 83 ji 1) II I I i H oosAic TU N N E L Fig. 83c. IC Page f B > *A, 'D Fit. 88 B FiS 87 lb7 Pag e 14. Fit. o9 It I.) FiS.?I I / I II H IK I=- /, t I I - I,I i ^t N. rI I.- tE I... -J_ i6. 96. ) C R D P.. E F i-i"' 4 "= ' - ^*5:;~~~~~~~~~~~~~~~~~~~~~~~"'"....:. t^ ^: tIjC:!~!'*i I... I z ~ ~~~ ~ ~~~ ~ ~~~ ~ ~~~ ~ ~~~ ~ ~~~ ~ ~~~ ~ ~~~ ~ ~~~ ~ ~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ^ T ' iili,! ^1:^^~~~~~~~~~~~~~~~~~i rIII* I j i S( I i "'!;- l " i <i'. 5 ~ ~ ~ ~ ' -:1.%r~:i l o? J ^1~~~ N'iic ~' E^' i^~ r' I,I I P^^l~\ Lt I ' I "^ ^^'iN Cu 'H! ~ ~~~~~ ': j III~~ ~ - I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I _ B I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/ H I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I *1 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,~ ~~~ ~~~~~~~~~~~~~~ i i II $'ii *, II I I * III.- I i ~I I ~j~II I i TABLE A. NATURAL SINE. 72i* 00 10 20 30 40 50 60 70 80 0 000 0006174 46034 90052 3406 9 76 087 16 104 58 121 87 139 17 60 1 29 714035 1 9 63 070 05 45 82 122 16 46 59 2 58 018 03 48 92 34 74 105 11 4b 75 58 3 87 32 77 053 21 63 088 03 40 74140 04 57 4 001 16 62 036 06 50 92 31 69 123 02 33 56 5 45 91 35 79 071 21 60 97 31 61 56 6 75")019 20 64 054 08 50 89 106 26 60 90 5 7 002 04 49 93 37 719089 18 55 89 141 19 53 8 33 78 037 23 66 07-208 47 84 124 18 48562 9 62 020 07 52 95 37 76 107 13 47 77 51 10 91 36 81 055 24 66 090 05 42 76 142_05 50 AiO'nQ ~ I ~ ~ I 1 2 2 2 2 2 2' 21 21 31 3-'I 38 39 40 342 43 44 45 47 48 49 52 53 54 65.2 49 3 78 4 004 07 5 36 6 6~5 7 95 8 005 24 9 53 0 82 1 006 11 2 40 3 69 4 98 5 007 27 3 56'1 7 85 3 008 14 D 44 ) 73( 16009 02 1 31 I 60( 90 i 010 1 8 76C (011 05 34 64 0 012 22 51 80 0 013 09 67 0 96 014 25 54 83 015 13 42 71 0 016 00 9 021 2 51 8 44 61, 91 023 2 8,1 024 1 025 01 )26 18E 47 7 6 )27 05 34 63 92 128 2 1 50 7 9 '29 08 38 07 96 30 25 54 4 39 3 68 2 97, 1 039 26 0 8. 3 040 18 3 42 71 31074-100 5 29 t 69 1 88 11042 1 7 75 (043 04 33 62' 91.044 20 49 78( 045 07.36 65( 94 046 23 53 047 11 40 69 0 98 8 ' 056 1' 6 I 057 2, 058 14 44 73 059 09 31 60 89 060 18 47 7IT6 061 05 34 6 3 92 )62 2 1 50 7 9 )63 08 3 7 66 95 164 24 53 821 165 1 1 40 D V1D 2 073 24 1 53 3 82 3 074 1 1 ~ 40 6 9 1 98 i 075 27 56 85~ 076 14 43 724 '077 01 30 59 88 078 1 7 46 75 079 04 3 3 62( 9 1 080 2 49 780 081 07 3 6 650 94 082 23 52 81 1'.6 6 9' 091 2 54 092 01 3, 91 51 69 3~ 8c )96 14 42 71 29 58 87 -498 16 45 74 )99 03 329 61 99 0 00 19 3 108 0 2 2 1 5 0 8 3 4' I 7: 3 110 0:, 5 3 81. 1112 0~ 3 4 9 1 113 2C * 49 7 8 114 07 3 6 65 94 115 23 5 2 80 116 09 38 6 7 96 117 25 5 4 I Izo u 0 33 9 62 8 91 7 126 20 6 49 5 78 3 127 06 2 35 1 64 11 93 3128 22 80 1129 08 37 66 95 130 24 4 53 81 131 10 39 68 97. 132 26 54 831 133 12 41 7C 99 1 134 27 566 85 1 92 143 2C 49 78 144 07 36 64 93 80 146 08 3 7 66 95 147 23 62 81 148 10 38 67 96 149 25' 54 82:150 11, 40, 6914 97j 561 261 55 1 84 i 52 12 1 [ 4 II4: 4 ' 4 44 '4 4 4 4 4 3~ 3' 34 3,1 3q 31 2i 23 27.6..5r ~9.8 7 6 5 3 2 0 9 -8 7 I 5 -I 8I 31 12 41 70 99 12 28 57 86 1 3 16 45 048 27 566 85 049 14 43 72 050 01 30 59 88 I I 6U 98 066 27 56 85 067 14 43 73 368 02 31 I I I - - I - -1 - 083 10 39 68 97 084 26 55 84 085 131 421 71 48 77 101 06 35 64 92 102 21 50 79 103 08 83 118 12 40 694 98 119 27 56 85l 120 14 43 I I Z 13b 14 43 72 136 O00 29 *85 87 137 16 I 41 7C 99~ 153 27 56 85 154 14 42 71 155 00 I I I - 14 13 12 1 1 10 8 7 6 5. Sb 29 7 051 17 60108-6 00 37 71 138 02 294 67 58 034 03 46 891 29 66 121 00 31 57 3 68 87 32 76 069 18j 58 95 29 60 86 2 69 017 16 61 052 05 47J 87 104 24 58 89 156 15 1 60 45 90 34 761087 16 53 87 139 17 43 0 NTRLCOSINE. q 72* NATURAL SINE. TABLE A. 9 — 0 | 100 111 12 13" 140 150 16~ 17~, 0156 43 173 65190 81 207 91 224 95 24 25882276 64 292 3760 1 72 93 191 09 208 20225 23 242 20259 10 92 65659 2157 01174 22 38 48 62 49 38 276 20 93 58 3 30 61 67 77 80 77 66 48 293 21 57 4 68 79 951209 05 226 08 243 05 94 76 4856 6 87 176 08192 24 83 87 33 260 22 277 04 76 66 6158 16 6 37 2 62 65- 62 60 31 294 04 54 7 45 66 81 90 93 90 79 69 32 53 8 73 94 193 09210 19 227 22244 18 261 07 87 6052 91659 02 176 23 38 47 50 46 35 278 16 8751 10 31 61 66 76 78 74 63 43 295 16 50 11 69 80 95 211 04228 07245 03 91 71 43 49 12 88177 08 19423 82 35 31262 19 99 71 48 13 160 17 37 62 61 63 9 47 279 27 99 47 14 46 66 81 89 92 7 7 65296 26 46 15 74 94195 09 212 18229 20246 15 263 03 83 64 46 16 161 03178 23 388 46 48 44 31 280 11 82 44 17 82 62 66 75 77 72 69 39 297 10 43 18 60 80 95 213 03 280 05 247 00 87 67 37 42 19 891179 09 196 23 31 33 28 264 15 95 65 41 20162 18 37 2 60 62 56 43 281 23 93 40 21 -47- 66 80 88 90 84 71 602982139 22 75 95 197 09 214 17 231 18 248 13 265 00 78 49 38 23163 04180 23 37 45 46 41 28 282 06 76 37 24 83 52 66 74 75 69 66 34 299 04 36 26 61 81 94215 02 232 03 97 84 62 3235 26 90181 09 198 28 30 81 249 2266 12 90 60 34 27 164 19 38 61 69 60 64 40 2838 18 87 33 28 47 66 80 87 88 82 68 46300 1532 29 76 95 199 08 216 16 283 16 250 10 96 74 43 31 30566 05182 24 37 44 45 38 267 24 284 02 71 30 81 83 62 65 72 7 6 6 52 29 9829 32 62 81 94217 01 234 01 94 80 56 301 2628 33 91 183 09 200 22 29 29 261 22 268 08 86 64 27 84166 20 38 51 68 8 61 36 285 13 8226 8 48 67 79 86 86 79 64 41 302 09 2 86 77 95201 08 218 14 235 1422 07 92 69 3724 87 167 061184 24 86 43 42 36 269 20 97 66 23 88 34 52 65 71 71 63 48 286 25 92 22 89 63 81 93 99 99 91 76 62 303 20 21 40 92 185 09 202 22 219 28 236 27263 20 270 04 80 4820 41 168 20 38 50 66 56 48 82287 08 76 19 42' 49 67 79 85 84 76 60 36 304 03 18 43 78 96 203 07 220 13287 12254 04 88 64 3117 44 169 06 186 24 36 41 40 32 271 16 92 69 16 45 85 62 64 70 69 60 44 288 20 8616 4 f;4 81 93 98 97 88 72 4730 1414 47 92 187 10204 21 221 26238 25 265 16 272 00 76 42 13 481170 21 38 60 65 53 46 28 289 03 7012 49 60 67 78 83 82 73 66 81 9711 60 78 95206 07 222 12 239 10 256 01 84 9 06 26 10 i 171 07 188 24 35 40 88 -29 273 12 87 63 9 62 86 62 63 68 66 67 40 290 16 80 8 53 64 81 92 97 95 86 68 42 307 08 7 64 93 189 10 206 20 223 25 240 238267 18 96 70 86 6 66 172 22 88 49 68 61 41 274 24 98 68 6 66 60 67 77 82 79 70 52 291 26 91 657 79 96 207 06 224 10 241 08 98 80 64 308 19 8 658t73 08 190 24 84 8 86258 26 276 08 82 46 2 69 36 62 63 67 64 64 86 292 09 74 1 60 65 81 91 96 92 82 64 87 3809 02 0 O — I 7FT80 ~ 750 7- 78~ 7, NATURAL COSINE. I I TABLE A. NATURAL SINE. 72x* 1 180 190 200 210 220 280 240 250 260 f 0309 02 325 678342 02 358 37 374 61 390 73 406 74 422 62 438 37 60 1 29 84 29 64 888391 00 407 00 88 63 59 2 67 326 12 67 91 375 15 27 27 423 15 8968 3 85 89 848359 18 42 53 53 41 439 1657 4 310 12 67 343 11 45 69 80 80 67 4256 6 40 94 39 73 956392 07 408_06 94 6855 6 7 8 9 10 11 12 13 14 15 17 181 19 20 11 22 23 24 26 27 28 29 30 31 32 33 34 186 37 38 39 40 68 95 311 23 61 78 312 06 33 61 89 813 16 44 72 99 314 27 64 82 315 10 37 65 913 316 20 48 76 317 03 30 58 86 318 13 41 68 96 319 24 61 79 320 06 327 22 49 77 328 04 32 69 87 329 14 42 69 97 330 24 61 79 331 06 34 61 89 332 16 44 71 98 333 26 53 81 334 08 36 63 90 335 18 45 78 336 00 27 56 fit 93 344 21 48 76 345 03 8(1 67 84 346 12 39 66 94 347 21 48 75 348 03 80 57 84 349 12 39 66 93 350 21 48 75 351 02 30 57 84 352 11 39 66 93 i II I I I I I i I I I I Mu1) uu 27 54 81 361 08 35 62 90 362 17 44 71 98 363 25 62 79 364 06 34 61 88 865 15 42 69 96 366 23 50 77 367 04 31 58 85 368 12 39 67 94 369 21 3(0i lZ 49 76 377 03 30 57 84 378 11 38 65 92 379 19 46 73 99 380 26 53 80 381 07 34 61 88 382 15 41 68 96 383 22 49 76 384 03 30 66 83 385 10 37 64 60 87 398 14 41 67 94 394 21 48 74 395 01 28 55 81 396 08 35 61 88 397 15 41 68 95 398 22 48 75 899 02 28 55 82 400 08 85 62 88 401 15 421 60 86 409 18 39 66 92 410 19 45 72 98 411 25 61 78 412 04 31 67 84 113 10 37 63 90 414 16 43 69 96 416 22 49 75 416 02 28 65 81 417 07 34 46 73 99 425 25 62 78 426 04 31 57 83 427 09 36 62 88 428 15 41 67 94 429 20 46 72 99 430 25 51 77 431 04 30 56 82 432 09 36 61 87 433 13 I i I I I I I 440 2C 46 72 9E 441 24 51 77 442 03 2q, 55 81 443 07 33 59 85 444 11 37 64 90 445 16 42 68 94 446 20 4C 72 98 447 24 60 76 448 02 28 54 80 of 53 62 51 60 49 48 47 46 46 44 43 42 41 40 39 38 37 36 36 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 47 48 49 50 C,1 62 63 64 65 I 84 61 89 321 16 44 71 99 322O 27 54 82 323 09 87 64 92 324 19 82 337 iC 37 64 92 338 19 46 74 839 01 29 56 83 340 11 88 66 363 20 47 75 854 02 29 66 84 855 11 38 65 92 356 19 47 74 367 01 48 76 370 02 29 66 83 371 10 37 64 91 372 18 45 72 99 373 26 64 91 386 17 44 7i 98 387 25 62 78 388 05 32 69 86 389 12 39 95 402 21 48 76 403 01 28 55 81 404 08 34 61 88 406 14 41 60 87 418 13 40 66 92 419 19 45 72 98 420 24 61 77 421 04 30 40 66 92 434 18 45 71 97 435 23 49 75 436 02 28 541 80 437 06 44~ 00 32 68 84 450 10 36 62 88 451 14 40 66 92 462 18 43 69 ll 18 17 16 16 14 13 12 11 10 9 8 66 47 93 28 53 66 67 964 67 74 341 20 66 80 93 94 83 69 463 21 3 68325 02 47 82 874 07 390 20406 21 422 09 86 47 2 69 29 76 358 10 34 46 47 66 438 11 73 1 60 67342 02 37 61 73 74 62 87 99 0 710 ' 70f 680 680 87W 680 660 64 680 NATURAL COSINE. 72L* NATURAL SINE. TABLE A. 27o0 280 290 300 310 32 33 340~ 50 1 0458 994(i9 47484 81500 00516 04529 92544 64559 19573 5860 1454 25 73485 06 25 29 530 17 88 43 8159 2 51 99 32 50 64 41 545 13 68574 0558 3 77470 24 57 76 79 66 37 92 2957 4455 03 50 83501 01 516 04 91 61560 16 5356 5 29 76 486 08 26 28531 15 86 40 77 55 6 54 471 01 34 51 53 40 546 10 64 575 0154 7 80 27 59 76 78 65 35 88 2453 8456 06 53 84502 01 517 03 89 59561 12 4852 9 32 78487 10 27 28532 14 83 36 7251 10 58 472 04 35 52 53 38 547 08 60 96 50 ii 84 29 61 77 78 63 32 84 576 19 49 12457 10 55 86503 02518 03 88 56562 08 4348 13 36 81488 11 27 28533 12 81 32 6747 14 62473 06 37 52 52 37 548 05 56 9146 15 87 32 62 77 77 61 29 80577 15145 __ f I 16458 13 17 39 18 65 19 91 20 459 17 21 42 22 68 23 94 24460 20 25 46 26 72 27 97 28461 23 29 49 30 75 31462 01 32 26 33 52 34 78 35463 04 36 30 37 55 38 81 39464 07 40 33 41 58 42 84 43466 10 44 36 46 61 46 87 471466 13 48 39 49 64 50 90 51467 16 52 42 53 67 54 93 55468 19 66 44 57 70 58 96 59469 21 60 47,no 85 8~,474 09 34 6C 86 475 11 37 62: 88 476 14 39 65 90 477 16 41 67 93 478 18 44 69 95 479 20 46 71 97 480 22 48 73 99 481 24 50 75 482 01 26 52 77 483 03 28 54 79 484 05 80 56 81 610 i 88:489 13 38 64 89 3490 14 40 65 90 491 16 41 66; 92 )492 17 42 68 93 493 18 44 69 94 494 19 45 70 95 495 21 46 71 96 496 22 47 72 97 497 23 48 73 98 498 24 49 74 99t 499 24 50 75 500 00 600 504 03 28 53 79 505 03 28 53 78 506 03 28 54 79 507 04 29 54 79 508 04 29 54 79 509 04 29 64 79 510 04 29 54 79 511 04 29 54 79 512 04 29 54 79 513 04 29 54 79 514 04 29 54 79 515 04 690~ 519 02 27 52 77 520 02 26 51 76 521 01 26 51 75 522 00 25 60 75 523 00 24 49 74 99 524 23 48 73 98 525 22 47 72 97 526 21 46 71 96 527 20 45 70 94 528 19 44 69 93 529 18 43 67 92 680 86 534 11 35 60 84 535 09 34 58 83 536 07 32 56 81 537 05 30 54 79 538 04 28 53 77 539 02 26 51 75 540 00 24 49 73 97 541 22 46 71 95 542 20 44 69 93 543 17 42 66 91 544 15 40 64 670 54 78 J549 02 27 51 75 550 00 24 48 72 97 551 21 45 60 94 552 18 42 66 91 553 15 39 63 88 554 12 36 60 84 555 09 33 57 81 556 05 30 54 78 557 02 26 50 75 99 558 23 47 71 95 559 19 660 563 05 38 29 62 53 86 77578 10 564 01 33 25 57 49 81 73 579 04 97 28 5665 21 652 45 76 69 99 93 580 23 '566 17 47 41 70 65 94 89581 18 567 13 41 36 65 60 89 84 582 12 568 08 36 32 60 66 83 80683 07 569 04 31 28 64 52 78 76584 01 570 00 25 24 49 47 72 71 96 95585 19 571 19 43 43 67 67 90 91 586 14 572 15 37 38 61 62 84 86587 08 573 10 31 34 65 68 79 66~ 64~ 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -r I m. M NATURAL COSINE. I TABLE A. NATURAL SINE. 72M* Ii1 860 1 370 1 380 1 390 410 1 420' 430 i 440 i - 1 - - i 0 1 2 8 4 6 6 7 8 9 10 Ti 12 13 14 15 16 1 7 18 19 20 21 22 23 24 25 26 27 28 29 30 31 82 34 35 36 37 38 39 40 41 42 43 44 46 47 48 49 60 62 63 64 65 6'6 57 68 691 60 -7 - 587 79 688 02 26 49 73 96 589 2C 43 67 90 590 14 87 61 84 591 08 31 54 78 592 01 25 48 72 95 593 18 42 65 89 594 12 36 69 82 595 06 29 62 76 99 596 22 46 69 93 597 16 39 63 86 598 09 32 56 79 599 02 26 49 72 95 600 19 42 66 89 601 12 86 68 82 680 6ul 82 602 06 28 61 74 98 603 21 44 67 90 604 14 37 60 83 605 06 29 63 76 99 606 22 45 68 91 607 14 38 61 84 608 07 30 53 9.9 609 22 45 68 91 610 15 38 61 84 611 07 30 58 76 99 612 22 316 66 89 316 12 85 68 81 517 04 26 49 72 95 318 18 41 64 87 519 09 32 65 78 320 01 24 46 69 92 321 15 38 60 83 322 06 29 61 74 97 328 20 42 65 88 324 11 33 66 79 325 02 24 47 70 92 s26 15 38 60 83 327 06 129 32 66 77 180 00 22 46 68 90 631 18 85 68 81) 632 03 25 48 71 93 633 16 38 61 83 184 06 28 61 73 96 185 18 40 68 85 636 08 30 63 75 98 137 20 42 65 87 638 10 82 54 77 99 639 22 44 66 89 140 11 33 56 78 141 00 23 45 67 90 542 12 34 56 79 500 142 79 643 01 23 46 68 9( 644 12 35 6 7 79 645 01 24 46 68 90 646 12 35 57 79 647 01 23 46 68 90 148 12 34 56 78 649 01 23 45 67 89 650 11 33 65 77 651 00 22 44 66 88 652 10 82 64 76 98 658 20 42 64 86 654 08 30 62 74 96 665 18 40 62 84 156 06 4V 656 06 28 60 72 94 657 16 88 69 81 658 03 25 47 69 91 659 18 8.5 66 78 660 00 22 44 66 88 661 10 31 63 75 97 662 18 40 62 84 663 06 27 49 71 93 664 14 86 68 80 665 01 23 45 66 88 666 10 32 63 75 97 667 18 40 62 83 668 05 27 48 70 91 669 13 480 669 18 35 66 78 99 670 21 43 64 86 671 07 29 51 72 94 672 16 87 80 678 01 28 44 66 87 674 09 30 62 95 675 16 38 69 80 676 02 23 45 66 88 677 09 80 62 73 678 16 37 69 80 679 01 23 44 65 87 680 08 29 61 72 93 681 15 36 67 79 682 00 470 682 00 21 42 64 85 688 06 27 49 70 91 684 12 34 65 76 97 685 18:3 q 61 82 686 03 24 45 66 88 687 09 80 61 72 93 688 14 85 67 78 99 689 20 41 6'~ 83 690 04 25 46 67 88 691 09 51 72 93 692 14 85 66 77 98 698 19 40 61 82 694 03 24 45 6f 460 694 66 87 696 08 29 49 70 91 696 12 33 64 96 697 17 37 68 79 698 00 21 42 62 83 699 04 25 46 66 87 700 08 29 49 70 91 701 12 82 58 74 95 86 67 77 98 708 19 89 60 81 704 0 1 60 69 68 67 56 65 53 63L 52 61 5 0 49 48 47 46 46 43 42 41 40 39 38 37 36 36 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 16 I 4 j 68 91 618 14 37 60 83 614 06 29 51 74 97 615 20 43 66 200,22 43 63 84 705 06 14 13 12 11 10 28 51 74 96 628 19 42 64 87 629 09 32 5V0 46 67 87 706 08 28 49 70 90 707 11 450 8 7 6 6 8 3 2 1 0 -7 - NATURAL COSINE. z 72N* NATURAL SINE. TABLE A. 1 460 46 ~ 470 480 490 ~ ~o 61~ 62 -0707 11 719 34731 358743 147564 71 766 04777 16788 01798 64 60 1 31 64 65 34 90 23 33 19 81569 2 52 74 75 63755 09 42 51 37 9958 3 72 95 95 73 28 61 69 66799 1667 4 93720 15 732 15 92 47 79 88 73 3456 6708 13 36, 34744 12 66 98778 06 91 61 55 6 34 66 4 31 85 767 17 24 789 08 68 54 7 66 75 74 61766 04 35 43 26 8653 8 75 95 94 70 23 64 61 44800 0852 9 96721 16733 14 89 42 72 79 62 2151 10709 16 36 33745 09 61 91 97 80 38650 11 37 66 63 28 81768 10779 16 98 6649 12 67 76 73 48767 00 28 34790 16 7348 13 78 96 93 67 19 47 62 33 9147 14 981722 16734 13 86 38 66 70 61801 0846 16710 19 36 32 746 06 67 84 88 69 2545 T6. 39 67 52 25 75 769 03 780 07 87 43 44 17 59 77 72 44 94 21 25791 05 6043 18 80 97 91 64768 13 40 43 22 7842 19711 00723 17735 11 83 32 69 61 40 9641 20 21 37 31 747 03 51 77 79 568302 1240 21 - 41 57 61 22 70 96 98 76 8039 22 62 77 70 41 89 770 14 781 16 93 47 38 23 82 97 90 60 759 08 33 34792 11 6437 24712 03724 17736 10 80 27 51 62 29 82 36 25 23 37 29 99 46 70 70 47 9936 Y26- 43 57 49748 18 65 88 88 64803 1634 27 64 77 69 38 84771 07 782 06 82 3433 28 84 97 88 67 760 03 25 256 793 00 6132 29 713 05725 17737 08 76 22 44 43 18 6831 30 25 37 28 96 41 629 61 35 8630 31- 45 57 47749 15 59 81 79 63804 0329 32 66 77 67 34 78 99 97 71 2028 83 86 97 87 63 97772 18783 15 88 3827 34714 07726 17738 06 73761 16 36 33794 06 65526 35 27 37 26 92 35 65 61 24 72 26 36 47 57 46750 11 64 73 69 41 8924 37 68 77 66 30 73 92 87 69805 0723 38 88 97 85 60 92773 10784 06 77 2422 397165 08727 17739 04 69762 10 29 24 94 4121 40 29 37 24 88 29 47 42795 12 56820 41 49 567 447561 07 48 66 60 30 7619 42 69 77 63 26 67 84 78 47 9318 43 90 97 83 46 86 774 02 96 656806 1017 44716 10728 17740 02 66763 04 21785 14 83 2716 45 30 37 22 84 23 39 32796 00 4415 46 -- 60 67 41752 03 42 58 60 18 6214 47 71 77 61 22 61 76 68 35 7918 48 91 97 80 41 80 94 86 63 9612 49717 11729 17741 00 61 98776 13786 04 71807 1311 50 32 37 20 80764 17 31 22 88 3010 51 62 57 39 99 36 50 40797 06 489 52 72 76 69 763 18 655 68 68 23 66 8 53 92 96 78 37 73 86 76 41 82 7 54718 13 730 16 98 66 92776 05 94 58 99 6 55 33 36742 17 75766 11 23 787 11 76808 16 5 566 53 566 37 95 30 41 29 9 83 4 57 78 76 66754 14 48 60 47 798 11 50 3 58 94 96 76 33 67 78 65 29 67 2 69719 14731 16 95 62 86 96 83 46 86 1 60 84 35 743 14 71 766 04 777 16 788 01 64 809 02 0 - 440 48~ 42~0 410 40~ 89 3 880~ O. o 'II ~I ~NATURAL COSINE...... —.-;...~,......,,,.~, ~ - -.~~~~~~~~I il TABLE A. NATURAL SINE. 720*..1 0 809 02 1 19 2 36 3 53 4 70 5 87 6 810 04 7 21 8 38 9 55 10 72 Ti 89 12 811 06 13 23 14 40 16 67 Y6 74 17 91 18 812 08 19 25 20 42 21 59 22 76 23 93 24 813 10 26 27 Y6 44 27 61 28 78 29 95 30 814 12 ai 28 32 45 33 62 84 79 35 96 36 815 13 87 30 38 46 39 63 40 80 44I 97 42 816 14 43 31 44 47 45 64 46 81 47 98 48 817 14 49 31 60 48 61 65 52 82 53 98 64 818 16 65 82 66 48 67 65 68 82 69 99 60 819 15, I50 660 819 15 82 49 65 82 99 820 15 32 48 65 82 9 821 16 32 48 65 81 98 822 14 81 48 64 81 97 823 14 80 47 63 80 96 824 13 29 46 62 78 95 825 11 28 44 61 77 93 826 10 26 43 59 75 92 827 08 24 41 67 73 90 828 06 22 89 66 71 87 829 04 340 660 670 829 04 838 67 20 83 36 99 63 839 15 69 30 85 46 830 01 62 1 7 78 34 94 50 840 09 66 25 82 41 98 67 831 16 72 31 88 47 841 04 63 20 79 35 96 61 832 12 67 28 82 44 98 60 842 14 76 30 92 45 833 08 61 24 77 40 92 66 843 08 73 24 89 39 834 05 65 2 1 70 87 86 63 844 02 69 17 85 83 835 01 48 17 64 83 80 49 95 665845 11 81 26 97 42 836 1 3 57 29 73 46 88 61 846 04 76 19 92 85 887 08 50 24 66 40 81 56 97 72 847 12 88 28 888 04 48 20 69 85 74 51 89 67 848 05 O 820 580 W 848 051867 17 20 32 36 47 51 62 66 77 82 92 97 858 06 849 13 21 28 36 43 51 59 66 74 81 89 96 850 05 859 11 20 26 35 41 51 56 66 70 81 85 96 860 00 851 12 15 27 30 42 45 57 69 73 74 88 89 852 03 861 04 18 19 34 33 49 48 64 63 79 78 94 92 853 10 862'07 25 22 40 37 66 61 70 66 85 81 854 01 95 16 868 10 81 25 46 40 61 64 76 69 91 84 855 06 98 21 864 13 36 27 61 42 67 57 82 71 97 86 866 12 865 01 27 15 42 80 57 44 72 59 87 78 857 02 88 17 866 03 810 800 66w 866 03 17 32 46' 61 76 90 867 04 19 33 48 62 77 91 868 05 20 34 49 63 78 92 869 06 21 35 49 64 78 93 870 07 21 36 50 64 79 93 871 07 21 36 60 64 78 93 872 07 21 86 60 64 78 92 878 06 21 36 49 63 77 91 874 06 20 84 48 62 290 874 62 76 90 875 04 18 32 46 61 75 89 876 03 17 31 45 69 73 87 877 01 16 29 43 66 70 84 98 878 12 26 40 54 68 82 96 879 09 23 37 51 65 79 93 880 06 20 34 48 62 75 89 881 03 17 80 44 58 72 86 99 882 13 26 40 64 67 81 96 280 382 95 383 08 22 36 49 63 77 90 384 04 17 31 45 58 72 85 99 885 12 26 89 53 66 80 93 886 07 20 34 47 61 74 88 887 01 15 28 41 55 68 82 95 888 08 22 35 48 62 75 88 889 02 15 28 42 65 68 81 95 890 08 21 85 48 61 74 87 891 01 270 596 58 57 56 65 54 53 52 51 50 49 48 47 46 46 44 43 42 41 40 39 38 37 36 85 34 33 32 31 30 29 28 27 26 25 24 28 22 21 20 19 18 17 16 15 14 18 12 11 10 9 8 7 6 16 -44 8 2 1 0 'Q I' NATURAL COSINE. 72p* NATURAL 8INE. TABLE A. 8 6 01 640 660 6 670 680 690 700 710 7 0891 01 898 79906 31913 65920 640927 18933 58939 69945 6260 1 14 92 43 66' 62 29 68 79 61 59 2 27899 05 65 78 73 40 79 89 7158 3 40 18 68 90 85 61 89 99 8057 4 683 30 80 914 02 96 62 934 00 940 09 90 56 5 67 43 92 14921 07 73 10 19 99655 6 80 56907 04 25 19 84 20 29946 0954 7 93 68 17 37 30 94 31 39 1853 8892 06 81 29 49 41928 05 41 49 2752 9 19 94 41 61 62 16 62 68 3751 10 32900 07 563 72 64 27 62 68 46 50 11 45 19 66 84 75 38 72 76 66 49 12 69 32 78 96 86 49 83 88 6548 13 72 45 90915 08 98 59 93 98 7447 14 86 657908 02 19922 09 70935 03941 08 8446 15 98 70 14 31 20 81 14 18 93845 16893 11 82 z2 43 i1 92 24 27947 0244 17 24 95 39 65 43929 03 34 37 1243 18 37901 08 61 66 54 13 44 47 2142 19 50 20 63 78 65 24 65 57 3041 20 63 33 75 90 76 835 65 67 4040 21 76 40 87 916 01 87i 45 75 76 4939 22 89 68 89 13 991 66 85 86 68'38 23894 02 71909 12 25923 10 67 96 96 6837 24 15 83 24 36 21 78936 06942 06 77 36 25 28 96 36 48 32 88 16 16 8635 26 41 902 08 48 6u 43 99 26 25 9534 27 64 21 60 71 65930 10 37 35948 0533 28 67 33 72 83 66 20 47 465 1432 29 80 46 84 94 77 31 57 54 2331 30 93 59 96917 06 88 42 67 64 3230 31-895 06 71910 08 18 99 2z 77) 74 4229 32 19 84 20 29 924 10 63 88 84 61 28 33 32 96 32 61 21 74 98 93 6027 34 45903 09 44 62 32 84937 08943 03 6926 35 68 21 66 64 44 95 18 13 7825 36- 71 34 68 75 65931 06 28 22 8824 37 84 46 80 87 66 16 38 42 9723 38 97 68 92 99 77 27 48 42949 0622 39896 10 71911 04918 10 88 37 69 61 1521 40 23 83 16 22 99 48 69! 61 24!20 41 36 96 28 33925 10 5 69 79 70 3a 19 42 49904 08 40 45 21 69 89 80 4318 43 62 21 62 66 32 80 99 90 6217 44 74 33 64 68 43 90938 09 99 6116 46 87 46 76 79 64932 01 19944 09 70156 46897 00 68 88 91 66 1 29 1l 7914 47 13 70912 00919 02 76 22 39 28 8813 48 26 83 12 14 87 32 49 38 9712 49 39 95 24 25 98 43 69 471960 0611 60 62905 07 36 36926 09 63 69 567 1610 61 64 20 48 4'~ 20 64 79 66 24 9 62 77 82 60 69 31 74 891 76 33 8 63 90 45 72 71 42 85 99 85 43 7 64898 03 67 83 82 63 95939 09 95 62 6 65 16 69 95 94 64933 06 19945 04 61 6 66 28 82 913 07 920 06 76 16 29 14 7 4 67 41 94 19 16 86 27 39 23 79 3 68 64906 06 31 28 97 37 49 33 88 2 69 67 18 43 39927 07 48 69 42 97 1 60 79 31 55 50 18 68 69 62951 06 0 -r 36 Z 24' "t 283- 22 210 ~ 1 89 _8 NATURAL COSINE. TABLE A. NATURAL SINE. 7Q 1 2 3 4 5 7 8 9 10 11 12 13 14 15 17 18 19 20 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 42 43 44 45 47 48 49 50 52 53 54 55 951 06 15 24 33 42 51 59 68 7 7 86 95 952 04 1 3 22 31 40 48 57 66 75 84 93 953 01 10 119 28 37 45 54 63 7-2 80 89 98 954 07 15 24 33 41 50 59 67 76 85 93 955 02 11 28 36 45 54 62 71 79 88 730 956 32 39c 47 Sc 64 78 8 1 90 98 957 0 7 I15 24 32 4C 49 5 7 6 C 74 82 9 1 99 958 07 16c 24 32 41 49 5 7 65f 74 82 9c 959 07 1 5 23~ 3 1 40 48 56 6 4 7 2 8 1 89 97 960 05 138 2 1 29 3 7 46 54 62 70 78E 86 I 961 26 34 42 50 58 66 74 82 90 98 962 06 14 22 30 38 46 53 61 69 77 85 93 903 01 08 16 24 32 40 47 55 63 71 79 86 94 964 02 10 17 25~ 33 40 48 56 63 71 79 86 94 965 02 09 17 24 32 40 47 55 I 965 93 996 00 08 15 23 30 38 45 53 60 6 7 756 82 90 97 167 05 12 19 27 34 42 49 56 64 71 78 86 93 00 168 07 1 5 22 29 37 44 51 58 66 73 80 87 94 169 02 -.09 1 6 23 30 37 45 52 59 66 73 80 87 94 I 760 970 30 37 44 51 58 65 72 79 86 93 971 00 06 13 20 27 34 41 48 55 62 69 76 82 89 96 172 03 10 17 23 30 37 44 51 57 64 71 78 84 91 98 173 04 11 18 25 31 38 45 51 58 65 71 78 84 91 98 974 04 I 770 9 74 37 44 50 57 63 70 76 83 96 9-75-02 08 16 21 28 34 41 47 53 60 66 73 7 9 85 92 98 976 04 11 17 23 30 36 42 48 61 67 80 86 92 977 05 I11 17 23 29I 36 42 48 54 60 66 7i2 78 84 Thu 978 15 21 27 33 45 51 57 63 69 75 81 87 93 99 979 05 10 16 22 28~ 34 40 46 52 5,8 63 69 75 81 871 92 980 04 10 16 211 271 331 39 44 50 566 61 67 73 79 84 90 96 981 01 07 18~ 24 29 35 181 63 68 74 79 85 90 96 1482 01 07 12 23 29 34 40 45 50 566 61 67 72 77 83 88' 94, 99, 183 04, 10 15 20 25 31 36 41 47 52 67 62 68 73 78 83 89 94 99 184 04 09 14 20 26 80 35 40 45 50 55 18481 6 9849 6 1850 1 6 9861 1 6 8862 1 6 1853 1 6 1854 1 6 1865 1 6 9866 1 1857 0 5 1858 0 869 859 9860 0 4 1861 4 9 19862 4 9 9863 3 8 1864 8 8 1866 2 7 1866 2 7 9867 1 6 9868 1 6 1869 0 S 1870 0 4 9 9871 4 8 1872 3 8 9873 2 7 8874 1 6 69 58 57 56 55 53 62 51 50 49 48 47 46 45 43 42 41 40 38 37 36 35 33 32 31 30 28 27 26 25 23 22 21 20 18 17 16 15 14 13 12 11 10 -w 8 7 6 6 56 96 94 62 970 01 11 91 40 61 987&,1 4 S7 966 06 961 02 70 08 17 97 46 66 ra 8 68 13 10 78 15 24 978 03 62 71 9878 0 2 69 22 18 86 23 30 09 67 76 4 1 60 30 26 93 30 37 15 63 81 9 0 NATURAL COSINE. r 4 i i 4 I 4. i q i I i q 4 A t A L f t t I 6 6 6 c 72R* NATURAL SINE. TABLE A..11 I -i 1 1 1 1 2 1 1 1 2 2 2 3 ' 3': 3: 31 V VI tc 7 -I ( Al f2 3 4 7 8 9 0 i 2 3 4 5 8 9 9 i 2 3 4 5 7 3 )I I I F I II i t I I I I I 810 8201 9876 99902 7 9877 3 9903 1 8 5 9878 2 9 7 9904 3 9879 1 7 6 9905 1 9880 0 5 5 9 99906 3 9881 4 7 8&9907 1 9882 3 5 7 9 ~9883 2 9908 3 6 7 98~84 1 9909 1 5 4 9 8 9885 4 9910 2 8 6 9-886 3 9911 0 7 4 9887 1 81 6 9912 2 9888 0 5 4 9 99913 3 9889 3 7 7 9914 1 9890 2 41 830 9925 9 8.9926 2 9 9927 2 6 9 9928 3 6 9929 C 3 7 9930 0 3 7 9931 0 4 7 9932 0 4 9933 1 4 7 9934 1 7 9935 1 4 7 84c) 850, p9945 2;9961 9 5 9962 2 8 5 9946 1 7 4 9963 0 7 2.9947 0 3 7 6 9 9 9964 2 9948 2 4 8 9 9949 1 9965 2 4 41 7 7 99-500 9 3 9966 1 6 4 8 6 9951 1 8 49967 1 7 3 9952 0 6 3 8 6 9968 0 8 3 9953 1 5 4 7 7 9 9954 O 9969 2 8601 9975 6 8 997 6 0 2 4 6 8 9977 0 2 4 6 8 9978 0 2 4 6 8 99719.0 31 S 7 9 9980 1 S 6 8 9981 0 2 3 870 9986 3 4 6 7 9 9987 0 2 3 5 6 8 9988 1 2 3 5 8 9 9989 0 2 3 4 6 7 8 9M9 0 1 2 4 5 830 9993 9 19994 C 1 2 3 4 5 6 7 8 9 9995 0 1 2 2 3 4 5 6 7 8 9 19996 0 0 2 3 3 4 5 6 890 9~ 998- 660 556 9 6 58 6 57 7 566 7 55 854 8 53 9 52 9 51 9 50 9999 049 0 48 1 47 1 46 1 45 2 44 2 43 3 42 3 41 3 40 439 4 38 4 37,536 6 85 5 34 5 33 6 32 6 31 6 30 -I 6 8 9891 0 9915 2 4 6 9 9916 0 9892 3 3 7 7 9893 1 9917 1 6 5 9894 0 8 4 9918 2 8 6 9895 3 9 7 9919 3 9896 1 7 5 9920 0 9 4 9897 3 8 8 2921 1 9898 2 6 6 9 9899 0 9922 2 4 6 89923 0 9900 2 3 6 7 9901 1 9924 0 6 4 9 8 )902 319925 1 7 5 I 9936 u 4 7 9937 0 4 7 9938 0 3 6 9939 0 3 6 9 9940 2 6 9 9941 2 8 9942 1 4 8 9943 1 4 7 9944 0 3 6 9 9945 21 I 2 9955 1 6 9 9956 2 4 7 9957 0 2 5 8 9958 0 3 6 8 9959 1 4 6 9 9960 2 4 71 9961 4 7 9 'I 4 6 9 9970 1 3 8 9971 0 2 4 9 9972 1 3 5 7 9 9973 1 '4 6 8 99 74 0 2 4 6 8 9975 0 2 4 6 I 5 7 9 9982 1 2 4 6 7 9 9983 1 3 4 6 8 9 9984 1 2 6 7 9 9985 1 2 4 S 7 8 9986 0 1 3 I 6 7 9 9991 0 1 2 4 5 6 7 7 9 9992 1 2 3 4 5 6 7 9: 9_993 0 1 2 4 6 7 8 9 I c 7 8 9 9 9997 0 I 2 2 3 4 4 5 6 6 7 7 8 9 9 9998 0 I1 2 3 4 4 4 C 7 7 8 8 8 8 8 9 9 9 9 19 9 1000 0 0 0 0 0 0 0 0 0 0 29 28 27 26 25 23 22 21 20 19 18 17 16 15 13 12 11 10 8 7 6 S 3 2 0 I 1 I 'I 30 7 0 4 0 0 I 1 0, NATURAL COSINE. TABLE B. NATURAL TANGENT. 72s* __I___I_0 20____ 30 40 50 60 70 j 80 T 11-4.l - -00 1 10 - 20 -, I_ _ _ _ _ __n _ _ _ _A _1 i r- 1 1 0 ' Q 1 f1 r 1 L 4 C 7 3 101 12 130 14 1 7 13 20 22 2 q 24 25Ir Out) Ut 29 68 87 001 16 45 75 002 04 33 62 91 003 20 49 78 004 07 36 65 95 005 24 53 82 006 11 40 6.9 98 007 27 J I ' 75 318 04 833 62 91 [)19 20 49 78 020 07 37 66 95 321 24 53 82 322 11 40 69 98 323 28 57 86 324 15 44 73 0)25 02 31 60 89 026 19 48 77 027 06 35 64 93 028 22 51 81 029 10;15 '1 v z 035 21 50 79 036 09 38 67 90 037 25 54 83 038 12 42 71 039 00 29 58 87 040 16 46 75 041 04 33 62 91 042 20 50 79 043 08 37 66 95 044 24 54 83 045 12 41 70 99 046 28 58 U0Z %I 70 053 00 28 57 87 054 1U 45 74 055 03.33 62 91 056 20 49 78 057 03 37 66 95 058 24 54 83 059 12 41 70 99 060 29q 58 87 061 16 45 75r 062 04 33 62 91 063 21 Sc 79 064 03E 070 22 51 86 071 16 39 63 97 072 27 soc 85 073 14 4J1 73 074 02 3 1 6 1 96 075 19~ 43 73 076 07 36 65' 95r 077 24 78 388 07 37 66 95 389 25 64 83 390 13 42 71 391 01 30 59 89) 392 18 47 77 393 06 35 65 94 394 23 53 82 395 11 41 70 396 00 29 68 88 097 17 46 76 098 05 34 64 93 099 23 40 69 99 106 28 158 87 107 16 46 75 108 05 34 63 93 109 22 52 81 110 11 40 70 99 111 28 58 87 112 17 46 76 113 05 85 64 94 114 23 53 82 115 11 41 7U 116 00C 29 59 88 123 08 38 67.97 124 26 56 85 125 16 44 74 126 03 833 62 92 127 22 Si 81 128 10 40 69 99 129 29 68 88 130 17 47 76 131 06 36 66 95 132 24 64 84 133 13I 42 72 134 02f 32 6 1 84 141 13 73 142 02 32 62 91 1 48 21 51 81 144 10 40 76C 145 00C 29~59 83 146 13 43 73 147 071 37 67 96 59 58 57 56 65 53 52 51 50 48 47 46 45 43 42 41 40 38 37 36 35 r 26 27' 281 29 30 32 33 34 35 37 38 39 40 56 85 308 iS 44 73 309 02 31 60 89 310 18 47 7 6 311 05 35 64 82 078 12 41 70 99 079 29 58 87 080 17 46 76 081 04 84 63 148 26 66 86 149 15 46 75 150 05 34 64 94 151 24 63 83 152 13 43,34 33,32 31 30 28 27 26 25 23 22 21 20 II - I 41 93 39 87 88 92 52 117 18 91i 72 19 42 012 22 68 047 16 67 082 22 81 47 135 21 153 02 18 43 51 97 45 96 61 100 11 77 60 32 17 44 80 030 26 74 065 26 80 40 118 06 80 62 16 45 013 09 655048 03 64 083 09 69 36 136 09 91 15 46 38 84 33 84 39 9~~9 65 39 15421 14 4 7 67 031 1 4 62 066 1 3 68 101 2 8 9 5 69 61 48 9 6 43 9 1 42 9 7 58 119 24 9 8 81 12 49 014 2 5 72 049 2 0 71 084 2 7 8 7 54 137 28 166 11 11 5 0 55 032 0 1 49 067 00 56 102 1 6 8 3 6 8 4010 51 84 30 30 0 6 46120 13 87 709 62 015 13 59 050 07 59 085 14 75 4213 1716 00 8 53 42 88 37 88 44 10305 7 47 3 7 54 71 033 17 66 068 17 73 34 121 01 76 60 6 65 016 00 46 95 47 086 02 63 31 139 06 89 6 5F6 29 76051 24 76 32 93 6 66 9 67 68 034 05 63 069 06 61 104 22 90 66 49 3 58 8 7 34 82 34 90 62 122 19 95. 79 2 69 017 1 6 63 062 12 63 087 20 81 49 140 24168 09 1 60 46 92 41 93 49 105 10 78 64 3810 890 80 87-0 8-6-0 860 84 83 82 81 / NATURAL COTANGENT. I I I 72T* NATURAL TANGENT. TABLE B. I -I 1 1 1 1 -I 1 1 1 2 2 2 2 2, 2' 2: 21 34 3: 3' 31q 3,1 44 4 3 4c 52 54t 515 66 67 58.59 60 90g 100 0 158 388176 3 1 68 6: 2 98 9: 3 159 28177 2. 4 68 &I 5 88 8& 6~ 160 17 178 1: 7 47 4: 8 77 71 9 161 07 179 Oi.0 37 3 t 1 67 611 2 96 9~ 3 162 26 180 21L 4 56 51 6 86 8f 69163 I618-1 - 7 46 48 8 76 78 9 164 06 182 08 0 35 38 1 66 68q 2 95 98 3 165 25 183 28 4 55 58 6 85 84 R6166 1184 14 7 45 44 8 74 74 9 167 04 185 04 [1 34 34 f ~64 64 2 94 94 3 168 24 186 24 4 54 54 5 84 84 3169 14 187 14 7 44 45 3 74 75 3 170 04 188 05 ) 33 36 (3 65' 1 193 195. 1 171 12 3 189 25 1 63 55 i.83 -86 u~172- 1190 16 43 46 4173 '03 191 066 33 36 63 66 93 97:174 23 192" 27 53 67 83 87 1175 13193 17 43 47 73 78 176 03 194 08 33 38 800 790 110 120 31904 -38 212 56 3 68 86 3 98 213 16 3 195 29 47 3 69 77: 3 89 214 08 3 196 19 38 3 49 69! 3 80 99 3 197 10 215 29 3 40 60 i 70 901, 198 01 216 21 3 1 51 1 61 82~ 91 217 12 19921 43 52 732 82 218 04:200 12 34 42 642 73 95 201 03 219 25 33 SO6 64 86: 94 220 17:202 24 47 64 78 2 85 221 08 203 iS 39 45 69 2 76222 00 204 06 31 36 612 66 92 97 223 22 2052 27 63 67 83 2 88 224 14 206 18 44 48 75 2 7'9225 05 207 09 36 39 67 2 70 97 208 00 226 28 30 682 61 89 91 227 19 209 21 50 62) 81 2 8228 11 210 13 42 43 -72 2 73 229 03 211 04 34 34 64 64 915 95 230 26 212 26 66 2: 66 87 7-8-0 770 230 87 231 17 48 79 232 09 40 71 233 01 32 63 93 2.3 24 5 5 85 236 16 47 78 136 08 39 70 113 7 00 31 62 93!38 23 64 85 '39 16 46 77 140 08 39 69:41 00 31 62: 93 ~42 23 54, 85 43 16 47: 77 44 08 39 70 45 01 32 622 93 46 24 55 86 47 17 482 78 48 09 402 71 39 02 33 I I I I 249 33 64 95 260 26 66 87 261 18 49 80 '2 52 11 4 2 7 3 263 04 3 5 6 6 9 7 I I I 267 95 286 73 268 26 287 0( 57 3E 88 6 1 269 20 288,01 51 32 82 61 270 1 3 9 15 44 289 27 76 68 271 07 90 38 290 21 69 63 272 01 84 32 291 1 6 63 47 V 11 I I 130 140 1510 160 170 / 306 73 306 05 37 6(9 307 00 32 64 96 308 28 60 91 309 23 55 87 310 191 51 Sc 50 546 45 254 28 59 90 2)56 21 52 83 256 14 45 76 257 07 38 69 258 00 31 62 93 269 24 65 86 260 17 48 79 261 1 0 41 72 I 94 273 26 57 88 i274 19 151 82 276 13 45 76i 276 07 39 70 277 01 32 64 95 278 26 68 89 279 21 62 83 280 16 46 I 79 292 10 42 74 293 05 37 68 294 00 32 63 96 296 26 58 90 296 21 513 86 297 16 48 80 298 1 1 43 76 299 06 38 I - 83 311 15 47 78 312 10 4 2 7 4 313 06 38 7 0 314 02 3 4 66 98 316 30 62 941 316 2O,6 68 90 317 2 2 54 86 318 1 8 50 I I I I I I I I j 4 i I 4 I II 44 43 42 41 40 38 37 36 35 34 33 32 31 30 28 27 26 26 24 23 22 21 20 I 0 F II II I I 462 03 36 66 97 263 28 69 90 )164 21 62 8.3 )195 15 46 77!66 08 319 70 67 01 33 64 95 I - 77 281 09 40 72 282 03 34 66 97 283 29 60 91 284 23 54 861 49 80 284$ 12 43 74 I - I I 70 -82 300 01 319 14 33 46 66 78 97 320 10 301 28 42 60 74 92 321 06 302 24 39 66 5 71 878322 03 303 19 36 51 67 82 99 1304 14 323 81 46 63 78 96 305 09 324 28 41 60 73, 92 I I I 19 18 17 1 6 15 13 12 11 10 8 7 6 6 3 2 1 0 F I - -r 760 750 17 W1 — 780 I- 720 [T/ NATURAL COTANGENT. TABLE B. NATURAL TANGENT. 72u* i 180 190 200 210 22I J 23I 240~ 250 260 0 324 92344 33363 97 383 86404 03424 47 445 28 466 31487 7360 1 325 24 65 364 30 384 20 36 82 68 66488 0959 2 56 98 63 53 70 425 16 93 467 02 4558 3 88345 30 96 87 405 04 51446 27 37 8157 4326 21 63365 29385 20 38 85 62 73489 1756 5 53 96 62 53 721426 19 97 468 08 6355 6 85346 28 95 87 406 06 54 447 32 43 8954 7 327 17 61366 28386 20 40 88 67 79490 2653 8 49 93 61 54 741427 22448 02469 14 6252 9 82347 26 94 87 407 07 57 37 50 9851 10328 14 58 367 27 387 21 41 91 72 85491 3450 11 46 91 60 54 75428 26449 07 470 21 7049 12 78 348 24 93 87 408 09 60 42 56492 0648 13329 11 56368 26 388 21 43 94 77 92 42 47 14 43 89 59 54 77 429 29 450 12 471 28 7846 15 75349 22 92 88 409 11 63 47 63 493 1545 16330 07 54369 25389 21 45 98 82 99 5144 17 40 87 58 55 79430 32451 17 472 34 8743 18 72350 20 91 88410 13 67 52 70494 2342 19331 04 52370 24390 22 47 431 01 87 473 05 5941 20 36 85 57 55 81 36 452 22 41 95 40 21 6990 89411 15 70 57 77495 3239 22 332 01 50371 23391 22 49 432 05 92474 12 68138 23 33 83 57 56 83 39453 27 48496 04 37 24 66352 16 90 901412 17 74 62 83 4036 25 98 48372 23392 23 51 433 08 97 475 19 7735 26 333 30 81 6 5 85 43454 32 55497 1334 27 63353 14 89 901413 19 78 67 90 49 33 28 95 46 373 22393 24 53 434 12455 02476 26 8632 29 334 27 79 55 57 87 47 38 62 498 22 31 30 60354 12 88 91414 21 81 73 98 5830 311 92 45 374 22 394 25 55 435 16456 0 477 33 9429 321335 24 77 55 58 90 50 43 69 499 3128 33 57355 10 88 92415 24 85 78478 05 6727 34 89 43375 21395 26 581436 20457 13 40500 0426 35336 21 76 54 59 92 54 48 76 4025 36 54356 08 88 93 416 26 89 84479 12 7624 37 86 41376 21396 26 60437 24458 19 48501 1323 38337 18 74 54 60 94 58 54 84 4922 39 51 357 07 87 94417 28 93 891480 19 8521 40 83 40377 20397 27 638438 28459 24 55502 2220 41338 16 72 54 61 97 62 60 91 5819 42 48358 05 87 95418 31 97 951481 27 9518 43 81 38378 20398 29 65439 32460 30 63503 3117 44339 13 71 53 62 99 66 65 98 6816 45 45359 04 87 96419 33440 01461 01482 34504 0416 46 78 837379 20 399 30 68 36 36 70 4114 47340 10 69 53 63420 02 71 71483 06 7713 48 43360 02 86 97 36441 05462 06 42505 1412 49 75 35380 20400 31 70 40 42 78 5011 50341 08 68 53 65,421 05 75 77484 14 8710 51 40361 01 86 98 39442 10463 12 50506 23 9 52 73 34381 20401 32 73 44 48 86 60 8 531342 05 67 53 661422 07 79 831485 21 96 7 54 38 99 86402 00 42443 14464 18 57507 33 6 55 70362 32382 20 34 76 49 54 93 69 6 66343 03 65 53 671423 101 84 89486 29508 06 4 57 36 98 86403 01 45444 18465 25 65 43 3 58 68363 31383 20 35 79 53 60487 01 79 2 69344 00 64 53 691424 13 88 95 37509 16 1 60 33 97 86 404 03 471445 23 466 31 73 53 0 710 70o~ 690 68~0 60 66 65~0 640 M630 NATURAL COTANGENT. ~~~~~..._....,...-,, 7 2v* 72v* ~~NATURAL TANGENT.TALB TABLE B. 1 2 3 4 6 7 8 12 13 14 169 17 18 20 22 23 24 26 27 28 20 -30 32 33 34 37 38 30 40 270 280 5~096 6 531 71 89 532 08 510 26 46 63 83 99 533 20 5 1 136 58 73 95 512 09 534 32 46 70 83 535 07 513 20 45 56 82 93 536 20 514 30 57 67 94 515 03 537 32 40 619 77 138 07 516 14 44 51 82 88 539 20 51 7 24 57 61 95 98 540 32 518 35 70 72 541 07 519 09 45 46 83 83 542 20 520 20 58 57 96 94 543 33 521 31 71 68 544 09 522 05 46 42 84 79 545 22 523 16 60 53 97 90 546 35 524 27 73 290 654 31 69 555 07 45 83 556 21 59 97 557 36 74 5058 12 50 88 559 26 64 560 03 41 79 561 17 56 94 562 32 70 563 09 47 85 564 24 62 565 01 39 77 566 16 54 93 567 31 69 568 08 46 85 569 23 62 570 00 39 78 571 16 55 93 572 32 71 573 09 48 *86 574 25 64 575 03 41 86J 576 10 57 90 577 36 800) 577 St 74 578 13 51 90 579 29 68 580 07 46 86 581 24 62 582 01 40 70 583 18 57 90 584 36 74 585 13 52 91 586 31 70 587 00 48 87 588 20 66 589 06 44 83 590 22 61 591,01.4U 70 592 18 58 97 810 600 86 601 26 65~ 602 05 45~ 84 603 24 64 604 03 43 83 605 22 62 606 02 42 81 607 21 61i 608 01 41 81' 609 21 60 1610 00~ 40' 80 611 20 60 612 00 40 80 613 20 60 ~614 00 40 80 615 20 61 616 01 41 81 820 524 87 125 27 68 12 608 49 89 127 30 70 128 1 1 52 92 129 33 73 130 14 55 95 131 36 7 7 132 1 7 58 99 133 40 80 134 2 1 62 135 03 44 84 136 25 66 137 07 48 89 138 30 7 1 139 1 2 63 94 640 35 76 041 1 7 58 99 642 40 81 643 22 62 644 04 46 87 645 28 69 646 10 25 93 647 34 7 5 648 17 58 99 649 41 330 649 41 82 650 24 65 651 06 48 8.9 652- 31 72 653 14 55 97 654 38 80 6 55' 21 63 656 04 46 88 657 29 7 1 658 3 1 54 96 659 38 80 660 2 1 63 661 05 47 89 662 30 72 663 1 4 56 98 664 40 82 665 24 66 666 08 50 92 667 34 76 668 1 8 60 669 02 44 86 670 28 7 1 671 138 655 97 672 89 82 673 24 66 674 00 51 340 93 675 36 78 676 20 63 677 05 48 90 678 32 75 679 17 60 680 02 45 88 681 30 78 682 15 85 683 01 43 86 684 29 71 685 14 75 686 00 42 85 687 28 71 688 14 57 689 00 42 86 690 28 71 691 14 57 692 0C 43 80 693 20. 72 694 61 50 695 02 46 88 696 31 76 697 31 61 698 04 74 91 699 34 77 700 21 350 700 21 64 701 07 51 94 702 38 81 703 25 68 704 12 55 99 705 42 86 706 29 73 707 17 60 708 04 48 91 709 35 79 710 23 66 711 10 54 98 712 42 85 713 29~ 73 714 17~ 61 715 05 49 93 716 37 81 717 25 69 59 58 57 56 55 53 52 51 50 49 48 47 46 45 44 43 142 141 40 ~38 137 36 ~35 33 '32 31 30 28 27 26 25 23 22 21 20 41 42 43 44 45 471 48~ 49 50~ 52~ 54 55 57 58 59 60 64 525 01 38 75,526 13 50 87 527 24 61 98 528 36 73 529 10 47 85 530 22 59 '96 531 34 71.547 11 48 86.548 24 6 22 549 00 38 75 550 1 3 51 89 551 27 65 552 03 41 79 553 1 7 55 93 554 3 1 593 f6 76 594 15 54 94 595 33 73 596 12 51 91 597 30~ 70 598 09 49~ 88 599 28 67 1600 07 46 86 317 21 61 118 01 42 82 11 9 22 62 120 02 43 83 321 24 64 122 04 45 85 123 25 66 124 06 47 87 ~718 13 57 719 01 46 90 720 34 78 721 22 67 722 11 65 99 723 44 88 724 32 77 725 21 65 ~726 10 64 19 18 17 16 15 i4' 13 12 11 l0 8 7 6 5 3 2 1 0 620 610 ] 5~~~~~~~~~0 1 590 I I 570-6- — 0- 660 5150 54 NATURAL COTANGENT. I TABLE B.. NATURAL TANGENT. 72w* 60 370 80 39o[ 401 __41 __1430 1__40I?i 2 3 4 5 7 8 9 10 Ti 12 13 14 15 16 17 18 19 20 22 23 24 25 4lti L4 99 727 43 88 728 32 77 729 21 66 730 10 55 731 00 44 89 732 34 78 733 23 68 734 13 5 7 735 02 47 92 736 3 7 81 737 26 71 754 01 47 92 755 38 84 756 29 76 757 21 67 758 12 58 759 04 50 96 760 42 88 761 34 80 762 26 72 763 18 64 764 10 56 765 02 77 782 22 6c 783 19 63 784 iC 57 785 04 51 98 786 47 92 787 39 89 788 34 81 789 28 76 790 22 7 0 791 17 64 792 12 59 793 06 I I II II II I I II I I I I 6uu I 810 27 75 811 23 71 812 20 68 813 16 64 814 13 61 58 816 06 65 817 03 52 818 00 49 98 819 46 95 820 44 92 821 41 90 bd u 10 60 840 09 59 841 08 58 842 08 58 843 07 57 844 07 67 845 07 56 846 06 66 847 06 56 848 06 56 849 06 56 850 06 57 851 07 57 669 29 80 870 31,82 871 33 84 872 36 87 873 38 89 874 41 92 875 43 95 876 46 98 877 49 878 01 62 879 04 55 880 07 59 881 10 62 882 14 900 4R 93 901 46 99 902 51 903 04 57 904 10 63 905 16 69 906 21 74 907 27 81 908 34 87 909 40 93 910 46 99 911 53 912 06 59 913 13 66 932 52 933 09 934 1I 69 935 24 78 936 33 88 937 42 97 938 52 939 09 61 940 19 71 941 26 80 942 35 90 943 45 944 00 55 945 10 65 946 20 I 0 1 i 0I 1 11 II I I I 0 1 1 I I I I 965 69 966 25 81 967 38 94 968 50 969 07 63 970 20 76 971 33 89 972 46 973 02 59 974 16 72 975 29 86 976 43 977 00 56 978 13 70 979 27 84 09 59 5E 57 59 57Ir 6-4 52 51 5C 48 42 47 41 48 44 40 42 41 49 9-9 38 37 36 36 zi -138 16 48 27 61 94 28 739 06 766 40 29 51 86 30 96 767 33 31T740 41 79 32 86 768 25 33 741 31 71 34 76 769 18 35 742 21 64 T6 67 770 1 37 743 12 57 38 67 771 03 39 744 02 49 40 47 96 41i 92 772 42 42 745 38 89 43 83 773 35 44 746 28 82 45 74 774 28 46 747 119 75 47 64 775 21 48 748 10 68 49 55 776 15 50 749 00 61 -cI 46 777 08 52 91 54 53 750 37 778 01 54 82 48 655751 28 95 T6 732779 41 67 752 19 88 58 64 780 35 59 753 10 82 60 55 781 29 530 620 64 794 01 49 96 795 44 91 796 39 86 797 34 81 798 29 77 799 24 72 800 20 67 801 15 63' 802 11 681 803 06 54 804 02 50 98 805 46 94 806 42 90 807 38 I 41 41 I I I I 822 38 87 823 36 85 824 34 83 825 31 80 826 29 78 827 27 76 328 25 74 329 23 72 330 22 71 331 20 69 332 18 68 333 17 66 334 15 65 335 14 64 336 13 621 I I I I I I 852 07 57 853 07 58 854 08 58 855 09 69 856 10 60 857 10 61 858 11 62 859 12 63 860 14 64 361 15 66 362 16 67 363 18 68 364 19 70 365 21 72 366 23 74 67 883 17 884 21 73-c 885 24 79 886 28 89 887 32 84 888 36 88 889 40 92 890 46 97 891 49 892 01 63 893 06 68 894 10 63 895 15 67 896 20 72 397 25 77 914 19 73 915 26 80 916 33 87 917 40 94 918 47 919 01 55 920 08 62 921 16 70 922 24 77 923 31 85 924 39 93 925 47 926 01 65 927 09 63 928 17 72 929 26 80 76 947 31 86 948 41 96 949 62 950 07 62 951 18 73 952 29 84 953 40 95 954 51 955 06 62 966 18 73 957 29 85 958 41 97 959 52 960 08 64 961 20 76 962 32 88 1; UM51) 41 98 981 56 982 18 70 983 27 84 984 41 99 985 56 986 13 71 987 28 86 988 43 989 01 58 990 16 73 991 31 89 992 47 993 04 62 994 20 78 995 36 94 996 52 997 10 I 33 32 31 30 59 28 27 26 25 Hi 23 22 21 20 09 18 17 16 15 14 13 12 11 10 9 8 7 6 5 iI i I 86 837 12867 26898 830 930 34 963 44 684 808 34 61 76 83 88 964 00 998 26 3 82 838 11868 27 899 35 931 43 57 84 2 809 30 f0 78 88 97 965 13 999 42 1 78 839 10 869_29 900_40 932 52 691.000000 5610 500 490 480 4 460 450 NATURAL COTANGENT. I 72X* NATURAL TANGENT. TABLE B. 450 460 470 480~ 49~ 500 ~ 510 520, 01.00000 1.035531.07237 1.110611.15037 1.191751.234901.27994 60 1 058 613 299 126 104 246 563 1.28071 59 2 116 674 362 191 172 316 637 148 58 3 175 734 425, 256 240 387 710 225 57 4 233 794 487 321 308 457 784 302 56 5 291 855 550 387 375 528 858 379 55 6 350 915 613 452 443 599 931 456 54 7 408 976 676 517 511 6691.24005 533 53 8 4671.04036 738 582 579 740 079 610 52 9 525 097 801 648 647 811 153 687 51 10 583 158 864 713 715 882 227 764 50 T1 642 218 927 778 783 953 301 842 49 12 701 279 990 844 851 1.20024 375 919 48 13 759 3401.08053 909 919 095 449 997 47 14 818 401 116 975 987 166 5231.29074 46 15 876 461 179 1.120411.16056 237 597 152 45 16 935 -522 -243 106 124 308 672 229 44 17 994 583 306 172 192 879 746 307 43 18 1.01058 644 369 238 261 451 820 385 42 19 112 705 432 303 329 522 89 463 41 20 170 766 496 369 398 593 969 541 40 21 229 827 559 435 466 665 1.25044 619 39 22 288 888 622 501 535 736 118 696 38 23 347 949 686 567 603 808 193 775 37 24 4061.05010 749 633 672 879 268 853 36 25 465 072 813 699 741 951 343 931 35 26 524 133 876 765 809 1.21023 417 1.30009 34 27 583 194 940 831 878 094 492 087 33 28 642 2551.09003 897 947 166 567 166 32 29 702 317 067 9631.17016 238 642 244 31 30 761 378 131 1.13029 085 310 717 323 30 31 820 439 195 096 154 382 792 401 29 32 879 501 258 162 223 454 867 480 28 33 939 562 322 228 292 526 943 558 27 34 998 624 386 295 361 698126.018 637 26 35 1.02057 685 450 361 430 670 093 716 25 36 -117 747 514 428 500 742 169 795 24 37 176 809 578 494 569 814 244 873 23 38 236 870 642 561 638 887 320 95222. 39 295 932 706 627 708 959 3951.81031 21 40 355 994 770 694 777 1.22031 471 1:100 41i 4141.06056 834 761 846 104 546 r90 19 42 474 117 899 828 916 176 622 269 18 43 633 179 963 894 986 249 698 348 17 44 593 241 1.10027 961 1.18055 321 774 427 16 45 653 303 091 1.14028 125 394 849 507 156 46 713 365 156 095 194 467 925 686 '-14 47 772 427 220 162 264 5391.27001 666.13 48 832 489 285 229 334 612 077 745 12 49 892 551 349 296 404 685 153 825 11 50 952 613 414 363 474 758 230 904 20 511.03012 676 478 430 544 831 306 984 9 52 072 738 543 498 614 904 382 1.32064 8 53 132 800 608 565 684 977 458 144 7 54 192 862 672 632 7541.23050 535 224 6 55 252 925 737 699 824 123 611 304 &> -6 312 987 802 767 894 196 688 384 4 57 3721.07049 867 834 964 270 764 464 3 58 433 112 931 902 1.19035 343 841 544 2 59 493 174 996 969 105 416 917 624 1 60 553 237 1.11061 1.15037 175 490 994 704 0 -- ~44~ 43 420 410 400 890 ~-..o " 3 3 NATURAL COTANGENT. I 1 I 1. I. TABLE B. NATURAL TANGENT. 72y* 6350 5640 660 660 670 580 590 600O l 1.32704 1.376381.42815 1.482561.639871.60033 1.664281.73206 60 1 785 722 903 3491.54085 137 538 321 59 2 865 807 992 442 183 241 647 488 58 3 946 891 1.43080 536 281 345 757 6555 567 41.33026 976 169 629 379 449 867 671 56 5 1071.38060 258 722 478 653 978 788 55 6 188 145 347 8166 576 657 1.67088 906 54 7 268 229 436 909 675 761 198 1.74022 53 8 349 314 525 1.49003 774 865 309 140 52 9 430 399 614 097 873 970 419 257 51 10 511 484 703 190 972 1.61074 530 376 50 TI 592 568 792 284 1.55071 179 641 492 49 12 673 653 881 378 170 283 752 610 48 13 764 738 970 472 269 388 863 728 47 14 835 824 1.44060 566 368 493 974 846 46 15 916 909 149 661 467 598 1.68085 964 45 Ti 998 994 239 755 6 567 7U 3 196i 1.75082 44 171.340791.39079 329 849 666 809 608 20043 18 160 165 418 944 766 914 419 31942 19 242 250 6081.50038 866 1.62019 631 437 41 20 323 336 598 133 966 125 643 556 40 21 405 421 688 228 1.56065 230 754 6765 39 22 487 507 778 322 165 336 866 794 38 23 568 693 868 417 265 442 979 91337 24 650 679 958 612 366 548 1.69091 1.76032 36 25 732 7641.450-49 607 466 654 203 151 135 2 6 814 850 139 702 566 760 316 271 34 27 896 936 229 797 667 866 428 390 33 28 9781.40022 320 893 767 972 541 51032 291.35060 109 410 988 868 1.63079 653 630 31 30 142 195 601 1.51084 969 185 766 749 30 31 224 281 5692 *1791.67069 292 8794 869 29 32 307 367 682 275 170 398 992 990 28 33 389 454 773 370 271 505 1.70106 1 77110 27 34 472 540 864 466 372 612 219 23026 36 664 627 955 562 474 719 332 351 265 36 637 714 1.46046 658 675 826 446 471 24 37 719 800 137 754 676 934 560 692 23 38 802 887 229 850 778 1.64041 673 713 22 39 885 974 320 946 879 148 787 834 21 40 9681.41061 411 1.62043 981 256 901 965 20 41 1.36051 148 603 1391.68083 363 1.71015 1.78077 19 42 134 235 595 235 184 471 129 198 18 43 217 322 686 8332 286 579 244 319 17 44 300 409 778 429 388 687 358 441 16 45 383 497 870 626 490 795 473 663 15 46 466 684 962 622 593 903 568 685 14 47 649 6721.470654 719 695 1.66011 702 807 13 48 633 769 146 816 797 120 817 929 12 49 716 847 238 913 900 228 932 1.7906111 60 800 934 3301.630101.569002 337 1.72047 174 10 61 8831.42022 422 107 105 445 163 296 9 52 967 110 514 205 208 554 278 419 8 631.37050 198 607 302 311 663 393 642 7 64 134 286 699 400 414 772 609 665 6 55 218 374 792 497 617 881 625 788 5 56 302 462 885 695 620 990 741 911 4 57 886 650 977 693 723 1.66099 857 1.80034 3 68 470 63881.48070 791 826 209 973 168 2 69 5664 726 163 888 930 818 1.73089 281 1 60 638 816 256 987 1.60033 428 205 405 0 860 ~ 860 3840 3380 820 810 380 29 T NATURAL COTANGENT. I ( s 72Z* NATURAL TANGENT. TABLE B. 61~ 620 630 64 65 66~ 67~ 68~ 0 1.80405 1.88073 1.96261 2.050302.14451 2.24604 2.85585 2.47509 60 1 529 205 402 182 614 780 776 716 &9 2 653 337 544 333 777 956 967 924 58 3 777 469 685 485 940 2.25132 2.36158 2.48132 57 4 901 602 827 637 2.15104 309 349 340 56 6 1.81025 784 969 790 268 486 541 549 55 6 150 867 1.97111 942 432 663 733 75854 7 2741.89000 253 2.06094 596 840 925 967 53 8 399 133 395 247 760 2.26018 2.37118 2.49177 52 9 524 266 538 400 925 196 311 38651 10 649 400 681 553 2.16090 374 504 597 50 11 774 533 823 706 255 552 697 807 49 12 899 667 966 860 420 730 891 2.50018 48 13 1.82025 801 1.98110 2.07014 585 909 2.38084 229 47 14 150 935 253 167 751 2.27088 279 440 46 15 2761.90069 396 321 917 267 473 65245 16 402 203 540 4762.17083 447 668 86444 17 528 337 684 630 249 626 863 2.51076 43 18 654 472 828 785 416 806 2.39058 289 42 19 780 607 972 939 582 987 253 502 41 20 906 741 1.99116 2.08094 749 2.28167 449 715 40 21 1.83033 876 261 250 916 348 645 92939 22 1591.91012 406 405 2.18084 528 841 2.52142 38 23 286 147 550 560 251 710 2.40038 357 37 24 413 282 695 716 419 891 235 571 36 25 540 418 841 872 587 2.29073 432 786 35 26 667 554 986 2.09028 755 254 629 2.53001 34 27 794 6902.00131 184 923 437 827 21733 28 922 826 277 341 2.19092 619 2.41025 432 32 291.84049 962 423 498 261 801 223 648 31 30 1771.92098 569 654 430 984 421 865 30 l31 305 235 715 811 599 2.30167 620 2.54082 29 32 433 371 862 969 769 351 819 299 28 33 561 5082.010082.10126 938 534 2.42019 51627 34 689 645 155 2842.20108 718 218 73426 35 818 782 302 442 278 902 418 952 25 l36 946 920 449 600 449 2.31086 618 2.55170 24 371.850751.93057 596 758 619 271 819 38923 38 204 195 743 916 790 456 2.43019 608 22 39 333 332 891 2.11075 961 641 220 827 21 40 462 470 2.02039 233 2.21132 826 422 2.56046 20 4-1 591 608 187 -392 304 2.32012 623 266 19 42 720 746 335 552 475 197 825 487 18 43 850 885 483 711 647 383 2.44027 707 17 44 9791.94023 631 871 819 570 230 928 16 451.86109 162 780 2.12030 992 756 433 2.57150 15 46 239 301 — 929 — ]90 2.22164 943 636 371 14 47 369 440 2.03078 350 337 2.33130 839 593 13 48 499 679 227 611 6510 317 2.45043 8156 12 49 630 718 376 671 683 506 246 2.68038 11 60 760 858 626 832 857 693 451 261 10 61 891 997 675 993 2.23030 881 665 484 9 621.870211.96137 8252.13164 204 2.34069 860 708 8 63 162 277 975 316 378 258 2.46065 932 7 64 283 4172.04125 477 553 447 270 2.69166 6 55 416 667 276 639 727 636 476 881 6 66 646 698 426 801 902 825 682 606 4 67 677 838 677 9632.240772.856015 888 831 3 68 809 979 7282.14126 262 2062.47095 2.60057 2 69 9411.96120 879 288 428 396 302 283 1 601.88073 261 2.06030 461 604 685 609 609 0 I 2 7~ — 0I 260 250 s- o 280 220 21 NATURAL COTANGENT. --------— —C- ..__.._.:. ---,. —. --— I -------- -----—.. -- -- — ---- — TABLB B. ' 69w'.1 736 2 963 2.7 832.61190 4 418 5 646i -6 8742r.7 7 2.62108 8 832 9 561 2.7 10 791 11 2.63021 -12 252 13 488 2.7 14 714 15 945 1-6 2.641M77 -17 410 2.7 18 642 19.875 20 2. 65109 Yl 3 422.8 22 576 23 811 24 2.66046 25 281 2.8 Y6 516 27 752 28 989 29 2.67225 2.8 30 462 3 700 32 937 33 2.68175 2.8 34 414 85 653 36 892 87 2.69131 2.8, 38 371 39 612 40 8582 8. 4-1 2.70094 42 835 43 577 44 819 2.8i 45 2.71062 i6 ~30~5 47 548 48 792 2.8' 49 2.72086 50 281 *CT 526 52 771 2.81 58 2.78017.54 268 55 509 2.81. -6 75 57 2.74004 58 251 59 499 2.9( 60 748 ' 201 B(.4740 997, 5624( 49( 74( 99( '6247 49~ 75( '7 00'~ 254 507l 761 '801'4 266 77h '9035 28& 802 816 574 833 1091 350 610 870 2130 391 658 914 3176 439 702 965 4229 494 758 5028 289 6555 822 6089 856 624 892 7161 480 700 970 3240 511 788 600 878 3147 421 2.9042 66 97 12.9124 2.9207 63 91 12.9318 44' 74 12.9402 86 59 87 12.9515 43 72:2.9600 28 57 85.2.97 14 43 71,2.9800 29 58 86 29 9-15 44 73 3.0002: 81' 61 90: 3.01191 481 78i 3.0207' 3 7, 66' 961 3. 08264 554 85' 3.0415, 451 741 8.05041 341 641 95( 3.0625' 54~ 857 3.0716( 464 76 180 NATUJRAL TANGE~NT. -72u 73i 740 13.077-68 3.27085 3.48741 46 8.08073 426 3.49125 '1 879 767 509 6 685 3.28109 894:3 991 452 3.50279 19 8.092198 795 666 6 606 3.- 29139 3.5105.3 14 914 483 441 283.10223 829 829 0 532 3.30174 3.52219;9 842 521 609 S8 3.11153 868 3.53001:8 4643.81216 393:8 775 565 78.5 193.12087 914 3.541 79 '1 4008 32264 5783 ~ ~718 614 19 68 5 3.13027 965 3.55364 7 341 3.33317 761 1 656 670 3.56159 4 97213.34023 557 8 3.14288 377 957, 3 605 732 3.57357 8 922.3.5087 75 4 3.15240 443 8.58160 0 558 800 562 7 877 8.86158 966 4 3.16197 516 3.59370 2 517 875 775 0 888 3.87234:3.60181 983.17159 594 588 8 481 955 996 7 804 3.88317 8.61405 83.18127 679 814 8 451 8.39042 3.62224 3 775 406 636 I 8.19100 771 3.63048 '3 426 3.40136 461 7 752 502 874 343.20079 869 3.64289 3 406 8.41236 705 i734 604 3.65121 2~3.21063 9713 5388 8 92 3.42343 957 3 722 713 3.66376. 33.22053 3.43084 7196 3 84 456 3.67217. 715 829 638 ~ 3.23048 3.44202 8.68061 381 576 485 3 714 951 909. 3.~24049 3.45327 8.6938'5 883 703 761 3 719 3.46080 3. 701 88 33.25055 458 616: 8 92 837 3.71046 1 729 3.47216 476: r 3.26067 5946 907 406 977 3.72838 I 74,5.8.48359 771 3 3.27085~ 741 3.73205 170 I 163 -160 72A** z 3.73205 640 8.7-4075 950 3.75388 828 3.76268 709 3. 77152 595 3.78040 485 931 3.793 78 827 3.80276 726 3. 81177 680 3.82088 992 3.83449 906 3.84364 824 3.85284 745 3.86208 671 3.87 136 601 3.88068 536 3.89004 474 945 3.90417 890 8. 913864 839 3.92816 793 3.98271 751 3.94232 718 3.95196 680 3.96165 651 3. 97189 627 3.98117 607 3. 99099 592 4.00086 582 4.01078 140 4.01078 576 4.02074 574 4.03076 578 4.04081 589 4.05092 599 4.06107 616 4.07127 639 4.08152 666 4.09182 699 4. 102 16 736 4. 11256 4. 123017 825 4. 13850 877 4. 14405 934 4. 15465 997 4. 16530 4.17064 600 4.18187 675 4.19215 756 4.20298 842 4. 21387 933 4.22481 4.28080 580 4.24182 685 4.8 523H9 7-95 4.26852 911 4. 27471. 2 803H2 595 4. 29159 724 4. 30291 860 4.31430 4.32001 573 4.33148 159 58 57 56 55 53 52 51 50 48 47 46 45 44 48 42 41 40 38 37 86 35 38 32 81 30 28 27 26 25 23 22 21 20 18 17 16 1 5 14 13 12 1 1 10 8 7 6 5 3 2 0 I NATURAL COTANGENT. li il. NATURAL TANGENT. TABLE l 4 2( C 11 2'1 15 1,9 24 25 27 28 29 30 3 1 32 39 34 35 37 38 39 40 42 43 44 45 46 47 48 49 50 52 53 54 L5 66 57 58 59 60 -r 770 )4.33149 728 4.3430C 879 [4.35459 i 4.3604C 628 4.37207 798 4.38381 969 4.39560 4.40152 7 45 L4.41340 4.42,534 4.43134 735 1.44338 942 4.455-4 4.46155 7 64 4.47374 986 [.4860i. 4.49215 832 I 4.50451 4.51071 693 4.52316 941 4.53568 4.54196 826 4.55458 4.56091 726,4.57363 4.58001 641 4.592831 927 4.60572 4.61219 868 4.62518 4.63171 825 4.64480 4.65138 797 4.66458 4.67121 786 4.68452 4.69121 791 4.70463 120 780 790 4.70463 5.14455 4.71137 5.16265 813 5.1605F 14.72490 86 4.473170 5.17671 851 5.1848( 4.74534.5.1 929 4.75219 5.20107 906 925 4. 76595 5.2174A '4.77286 5.2256C 978 5.2339,1 4.78673 5.2421E,4.79370 5.25049 14.80068 88C 769 5.26715 4.81471 5.27558 4.82175 5.28393 * 882 5.29235 * 1.83590 5.30080 4.84300 928 4.8 -t)13 5.31778 727 5.32631 4.86444 5.33487 4.87162 5.34345 882 5.35206 4.88u_01 5.36070 4.89330 936 4.90(056 5.3780b 785 5.38677 4.91516 5.39,552 4.9224-9 5.40429 984 5.41309 4. 93721 5.42192 4.94460 5.43078 4.95201 966 94.5 5.44857 4.96690 5.45751 4.97438 5.46648 4.98188 5.47548 940 5.48451 4.99695 5.49356 5.00451 5.50264 5.01210 5.51176 971 5.52090 5.02734 5.53007 i5.03499 927 5.04267 5.54851 5.05037 5.65777 809 5.56706 5.0658456.67638 o.07360 5.58573 5.08139 6.59511 921 5.60462 5.09794 5.61 397 5.10490 6.62344 5.112799. 63295 5.12069 5.64248 86265.65205 5.13658 6.66165 5.14455 5. 67128 110 100 800 5.67128 8094 9064 15.70037 1013 1992 2974 3960 4949 5941 6937 7936 8938 9944 5.80953 1966 29482 4001 5024 6051 7080 8114 9151 5.90191 1236 2283 3335 4390 5448 6510 757 6 8646 9720 6.00797 1878 2962 4051 5143 6240 7340 8444 9552 6.10664 1779 2899 4023 5151 6283 7419 8559 9703 6.20851 2003 3160 4321 5486 6655 7829 9007 6.80189 1375 90 810 820 8 840 6.3137T5 7.11537 8.14435 9.51436 2566 3042 6398 4106 3761 4553 8370 6791 4961 6071 8.20352 9490 6165 7594 2344 9.62205 7374 9125 4345 4935 8587 7.206t1 6355 7680 9804 2204 8376 9.70441 6.41026 3754 8.30406 3217 2253 5310 2446 6009 3484 6873 4496 8817 4720 8442 6555 9.81641 5961 7.30018 8625 4482 7206 1600 8.407(05 7338 8456 3190 2795 9.90211 9710 4786 4896 3101 6.50970 6T 7007 6007 2234 7999 9128 8931 3503 9616 8.51259 10.0187 4777 7.41240 3402 0483 6055 2871 5555 0780 7339 4509 7718 1080 8627 6154 9893 1381 9921 7806 8.62078 1683 6.61219 9465 4275 1988 2523 7.51132 6482 2294 3831 2806 801 2602 5144 4487 8.70931 2913 6463 6176 3172 3224 7787 7872 5425 3538 9116 9575 7689 3854 6.70450 7.61287 9964 4172 1789 3005 8.82252 4491 3133 4732 4551 4813 4483 6466 6862 5136' 5838 8208 9185 5462, 7199 9957 8.91520 5789. 8564 7.71715 3867 6118 9936 3480 6227 6450' 6.81312 5254 8598 6783, 2694 7035 9.00983 7119 4082 8825 3379 7457 5475 7.80622 5789 7797 6874 2428 8211 8139' 8278 4242 9.10646 8483 9688 6064 8093 8829 6.91104 7895 5554 9178 2625 9734 8028 9529 3952 7.91582 9.20516 9882 5385 3438 3016 11.0237 6823 5802 5530 0594 8268 7176 8058 0954 9718 9058 9.30599 1316 7.01174 8.00948 3165 1691 2637 2848 5724 2048 4105 4756 8307 2417 5579 6674 9.40904 2789 7059 8600 8516 3163 8546 8.10536 6141 3540 7.10038 2481 8781 3919 1537 4435 9.51436 4301 80 70 60 0 B. 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 299 28 27 26 25 f14 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 S 4 3 2 0 0 I I L L NATURAL COTANGENT. I11 TRAVERSE TABLE; OR, LATITUDES AND DEPARTURES TO EVERY MIN U TE: AND CALCULATED TO FOUR PLACES OF DECIMALS. BY MICHAEL McDERMOTT, CIVIL ENGINEER AND SURVEYOR. A I --------------------- - ------ 74 1 4 6 1 1.00oo0 L 0 00 00 00 00 00 2.0000 00 00 00 00 00 3 3.0000 00 00 00 00 00 LATITU: 4 ) 4.000 I 00 00 00 00 00 DE 0 DEGREES. 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 2g6 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 556 57 58 59 60 -I 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00,00 99 0.9999 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 iO.9999 1 00 00 00 00 00 00 00 00 00 I 00 00 00 00 00 00 00 00 00 00 1.9999 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 98 98 98 98 98 98 98 98 98 98 98 97 97 97 97 97 97 9.9997 2 00 00 00 00 00 00 00 00 00 00 00 00 oo 00 00 00 2.9999 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 98 98 98 98 98 98 98 98 98 97 97 97 97 97 97 96 96 96 96 96 96 96 2.9996 8 )7 97 97 97 97 97 9, 96 2986( OC 00 0( 00 OC 00 0( OC OC Of OC 0( c00 oc00 3.9999 99 99 99 99 99 99 99 98 98 98 98 98 98 98 98 98 98 98 98 97 97 97 97 97 97 96 96 96 96 96 96 96 95 95 95 94 94 94 3.9994 4 3.~9 ), ) )\ ) ) ) )i I I I I I:;! I i 5 6 5.0000 6.0000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00( 00 00 00 00 5.9999 00 99 00 99 00 99 00 99 00 99 00 99 00 99 00 99 4.9999 99 9 99 99 99 99 99 99 99 99 98,., 99 98 99 98 98 98 98 98 98 97 98 97 98 97 98 97 98 97 -98 97 97 96 97 96 97 96 97 96 97 96 97 96 96 95 96 95 96 95 96 95 96 94 96 94 96 94 95 94 95 93 95 93 95 93 95 93 94 93 94 92 934 92 93 92 93 92 9t3 91 4.9993 5.9991 *)_} _ Il 7 7.0000 00 00 00 00 oc 0o Oc oc 00 9c 99 99 99 99 99 99 99 99 99 99 99 98 98 98 97' 97 97 97 97 97 97 97 97 97 937 96 96 96 95 95 94 94 94 94 93 93 92 92 90 90 6.9990 7 __, 8 9 i 8.0000 9.000) 60 00 00 59! 00 0058, 00 00 57 00 00 56 00 0055 00 0054 00 00 53 00 00.52 00 oo;051 00 8.9999!)50 7.79999 99 4'9 99 99 48 99 9 '9 47 99 9946 99 9945 99 99 43 99 9942 99 99 41!99 98 40 98 )8394 98 983885 98 98137 98 '3836 98 97135 98 97 34 98 97 33 98 97 32 98 97 31 97 96130 97 9629 97 96 28 97 96271 96 9626 96 96 25 96 '6124 95 93523 95 95 22 95 95121 95 94120 94 9419I 94 94118 94 9317 94 93116 93 9215 93 '9214 93 92113 92 91 12 92 91111 91 90110 91 90 8 90 891 7 90 89 6 C90 89 5 90 88 4 89 88 3 891 87 2 89 87 1 7.9988 (8.9987 0 _8 9 - I I 3 DEPARTURE!9 DEGREES. I DEPARTURE 0 DEGREES. 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 03 06 09 12 15 17 2 06 12 17 23 29 35 8 09 1 7 26 35 44 52 4 12 23 35 46 58 70 5 151 29 44 58~ 73 __89( 6 1 8 3.5 53 7 0 88 0.0105 7 20 4 1 6 1 8-2 0.0102 2 2 8 2 3 47, 70 93 1 7 40 9 2& J 79 0.0105 31 57 10 29 58 87 __ 616 46 75( ii - 32 65 96 28' 60 92 12 35 7100.0105 40 75029 13 8 76 13 51. 89 27 il14 41 81. 22 63 0.0204 44 bis5 44 87 31 74 18 __62( 16 47 9 3 40 86 33 79 1 7 50 99 48 98 48 96 18 52 0.0105 57 0.0210 62 0.0314 I19 55 11 66 21 77 32 I20 58 116 75 33 91 __49( 121 61 2 83 44 0.0306 67 22 04 28 92 56 20 84 2"3 67 34 0.0201 6)8 35 0.0401 24 7 0 40 09 79 49 19 2)5 73 45 1 8 91 64 36(l 26 76 51 7 0.0302 78 54 27 79 57- 36 14 93 71 28 81 63 44 26 0.0407 88 29g 84 69 53 38 22 0.5006 30 87 7 5 62 49 37 23( 9T 8 81 ~71 61 51 R 41 32 93 86 79 72 66 59 33 96 92 88 84 80 76 34 99 98 97 96 95 93 35 0.0102 0.0204 0.0305 0.0407 0.0509 0.0611 3P6 -0-5 -09 - -14 190 ~24 2 8 37 08 1.5 23 30 38 46 38 11 2)1 32 42 53 639.39 13 27 40 54 67 80 j40 16 33 49 66 82 __980 41 19 39 589-~M 7 7- 970. 0-7 16 4 2 2)2 44 67 89 0.0611 33 43: 25 50 7510.0500 26 5 1 44 28 56 84 12 40.68 45 3 1 6 2 93 24 55 85 0 46~ 4 ~ - 0.0 4 0-1 ~ 3 5- 69 ~0.0 803 47 37 P73 10 47 84 20 48 40 79 19 58 98 38 49 43 85 28 70 0.0723 55 50 45 91 36 82 27 720C 561 48 9 7 45 9 3 4 2 9 0 5 2 51 0.0303 54 0.0605 57 0.0908 53 54 08 63 16 71 25 5 4 5 7 14 7 1 28 8 6 43 0 556 60 20 80 4010.0800 6 0 566 3 26 89- 52 15 77 57 66 32 97 63 29 95 58 69 37 0.0506 75 44 0.1012 59 72 43 15 86 58 29 0 60 0.0175 0.0349 0.0524 0.0698 0.0873 0.1047 0 1 2 3 ~4 5,~ ~6 LATITUDE 89 DEGREES. 75 20 41 61 81. ).01021 23 63 83 ).0204 2~4 44 65 85 ).0305 47 67 87 ).0407 2-.8 48 68 89 ).0509 29j 50 70 91 ).0611 31 -52 72 92~ ).07 13 53 74 94 ).0815 55 76 96.0916 3-7 57 77 98 ~.1018 38 59 79,.1100 20 8 23 40 70 93 0.0110 40 63l 80 0.0216 33 0.0302 26C 49 * 72 96 0.0419 42 66 0.0512 35 58 82 0i.o605 28 51 75 98 0. 072)2 45 68 91 0.0814 38 61 84 0.0907 3 1 54 78 0. 1001 24 47 70 94 0.1117 40 63 86 0.1210 86 57 80 9 o.000o 26 p 52 78 0.0104 30 58 84 0.0210 36 62 88 0.0314~ 92 0.0419 46 72 98 0.0524 50 7 6 0.0602 28 54 s0 0.070-7 33 60 86 0.0802) 38 64 90 0.0916 42 68 95 0. 1021 48 74 0. 1100 26 52 78 0. 1204 30 56 83 0.1309 35 62 88 0.1414 40 60 59 58 571 56 55 547j 53 52 51 50 48 47 46 45 44 43 42 41 40 38 37 36 35 33 32 31 30 28 27 26 25 24 23 22 21 20 18 17 16 15 14 13 12 11 10 8 7 6 40 0.1303 66 4 61 26 92 3 81 50 0.1518 2,.1201 73 44 1.1222 0.1396 0.1571 0 7- 8 9 I I I I i I i 76 LATITUDE 1 DEGREE. r: 7: i 1 0 0.9999 1 99 2 98 3 98 4 98 5 98 6 98 7 98 8 98 9 98 10 98 1 98 12 98 13 98 14 98 15 98 16 9.8 17 97 18 97 19 97 20 97 21 97 22 97 23 97 24 97 25 97 26 97 27 97 28 97 29 97 30 97 31 97 32 96 33 96 34 96 35 96 1.999T 97 97 97 97 96 96 96 96 96 96 96 96 956 95 95 95.95 95 95 95 04 94 94 94 94 94 93 93 93 93 93 93 93 93 92 -- 2.9996 95 95 95 95 95 95 94 94 94 94 93 93 93 93 _93 93 92 92 92 92 92 91 91 91 91 90 90 90 90 89 89 89 89 88 4; 3.9994 94 94 93 93 93 93 92 l 92 92 932 91 91 91 91 9O (,) 90 89 89 89 89 88 88 88 88 87 87 87 86 86 86 85 85 84 84 I b 4.9993 92 92 92 92 91 91 90 90 90 90 89 89 89 89 88 88 87 87 87 87 86 86 85 85 85 84 84 83 83 83 82 82 82 81 b 5.'39991 91 90 90 90 89 89 88 88 87 87 87 87 86 86 86 85 85 84 84 83 83 82 82 81 81 81 80 80 80 79 78 78 78 77 '1 6.999C 8C 89 88 88 87 87 86 86 85 85 85 85 84 84 83 83 82 82 81 81 80 80 79 79 78 78 77 77 76 76 76 75 75 74 74 7.9988 88 87 86 86 86 86 85 84 83 83 82 82 82 82 81 81 80 79 79 79 78 78 76 76 75 75 74 74 73 73 72 71 71 70 70 8.9987 86 86 86 85 84 84 82 82 81 81 80 80 79 79 78 78 77 77 76 76 75 75 74 73 72 72 70 70 69 69 68 68 67 67 66! ';/ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 341 33 32 31 30 29 28 27 26 25 I I 4 I; I., e e I 36 96 92 88 84 81 77 73 69 6524 37 96 92 88 84 80 76 72 68 6423 38 96 92 88 84 80 75 71 67 6322 39 96 92 87 83 79 75 71 67 63 21 40 96 92 87 83 79 75 71 66 62 20 41 96 91 83 78 74 70 66 6119 42 96 91 87 82 78 74 69 65 6018 43 95 91 86 82 77 73 6) 64 6017 44 95 91 86 82 77 72 c8 63 5916 45 95 90 86 81 76 72 67 63 5815 46i 95 90 86 81 76 71 66 62 5714 47 95 90 85 80 76 71 66 62 5713 48 95 90 85 80 76 71 66 61 5612 49 95 90 85 80 75 70 65 60 5511 50 95 90 85 80( 75 69 64 59 54 10 51 95 90 84 79 74 )69- 64 59 53 9 52 95 89 84 79 74 68 63 58 52 8 53 95 89 84 78 73 67 63 57 51 7 54 95 89 83 78 73 67 62 56 61 6 55 94 89 83 77 72 66 61 55 50 5 56 94 89 83 77 72 66 60 54 49 4 57 94 89 82 76 71 65 60 54 48 3 58 94 88 82 76 71 65 59 63 47 2 59 94 88 82 76 70 64 58 52 46 1 60 0.9994 1.9988 2.99382 3.9976 4.9970 5.9963 6.9957 7.9951 8.9945 0 1 2 83 4 6 6 7 8 9 DEPARTURE 88 DEGREES. I DEPARTURE 1 DEGREE. 77 1 2 3 4 5 6 7 8 9 0.O 0.0175 0O.03~4-9 - 0.05'2-4 0.06~9-8 06.0 87 3 0.1470.22 0-1 96 0.1571 60 1 7I7 55 32 0.0710 87 64 42 0.1419 97 59 2 80 61 41 21 0.0902 82) 62 42 0.1623 58 3 83 66; 50 313 1 6 99 82 66 49 57 4 86 7I2 59 45 31 0.1117 0.1303 90 76 56.5 89 78 67 56 46 35 24 0.1518 0.1702 55 6 92 8-~4 ~726 ~68 60 52 4 ~ 36 2854 95 90 85 80 75 69 64 59 54 53 8 98 9)6 93 91 89 871 84 82 80 52 9 0.0201 0.0401 02 0.0803 0.1004 0.1204 0.1405 0.1606 0.1806 Si 10 04 0 7 11 14 18 22 25 29 32 50 11 06 13 2u 2 38 9 46 52'- 5949 12 09 19 28 38 47 56 66 75 85 48 13 12) 25 3 7 49 62 74 86 98 0.1911 47 1 4 1 5 30 46 6 1 7 6 9 1 0.1506 0.17-22 37 46 1 5 1 8 36 5 4 7 2 9 1 0.1309 27 45 63 45 T6 ~ ~ 483 --- ~ 8-o. Io~6- 27 4-. 68 - 9 90O44 17 24 48 7 2 196 20o 44 68 92 0.2016 43 1 8 27 54 81 0. 0908 35 6 1 88 0.1815 42 42 1 9 30 60 89 1 9 49 80 0.1609 38 68 41 20 33 65 98 3 1 64 96 29 62 94 40 i 2,1 22 2~.3 24 25 2 7 2 8 2 9 3 0 3 2 3 3 3 4 3 5 37 38 89 4 0 If 42 43 44 45 47 48 49 50 52 53 54 55 57 58 59 60 36O 38 41 44 47 50 53 56 59 62 68 71 703 76 79,82) 85 88 91 94 97 0.0300 03 05 1 1 14 17 20;, 23 26 2 9 32 3 5 37e 40 43 4 6 0.0349 f-~1 71i 89i 94 0.0500 06 18 24 29 35 41 47 53 64 70 76 82) 93 99 0.0605 11 17 22 28 34 40 46 51 57 63 69 0.0707 16 24 33 42) 50 59 i 68 7 7 85, 94' 0.0803 12 20 29 38 46 64 72 81 90 99 0.0908 62 2)5 34 42 51 60 68 77 86fl 95 0. 1004 42 54 66 77 89 0.1000 1 2 24 3 6 4 7 7 0 8 2 94 0.1105 28 40 52 6 3 871 0.1210 2)2 3 3 45 56 68 80 9 1 0. 1303 1 4 26 38 93 0. 12)07 36C 5 1 65 80 95 0. 1309 24 38 53 67 82 96 0.1411 25 40 54 69 84 98 0. 1513 27 42 56 71 85 0. 1600 1 4 299 43 58 703 0. 1414 31 48 66 83 18i 36 53 61 88 0.1606 23 40 58 75 93 0.17 10 27 45 63 80 98 0. 1815 32 50 67 8 5 0. 1 90 2 1 9 3~7 54 7 2 90 0.2007 49 70 90 0. 1710 30 51 71 92 0. 1808 33 53 73 93 0. 1914 34 54 74 0.2015 36 57 97~ 0.2118 38 58 7I8 99 0.2219 39 80 0.2300 21 42 85 0. 1908 3 1 54 78 0.2001 24 48 7 1 94 0.2118 41 64 87 0.2210 57 80 0.2303 26 50 74 97 0.2420 4 3 66 90 0.2513 36J 591 82 0290 02906 53 7 6 0.2,12 U 47 73 99 0.2225 Si 77 0.2304 30 56 82 0.2408 35 61 87 0.2513 39 65 91 0.2617 44 70 96 0.2722 49. 75 0.2801 27 53 79' 06. 29 05N 31 57 84 0.3011 39 38 37 3l 6 35 33 32 3 1 30 28 2 7 26 25 23 22 22 20 1 8 1 7 1 6 156 1 3 12 1 1 10 8 7 6 5 I. 75 81 86 92 0.0698 2 21 3C 38 0. 1047 0 i I I I 510 61 73 84 0.1396 I 87 0. 1702'" 16 31 0. 1745 24 42 59 77 0.2094 7 1 62 99 82 0.2722 0.2402 46 2)3 6 9 0.2443 0.2792 87 63 89 0. 3115 0. 3141 I 4 3 2 1 0 7 1 8 LATITUIME88 DEGREES. I I j __ ____ 78 LATITUDE 2 DEGREES. - -1 1 s2 3 4 5 6 7 8 9 r 0 0.9994 1.9988 2.9982 3.9976 4.9970 5.9963.9957 7.9951 8.J9945 0 1 94 88 81 75 69 3 5 7 50 44 5 2 94 87 81 75 69 62 56 50 4"58 3 94 87 81 74 68 62 55 49 4257 4 94 87 81 74 68 61 55'r 48 4256 5 93 87 80 74 67 60 () 54 48 41 55 6 93t 87 80 73 67 60 5 46 4; 54 7 93 87 80 73 66 59 52 46; 3 l53 8 93 87 79 72 58 52 45 3852 9 93 87 79 72 65 57 51 44 37 1 10 93 86 79 71 65 57 )() 438 3 __3650 11 93 85 78 70 64 56 49 -42 34i49 12 93 85 78 70 6.3 55 441 3348 13 93 85 78 70 63 55 48 40 833 47 14 92 85 77 69 62 54 47 3!9 32 46 15 92 85 77 69I 62 54t 4(; 38 ) 1 4 16 99 84 77 68 61 531 4.5 38 30 44 17 92 84 76 68 61 53 45 37 2943 18 92 84 76 67 (60 51 43 35 2742 19 92 84 75 67 60 51 43 34 2641 20 92 83 75 67 5 6(__ 50 42 34 25. 40 21 92 83 75 66 (59 50,l 41 33 24 39 22 92 83 75 66 58 49 41 32 24 38 23 91 83 74 65 58 48 39 30 2237 24 91 82 74 65 56 47 38 30 2136 25 91 82 73 64 56,) 47 38 29 20 ' 35 26 91 82 73 64 55 46 37 28 19 34 27 91 82 73 64 55 45 36 27 18133 28 91 81 72 63 54 44 35 26; 16.;32 29 91 81 72 62 54 44 35 25 1531 30 91 81 72 62 53 43 34 24 1 5l30 31 90 81 71 61 52 42 33 23 14 2 32 90 80 71 61 61 41 31 22 1228 33 90 80 70 60 51 41 31 21 10127 34 90 80 70 60 50 40 30) 20 10126 35 90 80 69 59 50 __39 29 18 08 25 36 90 79 69( 59 49 38 28 -8 0(-7 -24 37 90 79 6 9 58 48 38 28 17 ()0623 38 89 79 68 58 47 36t 26i 15 05122 39 89 79 68 57 47 36i 25 14 04121 40 89 78 68 67 46 365 24 14 03120 41 89 78 67 56 45 34 2.3 12 0 19) 42 89 78 67 66 45 33 22 11 00118 43 89 78 66 55 44 33 22 10 8.9899 17 44 89 77 66 54 43 32 20 09 971l6 45 89 77 66 54 43 31 20 08 97 15 46 88 77 65 53 42 30 18 06 9 14 47 88 76 65 63 41 29 17 05 94113 48 88 76 64 52 41 29 17 05 93112 49 88 76 64 62 40 27 16 03 91 11 50 88 76 63 51 39 27 15 02 90 1 51 88 75 63 50 38 26 1-3 1 88-o 9 62 88 75 63 50 38 25 13 00 88 8 53 88 75 62 49 37 24 12 7.9898 8(; 7 54 8 74 62 49 36 23 10 98 85 6 55 87 74 61 48 35 22 (9 96 83 5 66 87 4 61 48 35 21 08 95 8 4 67 87 73 60 47 34 20 07 94 80 3 68 87 73 60 46 33 20 06 93 79 2 59 87 7 3 59 46 32 18 05 91 78 1 60 0.9986 1.9973 2.9959 3.9945 4.9932 5.9918 6.9904 7.9890 8.9878 0 1 2 3 54 - -6 7 8 9 DEPARTURE 87 DEGREES. I I =I 'l DEPARTURE 2 DI)EGREES. 79.49 1 02 3 T — 4 4~46~ 7 8 ~ 9 34 1Oi 0.3490 ).0698 0.1047 0. 1396 0145. 0.217457 0.20 3141 1 520.0704 56 0.1408 60 0.2111 63 0.2815 67159 2 55 10 64 1 1 74 29 84 38 93158 3 58 15 69 31 89 48 0.2504 62 0.321957 4 61 21 82 42 0.1803 64 24 85 4556 5 64 27 91 54 18j 81 445 0.2908 72 55 66 - 33 -99 6- 32 X98 63 — 31. 8 54 7 69 ] 39 0.1108 77 47 0.2216 85 54 0.3324 53 8 72 45 17 89- 62 34 0.2606 78 51 52 9 75 50 2( 0.1500 7 51 26 0.3002 7751 110 8 56 34 12 9 1 69 47 25 0.3403 50 11 81 6 43 24 0.1905 86 67 48 29 49 12 84 (8 52 '36] 2010.2303 87 71 55 48!13 87 74 0 47 34 21 0.2708 94 81 47 14 90 79 69 59 49 38 28 0.3118 0.3507 46 15 938 85 78 70 (,3 _56 48 41 33 45 16 96 (91 87 82 7 '73 69 64 60 44 117 98 97 5 94 94 90 89 87 8(643 18 0.0401 0.0901 0.31204 0.1605 0.2007 0.2408 2.2809 0.3210 0.3612 42 1!) 04 08i 13 17 21 25 29 34 18 41 20 ) 07 14 21 28 36 43 50_ 57_ 64 40 i21 10 201 80 4( 5)1 60 70 80 90 39 I 22 13 26i 39 52 65 7 7 90.330 0.33030.31 38 2/3 16(; 31 48 6i4 7 9)5 0.29111 27 43 37 i24 19. 38 56; 75 940.2513 32 50 69136 25 21 4 43 ( 87 0.2109 301 52 74 95 35 2; 25; 4 74-1 98 23! 48 72 9 '7 0.3821 34 127 28 55, 88 0.1710 38 651 90310.3420 48 33 28 3o 61 91 22 52 82 0.301 3 43 74132 129 33 6710.1300 33 670 0.2600) 331 66fi0.3900131 130. 36 _ 72 09 45 0.21811 171 53 90 26 30 31 3' 78 17 56 196 3 74 0.3513 52 29 132 42 84 26 680.22101 2 94 36 78128 33 45 90 35 801 2 69 0.3114 59 0.4004 27 134 48 961 43 931 39 87 35 82 3026 35 51 0.0901 52 0.1803 54I 0. 204 55 0.3606 66 25:36 54 07 61 14 68 22 75 29 82 24 37 56 13 69 26f 82 38 95 52 0.4108 23 38 59[ 19! 78 38 97 56 0.3216 75 3522 139 62 256 87 49 0.2312 74 36 98 61 21 i40 65 31 961 661 27 92 57 0.3722 88 20 i41 68 36 0.14()5 7 41 0.2809 77 46 0.4214 19 42 71 42 13 84 56 27 98 69 4018 1 43 74 48 22 96 70 4410.3318 92 66 17 44 77 54 3110.1908 85 62 3810.3815 92 16 45 8() 60 319.19 99 _79 59 38 0.4318 15 1l4 83 65 48 3 1 0.2414 96 79 62 4414 47 86 71 57 42 2810.2914 99 85 70113 148 89 77 66 54 43 3110.3420 0.3908 9712 149 91 83 74 66 57 48 40 31 0.442311 50 394 89 83 77 72 66 360 546 49 10 51 '37 94 92 89 86 88 801 78 75 ~9 52 0.0500 0.1000 0.1500 0.2000 0.2501 0.3001 0.3501 0.4001 0.4501 8 53 03 06 09 12 15 18 21 24 27 7 54 06 12 18 24 30 35 41 47 63 6 j55 09 18 26; 35 44 ' 53 62 701 79 5;56 1'2 231 3.51 471 691 701 82 9410.4605 4 57 15 29 44 58 73 88 0.3602 0.4117 31 3 58 18 35; 53 70 88 0.3105 23 40 68 2 i 59 21 41 2 82 0.2603 23 44 64 85 1 60 0.0o523 0.1047 0.1570 0.2094 0.2617 0.3140 0.3664 0.4187 0.4711 0 i — 1 -- 2 ---_ —3 | 4- |5 6-J - 7 — — 8 ~ 9 ILATITUIJE 87 ])E(IREES. so LATITUD)E 3 DEGREES. ~~ 1 2 3 ~~~~~~ 4 5 6 7 8 9 0 0. 99 86 1-9 97 3 2-9 9-59 3.B5 4. 9932 5.9 9 18 6.9904 7.989., 89.9877T i 60.1 8 6 7 2 5 8 4 4 31I 1 7 0 3 8 9 75 59 2 8 6 7 2 5 8 4 4 3 0 1 6 02. 88 74 58 3 86 712 5 7 4 3 29 1 5 01 86 72 57 4 86 7 1 57 43 2 9 1 4 00 86 71 56 5 86 7 1 57 42 28 1 36.9899 84 7055 -85 71 56 42 27 12 98 8369 4 7 85 0 556 419 267 11 96 82 67 53 8 85 70 55 40 26 11 96 81 66 62 9 85 70 54 40 25 09 94 79 64 51 10 85 69 54 39 24 08 9, 78 65 11 8 5 69 54 38 23 08 9 7 7 61 49 12 84 69 53 38 22 06 91 75 60 48 13 84 69 53 37 21 ~~~ ~~~05 89 74 5i 47 14 84 68 52 36 21 05 89 73 57 46 15 84 68 52) 36 20 03 87 71 5545 67 ~84 68 5 389 3 87' 7 544 17 84 67 51 34 1 8 02 85 69 524 1 8 83 67 50 34 1 7 00 84 67 5142 1 9 83 67 510 33 1 75.9900 83 66 50 41 20 83 66 49. 32 1 65.98991 82 65 48 40 21 83 66 49 32 15 ld7' 80 6 3 46 39 22 82 65 48 31 14 96 79 62) 44 38 23 82 65 48 30 13 906 78 6 1 42 37 24 82 65 47 30 1 2 94 7 7 59 42 361 25 82 64 47 29 11 93 7 5 58 403 26 82 64 46 28 1 1 93 75 57 39 341 27 82 64 46 28 10 91 7i3 55 37 33~ 28 82 63 45 27 019 90 7T2 54 35 32 29 82 63 45 26 08 881 70 52 34 31 30 81" 63 44 25 07 881 6 9 50 32 3 0 81 81l ~62 44 25 01 87 68 605 19 32 81 6 2 4 3 24 05 86 67 4 8 29.)28 33 81 62) 42 2 3 04 85 66 46 27 27 34 81 61 42 22 03 84 64 45 2 O,2 6 35 80 61 41 22 02 82 63 43. 24 25 36 80 61 41 21 02 82 62 42 2832 4 37 80 6 o 40 20 01 81 61 41 21 23 38 80 60 40 20 00 79 5")9 39 1 9 22. 8 9 80 59 3 9 19(, 4.98~ 78 58 38 17 21 40 80 59 39 18 9 8 7 7 57 3 6 16 20 41 79 59 388 1 97 76 55 34 14 19 42 79 58 38 1 7 96 7,5 54 34 13 18 43 79 58 37 1 6 95 7 4 53 32 11 171 44 79 58 36 15 94 7 3 52 30 09 161 45 79 57 36 14 9 72 50 29 07 151 -46 ~78 57 35 ~14 92- ~70 -49 2Y7 06 141 47 78 ~~~56 35 1 91 69 47 26 04 13 48 7 8 56 34 12 910 68 46 24 02 12 49 78 56 33 11 89 67 45 22 00 11' 50 78 55 33 10 88 66 43 211 8.971 98S10 -6-1 ~777 5 ~32 10o 87 64 42 19 97 9 52 77 54 32 09 86 63 40 18 95 8 53 77 54 a 08 85 62 39 6 79 54 77 54 3`0 07 84 61 38 14 91 6 55 77 53 30 06 83 60 36 13 8 q 56 76 53 2)9 06 82 58 35 11 88 -4 57 76 52 29 05 81 57 33 10 86 3 88 76 52 28 04 80 56 32) 08 84 2 59, 76 52 2 7 03 79 55 3 1 06 82 1 60 0.9976 1.9951 2.9927~ 3.9902 4.9878 5.9854 6.9829 7.9806 8.9780 0 - 2 3 4 6-d 7f 89 DEPARTURE 86 DEGREES. t;~:~'~ ~'; ~ ~i ~ii ~~ ~* ":z ':~.P,: -- n,.a? i.;.~:;~ r'r iZ-i:%~ I DEPARTURB 3 DBWRESS. 81 7 1 2 8 4 5 6 7 8 9 7 0 0.0623 0.1047 0.1570 0.2094 0.2617 0.3140 0.3664 0.4187 0.4711 6' 1 26 63 79 0.2106 32 58 84 0.4210 3769 2 29 68 88 17 46 760.3704 34 6358 3 32 64 96 28 61 93 25 67 8967 4 36 700.1605 40 7560.3210 45 800.481566 6 38 76 141 62 90 27 65 0.4303 4166 6 41 82 22 63 0.2704 4 86 26 67~64 7 44 77 31 75 19 620.3806 60 9353 8 47 93 40 86 33 80 26 730.4919652 9 50 99 49 98 48 97 47 96 4661 10 562 0.1105 67 0.2210 62 0.3314 67 0.4419 7250 11 55 11 66 21 77 22 87 42 98549 12 68 16 75 33 91 490.3907 66 0.502448 13 61 22 83 44 0.2806 67 28 89 6047 14 64 28 92 56 20 84 48 0.4512 7646 16 67 34 0.1701 67 35 0.3401 68 3560.5102 46 18 70 40 09 79 49 19 89 58 1844 17 73 45 18 81 64 36 0.4009~ 82 4443 18 76 51 27 0.2302 78 64 290.4605 8042 19 79 67 36 14 93 71 50 28 0.520741 20 81 63 44 26 0.2907 88 70 51 3340 21 84 69 63 38 22 0.3506 91 76 6039 22 87 75 62 49 37 240.4111 98 8638 23 90 80 71 61 61 41 310.4722 0.5312 37 24 93 86 79 72 66 59 52 25 3836 265 96 92 88 84 80 76 72 48 6436 26 99 98 97 96 95 93 92 91 9034 27 0.0602 0.1204,0.1805 0.2407 0.3009 0.3611 0.4213 0.4814 0.6416 33 28 05 09 14 19 24 28 33 38 4232 29 08 15 23 30 38 46 53 61 6831 30 11 21 32 42 53 63 74 84 9530 31 13 27 40 64 67 80 94 0.4907 0.5521 29 32 16 33 49 65 82 980.4314 30 4728 83 19 88 68 77 960.3715 34 54 7327 34 22 44 66 880.3111 33 65 77 9926 35 24 50 75 0.2600 25 50 7560.60000.662626 36 28 66 84 12 40 67 95 23 5124 37 31 62 92 23 64 850.4416 46 7723 38 34 670.1901 35 690.3802 36 700.670322 39 37 73 10 46 83 20 66 93 2921 40 40 79 19 58 98 37 770.6116 6620 41- 42 85 27 700.3212 64 97 39 8219 42 45 91 36 81 27 720.4617 62 0.680818 48 48 96 45 92 41 89 37 86 3417 44 510.1302 630.2604 660.3907 680.6209 6016 46 54 08 62 16 71 24 78 32 8616 46 67 14 71 28 85 41 98 66 0.6912 1' 47 60 20 79 39 99 690.4619 78 3813 48 63 26 88 61 0.3314 76 39 0.6302 6412 49 66 31 97 62 28 94 69 26 8011 60 69 37 0.2006 74 43 0.4011 80 48 0.6017 10 61 71 43 14 86 57 280.4700 71 43 9 62 74 49 23 97 72 46 20 94 698 53 77 5566 31 0.2709 87 64 40 0.6422 96 7 54 80 60 41 21 0.3401 81 61 42 0.6122 6 66 83 66 49 82 16 99 82 65 48 6 6 —86 72 68 44 30 0.4116 0.4802 88 74i 57 89 78 67 66 46 33 23 0.556611 0.6200 8 58 92 84 75 67 69 61 43 34 26 2 59 95 89 84.79 74 78 63 58 52 1 60 0.0698 0.1396 0.2093 0.2790 0.3488 0.4186 0.4883 0.556661 0.6278 0 "'1- -- 2 8 4 5 6 7 8 9 LATITUDE 86 DEGREES. B ~~ -':4; ~: ~::; ~~ ~:;T ' 1 1 2 1 2 2 2. I 2 I B I I i r 3 2 LATITUDE 4 DORuBBE8...~~~~~~~~~~~~~~~~~~ 5 ~m 5 1 2 3 4 5 7 8 9 0 i 2 3;4:5!7 3O 0.9976 76 75 75 75 75 74 74 74 74 74 73 73 73 73 73 72 72 72 72 71 71 71 71 L 71 i 7C "7C r 0.997C 3 7( 7( ) 6' 2 8 1 I 4 I - 6 1, 6 7 1,,, _ 0 I 9 1.1951 2.9927 61 26 50 26 50 25 50 24 49 24 49 23 48 22 48 21 48 21 47 20 47 20 46 19 46 19 46 18 45 18 45 17 44 16 44 16 43 14 43 14 42 13 42 12 42 12 41 11 41 10 i 40 10 40 09 40 08 39 08 38 08 3.9902 02 01 00 3.9899 98 98 97 96 95 94 94 92 92 91 90 89 88 86 86 86 85 84 83 82 81 — 8 8C 7E 7E 77 3.9878 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 58 57 5 54 4I 5 ~i3 514 4 4; 7 4( 6.98654 6.92, 52 28 51 26 50 25 49 24 48 22 46 21 45 19 44 18 43 17 42 15 40 14 39 12 37 10 86 09 35 08 34 06 33 05 31 03 30 01 28 '00 27 6.9798 26 97 25 96 23 94 22 92 21 91 19 89 18 87 16 86 15 84 (.V~UO 03 02 00 7.9798 97 95 94 92 90 89 8o 85 83 82 80 78 77 75 73 71 70 68 66 64 62 61 59 57 5' 56 54 79 77 756 738' 71 70 - 68 66 64 62 51 58 56 54 53 51 49 47 44 43 41 39 37 35 33 31 29 26 25 23 20_ i\ B0 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 4C 38 3E 3(;3, 3' 31 3( I 3 7 I 5 i I I I 3 1 0 8 7 6 4).3.2.1 LO 11 32 81 36 351 40 42 43 44 45 46 47 49 41 I - - I 69 69 69 68 68 68 68 68 67 67 66 66 66 66 i 66 65 65 3 65 65 64 38 37 87 37 36 — 36 35 35 84 34 83 33 82 32 31 81 380 29 28c ~ I - - I - - I - A -,, i 07 06 06 05 04 03 03 02 01 00 00 2.9899 98 98 97 96 95 94 93 76 75 74 73 72 71 70 69 68 67 66 66 64 64 63 62 61 6a 58 6E 45 44 43 42 40 39 38 37 36 34 33 32 31 80 29 27 26 25 24 22 1l 12 11 10 08 07 06 04 03 01 00 5.9798 97 95 94 92 91 89 87 86 i oz 81 80 78 76 75 73 71 70 68 66 65 63 61 60 58 57 54 653 51 I - 51 50 48 46 44 42 41 38 37 34 33 81 29 27 26 23 22 19 18 L 15 20 18 17 15 12: 10 08 06 04 01 8.9699 98 95 98 91 87 87 85 82 80 21 2 2 2 2 1 1 1 1 1 1 ] I' i;::::.;Sz, .t~ ~'::'~-~~` f r i-i ~ -I- '~" i, ~~~:~ ~?: i ~~.~: 1 -- 64 28 93 7 21 85 49 14 78 9 62 64 28 92 56 20 83 47 11 7 8 58 64 27 91 55 19 82 46 10 78 7 64 64 27 91 54 18 81 46 08 72 6 66 68 26 90 63 16 79 42 06 69 "6 - 63- 26 89 52 15 78 41 04 67 4 67 68 25 88 51 14 76 39 02 64 3 88 63 26 88 60 13 75 38 00 63 2 59 62 24 87 49 11 73 35 7.9698 60 1 60 0.99621.9924 2.9886 8.9848 4.9810 5.9771 6.9733 7.9695 8.9657 0 1 9 2 8 D R4 A6T RE 8 9 D S. DEPABTURE 86 DEGREES. I,.~; c; -rl' r~ ~i., i k I DEPARTURE 4 DEGREBs. 88 1 - 2 I 8 4 6 I 6 7. _ _ 1. I j I u i I i L I 1 2 8 14 16 7 18 9 10 11 12 13 14 15 IG 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 48 44 46 46 47 48 49 5c U.Uoyu 0.0701 03 06 09 12 15 18 21 24 27, 30 32 35 38 41 44 47 50 53 56 59 61 64 67 70 73 76 79 82 85 88 90 93 9 99 0.0802 05 08 11 14 17 19 22 25 28 31 34 37 40 43 U. 1;iY 0.1401 07 13 18 24 30 36 42 47 63 58 65 71 76 82 88 94 0.1500 05 11 17 23 29 34 40 46 52 58 63 69 75 81 87 92 98| 0.1604 10 16 21 27 33 39 45 50 56 62 68 74 79 85 U. ZUV 0.2102 10 19 28 36 45 54 62 71 80 89 97 0.2206 15 23 32 41 49 58 67 76 84 93 0.2302 10 19 28 36 45 54 63 71 80 89 97 0.2406 15 23 32 41 50 58 67 76 84 93 0.2502 10 19 28 37 45 54 63 71 8C 89 98 0.2606 0.2615 0.279C 0.2802 14 25 37 48 6C 72 83 95 0.2906 18 3C 41 53 64 76 88 9j 0.3001 22 34 46 57 69 80 92 0.3104 15 27 38 50 62 73 85 96 0.3208 20 31 43 54 6C 78 89 0.3301 12 24 36 47 69 7C ri n nX00 U. 466 0.3503 17 32 46 61 75 89 0.3604 19 33 48 62 77 91 0.3706 20 35 49 64 78 93 0.3807 22 36 51 65 80 94 0.3909 23 38 52 67 81 96 0.4010 25 39 54 68 83 97 0.4112 26 41 55 70 84 99 0.4213 0.4186 0.4203 20 38 55 73 90 0.4307 25 42 60 77 94 0.4412 29 47 64 81 99 0.4516 34 51 68 85 0.4603 21 38 55 73 90 0.470O8 25 42 60 77 95 0.4812 29 47 64 82 99 0.4916 34 51 69 86 0.5003 21 38 56 I 0.4883 0.4904 24 44 64 85 0.5005 25 46 66 86 0.5107 27 47 67 88 0.6208 28 49 69 89 0.5309 30 50 70 91 0.5411 31 52 72 92 0.5513 33 53 73 94 0.5614 34 55 75 95 0.5716 36 56 76 97 0.5817 37 58 78 98 0.5919 89 59 79 0.6000 20 40 61 81 0.6101 0.6581 0.5604 27 50 74 97 0.5720 43 66 90 0.5813 86 59 82 0.5906 29 52 76 98 0.6022 45 68 91 0.6111 38 61 84 0.6207 30 54 77 0.6300 23 46 70 93 0.6416 39 62 86 0.6509 32 55 78 0.6602 25 48 71 94 0.6718 41 I I I I I I I t I 1 0.6278 0.6305 81 67 83 0.6409 35 61 87 0.6513 39 66 92 0.6618 44 70 96 0.6722 48 74 0.6800 27 53 78 0.6905 31 57 88 0.7009 851 61 98 0.7114 40 66 92 0.7218 44 70 96 0.7322 49 76 0.7401 27 68 79R 0.7506 81 67 88.., 60 69 68 57 56 655 64 [53 52 51 50 49 48 47 46 45 44 43 42 41 40 391 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 28 22 21 20 19 18 17 16 1i6 IT4 18 12 11 10 I,, 61 58 62 6f 54 55 67 6C 46 48 11 54 67 60 68 66 69 0.0872 91 97 0.1703 08 14 20 26 32 37 0.1740 82 94 0.3405 17 28 40 52: 63 75 0.8486 28 42 57 71 86 0.4300 15 29 44 0.4858 73 90 0.5108 25 43 60 17 95 0.5212 0.5230 64 87 0.6810 84 67 80 0.6903 26 60 0.6978 U.7610 86 62 88 0.7714 40 66 92 0.7818 0.7844 9 8:7 6 6 4 8 2 1 0 i I- 2 A D8 84 6 D6 T.j. 8E.,. LATITUDE 86 DEGREES.. -.. m c — ~r~~l ~.j —; ~ ~':: ~~~ ~~ ~;: ~r r I: ~ i `P: r.. 4.84 -LATITTUDN 6 DEGREBs..: 2 a 8 1 - -4 5 6 6 7 8 9_ ' 0 0.9962 1.4924 2.9886 3.9848 4.9810 5.9771 6.97338 7.9695 8.9657 60 1 62 23 85 47 -p9 69 81 94 56659 2 61 23 84 46 07 68 30 91 5868 3 61 22 84 45 06 67 28 90 61 57 4 61 22 83 44 05 65 26 87 48 56 60 21 82 43 04 64 24 86 46 55 6 60 21 81 42 02 62 23 83 44 54 7 60 20 81 41 01 61 21 82 42 53 8 60 20 80 40 00 59 19 79 8952 9 60 19 79 88 4.9798 58 17 77 37 51 10 59 19 78 38 97 56 16 75 35 50 11 59 18 - 77 386 96 55 14 73 32 49 12 59 18 76 35 94 53 12 70 2948 13 69 17 76 34 93 52 10 69 27 47 14 58 17 75 33 92 50 08 66 2546 15 58 16 74 32 90 48 06 64 22 45 16 58 16 73 31 89 47 05 62 20 44 17 58 15 73 30 88 45 03 60 18 43 18 57 14 72 29 86 43 6.9600 58 1542 19 57 1.4 71 28 85 42 99 56 13 41 20 57 13 70 27 84 40 97 54 10 40 21 56 13 6 26 82 38 95 52 08 39 22 56 12 69 25 81 37 93 50 06 38 23 56 12 68 24 80 35 91 47 0337 24 56 11 67 22 78 34 89 45 0036 26 56 11 66 21 77 32 88 42 8.9598 35 26 55 10 65 20 76 31 86 41 9634 27 55 00 64 19 74 29 84 48 93 33 28 55 09 64 18 73 27 82 36 91 32 29 55 08 63 17 71 25 79 34 88 31 30 54 08 62 16 70 24 78 32 86 30 31 54 07 61 15 69 22 76 30 8329 32 63 07 60 14 67 20 74 27 81 28 33 53 06 59 12 66 19 72 25 7827 34 53 06 58 11 64 17 70 22 7526 35 53 05 58 10 63 16 68 20 73 25 36 52 05 57 09 62 14 66 18 7124 37 52 04 56 08 60 12 64 16 6823 88 62 03 55 07 59 10 62 14 656 22 39 62 03 54 06 57 08 60 11 6321 40 61 02 53 _04 66 07 58 _09 60 20 41 1 02 52 03 54 05 56 07 657 19 42 51 01 52 02 53 04 54 05 5518 43 51 01 51 01 52 02 52 02 5317 44 50 00 50 00 50 00 50 00 5016 45 50 1.9899 59 3.9799 49 3.9698 48 7.9598 47 156 46 49 99 58 98 47 96 46 95 45 14 47 49 98 57 96 46 95 44 93 42 13 48 49 98 56 95 44 93 42 90 89 12 49 48 97 56 94 43 91 40 88 3711 651 48 96 55 93 41 89 37 86 83410 61 48 96 53 92 40 87 35 83 31 9 62 48 95 53 90 38 86 33 81 28 8 68 48 95 52 89 37 84 31 78 26 7 64 47 94 51 88 35 82 29 76 28 6 [665,47 93 50 87 34 80 27 74 20 56 66- 46 93 49 86 32 78 25- 71 18 4 67 46 92 48 84 31 77 23 79 15 3 68 46 92 47 83 29 75 21 66 12 2 69 46 91 47 82 28 73 19 64 10 1 60 0.9945 1.9890 2.9836 3.9781 4.9726 5.9671 6.9616 7.9562 8.9507 0 =1 _2 8_ 4 6 6 7 8 9W _ DEPARTURE 64 DEGREES. AJ ~rClrrrrrrrl,,.~II C C LII DEPARTURE s DEGR S. 86 0.082 8 4 8 __ 0 0.1743 0.2615 0.486 0468 0.520 0. 6101 0.i 1 76 49 24 98 ' 73 47 22 96 71 69 2 77 56 82 0.3510 87 64 42 0.7019 97 8 3 80 61 41 21 0.4402 82 62 42 0.7923 67 4 83 66 49 32 16 99 82 65 4856 6 85 72 58 34 30 0.5316 0.6202 88 74 5 6 8 78 67 66 46 38 22 0.711 0.800054 7 92 84 75 67 59 51 43 34 2663 8 95 89 84 79 74 68 63 58 5252 9 98 95 93 90 88 86 83 81 7851 10 0.0901 0.1801 0.3702 0.3602 0.4508 0.5403 0.6304 0.7204 0.8105 50 1 03 7 10 14 17 -- 20 24- 2 4 -81 12 06 13 19 25 32 388 44 50 6748 13 09 18 28 387 46 55 64 74 8847 14 12 24 36 48 61 73 85 97 0.8209146 15 15 30 45 60 75 9010.640650.7320 36545 T16 18 36U 541 72 9010.5507 25 — 43 - 61144 17 21 42 62 8310.4604 25 46 66 87143 18 24 47 71 95 19 42 66 90 0.831342 19 27 63 80 0.3706 3 60 8610.7413 8941 20 30 59 88 18 48 7710.6507 36 66140 2I1 32 651 - 7 621 94 2i 59 - 92139 22 35 7110.3806 41 7710.5612 47 8210.8418 38 23 38 76 15 53 91 29 6710.7506 4437 24 41 82 23 6410.4706 47 88 29 7036 25 44 88 32 76 20 6410.6608 62 961365 26 47 94 41 8 35 - 81| 28 7510.8522134 27 600.1900 49 99 4910.5709 49 98 48138 28 53 05 680.3811 64 16 6910.7622 74 32 29 66 11 67 22 78 34 89 45 0.8600831 30 59 17 76 84 93 51 0.6710 68 2730 31 611 2 843 46 0.4807 5- 30 1 91 63129 32 64 2 93 67 21 0.5803 4910.7714 78 28 33 67 3410.2901 68 36 20 70 3710.8704127 34 70 40 10 80 50 37 90 60 3026 35 73 46 19 92 65 5510.6810 83 6625 36 751 62 2710.3903 79j 721 310.78061 821 37 79 67 36 15 94 81 61 80 0.8808 23 38 82 68 45 2610.4908 90 711. 63 3422 89 85 69 64 38 23 0.6907 92 76 6121 |40 87 75? 62 50 37 24 0.6912 99 8720 41 — 90 81 71 61 - 2 - 320.7922s.89319 42 93 86 80 73 66 59 52 46 8918 43 96 92 88 84 81 77 73 69 6617 44 99 98 97 96 95 94 93 92 91161 46 0.1002 0.2004 0.3006 0.4008 0.6010 0.6011 0.7013 0.8015 0.9017 16 461 061 1 4 19 - 241 29 P 3 4f 47 '08 15 23 31 39 46 64 62 69113 48 11 21 32 42 63 64 74 85 96112 49 14 27 41 64 6 81 9510.8108 0.912211 60 16 33 49 66 82 9810.711 31 4810 61 191 38 4968 -77- 9610. s 34- 641 -78 9 62 22 44 66 89 0.5111 83 55 77 99 8 68 25 6~ 75 0.4100 25 60 7510.82000.9226 7 64 28 66 84 12 40 67 95 23 61 6 65 31 62 92 23 64 8610.7216 46 77 6 34 67610 3101 35 69 06-202- 86 70 1.98 021 - 67 87 73 10 46 83 20 66 93 29 8 68 40 79 19 68 98 3 7710.8316 66 2 69 42 865 27 7010.6212 64 97 39 82 1 600l.1046 0.2091 0.813610.4181 0.6226 0.6272 0.781710.8862 0.9408 o - 2 - | 4 6 6 D R 8 E LATITUDB 84 DEGRaES.S h I 88 LAt1TtTD 6 DEGREES. 1( 1( 5 7 9? I 46 45 44 44 43 43 43 43 42 42 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 41 41 41 41 40 40 40 40 39 38 38 38 38 38 37 37 86 36 36 36 1.9890 90 89 89 88 88 87 87 86 85 84 83 83 82 82 80 80 79 79 78 78 77 77 76 75 74 74 73 73 72 71 6 2.9836 33 34 33 32 31 _ 8. 30 29 28 27 26 4 3.9781 79 78 77 76 75 74 72 71 69 68 25 25 24 23 22 20 19 18 17 16 15 14 13 12 11 10 09 08 07 67 66 65 64 62 61 59 58 57 56 54 53 52 51 49 48 47 46 44 43 6 4.9226 24 23 21 20 18 17 15 14 12 11 09 08 OS 06 05 03 01 4.9699 98 96 95 93 92 90 89 87 85 83 82 80 79 6 5.9671 69 68 66 64 62 60 59 57 64 58 7 6.961d 14 12 1C OE 08 06 04 02 OC 6.9597 95 I ) I 1 I L-, I 51 49 47 46 43 41 39 38 36 34 32 3C 24 22 2C 18 16 14 93 91 88 86 84 81 79 77 75 73 70 68 66 64 62 59 57 55 52 50 I 34 32 30 27 25 22 19 17 14 12 09 06 04 02 7.9499 96 94 91 88 86 76 74 71 68 65 62 59 56 54 51 48 45 42 89 36 33 30 28 24 21 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 31 31 30 8 7.9562 59 57 54 52 50 47 45 42 39 37 r I 8.9507 04 01 8.9499 96 98 91 98 85 82 79 06 59 58 57 56 55 54 53 52 51 50 831 85 70 0-6 41 77 12 48 83 1929 82 85 70 05 40 76 11 46 81 1628 83 85 69 04 39 74 08 43 78 1827 84 34 69 03 38 72 06 41 7 1026 85 34 68 02 36 70 04 38 73 07 25 86 -34 67 01 35 69 02 36 70 03 24 87 83 66 00 33 67 00 34 67 0123 88 83 662.9799 32 665.9599 32 65 8.939822 89 83 65 98 31 64 96 29 62 9521 40 82 65 97 30 62 94 27 59 92 20 41 32 64~ 96 28 60 92 24 56 8819 42 82 63 95 27 59 90 22 54 8518 483 31 62 94 25 7 88 20 61 8217 44 81 62 93 24 55 86 17 48 7916 45 81 61 92 22 53 84 15 46 76156 46 30 61 91 — 21 52 82 12 42 J814 47 30 60 90 20 50 80 10 40 0 13 48 30 59 89 19 49 78 08 38 6712 49 29 58 88 17 47 76 05 84 6411 50 29 58 87 16 45 74 03 32 6110 561 29 57 86 14 43 72 00 29 68 9 62 28 67 85 13 42 70 6.9498 26 66 8 63 28 66 84 11 40 68 95 23 61 7 64 28 55 83 10 38 66 93 21 48 6 665 27 54 82 09 36 63 90 18 46 6 6 -27 54 81 08 35 61 88 15 42 4 657 27 63 80 06 83 p9 36 14 89 8 58 26 62 79 06 31 67 83 10 86 2 59 26 61 78 03 29 55 81 06 838 1 60 0.9926 1.9851 2.9777 8.9702 4.9628 5.9553 6.9479 7.9404 8.9880 0 DEPARTURE 83 iDEouss.; X..TVW.!.- 7^ -...,] I Ir 0i 971iTuz 6 1D nuus. 37 _ 4 6 6 _ _7 00.104U0.2091 0.4181 o.V27y.62 0.7817 0.8362 0.40 110.0748 97 48 93 741 89 87 86 84 69 2 61 0.2102 58 0.420 66 0.6807 68 0.8409 6058 3 64 08 62 16 70 24 78 82 8657 4 57 14 71 28 85 41 98 650.951256 5 60 1 79 39 99 68 0.7418 78 37875 6 j 25 88 31 7 8 63 64 66 81 97 62 28 93 59 24 90 53 9 71 43 14 85 57 28 99 70 42561 10 74 48 23 97 71 350.7519 94 6850 9110 j I -r 3 -11 77 N 0.E4308 53 40 0.80617~ 9449 9 12 80 0 40 200.5400 80 60 40 0.972048 13 83 6 49 32 15?0.6507 80 63 46S47 14 86 72 57 43 29 15 0.7601 86 7246 15 88 77 66 55 44 2 21 0.8710 984 T6 921 76 58 60 41 88 0.9824 4 17 95 89 94 78 73 77 6 66 51148 18 97 95 92 89. 87 84 81 78 76 42 190.1100 0.2200 81 0.4401.0.5501 0.6601 0.7701 0.8802 0.990241 20 03 06 0.3309 12 16 19 22 25 2840 i 06 121 18 24 350; - 42 48 T41W 22 09 18 27 6 45 53 62 71 808 23 12 24 85 43 59 71 83 94 1.0006 87 24 15 29 44 59 74 880.7803 0.8918 3236 25 18 35 53 70 88 0.6706 23 41 58236 26 21 |41 629 82 0.5603 23 44 66 | 853 27 28 47 70 94 17 40 64 871.011133 28 26 58 790.4505 82 58 840.9010 87 82 29 29 58 87 16 46 750.7904 83 6281 80 32 64 96 28 60 92 24 56 88830 31I 351 7008406 40 750.6809 44 79 T1.0O214)W 82 38 76 13 51 89 27 65 0.9102 4028 33 41 811 22 6. 0.5704 44 85 26 6627 34 44 87 1 74 1 62 0.8005 69 92 26 85 47 93 40 86 32 79 26 '92 1.0 19 26 4 99 48 98 47 46 95 624 87 62 0.2305 67 0.4609 62 0.6914 66 0.9218 71 23 88 55 10 66 21 76 81 86 42 9722 89 58 16 74 82 90 48 0.8106 64 1.0422 22 40 61 22 88 44 0.5805 65 26 87 48 20 ~41~ C41 llt) 91g 19 83 47 -.9-31o6- Z' 7.1W9 42 67 33 0.3500 34 0.7000 67 84 1.0500 18 43 70 39 09 78 48 18 87 57 3617 44 78 45 18 90 683 350.8208 80 58 16 45 75 51 26 0.4702 77 52 28 0.9403 79 15 46T 78 657`9 92 70 48 26TU 169 47 81 62 44 25 0.5906 87 68 50 31 13 48 84 68 52 86 200.7104 88 72 612 49 87 74 61 48 85 21'0.8308 95 821 l. 50 90 80 69 59 49 89 29 0.9518 1.0708 10 61 93 5 783 64 56 46 4 QU 9 52 96 91 87 82 78 74 69 65 0 8 58 99 97 96 94 98 91 90 88 87. 7 64 0.1201 0.2408 0.3604 0.4806 0.6007 0.7208 0.8410 0.9611 1.0813 6 66 04 09.13 17 22 26 80 84 8965 56l 07 1 42 f1 85 43 0 57 4 67 10 20 830 40 50 60 70 80 908a 68 18 25 89 62 65 77 90 0.9708 1.0916 2 69 16 81 47 63 79 95 21 26 421 60 0.1219 0.2487 0.86660.4875 0.6094 0.78120.85831 0.9750 1.0968 G I-8 42 - 3 6 r7 -rll LATITUDE 83 DEGRERzS. 8a 5.p I 41 4 1 8 0 1 2 3 1 5 I 1 0.992( 26 2E 24 24 23 I 5 5 I I I 2 1.9851 60 50 49 48 48 8 2.9777 75 74 73 72 70 U 3.9699 97 96 J94 24 22 20 18 I 01 49 46 44 42 ID 74 71 68 65 7.904 8.980 60 01 26 59 7.9398 2358 95 1957 92 1656 89 13655 6 23 47 70 93 17 40 63 86 1054 7 23 46 69 91 15 38 60 83 0658 8 23 45 68 90 13 36 58 81 03 52 9 22 44 67 89 11 33 55 78 0051 10 22 44 66 88 10 31 53 75 8.9297 50 11 21 43 64 86 08 29 50 72 93 49 12 21 42 63 84 06 27 48 69 90 48 18 20 41 62 83 03 24 45 66 87 47 14 20 41 61 82 02 22 43 63 84 46 15 20 40 60 80 00 20 40 61 80o45 16 20 39 59 79 4.9599 18 38 58 77144 17 19 39 58 77 97 15 35 64 73 43 18 19 38 57 76 95 13 32 51 7042 19 18 37 56 74 93 11 29 48 66 41 20 18 36 55 73 91 09 27 46 64 40 21 18 356 54 71 89 07 25 43 6139 22 18 35 53 70 88 05 23 40 58 38 23 17 34 51 68 86 02 20 37 54 37 24 17 33 50 67 84 00 17 34 50 36 25 16 33 49 65 82 5.9498 14 31 47 35 26 16 32 48 64 80 96 12 28 44 34 27 15 30 47 62 78 93 09 25 40 33 28 15 30 46 61 76 91 06 22 37 32 29 14 29 44 69 74 88 03 18 36131 80 14 29 43 58 72 86 01 15 30 30 31 14 28 42 56 70 84 6.9398 12 26 29 32 14 27 41 55 69 82 96 10 23 28 83 13 26 40 53 67 80 93 06 19 27 84 13 26 39 52 65 78 90 03 16 26 86 12 24 38 50 63 75 87 00 13 25 86 12 24 37 49 61 7 3 85 7.9298 10 24 87 11 23 35 47 59 70 82 94 06 23 88 11 23 34 46 57 68 80 91 03 22 89 11 22 33 44 55 66 77 88 8.9199 21 40 11 21 32 42 53 64 74 85 95 20 41 10 20 30 40 51 61 71 81 9119 42 10 20 29 39 49 69 69 78 8818 48 09 19 28 37 48 67 66 75 8517 44 09 18 27 86 46 65 64 73 8216 45 08 17 26 34 44 62 61 69 7815 4 08 17 25 3S 42 60 59 6 75- 47 08 16 24 31 40 47 56 63 7118 48 08 16 23 30 38 45 53 60 6812 49 07 14 21 28 36 42 60 57 6411 60 07. 13 20 27 34 40 47 64 6010 61 06 12 19 25 32 37 44 0 66 9 62 06 12 18 24 30 35 41 47 68 8 68 05 11 16 22 28 33 88 44 49 7 64 06 10 15 20 26 31 86 41 46 6 65 04 09 14 18 24 28 33 37 42 6 6 04 09 13 17 22 26 80 84 89 4 67 04 08 12 15 20 23 27 81 35 3 68 04 07 11 14 18 21 25 28 32 2 69 08 06 09 12 16 18 22 25 28 1 60 0.9908 1.9805 2.9708 3.9611 4.9514 6.9416 6.9319 7.9222 8.9124 0 l 3- 2 8 4 6 -~ 8-1 7 -8.DBPAUTURE 82 DEoRBE8. I1 DBPARTURB 7 DEGREES. 89 -\ l 7 |- 8 | 4 | 6 | 6 |- 7L | --- 8 J -- 6 I ] 1 1 I f 83 4 8 4 4 4 4 4 4 ] 4 4 4 5 6 6 6 61 5' 61 0 1 2 3 4 6 6 7 8 9 LO.1 L2 23 t4 15 18 t7 18 19 2O 21 12 ~3 24 25 06 ~.7 )8!9 ]0 0.1219 22 26 27 30 38 36 39 42 45 48 50 53 56 59 62 65 68 71 74 76 79 82 85 88 91 94 97 0.1300 02 05 I I I I I I 0.2437 48 49 55 60 66 72 78 84 89 95 0.2501 07 12 18 24 30 36 41 47 58 59 64 70 76 82 87 98 98 0.2605 11 0.8666 65 74 82 91 99 0.3708 17 25 34; 43 51 60 69 77 86 95 0.3803 12 21 29 38 47 55 64 72 81 90P 99 0.3907 16 0.4876 86 98 0.4910 21 82 44 56 67 79 90 0.5002 13 25 36 48 60 71 82 94 0.5106 17 29 30 52 63 75 86 98 0.5210 21 0.6094 0.6108 23 87 61 66 80 95 0.6209 24 38 52 67 81 96 0.6310 25 39 58 68 82 97 0.6411 26 40 54 69 83 98 0.6512 27 0.7312 29 47 64 81 99 0.7416 33 51 68 86 0.7502 20 37 55 72 89 0.7607 24 41 58 76 93 0.7711 28 45 62 80 97 0.7814 32 0.8631 51 72 92 0.8611 82 52 72 93 0.8713 33 53 73 93 0.8814 34 54 75 94 0.8915 35 55 75 96 0.9016 36 56 76 97 0.9117 37 0.9761 73 96 0.9819 42 65 * 88 0.9911 34 58 81 1.000j 26 5C 78 96 1.011l 42 65 88 1.0211 34 58 81 1.0304 26 50 73 96 1.0419 42 42 Ij r I 3 I I 1.0968 94 1.1021 47 72 98 1.1124 60 76 1.1202 28 654 80 1.1806 32 58 84 1.1410 35 62 88 1.1514 40 66 92 1.1617 43 69 96 1.1722 48 59 58E 5'i 5( of 56 56 54 51 5C 4i 47 46 45 44 48 42 41 4C 39 38 37 36 135 34 38 32 31 30 I1 12 13 4:5:6 17:8 39:0:2 4 5:6 7 8 9 0 08 11 14 17 20 23 25 28 311 34 371 40 43 46 49 51 64 67 60 63 I 16 22 28 34 39 45 51 57 62 68 74 80 85 91 97 0.2703 09 14 20 26 24 33 42 5C * 56 68 76 85 94 0.4002 11 20 28 37 46 54 63 72 80 89 32 44 56 67 79 90 0.5302 13 25 36 48 60 71 82 94 0.5406 17 29 40 52 41 55 70 84 99 0.6613 27 42 56 71 85 0.6700 14 28 43 57 72 86 0.6800 165 4b 66 83 0.7901 18 36 52 70 87 0.8005 22 39 566 74 91 0.8108 26 43 60 77 57 77 97 0.9218 38 58 78 98 0.9318 39 59 79 99 0.9419 40 60 80 0.9500 20 40 65 88 1.0511 34 58 81 1.0603 26 60 73 96 1.0719 42 65 88 1.0811 34 68 80 1.0903 78 99 1.1825 51 77 1.1903 29 65 81 1.2007 33 69 84 1.2110 37 63 89 1.2216 40 66 I I 29 28 27 26 26 24 23 22 21 20 19 18 17 16 16 14 18 12 11 10 F F F F I I I F t 5I 5 t 31 I I I' I II I I ) [ 1 2 3 4 5 6 7 81 9 0 66 69 72 74 77 80 83 86 89 0.1892 i 31 37 48 49 66 60 66 72 78 0.2783 97 0.4106 15 23 32 41 49 68 67 0.4176 0o 75 86 98 0.6509 21 32 44 66 0.6667 44 68 72 87 0.6901 16 30 46 0.6959 ub 0.8212 30 46 64 81 99 0.8316 33 0.8350 61 81 0.9601 21 41 61 82 0.9702 22 0.9742 2t 60 78 95 1.1018 42 65 88 1.1111 1.1134 I I I I I I - 1.2318 44 76 96 1.2422 48 74 1.260C 1.2526 I i 9 8 7 6 5 4 8 2 1 0 I_ — I 1 1 —2 -- 4 I 6 1 6.1 7 -1 8.|9~I LATITUDE 82 DEGREES. C w...... I*.-:: -,67; -9,)-~ 1 TLAT1D!,8 DEG11I98. _____ 8 4 6 ~~~~946 73 8___ 91 60 00.9908 1.980b 2.9708 8.9611 4.9B51 9T 6.917.228146 1 '02 05 07 09 1 2 1 4 1 6 1 8 21 59 2 02 04 06 08 09 1 1 1 3 1 5 17 58 3 01 08 05 06 08 09 1 1 1 2 1457I 4 01 02 03 04 06 07 08 09 10566 5 00 01 02 02 03 04 04 05 05 55 6 00 0 1 0 1 01 01 02 25 7 0.9899 00 2.9699 3.9599 4.9499 5.9399 6.9299 7.9198 8.9098 53 8 99 1.9799 98 98 97 96 96 95 95652 9 99 98 97 i 96 95 94 93 92 91 51 10 99 97 96 94 93 92 90 89 87 50 11 98 96 95 93 91 89 87 8 84 49 -12 98 96 98 91 89 87 85 82 80 48 13 97 95 92 89 87 84 81 78 77 47 14 97 94 91 88 85 81 78 75 72 46 15 97 93 90 86 83 79 75 72 69 45 16 96 92 8 4 81 -7 7 73 69 64 17 96 91 87 83 79 74 70 66 6143A 18 95 91 86 81 76 7 2 67 62 58 42 19 95 90 84 79 74 69 64 58 53 41 20- 94 89 83 78 72 66 61 55 50 40 21 94 88 82 76 710 ~64 58 5R2 ~4639 22 94 87 81 74 68 62 55 49 42 38 23 93 86 79 72 66 59 52 45 38 37 24 93 85 78 71 64 56 49 42 34836 25 92 85 77 69 62 54 46 38 31 35 'T 952 -— 8!4 7N6 ~68 60 51 ~43 35 27 34 27 91 83 74 67 57 48 40 31 23,33 28 91 82 73 64 55 46 37 28 19 32 29 91 81 72 66 53 44 84 25 15381 30 90 80 71 61 51 41 31 22 12 30 1 90 79 69 59~ 49 38 28 18 0829 32 89 79 68 57 47 36 25 14 04 28 33 89 78 67 56 44 33 22 10 00 27 34 88 77 65 54 42 30 19 07 8.8996 26 35 88 76 64 52 40 28 16 04 92 25 -6 8 8 ~ 75 63 5 ~38 ~26 13 01 ~ 882-4 8 7 8 7 74 6 1 48 3 6 2 3 10 7.9094 84 28 880 8 7 7 3 6 0 47 3 4 2 0 07 9 4 80 22 3,9 86 7 3 5 9 45 3 2 1 7 0 4 90 77 21 40 8 6 7 2 57 4 3 2 9 1 5 0 1 86 72 20 Ti ~85 7 1 56 ~42 207 12 6.9~198 83 ~69 19 42 85 '70 55 40 25 09 94 79 6418 43 84 69 54 38 23 07, 92 76 61 17 44 84 68 52 36 21 05 89 73 57 16 45 83 67 51 34 18 02 85 69 53 15, 46' 88 ~66 50 33 1656.9299 82 66 49 14 47 82 65 48 31 14 96 79 62 4418 '48 82 65 47 29 12 94 76 58 41 12, 49 82 64 45 27 00 91 73 54 311 60 81 63 44 26 07 88 70 51 33 10 -61 81 62 — 43 24 05 85 6 6 ~4~7 289 62 81 61 42 22 08 83 64 44 25 8 638 80 60 40 20 00 80 60 40 20 64 80 59 39 18 4.9398 78 57 37 16 6 55 79 58 3 7 1 6 96 75 54 33 12 5 75~~Y9 57 ~36 1 94 72 51 30 08~ 5 7 78 56 35 13 91 69 47 26 0483 58 78 56 33 11 89 67 45 22 00 2 9 77V 55 32 09 8 7 64 41 18 8.8896 1 80 09877 1.9754 2.9631 3.9508 4.19385 5.9261 6.91L38 7.9.015 8.8892 0 1 2 3 4 46 16 7 8 9 I 'I DEPARTURE 6S1 DEGREES. I I ; j, i 0., i qjlt DIBPAITUUI PGN.9, 1 2 8 ~ ~~~4 6 ~7 8 9 6.19202783 0.4-176 0.66567 0.6969 0.836 0.9742 1.11841226I 1 96 89 84 78 73 68 62 657 6159 2 98 95 94 90 88 85 83 80 7868 3 0.1400 0.2801 91 0. 6602 0.7002 0.8402 0.9803 1.1203 1.2604 67 4 03 M 0.4210 -13 17 20 23 26 81 66 6 06 12 18 24 31 87 43 49 66655 6ii-i -8 273~ 6 4554 ~63 ~ 72 81,64 7 12 24.36 48 60 71 83 95 1.27Q7 68 8 16 30 44 69 74 89 0.9904 1.1318 33 62 9 18 35 53 '71 89 0.8506 24 42 69 51 10 21 41 62 '82 0.7103 23 44 64 86650 11 23 ~~47 -70 94 17 40 64 87 4814 12 26 53 79 0.6705 32 58 84 1.1410 34 1:3 29 58 88 17 46 75 1.0004 34 63 47 14 32 64 96 28 60 92 24 66 88 46 15 35 700.4305 40 75 0.8609 44 79 1.29114 46 16 38 76 13 51 89 2 7 65 1.1502 4044 1 7 41 8 1 2 2 63 0.7204 44 85 26 66 43 1 8 44; 87 3 1 7 4 1 8 62 1.04105 49 9242 1 9 46 93 3 9 86 3 2 7 8 25 7 11.30118 41 20 49 99 48 9 7 47 96 45 94 44 40 21 520.'2904 ~57 0.5~8019 61087 5 1.161870O39 22 55 10 65 20 76 3 8 41 938 23 58 10 74 32 90- 48 1.0206 64 1.3122 3 24 61 22 82 430.'7304 65 26 86 47 36 25 64 27 91. 65 19 82 46 1.1770 73 35 ~~ 67~ ~~0.44001 66 330.8800 66 33 99 34 27 70 311 09 78 48 1 7 86 66 1.3226 33 28 72 45 17 89 62 34 1.0306 78 61 32 29 75 560 26 0.5901 76 51 26 1.1802 77 31 30 78 566 34 12 91 69 47 25 1.3303 80 31 1 6 ~43 24 0.740 86 67l ~48 02-92 32 84 68 51 35 19 0.8903 87 70 62 33 87 '73 60 471 34 20 1.0405 94 80 27.34 90 79 69 58 48 38 27 1.1917 1.3406 26 35 93 85 78 70 63 55 48 40 3325 36 99 186 82 77 7 ~68 ~6369245 37 98 96 95 93 91 89 87 86 842V 38 0.1601 0.3002 0.4503 0.6004 0.7606 0.9007 1.0508 1.2009 1.3510 Z 39 04 08 12 16 20 24 28 32 36 21 40 07 13 21 28 35 41 48 65 62 2( -4 1 10 19o 3i 9 3 9 49 58 6 8 ~ 788~ 7 1 42 1 3 25 38 60 63 7 6 88 1.2101 1.36131If 43 16 31 47 62 78 93 1.0609 24 40 1V 44 1 8 37 65 7 4 92 0.9110 29 47 66 14 45 21 42 64 -85 0.7606 27 48 70 91 1~ 4624 48 7 96 21 45 6 3.77 47 27 54 81 0.6108 35 62 89 1.2216 483t 48 30 60 90 20 50 79 1.0709 39 69 11 49 33 65 98 31 64 96 29 62 ~941 60 36 71 0.4607 42 78 0.9214 49 85 1.3820 1 51 3-9 ~7716 649 31012 87 62 41 83 24 66 0.7707 48 90 21 73 53 44 88 33 77 21 65 1.0809 44 9 *64 47 94 41 88 36 83 30 77 1.3924 66 50 0.3100 50 0.6200 50 0.9300 50 1.2400 0 T6 53 0 9 1 65 17 7 3 7T6 67 66 11 67 23 79 34 90 46 1AOOI 68 69 17 76 34 93 52 1.0910 69 2 69 62 23 85 46 0.7808 69 31 92 6 60 0.166 0.3129 0.4693 0.6257 0.7822 0.9386 1.0960 1.2,614 1.40 1 T 8 4 6 ~~ ~~~~6 7 LATITUDE, 81 DE9GRESES. I 92 __L1;TD 9 tzu' s ___ T 8 - ~~4 ___ 6 00.98771.95 2.9631 3904985. 59261 6.9'188 7.901 -8.88,9260 1 743 68 29 08 82 58.85 1 1 88 69 2 76 52 28 04 80 56 32 08 8458 3 75 51 2 7 02 78 5 3 29 04 80507 4 75 50 25 00 76 5 1 2 6 01 76 56 5 74 49 24 3.9498 73 '48 22 7.8997 71 56 6 74 48 22 96 7 1 45 1 9 93 67 64 7 78 4 7 2 1 95 69 42 1 5 90 63583 8 73 46 20 93 6 6 3 9 1 2 86 59 52 9 72 46 1 8 9 1 64 37 00 82 65551 10 72 45 117 89 62 34 06 78 5150i 1 1 7 1 44 1b 87 59 31 08 74 46419 12 71 43 14 86 57 28 00 71 43 48 13 70 42 13 84 55 25 6.9096 67 38 47 14 70 41 1 1 82 52 22 98 63 84 46 156 70 40 10 79 50 20 90 60 '30 45 H6 i 89 09 78 48 17 87 56 26 44 17 69 88 07 76 45 14 83 52 21 43 18 69 37 06 74 43 12 80 49 17 42 19 68 36 04 72 41 09 76 45 13 41 20 68 35 08 70 38 06 73 41 08 40 Yi 67 3N4 01l ~68 36 03 70 37 04 39 22 67 38 00 67 84 00 67 84 00388 23 66 32 1.9599 65 31 5.9197 63 30 8.8796 37 24 66;31 97 63 29 94 60 26 91 36 25 65 30 96 61 26 91 57 22 87 35 26 6-5 80o -94 509 24 89 54 18 88 34 27 64 29 93 57 22 86 50 14 78833 28 64 28 91 55 19 83 47 10 74 32 29 63 27 90 58 17 80 43 06 70 31 30 63 26 89 52 15 77 40 03 66 30 ~Y 62 25 87 50 1 74 3&6 7.8899 62 29 32, 62 24 86 48 10 71 33 95 57 28 83 61 23 84 46 07 68 29 91 63 27 84' 61 22 83 44 05 65 26 87 48 26 36 60 21 81 42 02 62 23 88 44 25 36 60 20 80 40 00 60 20 80 40 24 37 59 19 78 384.9298 57 16 76 35 23 38 59 18 77 86 95 54 13 72 31 22 39 58 17 76 84 93 51 09 68 27 21 40 58 16 74 32 90 48 06 64 22 20 41 57 16 78 30 88 45 02 60 119 42, 57 14 71 28. 8.5 42.6.89991. 561 l181 5 6 566 55 1 55 5 4 5 4 I 53 51, 3 I 12 11 09 08 07 06 I I I 68 66 63 61 59~ 26 24 22 20 18 16 14 12 83 81 78 76 73 71 68 66 I 37 34 31 28 25, 22~ 19 ~96 93 89 86 82 79 75 72 692 49 45 41 87 38.29 25 II I I I 05 00 8.8696 91 87 82 78 17 16 15 ii4 13 12 11 10 52 Ob 58 10 63 16 68 21 73 9 52 ",04 56 08 61 13 65 17 69 8 51.03 55 06 58 10 61 13 64 7 51 02 58 04 56 07 58 09 60 6 50 01 52) 02 58 04 54 05 6555 -g0 00 50 00 51 01 1 01 61 4 49 1.9699 49 8.9398 48 5.9098 47 7.8797 46 3 49 98 471 96 46 95 44 98 42 2 48 ~~97 46 94 48 92 40 89, 87 1 0848 1.9696 2.9544 3.9392 4.9241 5.9089 6.8937 8.8786 8.8688 0 2T 7-' 8 -4 5 7 8 DE~PARTUR)R 80 DEGIREES. I DNP'AUTUUEI 9 ~D;GRzxs. 98 b 0.1664 8129 10.-4693 0.26 0.78 —22 0.9886 1.0960 1.2614 1.407966 1 67 84 0.4702 69 36 0.9408 70 88 1.410669 2 70 40 10 80 61 21 191 61 81 68 8 78 46 19 92 66 38 1.1011 84 67 67 4 76 62 2710.6308 79 56 31 1.2606 8266 6 79 67 86 16 94 72 49 80 1.4208 56 6 82 68 46 2610.7908 90 71 68 8464 85 69 64 38 23 0.9607 92 76 61 63 87 76 62 49 37 241.1111 98 86 52 9 90 80 71 61 61.41 31 1.2722 1.431261 10 98 86 79 72 66 69 62 46 38 60 11 96 92 88 84 80 76 71 67 6849 12 99 98 96 96 94 98 92 90 8948 18 0.1602 0.8203 0.4806 0.6407 0.8009 0.9610 1.1212 1.2814 1.4416 47 14 06 09 14 18 28 28 82 37 41 46 16 07 16 22 80 87 44 62 69 67 46 16 10 21 3M 41 62 62 72 82 98 44 17 18 26 40 63 66 79 92 1.2Q06 1.4619 43 18 16 32 48 64 81 97 1.1318 29 46 42 19 19 88 67 7-6 96 0.9718 32 61 70 41 201. 22 44 66 87 0.8109 31 68 74 96 40 21 zl26 49 77 98 23 48' '73 907 1.4620839 22 28 66 88 0.6610 38 66 - 93 1.8020 48 38 28 30 61 91 22 62 82 1.1418 43 74837 24 83 67 0.4900 33 67 0.9800 33 66 1.4700 36 26 36 72 08 44 81 17 68 89 26835 26 39 78 17 66 96 34 7381.3112 61 34 27 42 84 26 68 0.8210 51 93 86 77833 28 46 89 34 79 24 68 1.1513 68 1.4802 32 29 48 96 48 90 38 86 33 81 28831 80 61 0.8801 62 0.6602 68 0.9908 64 1.3204 66 80 81 68 07 60 13 67 20 78 26 8029 82 66 12 69 25 81 87 98 60 1.4906 28 88 69 18 77 36 96 66 1.1614 78 82 27 62 24 86 48 0.8810 72 34 96 68 26 86 616 30 94 69 24 89 64 1.3318 88 26 861 68 8650.6008 71 3891.0006 74 42 1.6009 24 87 70 41 12 82 68 24 94 66 35623 38 73 47 20 94 67 40 1.1714 87 61 22 89 76 68 29 0.6706 82 68 84 1.8410 87 22 40 79 68 38 17 96 76 ' 64 34 1.6113 20 4 82 64 46 28 0.8410 92R 74 66 3819 42 86 70 66 40 26 1.0109 94 79 64 18 48 88 76 63 51 89 27 1.1816 1.3502 90 17 44 91 81 72 62 68 44 84 26 1.6215 16 46 94 87 81 74 68 61 66 48 4216 6 96 98 89 86 82 78 76 72 68 14 7 99 98 98 97 96 96 94 94 98 13 80.1702 0.3404 0.6106 0.6808 0.8611 1.0218 1.1916 1.3617 1.6819 12 9 06 10 16 20 26 30 86 40 4611 0 08 16 23 81 39 47 66 62 7010 1 11 21 82 48 64 64 76 86 96 9 2 14 27 41 54 68 82 96 1.8709 1.6422 8 8 16 88 49 66 82 98 1.2016 81 48 7 19 89 68 77 97 1.0816 86 64 74 6 6 22 44 67 89 0.8611 83 66 78 1.6600 6 267 60 7650.6900 26 60 76 1.8800 26 4 7 28 66 84 12 40 67 96 28 51 8 8 81 62 92 23 64 86 1.2116 46 77 2 834 67 0.6201 84 68 1.0402 36 68 1.6602 1 0.1786 0.4784 0.6210 0.6946 0.8683 1.0419 1.2166 1.3892 1.6629 0 4 6 6 7 LATITUPE 80 DEGREES. - E AT t in f: t:teL ad i:::AN W;:: v 94 0 4 CU D i:O 1 0 7 *T~!:::': ~: j:::1: ' ' ': '/~ -;:r ~.; +:. *r1':~... - _ 0.9848 1.9696 2.9544 3.2 4392 4i 5.9 89 6.887 7.8786 8.68 06 1 48 95 48 90 88 86 88 81 2869 2 47 94 41 88 86 83 80 77 2468 8 47 93 89 86 83 80 26 78 1957 4 46 92 88 84 81 77 28 69 1656 5 46 91 37 82 28 73 191 64 1055 -6 45 90 35 80 25 70 15 60 05B4 7 45 89 34 78 23 67 12 56 01 5 8 44 88 82 76 20 64 08 52 8.859652 9 44 87 81 74 18 61 05 48 9251 10 43 86 29 72 15 58 01 44 87560 ITI1 43 85 28 70 13 556.8898 40 8349 12 42 84 26 68 10 52 94 36 7848 18 41 88 g4 66 07 48 90 31 73 67 14 41 82 22 64 05 45 86 27 6846 15 40 81 21 62 02 42 83 23 6445 16 40 80 20 60 00 39 79 19 5944 17 39 79 18 581.9197 36 76 15 5548 18 89 78 17 56 95 33 72 11 5042 19 38 77 15 53 92 80 68 06 4541~ 20 88 76 13 51 89 27 65 02 40 0 21 -37 75 11 49 87 24 61 7.8698 353 22 37 74.10 47 84 21 58 94 3138 28 36 72 09 45 81 17 54 90 2637 24 86 71 07 43 79 14 50 86 2136 25 35 70 06 41 76 11 46 82 1785 2-6 35 69 04 39 74 08 43 78 1234 27 34 68 02 36 71 05 39 73 0733 28 34 67 01 84 68 02 35 69 0232 29 83 66 2.9499 32 66 5.8999 32 6.5 8.8498 81 80 83 65 98 30 63 95 28 60 9830 -81 82.. 64 96 28 60 92 24 56 82-29 82 82 63 95 26 58 89 21 52 8428 88 81 62 98 24 55 86 17 48 7927 34 30 61 91 22 52 82 13 43 7426 35 80 60 90 20 50 79 09 89 6925 86 29 59 88 18 47 76 06 85 652 87 29 58 86 15 44 78 02 80 6028 38 28 57 85 13 42 706.8798 26 5522 89 28 66 88 11 89 66 94 22 6021 40 27 54 82 09 86 63 90 18 4520 41 27 580o 0 -6 85 6o 87 14. 01 -42 26 52 78 04 31 57 83 09 8518 48 26 51 77 02 28 54 79 05 8017 44 25 50 75 00 25 50 75 00 2516 45 25 49 74 8.9298 28 47 72 7.8596 2016 46 24 48 72 96 20 44 68 92 1614 47 28 47 70 94 17 40 64 87 1018 48 28 46 69 92 15 87 60 88 0612 49 22 45 67 89 12 84 56 78 0111 60 22' 44 65 87 09 31 583 74 8.849610 61 21 42 64 85 06 27 48 70 91" 62 21 41 62 83 04 24 45 66 86 658 20 40 60 80 01 21 41 61 817 54 20 89 59 78 4.9098 18 87 67 76 665 19 88 57 76 95 14. 38 52 71 66 - 19- 87 — 56 74 93 11 80 4866 9 67 18 86 64 72 90 07 26 48 61 68 17 85 52 70 87 04 22 89 67 69 17 84 60 67 84 01 18 84 51 0 0.9816 1.96338 2.9449 38.9275 4.9082 5.8898 6.8714 7.8580 8.884:.... PDRPARTUR8 79 DEOGREES. A U If I .1737 7 0.6210.6946.68 1.0419.216 1.8892 1 29i0 1 89 89 18 57 97 36 75 1.8914 6459 2 42 84 27 69 0.8711 53 95 38 8058 8 45 90 36 80 25 71 1.2216 61 1.570657 4 48 96 44 92 40 87 35 83 8156 6 51 0.3502 52 0.7003 64 1.0505 56 1.4006 5755 -- 54 07 61 15 69 22 76 30 83- 4 7 57 13 70 26 83 39 96 52 1.580953 8 59 19 78 38 97 5661.2316 75 3552 9 62 25 87 490.8812 74 36 98 6151 10 65 30 95 60 26 91 56 1.4121 8650 1 -68 - 36 0.5304 72 — 40 1.0608 76 54 1.591249 12 71 42 12 83 54 27 96 66 3748 18 74 47 21 95 69 42 1.2416 90 63 47 14 77 53 30 0.7106 83 60 36 1.4213 8946 15 79 59 38 18 97 76 56 351.601545,-n --- i ' —, — A,- -on n on1o aA '7 F.8 41 44 Jt,/iYT 1 1!! C 2 e. f 19 i t i t I I I I 41 4 4 i I I I i. 11 5< L~ 5(!. > 3 8 3 3 3 8 3 4 4 4 4 4 4 i 11 t, 0 J 13!6 3 8 B I 4 4 4 I 7 9 1 2 3 4 5 6 7 8 9 0 1;6 4 18 19 L5 '4!5 6i6 t7 t8 50 58 52 Kr O 0Z 85 88 91 94 97 ).1800 02 05 08 11 14 17 20 22 I II Ot 7( 7( 8! 8' 91 0.3601 1( 14 2' 2r 3' 3 4 50 1) 8 3 2 9 5 56 64 72 81 90 99.5407 16 24 4. 41 5( 5c 6', ) ) I 3 t I 7,I I - zo 28 81 84 37 40 42 45 48 51 54 57 60 62 65 68 71 74 77 ) 80 82 85 3 88 91 CAL 50 56 62 68 73 — 79 85 90 96 0.3702 08 13 19 25 30 36 42 48 53 59 65 70 76 82 76 84 92 0.5501 10 19 27 85 44 53 61 7C 87 9( 0.5604 2] 3( 81 41 6 7: 3 8 41 52 63 76 87 98 0.7209 21 32 44 55 66 78 90 0.7301 12 24 35 47 38 70 81 92 0.7404 15 27 38 50 B 61 4 72 3 84 1 95 0 0.7507 9 18 7 30 41 4 52 3 64 1 75 26 40 55 69 83 98 0.9012 26 41 55 69 83 98 0.9112 26 41 55 69 84 98 0.9212 26 41 55 69 84 98 0.9312 26 41 55 6C 84 9f 0.941' 2( 4' 5~ 61 1.0711 28 45 62 80 97 1.0814 31 49 65 83 1.0900 17 34 51 69 85 1.1003 20 37 54 71 89 1.1105 23 40 57 74 91 1.1209 26 43 t 60 3 77 94 3 1.1311 2 29 5 46 I 63 96 1.2516 36 56 76 97 1.2616 36 57 76 97 1.2716 37 57 76 97 1.2816 37 57 77 97 1.2916 37 56 77 97 1.3017 37 56 77 97 1.3117 37 57 77 96 1.3217 37 57 82 1.4304 27 50 73 96 1.4418 42 65 87 1.4510 33 56 79 1.4602 25 47 70 94 1.4716 39 62 85 1.4807 30 54 76 99 1.4922 45 68 9C 1.5014 3( 6I 82 1.510p 2( 5( 67, 92 1.6118 43 69 96 1.6221 47 73 98 1.6325 49 76 1.6402 27 53 78 1.6504 30 56 82 1.6607 88 33 58 84 1.6710 86 62 87 1.6813 39 64 90 1 6916 42 67 93 1.7019 44 t8 42 tl 39 38 37 36 31 30 29 28 27 26 25 34 23 22 21 2( 1E 13 r< i 1 It II IV i ) 5 1 0 8 7 5 i g -I I 97 93 90 87 84 80 77 74 7 7 0.1900 99 99 98 98 9 97 96 96 8 68 02 0.8805 0.5707 10 0.9512 1.1414 1.3317 1.5219 1.7122 2 69 05 10 15 21 26 81 86 42 47 1 01908 0.8816 0.6724 0.762 0.9541 1.144 1.3867 1.5265 1.7178 0 T2- 6 3 4 4 8 _ 1._LATITu -- 79 DEG.ES8. - -....... '.............*ATITD1 79 DoE s....... 44 II 96 lATITUPR 1 1 DIGNEK8. p 17 i 2 - 8 4 6 - 6 7 __ _ V 0.9816 1.9633 2.9449 3.9266 4.9082 6 889-8 6.8714 7.8580 8.847 f 06 1 16 81 47 63 89 94 10 26 41 59 2 15 80 46 61 76 91 06 22 87568 8 1i 29 44 68 78 88 02 27 81 57 4 14 28 42 56 70 84 6.8698 12 26 56 5 14 27 41 54 88 81 95 08 22 55 138 26 39 52 65 77 90.038 1654 7 12 25 87 50 62 74 87 7.8599 12 58 8 12 24 85 47 59 71 83 94 06562 9 11 22 34 45 56 67 78 90 0151 10 11 21 82 43 54 64 75 86 8.8296 50 11 10 20 30 40 51 61 71 81 91 49 12 10 19 29 38 48 58 67 77 86 48 13 09 18 27 86 45 54 63 72 81 47 14 08 17 25 34 42 50 69 67 76 46 15 08 16 26 82 40 47 55 63 71 46 T6 07 15 22 29 37 44 51 58 66 144 17 07 13 20 27 34 40 57 54 60 43 18 06 12 18 24 81 87 43 49 55 42 19 06 11 17 22 28 84 39 45 60 41 20 05 10 15 20 25 30 35 40 45 40 21 04 09 18 18 22 26 33 85 40 39 22 04 08 12 16 20 28 27 81 85 38 23 08 07 10 18 17 20 23 26 80837 24 08 05 08 11 14 16 15 22 24836 25 02 04 06 08 11 13 18 17 20835 2 1 "02 -i 050 306 08 10 11 18 D14 34 27 01 02 08 04 05 06 07 08 09883 28 00 01 01 01 02 02 03 08 04 32 29 00 00 2.9399 3.9199 4.8999 5.8799 6.8599 7.8898 8.819881 80 0.9799 1.9598 98 97 96 95 94 94 98830 81 99 97 96 95 94 92 91 90 88 82 98 96 94 92 91 89 87 85 88 28 88 98 95 92 90 88 85 88 80 78 27 84 97 94 91 88 85 81 78 75 72 26 85 96 93 89 85 82 78 74 70 67 25 36 96 92 87 83 79 75 71 66 62 2 87 95 90 86 81 76 71 66 62 57 28 88 95 89 84 78 73 68 62 57 51 22 89 94 88 82 76 70 64 58 52 46 21 40 983 87 80 74 67 60 54 47 41 20 TT- 9R3 86 78 71 64 57 50 42 851 42 92 84 77 69 61 53 45 88 80 18 48 92 88 75 66 58 50 41 38 24 17 44 91 82 73 64 55 46 87 28 19 16 45 91 81 72 62 58 48 34 24 15 15 46 90o 80 70 60 50 39 29 19 09 f4f 47 89 79 68 57 47 86 25 14 04 18 48 89 77 66 55 44 82 21 10 8.809812 49 88 76 64 52 41 89 17 05 98 11 50 88 75 68 50 88 25 18 00 88 10 Wl 8 74 61 48 8b 22 08 7.8295 84 9 52 86 78 59 45 82 18 04 90 77 8 58 86 71 57 48 29 14 00 86 71 7 54 86 70 55 40 26 11 6.8496 81 66 6 55 85 69 54 88 28 07 92 76 61 5 u 68 52 86 20 03 87 71 5b14 57 88 67 50 88 17 00 88 66 508a 88 88 65 48 81 14 5.8696 79 62 54 2 59 82 64 46 28 11 88 75 57 89 1 60 0.9782 1.956812.9845 8.9126 4.8908 5.8689 6.8471 7.8252 8.8084 1 ~12 ~8 5 6 ~7 ~ 8 ~9 DEPARTURE -1 DEGREE8. ii I DEPARTURE 11 DEGREES. 97 j 1 2 3 4 5 6 7 8 9, 0 0.190T8 03~816 0.5724 0.71632 0.9541 1. 144 q 1.3357 1.5265 1.7173 60 1 11 22 33 44 55 (5 76 88 98 59 2 14 28 41 55 69 8 3 97 1.5310 1.7224 58 3 17 33 50 67 84 1.1500 1.3417 34 50 57 4 20 39 59 78 98 1 7 37 5 6 7656 5 22 45 671 90 0.9612 34 57 79 7.7302 55 6 25 50 76 0.7701 26 51 76 1.5402 27564 7 28 56 84 12 41- 69 97 25 5353 8 31 62 98 24 55 8 5 1.3516 4 7 7852 9 3 4 68 0.5861 35 691)1.1603 3 7 70 1. 7404 51 10 37 7-3 10 46 813 20 56 __93 2950 I I 1 12 13 1 4 15 17 18 19 20 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 -4' 42 43 44 45 47 48 49 50 Ti 52 53 54 515 57 58 59 60 4f 4 t 54 57 6C 62 65 68 7 1 7 4 82 8 5 88 9 1 94 97 99 0.2002 0 5 08 1 4 1.7 1 9 9.) 2 5 2 8 3 1 34 3 6 319 4 2 45 48 5 1 5 4 5 6 59 6 2 6 5 6 8 7 1 7 3 7 6 0.2079 1 79 19 85 2'7 90 36 96 44 0.3902 539 08 61 13 76( 19(" 79 25 8 7 3s0 96 36 0. 59 O4 42 1 3 47 2 1 53 30 59 38 65 4 7 70 55 76r 64 82~ 72 -871 81I 99 98 0.4004 0.6007 1 0 1.5 -16 24 2 7 41 33 50 39) 58 44 6 7 50 7 5 56 8 4 6 1 92 6 7 0.6101 18 84 2 90 3 5 96 43 0.4101 52 07T 61 13 69 1 8 7 24 86 30 95 35 0.6203 41 1 2 47 20 53 29 0.4 158 0.6237 2 3 69 81 0. '78 04 38 4 c 6 1 7 2 ~84 915 0. 7906 1 8 29 40 52 63) 98 0.8009 20 09 54 66 771 89 0.8112 34 46 68 80 91 0.8208 -F4 25 3 7 48 60 71 82 94 0.8305 0.8316 4 0.97 12 26 41 69 83 98 0.9812 26 40 5 h5 69 83 97 0. 9912 26 40 54 69,83 97 1.0011 26 40 54 68 83 9 7 1.0111 25'4 0 54 1 7 3 2 9-07 1.021.1 25" 39 54 82 96 1.0310 2 5 34 5 3 3 7 52 1.0396 07 54 71 8q9 40 74 91 1. 1808 25 42) 60 7 6 94 1.1911 2 8 4 5 62 79 96 1.2013 3 1 4 7 6.5 99 3 3 50 6 7 84 1. 22 0 2 1 8 36 53 70 87 1.2304 2 1 38 89 24 40 58 1.2475 6 37 1.37 17 39 56 76 9 6 1.3816 3 6 96 1.43916 36( 56 - 6 9 6 1.4016 365 56 965 1. 42116 3.5 75.95 1.4215 3.5 00 7 5 95 1.4315 35 754 94 1.4414 34 1.4554 7 31 160. 1.572:1. 5819.3 8 1 1.5904 26 56 7 2 9 5 1.6018 4 1 63 86 1.6109 32 5 5 78 1.6223 4 6 92 1. 63 14 3 7 60 82 1.6406 28 50 74 96' 1.6519 42 65 8 7 1. 6610 1.6633 8 3 81 1 1.7507 583 84 1. 17606 36 61 87 1.7712 38 63 89 41 67 92 1.7917 43 69 '1.8020 46 71 97 1. 8122 49 741 1.8200 26 51 76 1.83029 28 54 79 1.8405 30 56 82 1.8507 33 58 84 1.8609 35 61 87 1.8,7 12 -9 - o'49 48 '47 '46 '4544 143;42 41 40,38 37 36 35 33 32 31 30 28 27 26 25 23 22 21 20 18 17 16 15 13 12 10 8 7 6 S -4 I8 ~2 I 0 I I LATITUDE 76 DEGIItIKS. D 1. 98 LATITUDE 12 DEGREB8. ": i' " ~ I8 i 4 i.6 T 1 7 1 8 9". _ iI....... ~.??-0 i I I L _ I I I trII r 1 I - - t 1 P 0*X I s W onl I 9 11 2 8 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 28 29 80 34 38 84 37 87 4( 81 80 80 79 78 78 77 77 76 75 7 74 74 73 72 72 71 71 70 69 69 68 67 67 66 66 66 64 63 6i 61 6( 6C 5 I 3 6' 6i 0.95631 62 61 59 58 57 56 54 53 52 51 50 48 47 46 45 43 42 41 40 38 37 36 35 33 32 81 30 28 27 26 25 23 22 21 20 18 17 16 15 7 18 2.9345 43 41 39 37 35 33 32 30 28 26 24 23 21 19 17 15 13 12 10 08 06 04 02 00 2.9298 97 94 93 91 89 87 85 83 81 79 7( 74 72' 7C 3.9126 24 21 19 16 14 11 09 06 04 02 3.9099 97 94 92 89 87 84 82 79 77 74 72 69 67 64 5,62 59 57 54 52 49 47 44 L 42 ) 38 8 3 21 ) 2 4.89U t 05 02 4.8899 95 92 89 86 83 80 77 74 71 68 65 62 59 56 53 49 46 43 40 37 34 31 28 24 21 18 15 12 09 05 02 4.8799 96 93 90 9 86 83 ).8~8y 85 82 78 75 71 67 63 60 56 52 49 45 41 37 34 30 * 26 26 23 19 15 11 08 04 00 5.8597 93 89 85 82 78 74 7C 67 62 56 56 51 47 4z 44 4C A - - > a- 1 '!. U.UsI I, 66 62 58 54 49 45 40 36 32 28 24 19 15 10 06 02 6.8398 94 89 84 80 76 71 67 63 59 54 49 45 3 41 36 32 28 23 18 14 09 05 00 6.8296 I.M- so 47 42 38 33 27 22 18 13 08 03 7.8199 94 88 83 79 74 69 64 59 54 49 44 38 34 29 24 1E 14 04 7.809W 94 81 8; 71 1 6~ 6 6; 5 5r 8.8034 C 28 23 E 17 12 1 06t 00 8.7995t 891 84t 791 738 681 62 56 51 45 40 35 28 28 17 12 06 00 8.7895 t 90 83 78 72 1 67 8 61 4 55 9 50 3 44 38 8 33 8 27 3 21 8 16 3 09 iO i9 i8 57 i6 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 2E 24 28 2. 21 2( i I IF I I I i 1 9 8 7 6 5 4 8 2 1 0 9 8 7 6 5 4 8 2 1 o I I I -~ I 41 42 48 45 46 t48 49 60 52 58 - I 56 55 55 54 68 63 52 52 51 50 49 49 48 48 47 I I I I -,w- I - - I * 12 11 09 08 07 06 04 03 02 00 0.9499 98 96 95 94 68 66 64 62 60 58 56 66 55 52 51 49 47 45 43 41 i I I,. 21 18 16 14 11 08 06 03 01 3.8998 96 93 90 88 acx II "Irs I z5u 77 74 71 67 64 61 58 54 51 48 45 42 38 35 i - I 36 82 28 25 21 17 13 09 05 01 5.8498 93 90 86 82 92 87 83 79 74 70 65 61 56 51 -- 47 42 38 33 28 - I I r, - I.1. 47 42 88 33 27 22 17 12 07 02 7.7996 91 86 81 75 04 8.7798 92 87 81 75 69 64 58o 52 46 40 84 28 23 r II 1( 14 1i 1. 4t4 46 46 44.9744 1 i I I I I - 98 91 90 88 1.9487 -. -. n 89 87 85 88 2.9281 5b b2Z 83 28 80 26 77 22 8.8975 4.8719 4 5 6.. 74 7C 66 5.8462 6 I 24 70 20 65 15 60 11 55 6.8206 7.7950 r — i - I I 17 11 05 8.7699 8.7698 9! I I I __ i I I I. ~ I.. - _. -..., I DIPABTURB 77 DQBOREBS. ~ p, DEPARTURE 12 DEGRIREE F 1 2 8 4 5 68 7 8 '1 1 2 1 13 E019.24751 4 6 00.2079 0.4168 0.6237 08316 1.0396 1.2475 1 46641.6633 i1-8712 11 82 64 46 28 1.0410 92 74 66 8869 2 85 70 64 39 24 1.2509 94 78 68 68 3 88 76 63 61 39 26 1.4614 1.6702 89 67' 4 91 81 72 62 63 43 34 24 1.8815 666 6 93 87 80 73 67 60 53 46 4056 6 96 92 89 85 81 77 73 70 6654 7 99 98 97 96 95 94 93 92 9168 8 0.2102 0.4204 0.6306 0.8408 1.0510 1.2611 1.4713 1.6815 1.8917 62 9 05 09 14 19 24 28 33 38 42 61 10 08 15 23 30 38 46 5 3 61 6860 11 10 21 31 42 64 62 73 83 94 49 12 13 26 40 63 66 79 92 1.6906 1.9019 48 13 16 32 48 64 81 97 1.4813 29 4647 14 19 38 57 76 95 1.2713 32 51 7046 16 22 44 65 87 1.0609 31 68 74 9646 16 2 49 74 98 23 48 72 97 1.9121144 17 28 65 83 0.8510 38 65 92 1.7020 4843 18 30 61 91 21 52 82 1.4912 42 73 42 19 33 66 99 32 66 99 32 66 98 41 20 36 72 0.6408 44 80 1.2816 62 88 1.9224 40 21 39 78 16 55 94 33 M 72 1.7110 4939 22 42 83 25 67 1.0709 50 92 34 7538 23 45 89 34 78 23 67 1L5012 56 1.9301 37 24 47 95 42 90 37 84 32 79 2736 25 60 0.4300 51 0.8601 61 1.2901 5 1 1.7202 62 86 26 53 06 59 12 65 18 71 24 7784 27 56 12 68 24 80 35 91 47 9338 28 69 17 76 35 94 52 1.5111 70 1.9428 82 29 62 23 85 46 1.0808 70 31 93 5431 80 64 29 93 58 22 86 51 1.7815 8030 81 67 34 0.6502 69 36 1.3003 70 38 1.9506 29 32 70 40 10 80 51 21 91 61 3128 33 73 46 19 92 65 37 10 83 6627 84 76 62 29 0.8703 79 55 81 1.7406 8226 35 79 57 36 14 93 72 50 29 1.9607 26 36 8 1 68 44 261.0907 889 70M 516 8 24 37 84 69 63 37 23 1.8106 90 74 6928 88 87 74 61 48 36 231.5310 97 8422 39 90 80 70 60 60 39 29 1.7519 1.9709 21 40 98 86 78 71 64 67 50 42 3820 41 96 91 87 82 78 74 69 65 6019 42 99 97 96 94 93 91 90 88 8718 48 0.2201 0.4403 0.6604 0.8805 1.1007 1.8208 1.5409 1.7610 1.9812 17 44 04 08 12 16 21 25 29 38 8716 46 07 14 21 28 35 42 49 66 6316 46 47 48 49 60 62 63 54 66 67 68 69 60 16 13 16 18 21 24 27 30 83 86 38 41 44 47 0.2250 ~1b -26 31 37 42 64 6i9 71 76 82 88 0.4489 38 47 65 64 72 80 89 98 0.6706 15 28 81 40 0.6749 3" 40 62 78 85 96 07 0.8919 30 41 68 64 76 87 0.8998 7 E 92 1.1106 76 93 1.3310 6M 88 1.550Q 28 48 I 8 1.7701 24 46 z3~b 1.9918 40 66 91 14 18 12 11 34 49 6 I 77 91 1.120t 19 84 1. 1248 2 4 1i LATITUDE 77 DEGREES. I I I ll 100 LATITUDE 13 DEGREES. I 1 2 | 3 4 _I 6 I7 18 _ 9 J 8.. \_. * \ _, \,,_,>. \ _,\ <,1 0 1 2 3 4 5 6 8 9 10 11 12 18 14 15 18 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 86 37 38 39 40 41 42 43 44 45 4t 47 48 49 50 51 52 53 54 55 556 57 58 0.9744 4C * 42 42 41 4(1 4( 38 39 37 38t 38 385 35 33 84 38 32 31 30 30 29 28 28 27 26 26 25 24 24 28 22 22 21 20 20. 19 18 18 I17 16 16 15 14 13 18 12 11 11 10 09 09 08 07 07 06 05 04 04 0.9708 1.9487 86 85 83 82 81 81) 78 '77 76 74 73 72 70 69 68 66 65 64 62 61 60 58 57 56 54 53 51 50 49 47 46 45 43 42 41 39 38;6 35 34 3, 31 8) 28 27 25 24 23 21 20 19 17 16 15 18 12 10 09 07 1.9406 2.9231 29 27 25 23 21 19 17 15 13 11 09 07 05 04 01 2.919,i 98 95 93 91 8; 85 83 81 7I. 77 75 72, 71 6 ' 67 65 63 61 59 57 55 t)w 53 51 4t 47 44 42 40) 38 36 84 32 30) 28 26 24 22 20 19 15 13 11 2.9109 8.8975 72 70 67 64 62 59 56 54 51 48 46 43 40 38 35 30 9 -27 24 299 14 11 (08 t06 0( 00 3.8898 94 9. 89 87 84 81 78 76 73 70 68 65 62 59 56 54 41 48 45 42.40 3' 34 32 29 26 223 20 18 15 3.8812 4.8719 15 12 09 06 02 4.8699 96 92 8! 86i 82 79 76 73 6t) 66 56 52 4(, 46 42 39 30 ( 32 291 2f6 292 19 15 12 09 05 02 4.8598 95 91 88 85 81 78 74 71 67 64 60 57 53 _50 46 43 40 86 33 29 26 22 19 4.8515 5.8462 6.8206 58 01 54 6,8197 50 92 47 88 42 83 39 79 35 74 30 69 27 65 23 6( 18 55 15 51 11 46 07 42 03 37 5.889:$;2 95 28 91 23 87 18 82 13 79 09 75 04 70 6.8099 67 95 63 90 58 85 54 8( 51 76 4(6 71 42 66 38 61 34 't; 30 52 26 47 22 42 18 37 13 32 09 27 06 23 01 18 5.8297 13 93 09 89 04 85 6 7999 80) 94, t; O 72 84 68 79 64 74 60 70 56 65 52 60 47 55 43 50 39 46 35 41 31 36 26 31 22 26 5.8218 6.7921 6 7 7.7950 44 39 34 29 23 18 13 07 02 7.7897 91 86 81 76 70 t;5 60 54 49 43.8 33 27 22 17 11 06 01 7.7795 90 84 78 74 68 62 57 51 46 41 35 o2 24 18 13 07 02 7.7696 90 85 80 74 69 63 58 52 46 41 35 30 7.7624 8.7693 87 82 7, 7C 64 5 52 46 40 34 28 22 16 11 04 08 8.7594 86 80 74 68 62 56 50 44 38 32 26 19 13 07 01 8.7495 89 83 76 70 64 58 52 46 40 33 27 21 14 08 02 8.7395 90 84 77 71 65 59 52 46 40 33 8.7827 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 48 42 41 40 139 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 8 2 1 0: 8 DEPARTURE 76,l)GRfES.: S- r S,.,+ [:; -, \: R -1; I I -,, - I I ~ I r DEPARTURE 13 DEGOEES., 01.1 1 2 3 4 6 ' 6 18 9 _-L i~ ~' ~U 1 U 1 2 3 4 5 60 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.22bU 52 55 58 61 64 67 69 72 75 78 81 84 86 89 92 95 98 0.2301 03 06 06 12 16 18 2C U.44'JUy 0.4505 10 16 22 27 383 30 41 50 56 61 67 73 79 84 90 95 0.4601 07 12 18 24 29) 35 41 U.0f749 57 b6 74 82 91. 6800 08 17 25 33 42 52 69 68 76 84 93 0.6902 19 35 44 53 61 u.6YyO 0.9009 21 32 43 55 66 77 89 0.9100 11 23 34 45 57 68 79 91 0.9202 13 25 36 47 58 70 81 1.1Z48 62 76 94 1.1304 19 33 46 61 75 89 1.1404 18 32 46 60 74 89 1.1503 17 31 45 59 73 88 1.1602 1.64 Ji 1.3514 31 48 65 82 99 1.3616 33 50 67 85 1.3701 18 35 52 69 86 4.3803 20 37 54 71 88 1.3905 22 1.0 i i 66 86 1.5806 26 46 66 85 1.5905 25 45 65 85 1.6004 24 44 64 84 1.6104 23 43 63 83 1.6206 23 42 1. t ou 1.8018 42 64 86 1.8110 32 54 78 1.8200 22 46 67 90 1.8314 36 58 82 1:8404 26 50 72 94 1.8517 40 62 I 71 97 2.0322 47 73 99 2.0424 50 75 2.0500 26 52 77 2.0603 28 53 79 2.0705 30 56 81 2.0806 31 58 83 5 5 5 5 5 5 5 5 5 4 4 4 4 14 '4 '4 '4 '4 4 4 1 4 3 8 U 9 8 7 6 5 4 3 2 1 0 9 8 7 L6 5 T4 3 2 1 0 '9 38 7 36 35 I 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 52 53 54 55 23 26 29 31 35# 37 40 43 46 49 51 54 57 60 63 66 68 71 74 77 80 83 85 88 91 94 97 0.2400 02 05 46 52 58 63 69 75 80 86 92 97 0.4703 08 14 20 25 31 37 42 48 54 59 65 71 76 82 88 93 99 0.4805 10 691 781 86 95 0.7004 12 20 29 37 46 54 63 71 80 88 97 0.7105 14 22 31 39 48 56 65 73 81 90 99 0.7207 15 92 0.9304 15 26 38 60 72 83 94 0.9406 17 28 40 51 62 74 85 96 0.9508 19 30 41 53 64 75 86 98 0.9609 2C 16 30 44 58 73 87 1.1701 15 29 43 57 71 86 1.1800 14 28 42 56 70 85 99 1.1913 27 41 55 69 83 1.2000 12 26 39 56 73 90 1.4007 24 41 57 75 92 1.4108 25 43 59 _ 76 94 1.4210 27 44 61 78 95 1.4312 29 46 63 80 97 1.4414 31 62 82 1.6302 21 42 61 81 1.6400 21 40 60 19 39 59 79 98 1.6618 38 58 78 97 1.6717 37 57 76 97 1.6816 36 - = 1.8608 1.8608 30 53 1.8676 98 1.8721 43 66 89 1.8811 34 57 79 1.8902 25 47 70 92 1.9015 38 60 82 1.9106 28 50 73 96 1.9218 41 2.U UU 34 60 84 2.1011 36 61 86 2.1112 37 63 88 2.1214 39 64 90 2.1316 41 66 92 2.1417 48 68 94 2.1519 44 69 96 2.1621 46 4 I I I I I I II II I I I I.54 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 7 5 If _ II II 56 08 16 24 32 40 47 55 63 71 4 57 11 22 32 43 54 65 76 86 97 8 58 14 27 41 54 68 82 95 1.9309 2.1722 2 59 16 33 49 65 82 98 1.6915 31 48 1 60 0.2419 0.4838 0.7258 0.9677 1.2096 1.4515 1.6934 1.9354 2.1778 0 l-2 - 3 4.5 6 7 8-9 9 LATITUDE 76 DEGREES. lj I I w102 ILATITUDE 14 oB8RtBS. H 8 4 5 6 7 8 9 10 11 12 13 14 15 16 16 17 18 19 20 21 22 23 24 25 26 27i 28 29' 30 38 34 88 354 36 37 38 39 40 41 42 48 44 45 46 47 48 49 50 I 0.9708 02 02 01 00 0.9699 99 98 97 97 96 95 95 94 93 92 92 91 90 89 89 88 87 87 86 85 84 84 83 82 82 81 80 79 79 78 77 76 76 75 74 73 73 72 71 71 70 69 68 68 67 2 1.9406 05 03 02 00 1.9399 97 96 95 93 92 90 89 87 86 85 83 82 80 79 77 76 75 73 72 70 69 67 66 64 63 61 60 59 57 56 54 53 51 50 48 47 45 44 42 41 39 38 36 35 33 s 2.9109 07 05 02 00 2.9098 96 94 92 90 88 86 84 81 79 77 75 73 71 68 66 64 62 60 57 55 5X 51 49 47 45 42 40 38 36 33 31 29 27 25 23 20 18 16 14 11 09 O 07 05 03 00 4 3.8812 09 06 03 003.8798 3.8798 95 92 89 86 84 81 78 75 72 69 66 64 58 58 55 52 49 46 43 41 38 35 32 29 26 23 20 17 14 11 08 06 02 3.8699 97 95 91 88 85 82 79 76 78 70 67 64 61 58 55 52 49 46 43 40 3.8637 6 4.8615 12 08 04 01 4.8497 94 90 87 83 80 76 73 69 65 62 58 55 51 47 44 40 37 33 29 26 22 18 15 11 08 04 00 4.8397 93 89 86 82 78 75 71 67 64 60 56 53 49 45 41 38 34 6 5.8218 14 09 05 01 5.8196 92 88 84 80 75 71 67 62 58 54 50 45 41 36 32 28 24 20 15 11 06 02 5.8097 93 89 84 80 76 72 67 63 58 54 49 45 40 36 31 27 23 18 14 09 05 00 7 6.7921 16 11 06 01 6.7896 91 86 81 76 71 66 62 56 51 46 41 36 31 26 21 16 11 06 01 6.7796 91 86 80 75 71 65 60 55 50 45 40 35 29 24 19 14 09 03 6.7698 94 88 83 77 73 67 62 67 52 47 41 386 81 26 20 6.7616 8 7.7624 18 12 06 01 7.7595 90 84 78 73 67 62 56 50 44 39 33 27 22 15 10 04 7.7498 93 86 81 75 70 63 58 52 46 40 34 29 22 17 11 05 7.7399 94 87 82 75 70 64 58 52 46 40 34 8.7827 21 14 07 01 8.7295 88 82 76 69 63 57 51 43 37 31 24 18 12 05 8.7198 92 86 79 72 66 60 53 46 40 34 27 20 14 07 00 8.7094 88 80 74 68 61 54 47 41 35 27 21 14 08 00 60 59 58 57 56 55 64 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 51 52 53 54 55 57 58 69 6( 66 32 65 81 65 39 64 28 63 26 ' 62 25 62 23 61 22 60 20 0.965911.9319 2.8998 96 94 91 89 87 85 82 8C!2.8978 30 27 24 19 15 12 08 06 00 4.8297 5.7996 92 87 78 7E 74 66 6a 6C 5.795( 28 22 16 10 04 7.7298 92 86 80 7.7274 8.6994 8E 81 74 67 61 64 47 46 8.6984 J j T ' 2 3 l 4 I6 61 7 8 i 9 1 -DEPARTURE 75 D0GREE8.. 1 *;-; *: *:- -\ -! #F: I -C D.PA-TURJ~ 14 PEG tHE8. jqjo I 1 DxPA~Rx 14' Ds"9198 JUG I 2 8 4 6 7 T 0.2419 0T.4838 0.7258 6.9677 1.2096 1.4515 1.6934 1.9354.17760 1 22 44 66 88 1.2110 32 54 76 98 59 '2 25 50 75 0.9700 25 49 74 99 2.1824658 3 28 55 83 11 39 66 94 1.9422 49 57 4 31 61 92 22 53 83 1.7014 44 75566 5 83 67 0.7300 33 67 1.4600 33 66 2.1900 55 -6 36 72 09 45 81 17 53 90 26 54 7 39 78 17 56 95 34 73 1.9512 61153 8 42 84 25 67 1.2209 51 93 34 7652 9 45 89 34 78 33 68 1.7112 57 2.2001 61 10 47 95 42 90 37 84 32 79 27 50 11 50 0.4901 51 Ti9801 52 7.4702 52 1.9-602 5349 12 53 06 59 12 66 19 72 25 78 48 13 66 12 68 24 80 35 91 47 2.2103 47 14 59 17 76 35 94 62 1.7211 70 28 46 15 62 23 85 4'h 1.2308 69 31 92 54 45 16 64 29 93 58 22 86 51 1.9715 8044 17 67 34 0.7402 69 36 1.4803 70 38 2.2205 43 18 70 40 10 80 50 20 90 60 3042 19 73 46 18 91 64 37 1.7310 82 5541 20 76 51 27 0.9902 78 54 29 1.9805 8040 21 Y s78 67 3f5 14 92 70 49 27 2.2306 39 22 81 63 44 25 1.2407 88 69 50 32 38 23 84 68 52 36 21 1.4905 89 73 57 37 24 87 74 61 47 35 21 1.7408 95 8236 25 90 79 69 59 49 38 29 1.9918 2.2407 35 6 93 85 78 70 63 56 48 40 3334 27 95 91 86 81 77 72 67 62 58 33 28 98 96 95 93 91 89 87 86 84 32 29 0.2501 0.5002 0.7503 1.0004 1.2505 1 5006 1.7507 2.0008 2.2509 31 30 04 08 11 15 19 23 27 30 34 30 81 07 13 2 0 26 3 3 40 4 6 53 59 29 32 09 19 28 38 47 66 66 75 8528. 33 12 24 37 49 61 73 85 982.2610 27 34 15 30 45 60 76 9 11.7606 2.0121 36 26 35 18 36 54 72 90 1.5107 25 43 61 26 36 21 41U f62 831.2604 24R 45 6 6 8624 37 24 47 71 94 18 41 65 88 2.2712 23 38 26 53 79 1.0105 32 58 84 2.0210 37 22 39 29 68 87 16 46 75 1.7704 33 62 22 40 32 64 96i 28 60 92 24 56 88 20 41 35 700.7604 39 741T.5209 44 78 2.2813 19 42 38 75 13 50 88 26 63 2.0301 3818 43 40 81 21 62 1.2702 42 83 23 6417 44 43 86 30 73 16 59 1.7802 46 8916 45 46 92 38 84 30 76 22 68 2.2914 15 46il 49 98 46 95 44 93 42 90 39TT 47 62 0.5103 55 1.0206 58 1.5310 61 2.0413 6413 48 55 09 64 18 73 27 82 36 91 12 4 657 1 72 29 87 44 1.7901 58 2.301611 50 60 20 80 401.2801 61 21 81 4110 51~i sZ63 26 89 52 15 77 40 2.0503 66 -9 66 31 97 63 29 94 60 26 91 8 -53 69 37 0.7706 74 431.5411 80 482.3117 7 54 71 43 14 85 57 2 99 70 42 6 66 74 22 96 71 45 1.8019 93 67' 6 56 77 54 38 I lf.1 1.030 851 61l P 2.0615 992 57 80 60 39 19 99 79 69 88 2.3218 8 58 83 65 48 30 1.2913 96 78 61 43 2 59 86 71 56 42 27 1.5512 98 83 69 1 6010.2588 0.5176 0.7766 1.0568 1.2941 1.6529 1.8117 2.0706 2.3294 0 T W 8 6 5 6 7 T i' I 7 5 I LA ITtDz 75 Dicowsims II -3 I I ii I I I I I 104 LATITUDE 16 DEGREES. 1 2 3 4 5 6 7 8 0 0.9659 1.9319 2.897f8 3.86.3i 4.8297 5. 7956 6.765 7. 7274 8.6934 60 1 59 1 7 86 34 9 3 5 1 10O 68.27 59 2 58 16 73 31 89 4 7 05 62 20 58 3 57 14 71 28 85 42 6.7596 56 13 57 4 56 12 69 25 81 3 7 93 50 06 56 5 0 11 67. 22 76 33 88 44 00 55 6 5-5 08 64 1 9 74 2)8 83 38 8.6892 54 7 54 07 62 16 70 24 78 32 86 53 8 53 06 60 13 66 1 9 7 2 26 79 52 9 52 015 57 10 62 1 4 671 1 9 72 51 10 52 03 55"- 0 7 59 10( 62 14 65 50 1t 51 02 153 04 5 5 u S 56 07 58 49 1 2 a~ 00 5 1 01 51 01 151 02 52 48 1 3 49 1.93099 48 3.8598 47.5.7 896 4 6 7.7195 4 547 1 4 49 97 406 94 43 92 4( 89 37 46 1 5 481 96 44 92 40 87 35 83 3 145 1F6 47 9-4 ~41 — 88 6 83- 3~ 7-7 24444 17 46 93 39 85 32 7 8 24 70 17 43~ 1 8 46 91 397 82 28 74 19~1 65 10 42 19 4.5 90 34 79 24 69 14 58 03 41 20 44 88 32 76 20 64 08 52 8.6796 40 21 43 87 30 73 17 60 03 46 9039. 22 43 8 5 2 8 70 1 3 3556. 74 9 8 40 83 38 23.42 83 2 5 6 7 09 5 0 92 3 4 75 37 2 4 4 1 82 2 3 6 4 0315 46 8 7 2 8 69 36 2 5 401 8 0 2 1 6 1 0 1 4 1 81I 2 2 62 35 26 39 7~~~9 1] 8 5 8 4.8197 ~36 ~76 1 5534 2 7 3 9 7 7 1 6 5 4 93 32 70 09 47 33 2 8 3 8 7 6 1 4 5 2 90 2 7 6 5 0 3 41 32 2 9 3 7 7 4 1 1 4 8 8 6 2 3 6 07.7 096 03431 3 0 3 6 7 3 09 4 5 8 2 1 8 5 4 90 27 30 31 36 71 06. 42 78 13 48 84 20 29 32 35 69 04 39 74 08 43 718 12 28 33 34 68 02 36 70 04 38 72 06 27 34 33 66 00 33 66 5. 7799 3 2 66 8.6399 26 35 32 65 2.88971 30 62 94 27 59 92 25 36 32 63 9- -5 26 58~ 900 -21 53 8424 37 31 62 92 23 54 85 16f 46 78 23 38 30~ 60 90 20 Si1 81 1.1 4 1 71 22 39 29 59 88 17 47 76 05 34 64 21 40 29 57 86 1 4 43 71 00 28 57 20 41 28 55 83 11 3.9 66 6.7394 22 ~49 19 42 2)7 5 4 8 1 08 35 61 88 1 5 42 18 43 26 52 78 04 3 1 57 83 09 35 17 44 25 51 76 01 2)7 52 7 7 02 28 16 I45 25 49 73 3.8498 23 48 72 7.6997 21 15 46 24 48 71 9 19 43 67 90 14 14 47 23 46 619 92 15 38 61 84 07 13 48 22 44 67 89 11 33 5,5 78 00 12 49 21 43 64 86 07 28 50 71 8.6-593 11 50 21 41 62 82 03 24 44 65 85 101 51 20 40 5.9 794T.8O~ 99 109 3-9 58 78 9 52 1 9 3 8 157 176 95 14 33 52) 7 1 8 53 18 36 55 73 91 09 27 4 6 64 7 ~54 1 7 35 52 70 87 04 22 39 57 6 55 16 33 50 6 6 83 00, 1 6 338 49 5 56 16 32 471 63 76 5.7695 11 26 42 4 57 1 5 30 45 Of) 75 90 05 20 35 3 58 1 4 28 43 57 7 1 8S 6. 72-9.9 14 28 2 59 18 27 40 53 67 80 94 07 21 1 60 0.9613 1.9225 2.8838 3.8450 4.8063 5. 767 6 6.7288 7.6901 8.6513 0 - 1 2 3~~~~-g- 74- 56 7 $6 9~ DEPARTURE 74 DEGREJES. I :iS: DEPARTult315 brnnozs. J 1 2 8 4 6 6 7 8 9 7~ 00.2588 0.5176 0.7765 1.03531.2941 1.5629 — 1112.0706 2.32- 9460 1 91 82 73 '64 55 46 37 28 2.3319 59 2 94 88 81 75 69 63 57 60 4468 3 97 93 90 86 83 80 76 73 6957 4 99 99 98 98 97 96 96 95 95-56 5 0.2602 0.5204 0.7807 1.0409 1.3011 1.5613 1.8215 2.0818 2.3420 55 6l 05/ ioT~ 151 20 25 30 35 40 4554 7 08 16 24 32 40 47 55 63 7153 8 11 21 32 43 54 64 75 86 9652 9 14 27 42 54 68 81 95 2.0908 2.3522 51 10 16 33 49 65 82 98 1.8314 30 47 50 11 19 38 57 76 95 1.5715 34 53 72 49 12 22 44 66 88 1.3110 31 53 75 97 48 18 25 49 74 99 24 48 73 98 2.3622 47 14 28 55 83 1.0510 38 65 98 2.1020 48 46 iS 30 61 91 21 52 82 1.8412 42 7345 16 33 66 999 32 66 99 32 65 9844 17 36 72 0.7908 44 80 1.5815 51 87 2.3723 43 18 39 77 16 55 94 32 771 2.1110 4842 19 42 83 25 66 1.3208 49 91 32 74 41 20 44 89 33 77 22 66 1.8510 54 90 40 2Y1 47 94 41 88 3 6 83 30 77 2.882439 22 50 0.5300 50 1.0600 50 1.5900 50 2.1200 W038 23 53' 07 58 11 64 17 70 22 i537 24 55 11 6 7 22 78 34 89 45 2.3900 36 25 58 18 75 34 92 501.8609 6 7 26 35 26 61 22 84 45 1.330U6 67 28 90 5134 27 66 28 92 56 20 84 48 2.1312 76 33 28 67 34 0.8000 67 34 1.6001 68 34 2.4001 32 29 70 39 09 78 48 18 87 57 2631 30 72 45 17 90 62 34 1.8707 79 62 30 31 75 50 26 1.0701 76 51 26 2.1402 7729 32 78 56 34 12 90 68 46 24 2.4102 28 33 81 62 42 23 1.3404 85 66 46 2727 34 84 67 51 34 18 1.6102 85 69 52 26 35 86 7 3 59 46 32 18 1.8805 91 7825 36 895 7 8 68 57 46- 35 2q Y4 2.4T420324 37 92 84 76 68 60 S2 44 36 2823 38 96 90 84 79 74 69 64 58 5322 39 98 95 93 90 78 86 83 81 7821 40 0.2700 O.'401 0.8101 1.0802 1.3502 1.6202 1.8903 2.1603 2.4304 20 T41 03 06- 10 13 16 19 22 26 2919 42 06 12 18 24 30 36 42. 48 6418 43 09 18 26 35 44 63 62 70 7917 44 12 23 35 46 68 70 81 93 2.4404 16 46 14 29 43 58 72 86 1.9001 2.1715 3015 46 17 34 52 69 86 1.6303W 20 T818 651-4 47 20 40 60 80 1.3600 20 40 60 8018 48 23 46 68 91 14 37 60 82 2.4505 12 49 26 61 77 1.0902 28 54 79 2.1805 301 60 28 57 85 14 42 70. 99 27- 5610 51l 31 62 94 25 56 871.9118 '50 81i9 52 34 68 0.8202 36 70 1.6404 38 712 2.4606 8 53 37 74 10 47 84 21 68 94 317 54 40 79 19 58 98 38 77 2.1917 66 6 56 42 86 27 70 1.3712 54 97 39 82 6 56tji 456 90 36 81 26 71 1.9216 622.4707 57 48 96 44 92 44 88 36 84 ~ 323 8 51 0.5502 52 1.1003 54 1.6505 56 2.200e 57 27 59 64 07 61 14 68 22 75 29 821 60 0.2756 0.5513 0.8269 1.1026 1.3782 1.6538 1.9296 2.2051 2.4808 ~ 1 2 1 8 4 6 6 7 LATITUDB 74 DEGREEs. I E z I: C D I::-:;.............. - -.: I:E -, I::.......... ' - ATTVXV 16 SBGOB8s. f: f a E X.:. A, i..9.,,,,, 7., 1. -; ~~: ~ -- - -I 7 m o.968 T 1 12 2 11 8 10 4 09 5 09 ~ 6 08 7 07 8 06 9 05 10 05 11 04 12 08 18 02 14 01 15 00 16 00 17 0.9599 18 98 19 97 20 96 '21 96 22 95 28' 94 24 93 25, 92 26 92 27 91 28 90 29 89 0 88 8-1 87 82 87 881 86 84 85 35 84 86 88 87 82 88 82 89 81 40 80 41 79 42 78 48 77 144 76 45 76 41t6 75 47 74 48 78 49 72 fio 72 L9225 24 22 20 19 17 16 14 12 11 09 I " ---—, 2.88 85 81 31 28 26 23 21 1c 14..850 47 44 41 88 34 31 28 25 22 18 I! 55 66 51 61 47 56 43 52 39 47 35 42 81 37 27 32 23 28 6. 7288 88 77 71 66 60 55 49 43 88 832 7.( 7I 3: 2, 018 8.618 5894 06 89 8.6499 82 92 75 85 69 77 6'2 70 56 63 50 56 43 49 87 41 arl - 60 59 58 57 56 55 54;53 52 151 50 I 4' - I -I I-. I 07 06 04 03 01 L.9199 98 96 94 93 91 90 88 86 85 83 81 80 78 76 76 78 71 70 62 68 66 65 63 61 6( 5E r if 5: _54 45 4 4. 4 11 09 06 04 02 2.8799 3 97 94 92 89 87 84 82 79 77 75 72 69 67 65 62 60 57 55 52 50 47 45 42 40 87 85 82 3 80 1 27 3 25 S 22 6 20 5 17 3 15 10 12 08 05 02 B.8399 96 92 89 87 83 79 76 72 69 66 62 59 56 53 50 46 43 40 36 33 30 26 23 20 16 13 10 06 03 00 3.8296 98 90 86 19 15 11 07 03 L7999 95 91 86 82 78 74 70 66 62 54 64 49 45 41 37 8. 21 2t 2( 14 I' 0) OI 0' 4.789 9 8 8 7 7 7 6 6 6 22 17 13 08 03 5.7598 ~ 93 89 83 78 -74 69 64 59 54 49 44 39 34 29 24 3 19 ) 14 i 09 0 05 3 5.7499 2 94 8 90 4 84 0 79 6 75 1 69 7 64 3 60 9 54 9- 49 0 44;6 39,2 34 18 29 26 20 15 09 04 6.7198 92 87 80 75 69 64 58 52 46 -41 35 29 23 17 11 06 O0 6.7094 89 71 71 64 5' 4' 4' 38 3< 2' 1; 1' 0 0 bu 23 17 10 04 7.6798 91 85 78 71 65 58 52 45 38 32 26 18 12 06 7.669 92 8( 71 6f 51 l 5t 3 4( 7 2' 2 1 6 1 0O 9L 7.669 8 9 2 8 7 7 1 7 26 4) 194' 12 4, 054 8.63974 904 834 754 684 60 8 53 83 463 38 3 31 8 243 16 8 083 01 8.6294 i 872 79 71 64 3 57. 6 49 " 9 41, 3 34' 3 26, 9 19 3 11 6 04 9 8.6197 3 89 6 81 9 74 2 66 6 59 9 52 2 44 8 7 6 5 4 3 2 1 0 38 37 36 II 35 24 2 1 2( 21 I 2' 2! 2 1 1 1 1 1 1 1 1 ) I 3 2 1 f 3 2 0 8 7 6 5 i 8 2.1.0 j. -. 71 41 12 83 54 2 6.96995 66 36 9 70 40 09 79 49 19 89 58 28 8 69 88 07 76 45 14 83 52 21 7 68 86 04 72 41 09 77 45 13 6 67 34 02 69 86 08 70 88 05 5 -66 88 2.8699 66 32 5.7398 65 81 09 4 65 81 97 62 28 93 59 24 90 8 65 29 94 59 24 88 58 18 82 2 64 28 91 55 19 88 47 10 74 1 0 9668 1.9126 2.8689 3.8252 4.7815 5.7878 6.6941 7.6504 8.6067 0 1 T::8 P4 BE E. 7 8 _79 DEPARTURE 78 DEGREES.! - # i + a~~~~~~...... ',',',,: i'............. -..... -r#i'l D EPARTBUR 16 DQitES8. 10 2 8 4 6 7 8 9; ) 6 0.2760.6513 0.8269.1026 1.3782 1.6688 1.92965l.4086 1 59 18 78 37 96 55 1.9314 74 8 9 2 62 24 86 48 1.3810 72 84 96 668 3 65 30 94 59 24 89 54 2.2118 8367 4 68 35 0.8303 70 38 1.6606 73 41 2.4908 6 5 70 41 11 82 52 22 93 63 3466 6 731 46 19 92 6639.9412 85 564 7 76 2 28 1.1104 80 55 312.2207 0 83 58 8 79 57 36 15 94 72 61 30 2.6008 52 9 82 63 45 261.3908 89 71 62 34 61 10 84 69 3 37 22 1.6706 90 74 65960 11 871 74 61 48 36 231.9510 97 84 12 90 8 7 60 60 39 2 2.23191 2.10948 13 93 85 78 71 64 56 49 32 8447 14 96 91 87 82 78 73 6 64 6046 15 98 97 95 92 94 88 86 84 82464 1614 0.5602 0.84031.204 i4006 1.6807 1.9608 2.2409 2.521044 17 * 04 08 12 16 30 23 27 315 854 18 07 13 20 27 3 40 47 4 6042 19 10 19 29 38 48 67 67 76 8641 20 12 25 37 49 62 74 86 98 2.5311 40 _21 15 45 60 75 90 1.9705 2.2510 539 22 18 36 63 71 89 1.6907 25 42 6038 23 21 41 62 821.4103 24 44 65 8637 24 23 47 70 94 17 40 64 8712.64111 36 25 26 52 79 1.1305 31 57 8312.2600 36136 26 29 68 871 16 45 74 1.9803 32 61 l34 27 32 64 95 27 59 91 23 64 863 28 35 6910.8504 38 73 1.7008 42 77 2.5611132 29 37 75 12 50 87 25 62 99 3731 30 40 80 21 6111.4201 41 8112.2722 6210 31 43 86 291 72 15 581.9900 43 86 29 32 46 91 37 83 29 75 20 66 2.6611 28 33 49 97 46 94 43 91 40 8 8727 34 61 0.5703 54 1.1405 5711.7108 5912.2810 6226 36 54 08 62 16 71 25 79 33 8726 — 7 ------— 1 711 2851 41 98 55 2.71224 37 60 19 79 39 99 6812.0018 78 8723 38 63 25 88 501 1.4313 75 3812.290 622 39 65 31 96 61 26 91 56 22 8722 40 68 3610.8604 72 40 1.7208 76 442.581220 4-1 71 42 -12 83 54 26 96 66 371 9 42 74 471 21 94 68 4212.0115 89 6218l 43 77 63 29 1.1508 82 61 38 2.8016 8217 44 79 58 38 17 96 76 54 342.69116 i 45 82 64 46 281.4420 92 74 56 8815 46 85 69 54 39 2411.708 98 78 621r 47 88 75 63 50 38 25 2.0213 2.310 8818 48 90 81 71 61 52 42 32 22 2.601: 49 93 86 7 72 66 59 52 45 811 50 96 92 87 84 80 75 71 67 68910 511 99 971 96 959 92 91 0 4 88 52 0.2902 0.6803 0.8705 1.1606 1.4608 1.7409 2.0811 2.321 2.6114 1 53 04 09 13 17 21 25 29 84 87 64 07 14 21 28 35 42 49 66 68 65 10 20 29 39 49 69 69 7 88 6 661 26 38 50 63 761 s23801'T 4I 67 15 31 46 62 77 9212.0408 28 168 18 86 65 73 9111.7509 27 46 6 69 21 42 63 8411.4605 2 46 67 8 60 0.2924 0so,470.8771 1.1696 1.4619 1.7542 2.0466 2.8890 2. 0 i-:I 0 1 8 4 6 6 7 T ~ LATITUDE 78 DEGREES., 108 ~~~LATITUDE~ 17 DEGREES. p 1 2 ~ ~~~8 4 5 6 7 a 9~ 0 0.9563 1.9126 2.8689 8.8652 4.7815 5.7378 6.6941 760-4 8.6067 60' 1 62 24 87 49 11 78 85 7.6498 60 59 2 61 28 84 45 07 68 29 90 52 58 8 61, 21 82 41 03.63 24 84 45 57 4 -60 19 79 38 4.7798 58 17 77 36 56 s6 59 18 -76 85 -- 94 53 12 70 29 55 75 58 16 74 32 90 47 05 68 21 54 7 57 14 71 28 86 43 00 57 14 53 8 56 12 69 25 81 36 6.6893 49 06 52 9 55 11 66 22 77 32 88 43 8.5999 51 10 55 09 64 18 73 27 82 36 91 50 TT 54 07 61 14 68 22 75 2 9 82 49 1 2 53 06 5 8 1 1 64 1 7 7 0 22 75 48 1 3 52 04 5 6 08 60 1 1 63 1 5 67 47 1 4 5 1 02 5 3 04 5 6 07 58 09 60 46 1 5 50 00 51I 0 1 51I 0 1 5 1 0 1 52 45 1765 491. 90~99i 48 3.8197 ~47 5. 7 29 6 457.6394 44 44 1 7 49 9 7 4 6 94 4 3 9 1 40 88 37'43 1 8 48 95 43 9 0 3 8 8 6 3 3 8 1 28 42 1 9 4 7 93 40 8 7 3 4 80 2 7 7 4 20 41 20 46 92 3 8 84 30 75 2 1 6 7 13 40 Ti 4~5 90 3 5 80P 25 70 1O 5 60 05839 22 44 8 8 3 2 7 6 2 1 6 5 0 9 5 38.5897 38 283 4 3 8 6 3 0 783 1 7 60 03 46 90 37 24 42 85 27 70 12 54 6.6797 39 82 36 25 42 83 25 66 08 49 91 32 74 35 26 27 28 29 30 751 82 83 84 85 87 88 40 ~41 42 48 44 41 40 39 38 f87 86 85 35 84 133 82 81 80 29 28 128 9.7 81;,79 78 76 74 78 71 69 67 66 64 62 60 59 57 55 53 Rri 22 19 17 14 12 09 06 04 01 2.8598 96 93 90 88 85 88 80 77 74 72 69~ 67~ 64 61~ 59 56 58 50 48i 45 63 59 56 52 49 45 42 38 85 31 28 24 20 17 14 10 06 03 8.8099 96 92i 89 85 -82 74 71 67 64 60 04 4.7699 95 90 186 82 77 73 69 64 60 55 51 47 42 38 83 29 24 20 16 11 07 02 4.7598 93 89 84 80 75 44 89 33~ 28 23, 18~ 12~ 07 02 5.7197. 91 86 81 76 65 60 54~ 49 44] 89 83 - 28 22 117 12 06 01 5.7095 901 85 79 72 66 60 54 48 42 36 30 23 17 11 05 6.6699 74 68 62 55 4.9 43 37 30 24 18 11 05 25 18 11 04 7.6297 90 83 76 69 62 55 48 41 84 27 20 13 05 7.6198 92 85 77 70 63 56 49 41 84 27 20 13 06 7.6099 92 7.6085 66 58 50 42 35 27 19 11~ 03 8.5795 87 79 71 64, 56 48 89 81 23 16 08 00, 8.6692 84 76 67 59 51 43 85.34 33.32 31 30 28 27 26 25 23 22) 21 20 18 17 16 is 18 12 11 10 8 7 6 6 4~ 8 2 I 0] / 22 44 21 43 20 41 20 89 - P 9 87.18 85 17' 82 16i 84 15 80 14 28 18 27 12 25 12 28 511 1.9021 46 2.8582 57 53 50 46 3.8042 71 67 62 58 4.7568 85 8( 74 66 6.7064 6.6599 98 87 81 6.6574 28 20 12 04 8-.6959 DEPARTuRE 7~4 DEGRES8, DEPARTURE 17 DEGREES. 109 - 1 2 3 4 5 6 7 8 9 T ' 00.2924 0.5847 0.8771 1.1695 1.4619 1.7542 2.0466 2.883902.631306 1 27 53 80 1.1706 33 59 86 2.3412 89 59 2 29 59 88 17 47 762.0505 84 6458 3 32 64 96 28 61 93 25 57 8957 4 35 70 0.8804 39 741.7609 44 78 2.6413 56 5 38 75 13 50 88 26 63 2.3501 38 55 6 40 81 21 62 1.4702 42 83 23 64 564 7 43 86 30.73 16 592.0602 46 8953 8 46 92 38 84 30 76 22 68 2.651452 9 49 97 46 95 44 92 41 90 3851 10 52 0.5903 55 1.1806 58 1.7709 61 2.3612 64 50 11 54 09 63 17 72 26 80 34 2.6609 49 12 57 14 71 28 86 43 2.0700 57 1448 13 60 20 80 40 1.4800 59 19 79 3947 14 63 25 88 50 13 76 382.3701 6346 15 65 31 96 62 27 92 58 23 89 45 18 68 36 0.8905 73 41 1.7809 77 46 2.6714 44 17 71 42 13 84 55 26 97 ' 68 3943 18 74 47 21 95 69 422.0816 90 6342 19 77 53 30 1.1906 83 59 36 2.3812 8941 20 79 59 38 17 97 76 55 34 2.681440 21 82 64 46 281.4911 93 75 57 39139 22 85 70 55 40 251.7909 94 79 6438 23 88 75 63 50 38 26 2.0913 2.3901 8837 24 90 81 71 62 52 40 33 23 2.6914 36 25 93 86 80 73 66 59 52 46 39 35 26 96 92 88 84 80 76 72 68 6434 27 99 97 96 95 94 92 91 90 8833 28 0.3002 0.6003 0.9005 1.2006 1.5008 1.8009 2.1011 2.4012 2.7014 32 29 04 09 13 17 22 26 30 34 3931 30 07 14 21 281 34 43 50 57 6430 31 10 20 29 39 49 59 69 78 88 29 32 13 25 38 50 63 76 88 2.4101 2.7113 28 33 15 31 46 68 77 922.1108 23 3927 34 18 36 55 73 91 1.8109 27 46 6426 35 21 42 63 84 1.5105 25 46 67 8825 36 24 47 71 95 19 42 66 90 2.721324 37 27 53 80 1.2106 33 59 86 2.4212 3923 38 29 58 88 17 46 752.1204 34 6322 39 32 64 96 28 60 92 24 56 8821 40 35 70 0.9104 39 74 1.8209 44 78 2.731320 41 38 75 13 50 88 26 63 91 38 19 42 40 81 21 61 1.5202 42 82 2.4322 63 18 48 43 86 29 72 16 592.1302 45 8817 44 46 92 38 84 30 75 21 67 2.7413 16 45 49 97 46 94 43 92 40 89 8715 46 51 0.6103 54 1.2206 57 1.8308 60 2.4411 6414 47 54 08 63 17 71 25 79 34 8818 48 57 14 71 28 85 42 99 562.7513 12 49 60 19 79 39 99 582.1418 78 3711 50 63 25 88 50 1.5313 75 38 2.4500 63810 '51- 65 31 96 61 27 92 57 22 87 9 52 68 36 0.9204 72 40 1.8408 76 44 2.7612 8 53 71 42 12 83 54 25 96 66 37 7 54 74 47 21 94 68 42 2.1515 89 62 6 55 76 53 29 1.2305 82 58 34 2.4610 87 5 '6 79 -58 37 16 96 75 54 13 2.7712 4 57 82 64 46 28 1.5410 91 73 35 37 3 58 85 69 54 38 23 1.8508 92 77 61 2 59 87 75 62 50 47 24 2.1612 99 87 1 60 0.3090 0.6180 0.9271 1.2361 1.5451 1.8541 2.1631 1.4722 2.7812 0 -' %2 s3^ 4 6 5 -6.7 8. 9 - LATITUDE i DEGREEiS., I I "la 4i I I I I 110 ~~~LATITVDS~ 18 DEGREES. 2 4 -5 - 6 87 T 9 T 40.9511 1.9021 2.8582 3.8042 4.7553 5.7064 6.6574 7.6085 8.559660 1 10 19 29 89 49 58 68 78 87 59 2 09 18 26 85 44 53 62 70 7958 8 08 16 24 82 40 47 55 68 71 57 4 07 14 21 28 85 42 49 56 68 56 5 06 12 18 24 81 87 43 49 55555 f 05 10 16 21 26 31 86 42 47564 7 04 09 18 17 22 26 80 84 89 58 8 08 07 10 18 17 20 28 26 80562 9 02 05 07 10 12 14 17 19 22 51 10 02 08 05 06 08 09 1 1 12 14 50 1 01~01 02~O 0O2 03R 0~4 0~4 ~05 05r-49 12 00 1.8999 2.8499 3.7999 4.7499 5.6998 6.6498 7.5998 8.5497 48 18 0.9499 98 96 95 94 98 92 90 -89 47 14 98 96 94 92 90 87 86 88 81 46 15 97 94 91 88 85 82 79 76 78 45 16 96 9- 2 88 ~ 84 ~81 7~7 73 -69 ' 4 ~6544 1 7 9 5 90 86 8 1 7 6 7 1 6 6 6 2 57 43 1 8 94 8 9 88 3 77 7 2 6 6 60 54 49 42 1 9 983 8 7 80 783 6 7 60 5 3 46 40 41 20 92 85 7 7 7 0 6 2 5 6 47 89 82 40 2i 9 83 75 6 6 5 8 49 4 1 32 2339 22 9 1 8 1 7 2 '62 5 3 44 8 4 256 15388 28 90 7 9 69 5 9 49 8 8 2 8 1 8 07837 24 8 9 7 8 6 6 55 44 3 3 2 2 10 8.5899836 26 88 7 6 683 5 1 3 9 2 7 1 5 02 90 35 26 ~87 7 4 6 1 ~ 48 835 21 ~0-8 7.5895 82834 2 7 8 6 7 2 5 8 44 8 0 1 6 02 88 74883 2 8 85 70 55 40 2 6 1 1 6.6396 8 1 66832 2 9 84 6 8 58 837 2 1 05 89 7 4 58831 80 83 6 6 50 883 16 5.6899 82 66 49830 81 82 65 47 29 12 94 76 58 41 29 82 81 68 44 26 07 88 70 51 88 28 38 81 61 42 22 03 83 64 44 25 27 84 80 59 39 18 4.7898 77 57 86 16 26 85 79 57 86 14 93 72 50 29 07 25 86 7V8 -55 33 11 89 66 44 22~8.529924 87 77 54 30 07 84 ~61 88 14 91 28 88 76 52 27 08 79 55 31 06 82 22 39 75 50 25 00 75, 49 24 7.5799 74 21 40 74 48 22 8.7896 -70 44 18 92 66 20 41 73 46 19 92 65 88 11 84 57 19 42 72 44 16 88 61 88 05 77 49 18 43 71 42 14 85 56 27 98 70 41 17 44 70 40 11 81 51: 21 6.;6291 62 82 16 45 69 89 08 77 47 16 85 54 2415 46 6-8 37 05 74 42 10 ~79 47 1614 47 67 85 02 70 37 04 72 39 07181 48 67 88 00 66 88 5.6799 66 82 8.5199 12 49 66 81 2.8897 62 28 94 59 25 90 11 50 65 29 94 58 28 88 52 17 81 10 I bl 64 52 63 53 62 54 61 55 60 -R 59 57 58 58 57 59 56 860 0.9455 27 25 24 22 20 16 14 12 1.8910 91 88 85I 881 80 77 74 71 68 2.8866 6-5 51 47 44 40 36 82 28 24 8.7821 lb 14 09 05 00 4.7295 90 86 81 4.7276 71 64 87 5.6781 46 39 88 26 19 18 06 00 6.6193 6.6186 I C 02 7.5694 87 79 72 64 57 49 7. 5642 64 48 81 14 05 8.6097 8 7 6 5 8 2 1 0 DOEPARTURB 71 DEGREES. i I DEPARTURX 1 DXGURIEE8.11 o 0.0-90 0.6180 0.9271 1.2361 1.'5451 1.854-1 2.1631 2.4722 2.78126 1 93 86 79 72 65 57 50 43 36 59 2 96 91 87 88 79 74 70 66' 6158 3 99- 97 96 94 93 91 90 88 87567 4 0.3101 0.6202 0.9304 1.2405 1.5506 1.8607 2.1708 2.4810 2.7911 566 5 04 08 12 16 20 24 28 32 36 55 6 07 14 20 27 84 41 48 54 61 54 7 10 19 29 88 48 57 67 76 86563 8 12 25 37 49 62 74 86 98 2.8011 52 9 15 80 45 60 76 91.2.1806 2.4921 86 51 10 18 86 53 71 89 1.8707 24 42 60 50 Ti ~2-1 41 62 82 15 6083 24 ~44 6 5 85 4 9 1 2 2 3 47 70 9 3 1 7 40 6 8 8 62.8110 48 1 3 26 52 78 1.2504 8 1 5 7 88 2.5009 85 47 1 4 29 5 8 8 7 1 6 45 73 2.1902 8 1 60 46 iS5 32 6 3 9 5 2 6 5 8 90 2 1 538 84 4- 5 16 84 6 9 0. 94 0 88 72 1.8806 4 1 75 2.8210 44 17 37 74 12 49 86 2 3 60 9 8 35 43 1 8 40 80 20 60 1.5700 8 9 7 92.5119 59 42 1 9 43 8 5 2 8 7 1 1 4 5 6 99. 4 2 84 41 20 45 9 1 86 82 2 7 72 2.2018 68 2.8809 40 21 22 28 24 25 27 28 29 30 32 33 84 35 37 88 89 40 42 43 44 45 476 48 49 50 51 54 57 69C 62 65 68 7C 78 76 79 81 84 87 90 92 95 98 0.3201 03 06 09 1 2 14 17 20 28 25 28 96 0.6302 07 13 19 24 30 i41 46 i52 57 68 68 7 — i4 7 9 85 90 96 0.6401 07 1 2 1 8 23 29 34 40 45 51 58 45 53 61 70 78 86 94 0.9503 11 19 27 36 44 52 60 69 77 85 94 0.9602 10 18 27 35 43 51 60 68 76 85 1.2604 156 26C 8 7 48 59 70 81 92 1 2703 1 4 25 86C 47 58 69 8C 92 1.2802 1 4 24 36 46 58 68 80 91 1.2902 1 8 41 55 69 83 97 1.5810 24' 38~ 52' 65 79 93 1.5907 21 i34 48 62 I76 90 1.6003 17 31 45 58 - 721 861 1.61 05 14 27~ 41, 89 1.8906 22 39 56 72 89 1.9005 22 38 55 72 88 1.9105 21 38 54 71 87 1.9204 20 37 53 70 86 1.9303 19 86 52 69 I 87 5711 76 96 2.21 1 34 54 738 92 2.2211 3 1 Sc 69~ 89 2.2308 2 7 46C 66 85 2,2404 24 48 62 8 1 2.2501 20U 89 59 78 97 86 2.5208 80 52 74 96 2.53f8 62 84 2.5406 29 50 73 94 2.5517 38 61 83 2.5605 27 49 7 1 9:3, 2.5715 37 59 82 2.5808 84 59 83 2.8409 34 59 83 2.8508 33 57 82 2.8607 82 56 81 2.8706 81 56 81 2.8805 81 65 80 2.8904 80 54 79~ 2.9004 39 38 87 36 36 33 82 31 30 28 27 26 2S 23 22 21 20 19 18 17 16 15 i14 18 12 51 31 62 93 24 55 85 2.2616 52 34 67 0.9701 35 69 1.9402 36 53 36 73 09 46 82 18 55 54 39 78 18 57 96 35 74 2.51 55 42 84 26 68 1.62010 511 93 68 69 60 45 50 0.8256 89c 95 o.osoc 06 0.6511 34 42 51 59 79 90 1.3001 12 1.3023 6 LATITUDia 711 I.... 112 L~~~~~~ATITUDZ9 19 Dklro 2 8 4 6a 6 7 8 9 0 0.9455 1.8910 2.8366 3.7821 4.7276 5.6731 6.6186 T5.6642 &.5097 60 1 54 08 63 17 71 25 79 34 89 59 2 63 07 60 13 67 20 73 26 80 58 3 52 05 57 09 62. 14 66 18 71 57 4 51 03 54 06 57 08 60 11 63 56 5 50 01 51 02 52 02 53 03 54 55 6 50 1.8899 49 3.7798 48 5.6697 47 7.5596 46 54 7 49 97 46 94 43 91 40 88 37 53 8 48 95 43 90 38 86 33 81 28 52 9 47 93 40 86 33 - 80 26 73 19 51 10 46 91 37 83 29 74 20 66 11 50 11 45 89 34 79 2,4 68 13 58 03 49 12 44 88 31 75 19 63 0 7 50 8.4994 48 13 43 86 28 71 14' 57 00 42 85 47 14 42 84 29 67 09 51 6.6093 34 76 46 15 41 82 23 64 05 45 86 27 68 45 16 40 80 20 60 00o 39 79 19 5944 17 39 78 17 56 4.7193 34 73 12 51 43 18 38 76 14 52 90 28 66 04 42 42 19 37 74 11 48 8.5 22 59 7.5496 33 41 20 36 72 08 44 81 17 53 89 25 40 21 35 70 05 40 76 11 46 81 1i6 39 22 34 68 03 37 7 1 05 39 74 08 38 23 33 66 00 33 66 5.6599 32 66 8.4899 37 124 32 64 2.8297 29 6 1 93 25 58 90 36 25 31 63 94 2.5 57 88 1 9 50 82 35 26 30 61 91 21 52 82 1 2 42 73 34 27 29 59 88 18 47 76 05 34 64 33 28 28 57 85 14 42 70 6.5999 27 56 32 29 27 55 82 10 37 64 92 19 47 31 30 26 53 79, 06 32 58 85 11 38 30 31 25 51 76 02 27 522 78 03 39 29 32 25 49 74 3 7698 23 47 72 7.5396 21 28 33 24 47 71 94 18 4 1 65 88 12 27 34 23 45 68 90 13 35 58 80 03 26 35 22 43 (5 86 08 29 5 1 72 8.4794 25 36 21 41 62 82 03 24 44 65 8524 37 20 39 59 78 4.7098 18 37 57 76 23 38 19 37 5 6 74 93 12 30 49 67 22 39 18 35 53 70 88 06 23 41 58 21 40 17 33 50 67 84 00 17 34 50 20 4[ 16 31 47 63 79 5.649 4 100 26 41 19 42 15 29 44 59 74 88 03 18 32 18 43 14 27 41 655 69 82 6.5896 10 23 17 44 13 25 38 51 64 76 89 02 14 16 45 12 24 35 47 59 71 83 7.5294 0615 46 11 22 32 43 54 65 76 86 8.4697 14 47 10 20 29 39 49 59 69 78 88 13 48 09 18 26 35 44 53 62 70 79 12 49 08 16 23 31 39 47 55 62 7011 50 07 14 20 27 34 41 48 54 61 10 51 06 12 17 23 29 35 411 46 52 9 52 05 10 15 20 25 29 34 39 44 8 53 04 08 12 16 20 23 27 31 35 7 54 03 06 09 12 15 1 7 20 23 26 6 55 02 04 06 08 10 11 13 15 175 S7O 01 02 03 04 05 05 06 07 08 4 57 00 00 00 00 00 5.6299 6.5799 7.6199 8.4599 3 5 0.9899 1.8798 2.8197 8.7596 4.6995 93 92 91 90 2 5 98 96 94 92 90 87 85 83 81 1 0.9397 1.879412.8191 3.7588 46985 5.6381 6.5778 7.5175 8.4572 0 1 2 8 4 6 i6 T 8 9 DEPARTURE 70 DEGREES. i DEPARTURE 19 DIGRESS. la 1 2 8 4 6 6 7 8 9 e 0 0.325,6 0.6511 0.9767 1.3028 1.62718 1.9534 2.2790 2.6046 2.9801 60 1 68 17 75 84 92 50 2.2809 67 26 59 2 61 22 84 45 1.6306 67 28 90 61 58 3 644 28 92 56 20 83 47 2.6111 755 4 67 33 0.9800 67 34 1.9600 67 34 2.9400 56 5 69 39 08 78 47 16 86 55 25 55 6 72 44 17 89 61 332.2905 ~78 b5054 7 75 50 2 5 1.3100 75 50 24 99 74 53 8 78 55 33 11 89 66 44 2.6222 99 52 9 80 60 41 2 2 1.64&2 82 63 43 2.9524561 10 83 66 50 33 16 99 82 66 49 50 1 86 72 58 44 30 1.97152.3001 87 37849 12 89 77 66 55 44 32 21 2.6310 98 48 13 91 83 74 66 57 48 40 31 2.9623 47 14 94 88 83 77 71 65 59 54 48 46 15 97 94 91 88 85 81 78 75 72 45 166 0.3300 99 99 99 99 98 98 98 90744 17 02 0.6605 0.9907 1.3210 1.6512 1.9814 2.3197 2.6419 2.6722 48 18 05 10 15 20 26 31 361 41 46 42 19 08 16 24 32 40 47 55 63 71 41 20 11 21 32 42 53 64 74 85 95 40 21 13 27 40 56 67 80 94 2.6507 2.9 821 39 22 16 32 48 64 81 97 2.3213 29 45 38 23 19 38 57 76 95 1.9913 32 51 70 37 24 22 43 65 86 1.6608 30 51 73 94 36 25 24 49 73 98 22 46 71 95 2.9920 35 26 2? Y44 81 1.3308 3 6 63 902.6617 44 34 27 30 60 89 19 49 792.3309 38 68 833 28 33 65 98 30 63 96 28 61 93 32 29 35 711.0006 41 77 2.0012 47 82 3.0018 31 30 38 76 14 52 91 29 67 2.6705 48 30 31 41 82 22 631.6704 45 86 2 6 67 29 32 44 87 31 7-4 1 8 62 2.3405 49 92 28 83 46 93 39 85 32 78 24 70 3.0117 27 34 49 98 47 96 45 94 43 92 41 26 35 52 0.6704 55 1.3407 59 2.0111 63 2.6814 66 25 36 55 09 64 18 73 27 82 36 91 24 37 57 15 72 29 87 44 2.3501 58 3.0216 23 38 60 20 80 40 1.6800 60 20 80 40 22 39 63 25 88 51 14 76 39 2.6902 64 21 40 66 31 97 62 28 93 59 24 90 20 41 68 36 1.0105 73 41 2.0209 77 46 3.031419 42 71 42 13 84 55 26 97 68 39 18 43 74 47 21 95 69 42 2.3616 90 63 17 44 76 53 29 1.3506 82 58 35 2.7011 88 16 45 79 59 38 17 96 75 54 34 3.0413 15 467 82 64 46 2 8 c.6 1.6910 91 73 55 3714 47 85'a 69 54 38 23 2.0308 92 77 61 18 48 87 75 62 50 37 24 2.3712 99 87 12 49 90 80 70 60 51 41 31 2.7121 3.0511 l1 50 93 86 79 72 65 57 50 43 36 10 51 96 91 87 82 78 74 69 65 60 9 52 98 97 95 93 92 90 88 86 85' 8 53 0.3401 0.6802 1.0203 1.3604 1.7006 2.04071 1.3808 2.7209 3.0610 7 54 04 08 11 15 19 23 27 30 34O6 55 07 13 20 26 33 39 46 52 59 56, 56 09 19 28 37 47 56 65 74' 847 57 12 24 36 48 60 72 84 96 8.0708 8 68 1 5 29 44 59 74 88 2.3903 2.7318 32 2 69 18 35 53 70 88 2.0505 23 40 58 1 60 g.84l20 0.6840 1.2661 1.3681 1.7101 2.0521 2.3941 2.7362 3.0782 0 1 2 1 8 4 5 6 7 8 9 LATITUDE 70 DEGIlIREES. F 11 - F 1 t14 L & \ATItTDZ 20 31B. ji4 16' 8 4 8 9 ' 0.9897 1.8794 2.8191 3.7588 4.6985 6.6 6.5778 7.5175 8.4672 60 1 96 92 88 84 80 75 71 67 63 69 2 95 90 85 80 75 69 64 59 54 658 3 94 88 82 76 70 63 57 51 4557 4 93 86 79 72 65 57 50 43 3656 5 92 84 76 68 60 51 43 35 2755 6. 91 82 78 64 55 45 36 27 18 54 7 90 80 70 60 60 39 29 19 09153 8 89 78 67 56 45 33 22 11 0052 9 88 76 64 52 40 37 15 03 8.4491 51 10 87 74 61 48 35 21 08 7.5095 82150 11 86 72 58 44 30 15 01 87 7349 12 85 70 55 40 25 09 6.5694 79 64 48 13 84 68 52 36 20 03 87 71 5547 14 83 66 49 32 15 5.6297 80 63 46 46 15 82 64 46 28 10 91 73 55 37145.{ 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 85 36 37 388 89 41 4E 44 45 47( 4; 41 6( 6 65:6 I ' 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 65 6g 64 63 i 62 f1 60 59 58 57 - 56 64 53 52 651 3 Si 7 49 4E 9 47 " 4( 2 44 4f 4 4' 5 41. 4( 7 83 62 60 58 56 54 52 50 48 46 44 42 40 38 36 33 31 29 27 26 23 21 19 17 15 13 11 09 07 05 O03 01 Oi 1.869c 97 94 i 9', 9( ' 8( 2 84 8! D 8( 71 8 74 7 7 -6 1.867! 43 40 37 34 31 28 24 21 18 15 12 09 06 03 00 2.8097 94 91 88 85 82 79 76 73 70 66 63 60 57 54 51 48 45 1 42 2 39 3 36 8 82 6 29 4 26 2 23 20 8 18 6 14 4 10 2 2.8007 24 20 16 12 08 04 3.7499 95 91 87 83 79 75 71 67 63 59 55 50 46 42 38 34 30 26 22 18 14 10 06 01 3.7397 93 89 85 81 76 7. 6E 64 6( 5: 671 4, t8.7384 05 00 4.6895 90 85 79 74 69 64 59 54 49 44 39 34 29 24 19 13 08 03 4.6798 93 89 83 78 72 67 62 57 47 4 31 21 1f 3 1( 0( ) 04 6 4.669~ 91 7 8' 3 4.667 85 79 73 67 61 655 49 43 37 31 25 1 19 13 07 00 5.6194 88 82 76 70 64 58 51 45 39 33 26 20 14 08 02 5.6096 90 83 1 77 e 71 1 65 6 59 62 5 46 0 40 5 33 27 4 21 D 5.6016 66 59 52 45 38 32 24 17 10 02 6.5596 89 82 75 67 60 53 45 38 31 24 17 10 03 6.6496 89 81 74 67 60 52 45 8C 87 8( 72 61 6.5358 6.635] 47 39 31 23 15 07 7.4998 90 82 74 66 58 50 42 34 26 18 09 01 7.4893 856 77 68 60 52 44 35 27 19 02 7.4794 8( 7E 3 7( 61 5. 3 21 j 24 1: 5 0O 8 7.4694!17.4684 194 104 01 4 8.4392 4 833 733 64 558 4618 371 28 3 191' 10,t 00O 8.4291 82 ' 72 63 54 45, 36? 27 18 09 00 8.4190 81 72 63 563 i 44 5 85 25 16 - 07 3 8.4097 5 88 6 78 8 69 6 Q 60 1 50 3 41 4 81 6 8.4 02 4 3 2 1 0 19 38 17 16 15 14 13 12 31 19 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0O,I -2 _e I.. mr _ I i 'I; - I I T -- 'I 77 -- I 8 - I1 I t -.~~..r -.- __ -~ I DEPABRTURE 69 DBEGRES.. )4. -,: '.- I A E:,: no -W~ - 1a:'ll " - 1,! - ' - i -::: I, Id;, ' I ~ I p., I I 1 1I I I 1 I 1 1 1 2 2 2 2 2 DEPARTUR 20 lBQm3Bs. 116;,t-,:.:o i;; o --- t-t,, - 1 - - I,,_i-:~~~P~ I " + i I I i T r } i 2 1 f: rl P 3 3 \ K I 6 4 ^ q (1 ( PI I \ II 3 j 3 8 E 4 4 4 I I II i ) ) 2 3 5.s 7 r I 1 0.342 01 23 26 28 31 34 37 39 42 45 48 50 53 56 58 61 64 67 69 72 75 78 80 83 86 88 j,_ z I 8. 4 I ~ re I V I 4;. }-.v J I.-l ".6840 46 51 67 62 68 73 79 84 90 95 0.6901 06 11 17 22 28 33 39 44 5C 6S 61 61 71 7_ 1.0261 69 77 85 93 1.0302 10 18 26 34 43 51 59 67 75 84 92 1.0400 08 16 24 33 41 49 1 57 7 65 1.8681 1.3703 14 24 36 46 57 68 79 90 1.3801 12 23 34 45 56 66 78 88 99 1.3910 21 32 43 54 1.7101 16 29 42 56 70 83 97 1.7211 24 38 52 65 79 92 1.7306 2( 33 47 61 74 1.7402 11 2. 4' 2.U5b1 37 54 70 87 2.0603 20 63 53 69 85 2.0702 18 34 60 67 83 2.0800 16 33 t 49 65 82 98 9 2.0914 2 3C 2.4a;4 60 80 99 2.4018 37 56 75 95 2.4114 33 52 71 90 2.4209 28 47 S 66 8f 2.4305 24 4 62 81 L 2.440( 2.7862 83 2.7404 27 49 71 93 2.7514 37 58 80 2.7602 24 46 67 90 2.7711 33,3 7 98 5 2.7820 42 64 D f I 8.080669 3168 6667 8066 3.090666 2964 64 63 7962 8.1003 61 2850 63849 77 48 8.1101 47 26 46 6146 76544 99 43 3.1226 42 4941 78 40 i98 39 3.1323 88 4737 71386 i u,) 6 7 8 9 0 2 3 4 5 6 i7!8 19 [0 1[ [2 13 14 15 I -=7 'I - -,-II 91 94 97 99 0.3502 05 08 10 13 16 18 21 24 27 29 32 35 38 40 43 82 88 98 99 0.7004 10 15 20 26 31 37 42 48 53 59 64 69 73 8C 8f 74 82 90 98 1.0506 14 23. 31 39 47 -55 62 72 80 88 96 1.0604 13 21 29 I tfi 76 86 97 1.4008 19 30 41 52 63 74 84 96 1.4106 17 28 39 5C 61 72 - l. -I 56 70 83 -97 1.7511 24 38 51 65 79 92 1.7606 20 33 47 60 74 87 1.7701 15 47 38 3u0. 14z 's I 63 57 61 45 33 80 76 73 69 82 96 95 94 94 31 2.1013 2.4515 2.8017 3.1519 80 291 34 38 43 29 45 53 60 68128 61 71 82 92 27 78 91 2.8104 3.1617 26 94 2.4610 26 41 26 2.1110.29 47 -66 2T 27 48 69 9028 43 67 91 3.1716 22 60 86 2.8213 89 21 76 2.4705 34 64 20 92* 24 8 if1 2.1208 43 78 3.1812 18 46 46 1 9 71 3 8 2 8 7 47 48 97 46 94 42 9 48 61 0.7102 63 1.4204 66 2.130 49 64 08 61 15 69 2 60 57 13 70 26 83 3 61 59 18 78 37 96 6 52 62 24 86 48 1.7810 1 63 65 29 94 69 24 E 64 67 35 1.0702 70 87 2.14C 66 70 40 10 80 61 l65 73 46 18 91l 64 67 76 61 27 1.4302 78 B 68 78 66 36 13 91 f 69 81 62 43 24 1.7906 4 60 0.8684 0.7167 1.0761 1.4335 1.7919 2.151 LATITUDP 69 DIGRE 1 I; e ~ S 1 0 116 ~~~~~~LATITUJDE 21DGUFER8 i 1 2 8 4 6 ~ ~~ ~~ ~~~~6 7 8 9 o0.93 1.8672 2.8007 3.7343 4.6679 5.6015 6.5351 7.4686 8.4022 60 1 35 70 04 3 9 74 09 44 78 13569 2 34 67 01 35 69 02 36 70 03 58 3 83 65 92.7998 31 64 5.5996 29 61 8.3994 57 4 32 63 95 26 58 90 21 53 84 56 5 31 61 92 22 53 84 14 44 75 55 6 30 59 89 18 48 77 07 36 66 54 7 29 57 86 14 43 71, 6.5299 28 57 53 8 27 55 82 10 37 64 92 19 47562 9 26 53 79 06 32 58 84 11 351 10 25 51 76 01 27 52 7 7 02 28 50 11 24 49 73 3.7297 22 46C 69 7.45.94 19 49 12 23 46 70 93 1 6 39 62 86 09 48 13 22 44 67 89 1 1 33 55 78 00 47 1 4 21 42 63 84 06 2 7 48 69 8.3890 46 156 20 40 60 80 01 21 41 61 81 45 16 7 19 38 57 ~764T. 659.,5 1 4 33 52 714 4 1 7 1 8 3 6 5 4 7 2 9 0 0 8 2 6 4 4 62 43 1 8 1 7 3 4 5 1 6 8 8 5 0 1 1 8 3 5 52 42 19 1 6 32 48 64 80 5.5895 1 1 26 43 41 2 0 1 5 3 0 4 4 59 7 4 8 9 04 1 8 33 40 21 14 27 ~41 515 6.9 826.5 196 10 2339 22 13 25 38 51 64 76 89 02 14 38 23 12 23 35 46 58 70 81 7.4493 04 37 24 11 21 32 42 53 64 74 85 8.37-9536 25 10 19 29 38 48 -57 67 76 86 35 26 08 1 7 25 34 42 50 59 67 76 34 27 07 1 5 22 30 37 44 52 59 67 33 28 06 1 3 19 25 32 38 44 50 57382 29 05 10 1 6 21 26 31 36 42 47 31 30 04 08 1 3 17 21 25 29 34 38 30 Ti 03 06 ~09 12 16 1 9 ~22 ~25 28 29 32 02 04 06 08 10 1 2 14 16 18 28 33 01 02 03 04 05 05 07 08 09 27 34 00 00 00 00 00 5.5799 6.5099 7.4399 8.3699 26 35 0.9299 1.8598 2.7896 3.7195 4.6494 93 92 90 89 25 36 98 96 93 91 ~89, 8 7 85 8 2 8024 3 7 9 7,9 3 9 0 8 7 8 4 8 0 7 7 7 4 70 23 3 8 9 6 9 1 8 7 8 2 718 7 4 6 9 6 5 60 22 39 95 89 84 718 73 67 62 56 51 21 40 94 87 81 74 68 61 55 48 42 20 4 9 2 85 7 7 70o 62 54 47 39 32 19 42 91 83 74 65 57 48 39 30 22 18 43 90 80 71 61 51 41 31 22 12 17 44 89 78 68 57 46 35 24 14 03 16 456 88 7 6 64 52 40 29 1 7 05 8.3593 15 -46 87 74 61 48 35 22 09 7.429!i 83 14 47 86 72 58 44 30 15 01 871 73 13 48 85 70 55 40 25 09 6.4994 79 6412 491- 84 6 8 5 1 35 1 9 03 8 7 70 54 11 50 83 65 48 3 1 14 5.5696 79 62 44 10j 51 52 53 54 AA 82 81 719 78 7 7 76 75 74 -78 63 61 56 57 5 5 52 50 48 46 i I I I II 45 42 38 35 32 29, 25 22~ 19~ 2.7815 26 22 18 14 09 05 00 3.7096 91 3.7087 I 0 L 4.6397 92 87 81 76 76 65 4.6359 II I I I I 90 83 76 W1 64 57 51 44 37 5.5681 71 64 56 49 41 33 26 18 10 6.4903 I 53 44 35 2 7 18 101 02' 7.4192 -83 1.41714 34 25 16 06 8.3496 86 76 66 56 8.8446 9 8 7 6 S 3 2 1 0 I 'I DEPARTURE~ 68 DEGREES. j i I DEPARI~TuRp 21 DEGREES. 117 _LI 1 2 1814! 6LL.AA7K 1 9 I I 0 1 2 3 4 5 7 8 9 10 12 18 14 15 T1i 17 18 19 20 22 23 2-4 25 27 28 29 30 32 33 34 35 37 38.39 40 41 42 43 44 45 47 48 49 50 52 53 54 55 57 58 59 60 0.3584 86 89 92 95 97 0.3600 03 05 08 11 14 16 22 24 27 30 33 35 38 41 43 46 49 54 57 60 62 65 68 7-0 73 76 79 811 84 87 89 92 95 98 0.3700 03 06 08 11 14 16 19 22 25 '27 80 83 35 38 41 43 0.8746 0.7167 73 7 8 84 89 95 0.7200 05 11 16 22 27 32 38 43 49 54 60 65 70 76 81 87 92 98 0.7303 08 14 19. 25 30 35 41 46 52 57 62 68 73 79 84 90 95 0.7400 06 11 17 22 27 33 38 49 54 60 65 71 76 81 87 0.7492 1.0751 59 67 75 84 92 1.0800 08 16 24 32.41 49 57 65 73 81 89 98 1.0906 14 22 30 38 46 5r 63 79 87 95 1.1003 10 19 27 36 43 52 60 68 76 84 98 1.1101 09 17 25 33 41 49 57 65 74 82 90 984 1.1206 1 4 229 36 1.123E 1.43385 46 56 6 7 78 1.4400 11 21 82 43I 54 65 76 87 98 1. 45 08~ 19 30~ 41 62 74 84 95 1.4606 28 38 49 60 71 82 92 1.4703 14 25 36 47 58 68 79 90 1.4801 12 22 33 44 55 66 76 87 98 1.4909;,20 30 41 52 63 74,1.4984 1.7919 32 46 59 73 87 11.8000 14 27 41 54 68 81 9 5 1.8109 2 2 3 6 49 63 76 90 1.8 2-03 1 7 3 1 44 5 8 7 85 9 8 1.8312 2 5 3 9 52 6 6 7 9 93 1.8406 20 3 4 47 6 1 74 88 1.8501 1 5 2 8 42 5 5 6 9 82 96 1.8609 2 3 3 6 50 63 7 7 90 1.8704 1 7 1.8731 2.1502 18 35 51 67 84 2. 1600 16 32) 49 6,5 81 97 2.1714 30 46 639 79q 95 2.1811 27" 44 60 7 7 93 2. 1909 4 1 58 7 4 90 2.2006 2 2 39 556 7 1 87 2.21039 26 36 53 69 85 2.2201 1 7 3 4 56 66 82 98 2.2315 3 1 4 7 63 79 96 2.2412 28 44 60 2.2477 2.150UM 2.5105 24 43 62 81 2.5200 19 38 57 95 2.5313 33 52 71I 90 2.5409 46 65 84 2.5504 23 42 61 79 98 2.5617 36 55 74 93 2.5712 31 50 68 87 2.5807 26 45 64 83 2.5901 20 39 58 96 2.6015 34 53 72 90 2.6109 28 A '7 L2.bti U 91 2.8713 34 56 78 2.8800 22 43 65 86 2.8908 30 52 74 95 2.9017 38 60 82 2.9103 25 57 69 90 2.9212 34 55 77 98 2.9320 42 63 85 2.9406 28 50 71 94 2.9515 37 58 80 2.9602 23 45 66 88 2.9710 31 53 74 c96 2.9818 39 61 3.22bi8 78 3.2202 26 51 76 3.2300 24 49 73 97 3.2422 46 71 95 3.2520 44 68 98 3.2617 41 65 91 3.2715 39 64 88 3.2812 36 61 3.2985 3.3019 84 58 82 3.3107 31 55 80 3.3206 29. 58 78 3.8302 26 50 75 99 3.3428 48 72 96 3.3521 45 I I I I I I I I I I I I I I I I I I I I I I I i I f59 58 57 56 55 53 52 51 50 49j 48 47 46 45 4-4 43 42 41 40 38 37 36 85 33 32 31 30 28 27 26 25 23 22 21 20 18 17 16 15 14 18 12 11 10 8 7 -1 I 2 1 I 6 I I 8 LATITUDE, 68 DEGREES. II~~ ATITUDB 22 0tDREEB. 2 1 -8 I 4 4 1i i I 6 I Y / 0 0.9272 1.8644 2.7815 3.7087 4.6359 5.5631 6.4903 7.4174 8.344660 1 71 41 12 83 64 24 6.4895 66 36 59 2 70 39 09 79 49 18 88 58 27 58 3 69 37 06 74 443 12 80 49 17157 41 68 35 03 70 38 05 73 40 08 56 5 66 33 2.7799 66 32 5.5598 " 65 31 8.3398 55 6 t,5 31 96 61 27 92 57 22 8854 7 64 28 93 56 21 85 49 14 78153 8 63 26 89 52 16 79 42 ] 05 68 52 9 62 24 86 48 10 72 34 7.4096 58151 10 61 22 83 44 05 65 26 87 4850 -I 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 291 30 -T 31 32 33' 34 35' 36 37 388 39 40 41 42 ltu 59 58 57 55 64 53 52 51 50 49 48 47 46 44 43 42 41 40 39 38 37 36 34 33 32 31 30 29 28 27 25 24 23 22 21 20 19 18 16 Ztl 17 15 11 09 06 04 02 00 1.849' 95 93 91 89 86 84 82 80 78 75 73 71 69 66 64 62 60 57 55 58 51 49 46 44 42 40 37 35 33 79 76 73 70 66 63 60 56 53 60 46 43 40 37 33 30 26 23 20 16 13 10 07 03 00 2.7696 93 90 86 83 80 76 73 69 66 631 59 56 53' 49 ay 35 30 26 22 17 12 08 04 00 3.6995 91 86 82 78 73 68 64 60 55 51 46 42 37 32 28 24 20 15 10 06 02 3.6897 92 88 84 79 74 70 66 Ut 4.6294 88 83 77 72 66 61 55 50 4ft 39 33 28 22 16 11 05 00 4.6194 89 83 78 72 66 61 55 50 44 38 33 27 22 16 10 05 4.6099 93 88 82 I 09 52 46 39 33 26 19 13 06 5.5499 93 86 80 73 66 59 53 46 39 33 26 20 13 Otb 5.5399 93 86 79 72 66 59 52 46 39 32 25 19 12 05 5.5298 11 03 6.4796 88 80 72;5 57 49 42 34 27 19 11 02 6.4695 87 79 72 64 56 49 40 32 25 17 09 01 6.4593 86 78 70 62 54 46 39 30 23 15 06 6.4499 91 83 75 67 60 51 43 6.4435 7 7i 61 52 43 34 25 17 08 7.3999 90 82 73 64 55 46 37 28 19 10 02 7.3898 84 74 66 57 48 39 30 21 12 03 7.3794 85 76 67 58 49 40 31 22 13 06 7.3695 86 77 68 58 50 7.3640 Q 28 18 09 8.3299 89 79 69 59 49 39 29 19 10 00 8.3189 79 69 59 49 39 29 20 09 8.3099 89 79 69 58 48 39, 29 19 08 8.2998 88 78 67 58 48 40 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 i I i1 15 2 14 38 13 4 12 56 11 830 28 26 24 21 46 42 39 36 32 61 56 52 48 43 76 71 65 60 54 91 85 7E 71 64 37 27 * 17 07 8.2896 8 7 6 6 10 09 19 17 15 29 26 22 19 88 34 29 25 48 43 37 31 65 51 44 37 5.5230 6 8t 77 6( 66 8.2845 n9 67 DEGREES.. 1 t;t k 1 2 8 4 5..,,ri: '" 6 7 8 2. OT.38746 7.7-492 1f1238 1.4984 1.8731 2.2477 2.6223 42 7.9 315 0 1 49 98 46 95 44 93 42 90 8959 2 52 0.7503 55 1.5006 58 2.2509 61 38.0012 6458 3 54 08 63 17 71 25 79 34 8857 4 57 14 71 28 85 41 98 55 3.3812 56 5 60 19 79 38 98 57 2.6817 76 8655 62 ~8i- -- 491.8811 73 35 98 60 54 7 65 30 95 60 25 89 54 3.0119 84 53 8 68 35 1.1303 70 38 2.2606 73 41 3.3908 52 9 70 41 11 81 52 22 92 62 83351i 10 73 46 19 92 65 38 2.6411 84 57 50 11 76 —51 —2 1.5'5- 103 9 4 30 —.0206 81 49 12 78 57 35 14 92 70 49 273.400648 13 81 62 43 24 1.8906 87 68 49 8047 14 84 68 51 35 19 2.2703 87 70 54 46 15 87 73 60 46 33 19 2.6506 92 79 45 16 89 78 T 68 57 46 35 243.0314 3.410344 17 92 84 76 68 60 51 43 35 274 18 95 89 84 78 73 68 62 57 5142 19 97 95 92 89 87 84 81 78 7641 20 0.3800 0.7600 1.1400 1.5200 1.9000 99 99 99 9940 21Zil - 03 05 08 10O 13 2.2816.6618 3.04213.422339 22 05 11 16 21 27 32 37 42 48838 23 08 16 24 32 40 48 56 64 72371 24 11 21 32 43 54 64 75 86 9636 25 13 27 40 54 67 80 94 3.0507 3.4321 36 26 16- 32-48 64 81 972.6713 29 4534 27 19 38 56 75 94 2.2918 32 50 6933 28 22 43 65 86 1.9108 29 61 72 94 82 29 24 48 72 96 21 45 69 933.441731 30 27 54 80 1.5307 34 61 88 3.0614 41 80 31 30 59 89 18 48 772.6807 36 6629 32 32 64 97 29 61 93 25 58 9028 33 35 70 1.1505 40 75 2.3009 44 79 3.4514 27 84 38 75 13 50 88 26 633.0701 8826 35 40 81 21 61 1.9202 42 82 22 63 25 36 -43 86 29 H-72 15 T58 2.6901 44 87 24 37 46 91 3 7 82 28 74 19 65 3.461023 38 48 97 45 93 42 90 38 86 3522 39 51 0.7702 53 1.5404 55 2.3106 57 3.0808 5922 40 54 07 61 15 69 22 76 30 83820 41 56 -13 69 26 82 -638 95 513.470819 42 59 18 77 36 96 65 2.7014 72 3218 43 '62 23 85 47 1.9309 70 32 94 55171 44 64 29 93 58 22 86 51 83.0916 80 16 45 67 34 1.1601 68 36 2.3203 70 37 3.4804 15 46 70 40 -0 79 4 19 89 58 2814 47 73 45 18 90 63 3652.7108 80 6818 48 75 5 0 26 1.5501 76 57 26 3.1002 77 12 49 78 56 33 11 89 67 45 22 8.49 11 50 81 61 42 22 1.9403 83 64 44 210 51.. 838 66 50 16 99 821 66 9 52 86 72 58 44 80 2.3315 2.7201 87 7 8 53 89 77 66 64 43 32 20 3.1109 9: 7 64 91 82 74 65 56 47 38 80 3.6021 6 55 94 88 82 76 70 63 57 561 45 66 97 93-90 86 83 80 76 7 57 99 99 98 97 97 96 96 94 94 58 0.3902 0.7804 1.1706 1.5608 1.9610 2.8412 2.7314 3.1216 3.5118 2 59 05 09 14 18 23 28 32 37 41 1I 60 0.8907 0.7815 1.1722 1.5629 1.9537 2.8444 2.7851 3.1258 8.51 0 17' 2 -8 4-,, W...a6- 7 8 W - LATITUDEi 67 DEGIO S.rE. J~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-::~~~i I I i T 120 LATITUDE 23 DEGRRE$. 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I 1. I 1 4; i DEPARTURE 26 DEGREES. 126 p 1 2 3 4 6 6 7 8 9; 0 0.4226 0.8452 1.2679 1.6905 2.1181 2.5857 2.9683 3.3810 3.8086 06 1 29 68 86 15 44 78 2.9602 30 61969 2 82 63 95 26 68 89 21 62 8468 8 34 68 1.2702 86 71 2.6405 39 73 3.8107 57 4 37 78 10 47 84 20 671 94 80 66 6 89 79 18 68 97 86 768.8915 6666 6 42 84 26 682.1211 62 94 86 78 64 7 45 89 84 78 28 68 2.9712 67 8.8201 68 8 47 95 42 89 37 84 81 78 26 62 9 60 0.8600 60 1.7000 50 99 49 99 4961 10 58 05 58 10 63 2.5515 68 8.4020 78 60 11 655 10 66 21 76 31 86 42 97 49 12 58 16 73 31 89 47 2.9805 62 3.8820 48 18 60 21 81 42 2.1802 62 23 83 44 47 14 63 26 89 62 16 79 42 3.4105 68 46 16 66 31 97 63 29 94 60 26 9146 18 ~68 ~37 1.2805 73 ~42 2.5610 78 46 3.8 416 4 4 171 7 1 42 1 3 84 66 26. 96 6 7 3848 18 74 47 21 94 68 42 2.9915 89 62 42 19 76 52 29 1.7105 81 6 7 33 3.4210 86 41 20 79 58 36 15 94 73 52 30 3.8599 40 -21 82 63 45 262.1408 89 71 62 343-9 22 84 68 52 86 21 2.5705 89 73 67 38 23 87 73 60 47 34 20 3.0007 94 8037 24 89 79 68 58 47 36 26 3.4315 3.8605836 25 92 84 76 68 60 52 44 36 2836 26 95 89 84 78 78 68 62 57 5134 27 97 94 92 89 86 83 80 718 76833 28 0.4300 0.8600 1.2900 1.7200 2.1500 99 99 99 99 32 29 03 06 08 1 0 13 2 5815 3.0118 3.4420 3.8723~ 31 30 05 10 15 20 26 31 86 41 46830 31 0 lb 23 31 39 4 6 ~54 ~62 ~ 692 9 32 10 21 31 42 62 62 78 88 9428 33 13 26 39 52 65 78 91 3.4504 3.8817 27 84 16 3 1 47 62 78 94 8.0209 25' 4026 85 18 36.55 78 91 2.5909 27 46 64 26 36 21 42 63 84 2.1605 25 46 67 8824 87 24 47 71 94 18 41 65 88 3.8912 23 88 26 62 78 1.7804 31 67 83 8.4609 8622 39 29 57 86 15 44 72 8.0801 80 68 21 40 31 63 94 26 67 88 19 50 82 20 ITf 34i ~68 1.3 002 8 6 70N2.6 00 8R~~ 8 72 3.90061i9 42 37 73 10 46 83 20 66 98 2918 48 89 78 18 6 7 9 6 35 7 4 3.4714 68 17 4 4 42 84 2 5 67 2.1709 5 1 9 3 3 4 7616, 46 465 89 3 4 78 23 67 3.0412 6 6 3.9101 16 46 l~47 94 4 1 88M 36 83 30 7O 7 241 47 4-8 49 50 52 '58 54 66 67 68 69 60 - 60 62 65 58 60 63 65 68 71 76 79 81 0O.4384 0.870E 2(4 31 841 41 471 67 0.8767 49 57 65 73.81 88 96 1.81 04 12 20 28 86 48 1.8151 8 99 1.7409, 26 86 41 61 62 72 82 98 1.7504 14 24 1.7535 4 49 62 75 88 2. 1801 14 27 40 58 98 2.6114 29 45 61 77 92 2.6208 24 40 55 71.87 2.6302 671 841 9 Iq 2.19041 2.191c1 6 LATITUDE, 64 DEGRRES& I i I I I 12~~~~1 ~LATITUDE 26 DmapEus. 0 0.8988 1.962.6964 3.5952 4.4940 5.8927 6.2915 -7.1903- 8.0891 U 1 87 73 60 47 3:.3 20 70 7.1894 8059 85 71 56 42 27 12 6.2898 88 69 58 3 83 68 52 36 21 05 89 73 57 57 4 82 66 48 3 1 14 5.8897 80 62 45 56 5 81 68 45 26 08 90 71 53 84 55 6 0 61 41 21 02 82 62, 42 23 b4 7~ 79 58 87 16 4.4895 74 53 82 11563 8 78 55 33 11 89 66 44 22 8.0799 52 9 76 53 29 06 82 58 35 1 1 88 51 10 75 50 26 01 76 51 26 02 77 50 1 1 74 48 22 3.5896 70 43 1 77.1791 65 49 12 73 45 1 8 90 63 36 08 81 53 48 13 71 48 14 85 57 28 6.2799 70 42 47 1 4 70 40 10 p80 50 20 90 60 80 46 15 69 87 06 75 44 12 81 50 18 45 16 ~7 35 02 70 37 04 72 39 07 44 17 66 32 2.6899 65 31 5.37197 63 30 8.0696 48 ~18 65 30 95 60 25 89 54 19 84 42 19 64 27 91 54 18 82 45 09 72 41 20 62 25 87 49 12 74 36 7.1698 61 40 21 61 22 8 44 05 66 27 88 49839 22 60 19 79 39 4.4799 58 18 78 87 38 28 58 17 75 84 92 50 09 67 25 37 24 57 14 71 28 86 43 00 5 7 14 36 256 56 12 68 23 79 35 6.2691 46 02 35 26 55 09 64 18 73 27 82 36 8.0591 34 27 63 06 60 13 66 19 72 26 79 33 28 52 04 56 08 60 11 63 15 67132 29 51 01 52 02 53 04 54 05 65581 30 49 1.7899 48 3.5797 47 5.3696 45 7.1594 44 30 i 81 48 82 47 33 45 34 44 35 43 -6 42 37 40 38 39 39 38 40 86 41 35 42 34 43 32 44 31 45 30 iw 29 47 27 48 26 49 25 60 23 5 i22 52 21 53 19 54 18 656I 17 9c 98 91 86 83l 86 78 76 67 65 62 60 57 54 52 49 46 44 41 39 36 33 44 40 36 82 28 25 21 17 18 09 05i 01 2.6797 93 89 86 82 78 74 70 66 62 58 54 501 92 87 82 76 71 66 61 56 50 45 40 35 80 24 19 14 09 04 3.5698 93 88 821 77~ 72' 67~ I 40 34 27 21, 14 08 01 4.4695 88 82 75 69 62 56 49 43 36 30 23 16 10 03 4.4597 90 84 88 80 72 65 57 49 41 33 26 18 10 5.3594 87 79 71 63 55 47 39~ 82 24 16 08 00 I 3C 27 09 6.2591 81. 72 63 54 45 36 27 18 09 00 6.2490 81 71 62 44 35 1 7 84 74 63 53 42 82 22 11 01 7.1490 80 70 59 49 38 28 18 07 7.1896 86 75 65 54 44 34 32 20 09 97 8.0485 74 62 50 38 27 15 03 8.0392 80 68 571 45 33 21 09 8.029 -85 741 621 501 I 29 28 27 26 25 28 22 21 20 18 17 16 15 14 13 12 11 10 8 7 6 5 'II 31 1128 46 42 61 5e 51 I4F II I 7 715.3492 70 84I I.1 6.23c, )7 22 38 4 18 12 2638 ~ 9 02 14 2 W0 7. 1291 013 1 'I 7.1281 8.0191 0 — 9-w — - 5.34611M. DEPARTUREB 26 DOGREES. 1f 7 1 2 3: 4 6 6 7 8 9 0 0.4884 0.8767 1.8161 1.7585 2.1919 2.6302 3.0686 3.6070 3.946860 1 86 73 69 45 32 188.0704 90 7769 2 89 78 67 56 45 33 22 8.5111 3.950068 3 92 83 75 66 58 50 41 833 2457 4 94 88 83 77 71 65 69 54 4856 6 97 94 90 87 84 81 80 74 71 6 Ii It 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 28 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 60 51 52 53 64 55 66 57 58 69 60 0.4402 05 07 10 12 15 18 20 23 26 28 31 33 36 39 41 44 46 49 52 64 57 59 62 65 67 70 72 75 78 80 83 85 88 0.8804 09 14 20 25 30 35 41 46 51 56 61 67 72 77 82 87 93 98 0.8903 08 14 19 24 29 34 40 45 50 55 60 66 71 76 vt 1.3206 14 22 29 37 45 53 61 69 77 84 92 1.330U 08 16 23 31 39 47 55 63 70 78 86 94 1.3402 09 17 25 33 41 48 56 64 72 8C 87 95 1.3503 11 19 26 34 42 56 68 65 73 81 89 96 1.3604 12 1.3620 1.7608 18 29 39 50 60 71 81 92 1.7702 12 23 33 44 54 64 6 96 1.7806 17 27 88 48 58 69 79 90 1.7900 10 21 31 42 52 2.2010 23 36 49 62 76 89 2.2102 15 28 41 54 67 80 93 2.2206 19 32 45 58 71 84 97 2.2310 23 36 49 62 75 88 2.2401 14 27 40 y6 2.6412 28 43 59 74 91 2.6506 22 37 53 69 84 2.6600 15 31 47 62 78 94 2.6710 25 41 56 72 88 2.6803 19 34 50 66 81 97 2.6912 28 3.0814 32 50 69 87 3.0906 24 42 60 79 97 3.1015 33 51 70 88 3.1106 25 43 61 79 98 3.1216 34 52 70 09 3.1307 25 43 61 80 98 3.1416 3.5216 37 58 78 99 3.5321 42 62 83 3.5404 25 46 66 87 3.5508 29 50 71 92 3.5613 34 54 75 9c 3.5717 38 52 79 3.580C 18 42 62 83 3.5904 Vo 3.9618 41 65 88 3.9712 86 57 83 3.9806 30 63 76 3.9900 23 47 70 93 4.0018 41 64 88 4.0111 35 68 81 4.0205 28 52 75 98 4.0822 45 69 92 53 52 51 50 49 48 47 46 46 44 43 42 41 40 39 38 37 36 36 34 33 82 81 30 29~ 28 27 26 26 24 23 22 21 20 91 93 96 98 0.4601 04 06 09 11 14 17 19 22 24 27 30 82 85 87 0.4640 X1 86 92 97 0.9002 07 12 18 28 28 33 88 44 49 64 69 64 69 76 0.9080 62 53 73 66 83 79 94 92 1.3004 2.2505 14 18 25 31 35 44 46 57 66 70.66 83 77 96 87 2.2609 97 22 1.8108 35 18 48 28 61 39 74 49 87 1.8160 2.2700 44 59 7IL 9C 2.7006 22 37 53 6~ CE 84 2.7106 81 31 46 61 77 93 2.7208 24 2.7239 34 52 71 89 3.1507 25 43 62 80 98 3.1616 34 63 70 88 3.1707 25 43 61 3.1779 25 46 66 87 3.6008 29 5C 7C 91 3.6112 83 64 74 94 3.6215 D6 4.0415 89 62 86 4.0509 32 56 79 4.0603 26.^ 19 18 17 16 16 14 18) 10 l 3.6819 4. It 1 [-l. - - - 4 1 & I 1 7 81 7 - T1 718 -— _;- *~: S_ LATITUDE 68 DEGBBBS. ? I t I:, N, % I:! i. I: i.... I. I,.- % I I >fi TA'vIrTTD1 27 DEGREES.:4 -U. - _.. — _, 1 2 3 4 6 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 83j 37 38 41 4C 4t 4S 45 4^ 4' 5( 5 6 6 5 6;: & 1. I - -, r - a 1 09 17 07 15 06 12 05 10 04 07 02 04 01 02 2. 00 1.7799 0.8898 96 97 94 96 91 94 88 93 86 92 83 90 80 s89 78 88 75 86 72 85 70 84 67 82 64 81 62 80 59 78 56 77 54 76 51 74 48 73 46 72 43 70 40 69 38 67 35 66 32 65 29 638 27 62 24 61 21 59 19 58 16 ) 57 13 55 11 -54 08 53 05 1 51 02 5 50 00 49 1.7697 7 47 94 8 46 92 9 45 89 4.3 86 1 42 8.3 2 40 81 3 89 78 4 38 75 5 86 73 6 35 70 7 34 67 8 82 64 9 31 62 0.8830 1.7659 l 2 --- 3 3780 26 22 18 14 10 Ut 6602 99 94 90 87 83 78 71 6t 51 5z 5' 4' 4, 3' 3! 31 2 1 1 1 0 0 2.659 9 9 i 7 'i 2.61 2 64 f 4 6 3.5640 4.4551 5.3 35 44 30 37 24 31 19 24 14 18 08 11 03 04 3.5598 4.4498 5. 92 91 87 84 82 78 77 71 71 64 66 58 1 61 51 555 44 3 50 38 45 31 4 39 24 1 34 18 7 -29. 11 5) 2 23 04 9 18 4.4398 5 13 91 0 07 84 7 02 78 2 3.5496 71 8 91 64 5 86 58 0 80 51 _ 75s 44 )2 70 37 I8 64 31 14 59 24 )0 54 17 iT 48 10V 32 43 04 '8 37 4.4297 *4 32 90 70 26 83 6t;1 77 52 16 70 58 10 63 54 05 56 50 00 50 46 3.5 34 4 -12 89 36 37 83 29 34 78 23 29 72 16 2) 67 09 21 62 02 17 56 4.4195 13 51 89 09 45 82 - -i 40 75 01 34 68 97 29 61 92 23 54 89 3. 518 4.4148 _ 4 6 6 3461 52 44 37 29 21 13 05 3397 8a 81 7' 65 51 4( 41 4' 3: 2' 11 0O 0.329 8, 7 6 6 5 4 3 2 2 1 0 i.319 8 C 4 5.302 5.29 6 7 8 _ 6.2371 7.1281 8.' 61 70 52 59 43 49 34 38 25 28 T1 17 06. 06 6.2297 7.1196 8. 87 85 78 74 69 64 60 51 50 42 41 32 1 31 22.- 22 10 7 5 13 01 7 03 7.1090 o 6.2194 78 1 85 68 _ 75 58 5 66 46 7 57 36 9 47 26 1 38 14 7 3 29 04 5 19 7.0993 7 10 82 9 01 72 1 6.2091 61 3 82 50 )4 72 39 )7 63 29 8 53 18 10 44 07 34 7.0896 31 25 86 36 15 74 18 06 64 [O 6.199( 53 ^ 87 42' 23 77 31 16 68 2'1 )7 58 10 )9 49 7.0799 91 40( 88 83 30 ' 78 75 21 66 67 12 56 59 02 45 50T 6.1895 ' 34 42 83 23 34 73 12 26 64 02 18 54 7.0690 09 44 79 02 35 69 93 25 58 85 16 46 S77 6.1807 7.0636 7 - 9 r 019160 I 78 59 67 58 55 57 43 56 32 55 19 54 0753 0096 52 83 51 71 50 60 4{ 48 48 35 47 2446 12 45.999944 88 43 76 42 63 41 52 40 40 39 27 38 1637 0436.9891 35 80) 34 6733 5532 44 31 31 30 19 29 07 28 T.979527 82 26 71 25 58 24 4623 3422 2221 09 20 7.9698 19 85 18 7317 6116 49 15 8 — 14 2513 1212 0111 7.9588 10 75 9 64 8 51 7 39 6 27 5 14 4 02 3 7.9490 2 77 1 7.9466 O 9 - ----- ~~' - - ---- - II It 1)RPARTURE tO DEGREES. - - Z 11 v I E 27 ir 00.4640 1 7~ 1.860 ~ ~ ~ T~3~1. 1 48 8 28 7 110 55 98 40 2 45 90 35 80 26, 71 3.1816 6] 4.090668 8 48 95 43 91 89 86 34 82 2957 4 50 0.9101 511.8201 52'2.7302 52 3.6402 5866 5 53 06 59 12 65 17 70 28 76656 6 55 11 66 22 77 32 88 43 99 4 7 58 16 74 32 90 48 3.1906 64 4.1022658 8 61 21 82 42 2.2803 64 24 85 4562 9 68 26 90 63 16 79 42 3.6506 69651 10 66 32 97 63 29 95 61 26 92 50 II 68 37 1.3705 74 42 2.7410 79 47 4.11164 12 71 42 13 84 55 26 97 68 8948 13 74 47 21 94 68 42 3.2015 89 62 47 14 76 52 29 1.8305 81 57 38 8.6610 86 46 15 79 57 36 15 94 72 51 30 4.1208 45 16 81 63 44 25 2.2907 88 69 50 44 17 84 68 52 36 20 2.7503 87 71 55 43 18 87 73 60 46 33 19 3.2105 92 79 42 19 89 78 67 56 46 35 24 3.6713 4.1302 41 20 92 83 75 67 59 60 42 34 25 40 21 94 88 86 77 71 6b 59 50 48 89 22 97 94 90 8 7 84 81 78 74 71 38 23 99 99 98 98 9 7 96 9 6 95 95837 24 0.4602 0.9204 1.3806 1.8408 2.3010 2.7612 3.2214 3.6816 4.1418 36 25 05 09 14 18 23 28 3 2 3 7 41836 26 07 14 22 29 86 43 50 58 T 6 27 10 19 29 39 49 68 68 78 87 88 28 12 25 37 49 62 74 86 98 4.1511 82 29 15 80 45 60 75 89 3.2304 3.6919 3481 80 18 35 53 70 88 2.7705 23 40 68830 31 20 40 60R 80R 2.3101 21 41 61 81 29 32 23 45 68 90 18 36 58 81 4.1608 28 33 25 50 76 1.8501 26 51 76 3.7002 27i27 34 28 56 83 1 1 89 67 95 22 50 26 35 30 61 91 22 52 82 3.2413 43 7426 36 38f 66 99 32R 6i5 98 31 64 ~70 2 87 36 71 1.8907 42 78 2.7813 49 84 4.1720 28 88 38 76 14 52 91 29 67 3.7105 48 22 39 41 81 22 63 2.8204 44 85 26 66 21 40 43 87 30 73 17 60 3.2503 46 91 20 i1 42 43 44 45 4tE 51 64 5c 97 0.9302 07 12 6j1 45 53 61 68 56 i 94 1.8604 14 204 42 555 68 81 96 2.7906 22 37 Z 39 57 75 93 6ti 87 3.7208 29 49 4. 1612 86 82 4.1905 18 17 46 59 17 76 35 94 62 3.261-1 7 47 61 23 84 45 2.8307 68 - 29 90 48 64 28 92 56 20 88 47 8.7811 49 66 83 99 66 32 98 65 31 60 69 38 1 A007 76 45 2.8014 83 52 4.20 51 72 43 15 86 58 3083.2701 73 S2 74 48 23 97 71 46 19 94 68 77 68 30 1.8707 84 60 87 3.7414 64 79 69 88 17 97 76 55 3484.21 65 82 64 46 28 2.8410 91 73 65 6 84 69 63 88 22 2 8106 91 75 67 87 74 61 48 36 22 8.2809 96 68 90 79 70 68 48 88 27 3.76171 4.224 69 92 84 76 68 61 68 46 87 60 0.4695 0.9389 1.4084 1.8779 2.8474 2.8168 8.2868 8.7558 4.22 LATITUDE 62 DEGREES. H i; iL ~B a ~~ -i-e a:1 r ~ ~ X~fTI~Z 8 iur A ~iti:::!: 0 7 ~:i! 1 0 1 2 8 4 5 7 8 9 10 0.888C 2( 2, 21 24 2. 21 2( 1' 1, 1K 7 1 7 9 7 1.:765 56 53 61 48 45 43 40 37 34 32 II I I I 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 28 29 30 31 32 383 84 36 3T 37 38 39 40 41 42 43 44 45 46 47 48 AQ 14 13 12 10 09 08 06 05 03 02 01 0.8799 98 97 95 94 92 91 90 88 87 85 84 83 81 80 78 77 76 74 73 72 70 69 67 66 65 63 62 60 59 58 56 55 53 29 26 23 21 18 15 12 10 07 04 01 1.7599 96 93 90 87 85 82 79 76 74 71 68 65 62 60 57 54 52 49 46 43 40 37 35 32 29 26 23 21 15 12 03 06! m I i I I i Ii I i i I I I II I I.t I I II z:.648:9 84 8( 76 72 68 64 56 52 47 11 iI [ I I II^ I _ 8.5318 12 07 02 3.5296 90 85 80 74 69 63 -4 '5 4.4148 41 34 27 20 13 07 00 4.4093 86 79!7 I 43 39 35 31 27 23 19 14 10 06 02 2.6398 94 90 85 81 77 73 69 65 60 56 52 48 44 39 35 31 27 23 19 15 10 06 02 2.6298 94 89 85 81 77 73 68 64 60 I 58 52 47 41 36 30 25 19 14 08 02 3.5197 92 86 80 75 69 64 58 53 47 42 36 30 25 19 14 08 02 3.5097 92 86 80 75 69 64 58 52 47 41 36 30 24 18 13, 7L6 F ':7::8 -" I 72 65 59 52 45 38 31 24 17 10 03 4.3997 90 83 76 69 63 55 48 41 34 27 20 13 06 00 4.3892 85 78 72 65 58 51 44 37 r30 23 16 09 02 4.3795 8E 81 78 66 5.29177 69 60 52 44 36 26 19 11 03 5.2895 86 78 70 62 53 45 37 29 20 12 04 ).2796 87 79 70 62 53 45 38 29 21 12 04 5.2696 87 79 70 62 54 46 37 29 21 12 04 5.2595 87 79 70 62 53 45 37 28 19 6.10U7 6.1797 87 78 68 58 49 39 30 21 11 01 6.1691 82 72 62 53 43 34 24 14 04 6.1595 85 76 66 56 46 36 27.17 08 -6.1498 88 78 68 59 49 39 29 20 10 01 6.1391 81 71 61 52 41 32 22 12 03 6.1293 82 72 7.0636 25 14 03 7.0592 81 70 59 48 38 26| 15 04 7.0494 82 71 6( 50 38 27 16 05 7.0394 83 72 61 50 38 27 17 06 7.0294 83 72 61 50 38 27 16 05 7.0194 83 72 61 50 38 27 16 05 7.0094 82 71 6C 43q 37 2f: i:" 7.9466 53 40 29 16I 03 7.9391 79, 67 55 42 30 17 05 7.9293 80 68 56 43 31 18 05 7.9194 81 69 56 43 31 18 06 7.9094 81 69 56 43 31 18 06 7.8993 80 69 56 44 31 18 06 7.8893 81 68 55 43 30 18 05 7.8791 79 o5 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 f t _,,,...:....:-n i t _ I I - - -- - - - I - - - - I - I I 52 04 55 07 59 11 63 14 66 4 50 01 51 02 52 02 53 03 543 49 98 47 3.4996 45 5.2494 43 6.9992 41 2 48 1.7495 43 90 38 86 33 81 28 1.87 46 1.7492 2.6239 3.4985 4.3731 5.2477 6.1228 6.9970 7.8716 0.1.2 8 3.4 6 7 -. 8 9 _ il DEPARTURE 61 DEGREES. - - lpff -",:: x:a-~i DEPARTURE 28 DEGREES. 181 U - 0 1 2 3 4 5 T6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0.4-695 97 0.4700 02 05 08 10 13 15 18 20 28 26 28 31 33 36 38 41 43 46 2 0.938Y 95 0.940( PI 1C 2C( 361 3C 41 4eC 51 56 61 6C 72 77 82 87 92 3 1.4084 92 1.4100 07 15 23 30 38 46 53 61 69 77 84 92 1.4200 07 15 23 30 38 4 1.8779 89 1.8800 10 20 30 40 51 61 71 82 92 1.8902 12 22 33 43 53 64 74 84 6 5I 2.3474 87 2.3500 12 25 38 -51 64 77 89 2.3602 15 28 41 53 66 79 92 2.3705 17 30 6 2.8168 84 99 2.8214 30 46 61 76 92 2.8307 22 37 53 69 84 99 2.8415 30 45 60 76 7 3.2863 81 99 3.2917 35 53 71 89 3.3007 25 43 6C 79 97 3.3114 32 51 68 86 3.3204 22 8 3.7558 78 99 3.7629 40 61 81 3.7702 22 42 63 83 3.7804 25 45 66 86 3.7906 27 47 68 9 4.2252 76 99 4.2322 45 68 91 4.2414 38 60 84 4.2506 30 53 75 99 4.2622 45 68 91 4.2714 I 80 59 58 57 56 55 54 53 52 51 50 59 48 47 46 45 44 43 42 41 40 21 49 97 46 94 43 92 40 89 3739 22 51 0.9502 53 1.9004 56 2.8507 58 3.8009 6038 23 54 07 61 15 69 22 76 30 8337 24 56 12 69 25 81 37 93 50 4.280636 25 59 18 76 35 94 53 3.3312 70 2935 26 61 23 84 462. 3807 68 30) 91 5334 27 64 28 92 56 20 83 473.8111 7533 28 67 33 1.4300 66 33 99 66 32 99 32 29 69 38 07 76 45 2.8614 83 52 4.2921 31 30 72 43 15 86 58 30 3.3401 73 4430 '-'! ~- A A ~ O i] ~ fi 7-~ ~ '~~-. ~'"~* o~ tt 01 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 52 53 54 55 57 67 68 69 60 77 79 82 84 87 90 92 95 97 0,.4800 02 05 07 10 12 15 18 20 25 28 30 33 35 38 41 43 46 0.4848 4t 53 59 64 69 74 79 84 89 94 99 0.9604 10 15 20 25 30o 35 40 45' 50; 55; 61; 66i 71 76 81 86 91 0.96961 30 38 45 53 61 69 76 84 91 99 1.4407 14 22 30 37 45 53 60 68 76 83 91 98 1.4506 14 22 29 37 1.4544 1.9107 17 27 38 48 58 68 78 88 99 1.9209 19 29 40 50J 60 70 80 90 1.9301 11 21 381 42 52 62 72 82 1.9892 71 84 97 2.3909 22 356 48 60 73 86 99 2.4011 24 37 50 62 75 88 2.4101 13 26 39 52 64 77 90 2.4203 15 28 2.4241 40 60 76 91 2.8706 21 37 52 68 83 98 2.8813 29 44 59 74 90, 2.8905 21 36 51 66 82 97 2.9012 27 43 68 74 2.9089 19 37 65 73 91 3.3508 27 44 62 80 98 3.3615 34 51 69 87 3.3705 23 41 58 76 94 3.3812 30 48 65 84 3.3901 19 3.3937 Id a 3.8214 34 54 75 9 5 3.8316 36 67 77 98 3.8418 38 58 79 99 3.8520 40 61 81 3.8602 22 42 62 83 3.8703 24 44 65 8.8785 67 90 4 3014 36 60 82 4.3106 28 51 74 97 4.3220 48 66 89 4.8312 86 81 81 4.8403 27 49 73 956 4.8519i 65 87 4.8610 4.8683 zI 28 27 26 25 24 23 22 21 20 19 18 17 16I 16 14 fT; 18 12 11 10i 8 71 0:o: V 1 L KI % I g j 4 1 5 I 6 1 -6 t 8 LATITUDE 61 DEGRBES. 132 LATITUDE 29 DEGREES. 2 8 4 5 6 7 8 I J -0 08746 1.7492 2. 6239 3.4 985 4.3731 56.2477 6.1223 6.997- 7.871660 1 45 90 34 79 24 69 14 58 03 69 2 43 87 30 74 17 60 04 477.869158 3 42 84 26 68 10 52 6.1194 36 78157 4 41 81 22 62 03 44 84 25 65156 5 39 78 17 5614.3696 35 74 1 8 52155 6 38- 75 - 13 51 -89 26 64 02 8954 7 36 73 09 45 82 18 5416.9890 27153 8 35 70 05 40 75 09 44 79 14152 9 33 67 01 34 68 01 35 68 02151 10 32 6412.6196 28 61 5.2393 25 57 7.8589 50 11 31 61 92 22 53 84 14 45 7549 12 29 58 88 17 46 75 04 34 63148 13 28 56 83 11 39 6716.1095 22 50147 14 26 53 79 06 32 68 85 11 3846 15 25 50 75 00 25 50 75 6.9700 25145 16 24 47 4713.4894 18 41 65 88 1244 17 22 44 66 88 11 33 55 7717.8499143 18 21 41 62 83 04 24 45 66 8642 19 19 39 58 7714.3597 16 35 54 7441 20 18 36 53 71 89 07 25 42 60140 -21 16 33 49 -- 66 — 825.2298 15 31 4839 22 15 30 45 60 75 90 05 20 35138 23 14 27 41 54 68 82[6.0995 09 22837 24 12 24 36 48 61 73 8516.9697 09136 25 11 21 32 43 54 64 75 86 7.8396135 26 09 19 28 — 37 47 56 65 74 8434 27 08 16 24 32 40 47 55 63 71133 28 06 1 19 26 32 38 45 51 58132 29 05 10 15 20 25 30 35 40 45131 30 04 07 11 14 18 22 25 29 32 30 31 -02 04 5 06 08 - 111E 3 15 17 192 32 01 01 02 03 04 04 05 06 06128 33 0.8699 1.7399 2.6098 3.4797 4.3497 65.2196 6.0895 6.9594 7.8294 27 34 98 96 93 91 89 87 85 82 80126 35 96 93 8 86 82 78 75 71 68 25 36 95 90 85 80 75 69 64 59 64 24 7 94 87 81 74 68 61 55 48 42123 88 92 84 76 68 61 53 45 87 2922 39 91 81 72 62 53 44 34 25 1521 40 89 78 68 57 46 35 24 14 03120 41 — 88 76 63 51 — 39 —27 —15 — 02 7.819019 42 86 73 569 45 32 18 0416.9490 7718 48 85 70 55 40 25 0916.0794 79 6417 44 83 67 50 34 17 00 84 67 51 16 45 82 64 46 28 1065.2092 74 56 38815 46 -81 61 - 42 22 03 -- 83 64 44 2514 47 79 58 37 161 4.3396 75 54 33 1213 48 78 55 33 11 89 66 44 22 7.809912 4 76 52 29 05 81 57 33 20 8611 6 75 650 2413.4699 74 49 24 6.9398 73810 -51 73 47- 20 - 93 -67- 40 - 13 86 60 62 72 44 16 88 60 31 03 75 47 8 53 ~ 70 41 11 82 52 22 6.0693 68 34 7 56r 4 69 38 07 76 45 14 83 52 21 6 55 68 35 03 70 38 05 78 40 085 66 l -66 32L 2.5998 - i 31 6.1997 68 29 7.7995 4 57 66 29 94 58 23 88 52 17 81 3 58 63 26 90 53 16 79 42 06 69 2 59 62 23 85 47 09 70 382 94 65 1 60.860^ 1.7321 2.5981 8.4641 4.3302 5.19,62 6.0622 6.9282 7.7948 0 - Y- 8 4- 6. T 7 8 8 Snle-P8PAUT 60 iOB&uu _ I. I~ I I DEPARTURE 29 DEGREES. 313 i 1 2. 3 4 6 5 I 6 7 I 8 9 )T I 0!0.4848 0.9696 1.4544 1.9392 2.4241 2.9089 3.3937 3.8785 4.863360 1 51 0.9701 52 1.9402 58 2.9104 54 3.8805 5559 2 53 06 60 13 66 19 72 26 7958 8 56 11 67 23 79 84 90 46 4.8701 57 4 58 17 75 83 92 503.4008 66 2556 5 61 22 82 43 2.4304 65 26 86 4755 6 63 27 90 54 17 80 44 3.8907 7154 7 66 32 98 64 30 95 61 27 9353 8 68 37 1.4605 74 42 2.9210 79 47 4.3816!52 9 71 42 13 84 55 26 97 68 3951 10 74 47 21 94 68 41 83.4115 88 6250 11 7 52 28 1.9504 81 57 33 3.9009 85 49 12 79 57 37 14 93 72 50 29 4.8907 48 13 81 62 43 242.4406 87 68 49 3047 14 84 67 51 35 19 2.9802 86 70 53 46 15 86 72 59 45 31 173.4203 90 7645 16 89 78 66 55 44 33 223.9110 9944 17 91 83 74 65 57 48 39 30 4.402243 18 94 88 81 75 69 63 57 50 4442 19 96 93 89 86 82 78 75 71 6841 20 99 98 97 96 95 93 92 91 9040 21 0.4901 0.9803 1.4704 1.9606 2.4507 2.9408 3.4310 3.9211 4.4113 39 22 04 08 12 16 20 24 28 32 3638 23 07 13 20 26 33 39 46 52 5937 24 09 18 27 36 45 54 63 72 8136 25 12 23 35 46 58 70 81 93 4.420435 26 14 28 42 56 71 65 993.9313 27 34 27 17 33 50 66 83 803.4416 33 4933 28 19 38 58 77 962.9515 34 54 7332 29 22 43 65 87 2.4609 30 52 74 95 31 30 24 48 73 97 21 45 69 944.4318 30 31 27 54 80 1.9707 34 61 88 3.9414 41 29 32 29 59 88 17 47 768.4505 34 6428 33 32 64 95 27 59 91 23 54 8627 34 84 69 1.4803 38 72 2.9606 41 75 4.4410 26 35 37 74 11 48 85 21 58 95 3225 6 9 79 18 58 97 386 76 3.9515 5524 37 42 84 26 682.4710 51 93 35 7723 38' 45 89 34 78 23 67 3.4612 56 4.4501 22 39 47 94 41 88 35 82 29 76 2322 40 50 99 49 98 48 977 47 96 4620 41 52 0.9904 56 1.9808 61 2.9713 65 3.9617 6919 42 55 09 64 18 73 28 82 37 9118 43 57 14 71 28 86 43 3.4700 57 4.4614 17 44 60 19 79 38 98 58 17 77 3616 45 62 24 87 49 2.4811 73 35 98 6015 46 65 29 945 59 24 88 533.9718 82 14 47 67 341.4902 69 362.9803 70 384.470513 48 70 89 09 79 49 18 88 58 2712 49 72 45 17 89 62 34 3.4806 78 5111 50 75 50 24 99 74 49 24 98 7810 51 77 55 321.9909 87 64 41 3.9818 96 9 52 80 60 89 19 99 79 59 88'4.4818 8 53 82 65 47 30 2.4912 94 77 59 42 7 54 85 70 55 40 25 2.9909 94 79 64 8 55 87 75 62 50 37 24 3.4912 99 87 5 6 90 80 70 60 60 39 0 298.99194.4'9094 57 92 85 77 70 62 54 47 39 82:8 58 '95 90 85 80 75 70 65 60 6655 2 69 98 95 93 90 88 85 83 80 78 600.6000 1.0000 1.5000 2.0000 2.5000 3.0000.65000 4.0000 4.50 0 ^jI ZI ---1.1- -- - 8 T 5 6 7 4 6 LATITUoB 0 60 IIIBWSS. I 134 0 0.8660 1 59 2 571 8 566 4 541 5 53 -6 52 7 50 8 49 9 47 10 46 Ti 44 12 48 13 41 14 40 15 38 T6 37 17 85 18 34 19 83 20 31 21 30 22 28 23 27 24 25 25 24 26 22 27 21 28 19 29 18 30 16 31~ 15 32 13 33 12 84 10 35 09 -6 07 37 06 38 015 89 03 40 02 -41 00 42 0.8599 48 97 44 96 45 94 46 93 47 91 48 90 49 88 50 87 61 85 52 84 58 82 54 81 55 79 ~ 78 57 76 58 75 59 73 80 0.8572 LATITUDE 30 DEGREES. 2 3 1.7321 2.5981 18 76 15 72 12 68 09 63 06 59 03 55 00 50 1.7297 46 94 41 91 37 88 33 85 28 83 24 80 19 77 15 74 11 71 06 68 02 65 2.5898 62 93 59 89 56 84 53 80 50 7 5 47 71 44 671 41 62 88 58 36 53 33 49 30 44 27 401 24 36 21 311 18 271 15 22 12 18 09 14 06 09 03 05 00 00 1.7197 2.5796i 94 911 91 87' 88 82 85 78 82 73 79 69~ 76 64 78 60~ 70 5.5 67 '511 64 46i 61 42 58 88 55 88 52 29 49 24 4 6 20 1.714312.5715 ~2 8 4 3.4641 35 29 24 18 121 06 00~ 3.4594 88 83 77 71 65 59 54 48 42 36 30 24 18 12 06 00 3.4495 89 83 77 71 65 ~59 53 48 42 36 30 24 18 12 06 00 3.4394 88 82 76 70 64 58 52 46 34 28 22 17 11 05 3.4299 98 8.4287 5 4, 3 3021 14.3294 87 80 72 65 58 51 43 36 29 2 1 14 07 4.3199 92 85 7 7 70 63 55 48 4 1 33 26 19 11 04 4.3096 89 82 7 4 67 60 52 45 37 80 23 1 5 08 00 4.2993 85 7 8 7 1 63 56 48 41 33 25" 1 8 10 03 4.2895 88 81 74 66 4.285 q 6 5. 1962 53 44 35 26 18 09 0 1 5.1892 83 65 5 6 48 30 2 19 04 5.1795 86 7 7 691 601 51. 42 331 24' 151 07 5.1 698~ 89 80' 71 62~ 531 44~ 35 27 1 8 09 00 5. 1591 82 74 65 56 47 38 29 20 1 1 02 5. 1493 84 75 66 57 48 89 5.1480 7 6.0622 12 01 6.0591 81 71 61 51 40 30 20 09 6.0499 8q9 79 69 58 48 3 8 28 1 7 07 6.0397 86 76 66 55 45 34 25 1 4 04 6.0293 88 73 62 52 41 32 2 1 1 1 00 6.0190 7 9 69 59 48 37 27 1 7 06 6.0096 85 75 64 54 44 38 28 1 2 6.0002 7 8 6.9282 70 58 47 35 24 12 01 6.9189 77 V 6 54 42 30 18 07 -6. 90'95 83 7 2 60 48 3 6 25 1 3 01l 6.8990 7 8 66 5 4 42 30 1 8 06 6.8895 83 7 1 59 47 36 24 1 2 00 6.8788 7 6 65 538 4 1 29 1 7 015 6. 86 93 8 1 69~ 57 45 3 4 22 'C( 9E 6.858( 6.8574 8 9 6.94 3 29 16 03 7.7890 77 64 51 7.7798 84 72 58 46 32 19 06 7.7693 79I 66 53 39 26 13 00 7.7 586 73 60 47 33 20 07 7.74.94 80 6 7 53 411 27 14~ 00 7.73871 731 60' 47' 339 20 06 7.729P 7 IR 66 39 25 7N -199, 86 72 59 7.7145 59 58 57 56 55 53 52 51.50 48 47 46 45 43 42 41 40 38 37 36 35 33 32 31 30 28 i27 126 25 23 22 21 20 19j 1 8 17 16 15 1~4 13 12 ii 10 8 7 6 5 2 1 0 I- ------ - I DEGREES SEPArUJ 8011. RZ s. 8: I 6; a a8 4 5 6 7 8 T7p o0.500 1.00U 1.5(o o 2. 2.000 8.000 3.0t 8.5000 o4.-00i00 4.T0 60 1 03 05 08 10 13 15 18 20 23 59 2 05 11 15 21 25 0 35 40 4568 3 08 15 23 80 88 46 58 61 68 57 4 10 20 30 40 51 61 71 81 8 956 5 13 25 8 56 0 68 76 8824.0101 4.511356 6 15 3 45 6 76 91 3.6106 21 3654 11 28 55 83 6 (649 12 30 60 91 21 51 813.5211 42 7248 13 38 65 98 31 64 96 29 62 9447 14 38 701.5106 41 763.0211 4( 82 4.5317246 15 38- 75- - 13 5 —1 89 26 641 4.002 39145 T10 401 811 2]1V1jl 2.5202 421 8 2 22r 63844 17 43 86 28 71 14 7 0 42 8548 18 45 91 3(i 81 27 7235317 2 4.540842 19 48 9 4 91 39 8.31 82 80841 20 50 1.0101 51 2.0201 52 13.0308 52 4. 408 2 5340 214 35 0 8 31 64 96 2 70 947 22 55 11 66 21 76 321 874 42 93 38 2 58 16 731 31 89 4 3.540 6214. 5520137 24 60 21 81 41 2.5302 629 22 82 431386 25 63 26 88 51 14 75 404.002 65 35 21 8465 91 S 27 9222i 3.5.-357 6 89421 27 68 86 1.5204 72 40 8.0408 75 43 4.5611 33 28 70 41 11 82 52 22 93 63 8 4 32 30 75 51 2 2.0302 7 5228 4.0603 7930 31 789 56 34 8 90 67 45 4.57013 32 80 61 41 22 2.402 82 63 43 2428 33 83 66 49 32 15 97 80 63 465207 34 85 71 56 42 2 I3.0512 98 83 6926l 35 88 76 61 52 40 27.5615 4.003 91 25 36 9-16 6372 5-42 -- -- 779 90 4.0908 46016 15 87 93 36 79 72 65 57 503 8 43 36123 8 95 41 61 82 75607 72 68 63 59 22 39 98 96 94 92 590 87 85 83 68121 40.51.20111.5601 2.0402 2.55023.06028372 4.080814.5904 20 53 43 861 241 2 2.54702 678 45 23 — 6741 2 34 05 11 16 22 27 82 38 0 491 8 43 08 76 24 82 40 27 565 683 711 44 1: 0 21 31 42 5 62 73 88 9416 87 93 6 739 52 65 77 90 4.0903 4.6016 15 47 8 36 54 72 90 3.077 25 43 0611 20 48 20 41 61 82 2.5602 22 43 6:0 84.12 49 28 46 69 92 15 37 60 S83 4.6106 1 52 0 61 9 1 22 52 82 8. 918 43 74 8 58 0 66 99 32 65 97 30 63 96 7 4 85 7113.5406 42 77 3.0812 48 803 4.6219 6 57 1 88 76 14 52 90 87 0 6725 44. 3 4 1 5420 81 6 8 62 2.5702 42 83 23 64 4 57 43 86 29 72 15 57 8.6000 43 861 3 58 42 91. 86 82 27 72 18 684.6809 2 59 48 96 44 92 40 87 8S 83 3 6 1 00.150 1.0301 17 4 1 2.0602 272 3.0902 3.6 41208 4.6541 6 ^ ~i^ 1 2 | 1j 42^N 5 43 8 2 72 1 5736 0 4 86 2 143 2.5715328 4.259 028-r.14 18 21 5.9991 62 3259 69 37 06 75 44 12 81 0 1858 2 67 34 02 6 36 03 7 0t57 4 66 31 2.5697 63 29- 5.1394 60 26 7.7091156 4 663 85 49 1 ' 5, 8 60 19 7 39 4.2799 3 68 18 478 37352 9 8 16 75 33 91 49 07 66 2451 10 57 18 7 27 84 459 1050 — - -- 51 135 2 04 516 08 61 13 5 17 69347 14 51 01 6 2 02 53 04 6 54 05 546 15 41.7098 47.4196 46 5.1295 44 6.8393 42146 61s 2 52 78 37 152M3 17 46 92 38 84 31 77 23 6 18 45 89 78 23 68 g 12 7 0142 20 42 83 25 66 08 5.9791 3 74140 45 104 075 __H __14 —1~ — — 5 —..11 21 40 8 20 60 0 4191 21 139 22 39 77 1~6 54-4.269 31 70 08 47 38 23 37 74 11 48 8 22 565.8296 3337 ri 51251 61 14 64 9l 25 34 68 02 36 70 04 38 72 0635 27 31 62 93 244 3 8 17 4 2 793 28 2 59 88 18 47 76 06 3. 6582 31 2 50 75490 25 49, 74 6.8199 — 242 32 23 47 7 3.49 17 40 6011 428 33 22 44 65 87 09 31 53 74 7.6696927 34 20 41 61 81 02 22 42 62 83126 35 19 38 56 754.2594 13 52 50 69425 3617' 17-;3.j 619 87.04 212 38l 5o6124 38 14 28 43 57 71 855.9599 14 22sl 39 13 25 38 51 64 76 89 02 6421 40 11 22 34 45 56 67 786.800 01220 41 20 13 8 51 48 8 5991 14 212i 42 408 16 24 32 41 7 65 73118 43 07 13 20 2 3 40 46 53 917 0 10 15 20 2 31 36 41 46116 745 04 0 11 14 18 21 25 8 3210 5 4 06 04 3O 1 8 14 1 8 47 01 01 02 02 03 03 04 04 0513 4 97 5 92 90 87 84 82 79 7711 50 96 92 88 84 80 75 71 6 631 53 91 83 74 65 7 48 3 8 5 90 79 69 9 49 8 28 1 07 6 5 88 76 65 53 41 2 15 096 7.639 5 5 8 67 51 34 18 0 85 691 522 59 82 64 46 28. 105.0892 74 56 881 12 0 4 6 DEpARTUUB 58 DEORa E:1 I f 1 3.1 -1 4 a 2 I 01 DEPARTURE 31 DRGREE&. 13 - 4 6 6 7 - - - o 0.56 150 100 1.5451 2.0602 2.5752 3.0902 8.6053 4.1203 4.6854 6 1 53 06 59 12 65 17 70 23 76569 2.55 Ii 66 22 77 32 88 43 99568 3 58 16 74 32 90 47 3.6105 63 4.6421 57 4 60 21 81 42 2.5802 62 23 83 44566 5 63.26 88 51 14 77 40 4.1302 65 55 6~6 ~31 96 61 27 92 57 22 8854 7 68 36 1.5503 7 1 39 3.1007 74 42 4.6510 53 8 70 41 1 1 81 52 22 92 62 33 52 9 73 46 18 91 64 37 3.6209 82 65551 10 75 51 26 2.0701 77 52 27 4.1402 78 50 IP 7 8 56 33 1 1 89~ 67 44 22 9.6600 49 1 2 80 6 1 41 21 2.5902 82 62 42 23 48 13 83 66 43 3 1 14 97 80 62 45 47 1 4 85 70 56 4 1 26 3.1111 96 82 67 46 156 88 75 63 51 39 26 3.6314 4.1-502 89 45 ft 90 ~80 71 61 5 1 41 3 1 22 4.67124 17 93 85 78 71 64 516 49 42 34 43 18 95 90 86 81 76 71 ~66 62 57 42 19 98 95 93 91 89 86 84 82 79 41 20 0.5200 00 1.5601 2.0801 2.6001 3.1201 3.6401 4.1602 4.6802 40 03 UP -- 08 10o 13 1R6 18 21 23 39 22 05.10 15 20 26 31 36 41 46388 23 08 15 23 30 38 46 53'- 61 68 37 24 10 20 30 40 51 61 71 81 91 36 25 13 25 08 50 63 76 88 4.1701 4.6913 35 26 15 30 45 60 76 91 3.6506 21 36 31 27 18 35 53 70 88 3,1305 23 40 58 38 28 20 40 60 80 2.6100 20 40 60 80 32 29 23 45 60 90 13 35 58 80 4.700331 30 25 50 75 2.0900 25 50 75 4.1800 25380 NI 8 55 8 1 0 3 8 6 5 9 3 20 47'N 3 2 3 0 6 0 9 0 2 0 50 79 3.6609 3 9 69 28 3 3 3 2 6 5 9 7 3 0 6 3 9 4 2 7 59 92 27 3 4 35 7 0 1.5705 40 7 5 3.1409 44 79 4.7114 26 3 5 3 7 7 5 1 2 5 0 8 7 '24 62 99 37 25 36 40 80 20 60 2.6200 39 79 4.1919 59 24 37 43 85 27 70 1.2 53 96 38 81 23 38 45 90 34 79 24 69 2.6714 58 4.7203 22 39 47 95 42 89 37 84 31 78 26 21 40 50 1.0500 49 99 49 99 49 98 48 20 41 52 04 57 2. 1010 61 3.1514 65 4.2018 70 19 42 55 09 64 19 74 28 83 38 92 18 43 57 14 72 29 86 43 2.6800 58 4.7315 17 44 60 19 79 29 99 58 18 78 37 16 -45 62 24 86 49 2.6311 73 35 98 59 15 46 65 29 94 48 23 88 5624.2117 81i14 47 67 34 1.5801 68 36 3.1603 69 37 4.7404 18 48 70 39 09 78 48 18 87 57 26 12 49 72 44 16 88 60 322.6-904 76 48 11 50 75 49 24 98 7-3 47 22 96 71 10 51 77 64 31 2.1108 — 85 ~62 389 4.22-16 98 52 79 59 88 18 97 76 56 35 4.7515 8 53 82 64 46 28 2.6410 91 73 55 37 7 54 84 69 53 38 22 8.1706 91 75 60 16 55 87 7 1 48 35 21 2.7008 95 82 5 5 6 8 9 79 ~~~68 37 4 86 2 4.2314 4. Y~i 57 92 84 75 67 59 51 43 84 268~ 58 94 89 83 77 72 66 60 54 49 2 59 97 92 90 87 84 80 77 74 701 600.5299 1.0598 1.5898 2.1197 2.6496 3.1795 3.7094 4.2894 4.680 1 2 8 4 7 6 T W - I 1I LATITUDA bt5 DEGRESS. It, 1 - I I I 188 L~~~~ATITUDI 82 D-souims. 0 0848 1.9612.5442 8.8922 4.2408 5-.0883 5.9864 -6.7844 76260 1 79 58 87 16 4.2395 78 52 31 10569 2 77 55 82 10 87 64 42 19 7.F~297 58 8 76 52 28 04 80 55 81 07 83567 4 74 49 23 8.8897 72 46 20 6.7794 69566 5 78 46 18 91 64 87 10 82 55 55 6 71 42 1 4 85 56 2756.9298 70 4154 7 70 89 09 79 49 18 88 58 2758 6 8 68 86 04 720 41 09 77 45 18562 9 67 88 00 66 88 00 66 8337.6199 51 10 65 20 2.5395 60 25 5.0790 55 20 85 50 11 64 27 91 54 18 81 45 08 7249 1 2 62 24 8 6 48 1 0 7 1 383 6.7695 57 48 1 8 60 2 1 8 1 42 02 62 2 3 83 44 47 1 4 59 1 8 76 85 4.2294 513 1 2 70 29 46 1 5 57 1 5 72 2 9 87 44 01 5 8 16 45 16 56 1 1 67 23 79 345.9190 46 01 44 17 54 08 63 17 71 25 79 84 7.6088 48 18 58 05 58 10 68 16 68 21 78 42 19 51 02 58 04 56 06 58 09 60 41 20 50 1.6899 49 3.3798 48 5.0697 47 6.7596 46 40 Ti 48 — 96 44 92 40 88 36 84 32 39 22 46 93 89 86 82 78 25 71 18 38 28 45 90 34 79 24 69 14 58 03837 24 48 87 80 73 17 60 08 46 7.5990836 25,42 83 25 67 09 5056.9092 84 75 35 26 40 80 21 61 01 41 81 22 62834 27 89 77 16 54 4.2193 82 70 09 47833 28 37 - 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087.279759 2 87 73 60 47 34 20 07 6.4694 80 5H 3 85 70 55 40 25 10 5.6595 80 65 57 4 83 67 50 33 17 00 83 66 5056 5 82 63 45 26 08 4.8490 71 53 3455 6 80 60 40 22 00 79 59 39 19 54 -7 78 56 35 134.0391 69 47 26 0453 8 77 53 30 06 83 59 36 12 7.2689 52 9 75 50 24 3.2299 74 49 24 6.4598 73 51 10 73 46 19 92 65 38 11 84 57,50 11 71 43 14 85 57 28 5.6499 70' 42 49 12 70 39 091 78 48 18 87 57 2648 13 68 36 04 72 40 07 75 43 1147 14 66 32 2.4199 65 31 4.8397 63 30 7.2596 46 151 64 __29 93 58 22 86 51 15 80 45 16 63 25 88 51 14 76 39 02 64 44 17 61 22 83 44 06 66 276.4488 4943 18 59 19 78 374.0297 56 15 74 3442 19 58 16 73 30 88 46 03 61 1841 20 56 12 67 23 79 35 5.6391 46 0240 21 54 08 62 16 71 25 79 33 7.2487 39 22 52 05 57 10 62 14 67 19 7238 23 " 51 01 52 03 54 04 55 06 56 37 24 49 1.6098 47 3.2196 454.8293 42 6.4391 4036 25 47 94 42 89 37 83 30 78 2535 26 46 91:37 82 28 73 19 64 10 34 27 44 88 31 75 19 63 07 50 7.2394 33 28 42 84 26 68 10 52 5.6294 36 78 32 29 40 81 21 61 02 42 82 22 6331 30 39 77 16 54 4.0193 32 70 09 47 30 31 37 74 10 47 84 21 58 6.4294 31 29 32 35 70 05 40 76 11 46 81 1628 33 33 67 00 34 67 00 34 67 01 27 84 32 63 2.4095 26 58 4.8190 21 53 7.2284 26 35 30 60 90 20 50 79 09 39 6925 36 28 56 85 13 41 695.6197 26 54 24 87 26 53 79 06 32 58 85 11 3823 38 25 49 74 3.2099 24 48 73 6.4198 22 22 89 23 46 69 92 15 38 61 84 07 21 40 21 42 64 85 06 27 48 70 7.2191 20 41 20 39 59 78 4.0098 17. 37 56. 7619' 42 18 86 53 71 89 07 25 42 6018 48 16 32 48 64 81 4.8096 12 28 4417 44 14 29 43 57 72 86 00 14 2916 45 13 25 38 50 63 75 5.6088 00 13 15 46 1 1 22 32 43 54 65 76 6.4086 7.2097 14 47 09 18 27 36 46 55 64 73 8213 48 07 15 22 29 37 44 51 58 6612 49 06 11 17 22 28 34 39 45 5011 60 04. 08 11 15 19 23 27 30 8410 61 02 04 06 08 11 13 15 17 19 9 62 00 01 01 01 02 02 02 02 03 8 68 0.7999 1.5997 2.3996 38.1994 3.9993 4.7992 5.5990 6.3989 7.1987 7 64 97 94 90 87 84 81 78 74 71 6 655 95 90 85 81 76 71 66 61 56 6 6I 938 87 80s 74 67 60 54 47 41 4 67 92 83 75 67, 58 50 41 83 24 38 58 90 80 70 60 50 89 29 19 09 2 69 88 76 64 52 41 29 17 05 7.1893 1 600.7986 1.69783 2.3959 8,.1946 3.9932 4.7918 5.5905 6.8891 7.1878 0 IT_ 1,,,~ 2 8 4-~ 6 i6 7 6. 8 I I DEPARTUR 653 DEGREES. 11 -- DEPARTURE 36 DEGREES. 147 i 1 2 a 4 5 6 7 8 0 0.587-8 1.17-56 1.7634 2.3512 2.939t 3.5267 4.1145 4.7023 5.2901 60 1 80 60 41 21 2.9401 81 61 42 2259 2 83 65 48 30 13 96 78 61 4358 3 85 70 55 40 25 3.5309 94 79 6457 4 87 75 62 49 37 24 4.1211 98 8656 5 90 79 69 58 48 38 27 4.7117 5.3006 55 6 92 84 76 68 60 52 44 36 - -28 54 7 94 89 83 77 72 66 60 54 4953 8 97 93 90 87 84 80 77 74 7052 9 99 98 97 96 95 94 93 92 9151 10 0.5901 1.1803 1.7704 2.3606 2.9507 3.5408 4.1310 4.7211 4.3113 50 1 1 0 ~4 07 1 1 15 19 ~22 26 30 N3349 12 06 12 18 24 31 37 43 49 5548 1 3 0 8 1 7 25 34 4 2 50 5 9 6 7 7647 14 11 21 32 43 54 64 75 86 9646 1 5 13 26 39 5 2 6 6 7 9 92 4.7305 4.3218 45 16 1 5 3 1 46 62 77 92 4.1408 23 3944 17 18 36 53 71 89 3.5507 25 42 59 43 18 20 40 60 80 2.9601 21 41 61 81 42 19 23 45 68 90 13 35 58 80 4.3303 41 20 25 50 74 99 24 49 74 98 2340 21 27 54 ~ 82 23 709 36 6i3 90 4.7418 4539 22 30 59 p9 1 8 48 77 4.1507' 36 66 38 ~23 32 64 95 27 59 91 23 54 8637 ~24 34 68 1.7803 37 71 3.5605 39 74 4.3408 36 '25 37 7IT3 10 46 83 19 56 92 2935 i26 39 7 8 17 56 95 33 72 4.7511 5034 27 41 82 24 65 2.97-06 47 88 30 7133 28 44 87 31 74 18 61 4.1605 48 9232 29 46 92 38 84 30 75 21 67 4.3513 81 30 48 96 45 93 41 89 387 86 34 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 47 48 49 50 52 53 54 55 51 58 66 62 64 67 66c 7 2 74 76C 76E 8 1 83 86 88 96 93 -— 95 10.6000 02 04 07 01 1.1906 10 15 20 24 29 34 39 43 48 53 58 62 66 71 76 80 85 '90 52 59 66 73 86 87 94 1. 7901 08 15 22 29 37 43 50 57 64 71 78 85 92 99 1.8006 13 20 2.3802 12 21 30 39 49 5 8 68 77 86 96 2.3905 16 24 33 42 52 61 70 80 53 65 76 88 2.9800 11 23 35 47 58 70 82 95 2.9905 16 28 40 51 63 75 3.5704 17 31 46 59 73 88 3.5801 16 30 43 58 73 85 99 3.5914 27 41 56 69 83 97 3.6011 25 39 54 76 8f 4. 70 16IC 36 52 68.85 4. 1801 17 34 52 66 82 99 4. 1915 31 48 64 80 97 42.013 29 46 23 42 61 80 98 4.771 7 35 54 73 91 4.7810, 31 47 66~ 85 4.7903 22 41 55 76 97 4.3618 39 60 81 4.3702 24 44 65 87 4.3810 28 49 70 91 5.3912 29 28 27 26 25 28 22 21 20 18 17 16 94 99 1.2004 08i 13i 89 98 2.4008 17 26 8ci 98 3.001C 21 33 56 09 1 82~7 36 45 53 6,2 71 J 57 11 22 34, 45 56 67 78 90 58 14 27 41 64 68 81 4.2195 4.8108 6.412 59 16 32 47 63 79 95 11 26 60 0.6018 1.2086 1.8054 2.4072 3.0091 3.6106 4.2127 4.8145 5.414 _ _ _ _ _ _ _ _ _ _ _ 8 4 6 - 7 ' LATITUDE 53 DEIGREES. I 148 ~~~LATITUJDE 37 DEGREES. 142 8 4 7 8 9 00.79861.5978 2.3959 3.1946j'3.9932 4.98 5.5905 69.3-891 7.1878 60 1 85 69 54 38 23 08 5.5892 77 61 59 2 83 66 49 32 16 4.7897 80 63 46 58 3 81 62 43 24 06 87 68 49 30 57 4 79 59 38 17 3.9897 76 55 34 14 56 5 78 55 33 10 88 66 43 21 7.1798 65 ~i 765 7 3 79 55 3 1 06 8254 7 74 48 22 3.1896 71 45 1 95.3793 67 53 8 72 45 17 89 62 34 06 78 51 52 9 71 41 12 82 53 24 5.5794 65 35 51 10 69 88 06 75 44 13 82 50 19 50 1i ~67 34 01 6 8 3 6 038 7 0 3 7 04 49 1 2 656 31 2.3896 6 1 2 74.7792 5 7 2 27.1688 48 1 3 64 2 7 9 1 54 1 8 82 45 08 72 47 1 4 62 24 85 47 09 7 1 3 36.3694 56646 156 60 2 0 80 4 8 00 60 2 0 80 40 45 1-6 58 17 7 H333.9792 SU 08 66 25 44 17 57 13 70 26 83 39 2.5696 52 09 43 18 55 09 64 19 74 28 83 38 7.1592 42 19 53 06 5~~~9 12 65 18 71 24 77 41 20 51 02 54 05 56 07 58 10. 61406~ 5 21 49 1.5899 4.78 4.66 4.55 43 22 48 95 43 91 39 86 34 82 29 38 23 46 92 38 84 30 75 21 67 13 37 24 44 88 32 76 21 65 09 53 7.1497836 25 42 85 27 70 12 54 5.5597 39 82 35 2641 81 22~~~~ —6';2 - 03 44 8Q14 25 65 34 27 39 7 8 1 6 6553.9694 33 72 1 0 49 33 28 37 74 1 1 48 86 23 60 6.3497 34 32 29 35 7 1 06 41 7 7 1 2 47 82 18 31 30 34 67 0 1 3 4 68 01 35 68 02 30 31 382 64 2.795 2 7 ~ 59 ~4.7 591 23 54 7.1386 29 32 30 60' 90 20 50 80 10 40 70 28 33 28 56 85 13 41 69 5.5497 26 54 27 34 26 53 79 06 32 58 85 11 38 26 35 25 49 74 3.1699 24 48 73 6.3398 22 25 3t 23 46~69 92 1 5 3 7 60 83 06 24 37 21 42 63 84 06 27 48 69 7.1290 23 38 19 39 58 77 3.9597 16 35 54 74 22 39 18 35 53 70 88 06 23 41 58 21 40 16 32 47 63 79 4.7495 11 26 42 20 4-1 14 ~28 ~42 56 70 845-. 53 98 1 2 26 19 42 1 2 24 3 7 4 9 6 1 7 3 85 6.3298 10 18 43 11 2 1 3 2 42) 5 3 6 3 7 4 84 7.1195 17 44 09 17 26 35 44 52 61 7i0 78 16 45 07 14 21 28 35 41 48 55 62 15 4605 1 15 2 2 6 31 3 6 4 1 ~ 46 4 4 7 083 0 7 1 0 138 1 7 20 2 3 2 6 3013 48 02 0 3 05 06 0 8 0 9 1 1 1 2 14 12 4 9 00 00 12,.8699 3.1599 3.9499 4.7399 5.5299 6.3198 7.1098 1 1 600.78.98 1.5796 94 IN 90 88 86 84 82 10 53 9692 89 8 81 ~ 77 ~ 73 70 6 6 9 62 94 89 88 78 72 66 5 1 55 50 8 68 93 85 78 70 63 56 48 41 8337 64 91 82 72 63 54 45 36 26 17 6 65 89 78 67 56 46 35 24 13 0256 87 75 62 4 372 116.~30987.~0986 4 67 88 71 57 42 28 1a5.5199 84 70 3 68 84 67 51 85 19 02 86 70 53 2 6 ~82 64 45 28 10 4.7291 73 55 47 1 400.17880 1.5760 2.8640 3.1-520 3.9401 4.7281 5.5161 6.8041 7.092I 0 -1 A i o i , -; - DEA- TR 37 DER:8 149 ---; DEPARTURE 37 DBGRBES. 149 0 1 2 8 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 0.6018 21 28 25 27 3C 32 34 37 39 41 44 46 48 61 53 55 58 60 62 65 67 69 71 74 76 *78 81 83 85 88 1.2036 41 46 50 55 60 64 69 73 78 83, 87! 92 97 1.2101 06 11 15 20 25 29 34 38 43 48 52 57' 61 66 71 79 8 4 1.8054 2.4072 62 81 68 91 75 2.410( 82 1C 89 19 96 2~ 1.8103 38 10 47 17 56 24 66 31 75 38 84 45 93 52 2.4202 59 12 66 21 73 3C 80 40 87 49 94 58 1.8201i 67 07 76 14 86 21 95 28 5 4304 35 14 42 23 49 32 56 41 63 50 0 3.0091 3.0103 14 26 37 49 61 72 84 95 3.0207 19 30 42 63 65 77 88 3.0300 11. 23 34 46 57 69 81 92 3.0404 15 27 38 3.6109 23 37 51 64 79 93 3.6206 21 34 48 62 76 90 3.6304 17 32 46 59 73 87 3.6401 15 28 43 57 70 84 98 3.6512 26 7 4.2127 44 6( 76 92 4.2209 25 41 57 73 90 4.2306 22 38 64 7C 87 4.2403 19 35 52 68 84 4.2500 17 33 49 65 81 97 4.2613 8 4.8146 64 82 4.8201 19 88 57 75 94 4.8313 31 50 68 86 4.8405 23 42 61 79 98 4.8516 85 63 72 90 4.8609 27 46 64 83 4.8701 9 5.4163 85 5.4206 26 47 68 89 5.4310 30 51 73 93 5.4414 35 655 76 98 5.4518 89 60 81 5.4601 22 43 64 85 5.4706 27 47 68 79 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 88 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 to6 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 52 53 54 66 90 92 95 97 99 0.6102 04 06 08 11 13 15 18 20 22 26 27 29 31 34 36 38 41 48 45 80 85 89 94 98 1.2203 08 12 17 21 26 31 35 40 45 49 54 58 63 67 72 77 81 86 90 70 77 84 90 97 1.8305 11 18 25 32 89 46 53 60 67 74 80 87 94 1.8401 08 15 22 29 85 60 69 78 87 96 2.4406 15 24 34 43 52 61 70 80 89 98 2.4507 16 26 35 44 63 62 72 80 50 61 73 84 96 3.0508 19 31 42 54 65 77 88 3.0600 11 23 34 45 57 69 80 92 3.0703 15 26 39 53 67 81 95 3.6609 23 37 50 64 78 92 3.6706 19 33 47 61 75 88 3.6802 16 30 44 57 71 29 45 62 78 94 4.2711 27 43 59 75 91 4.2807 23 39 55 72 88 4.2904 20 36 62 68 84 4.3000 16 20 38 56 74 93 4.8812 31 49 68 86 4.8905 22 78 96 4.9014 83 61 70 88 4.9106 ~.0 I 5.4809 80 51 71 92 5.4914 34 55 76 96 5.5017 38 68 79 6.5100 21 6.5' 56 67 -fiR 42 90 AU\ Go 84 98 8.6912.).P 82 48 64 An 4 i. I i z - X ~, I X f. i I 160 LATITUDE.38 DEGREES. ) 1 ~ ~2 8 4 6 6 7- 8 9, '0 0.7880 1.5760 2.8640 8.1520 8.9401 4.7 28 5i.6161 6.8041 7.0921 60 1 78 67 85 1383.9892 70 48 26 05 59 2 77 58 80 06 83 59 86 12 7.0889 58 8 75 50 24 99 74 48 23 6.2998' 72 57 4 78 46 19 3.1492 65 37 10 88 56 56 5 71 42 1 3 84 56 2765.6098 69 40 55 6 69 39 08 77 47 16 85 54 24 54 7 68 85 08 70 38 06 78 41 08 63 8 66 32 2.3597 63 29 4.71 95 61 26 7.0792 52 9 64 28 92 56 20 84 48 12 765 1 10 62 24 87 49 1 1 73 35 6.27-98 60 50 Ti 60 21 ~8 42 02 62- 23 ~ 44 49 12 59 17 76 34 3.9293 52 10 *61 2 7 48 18 57 14 70 27 84 41 5.4998 54 11 47 14 55 10 65 20 75 30 85 4017.0695 46 115 53 06 60, 13 66 19 72 26 79 45 1 6 5 1 03 ~54 06 57 08 60 11 6344 17 50 00 49 3.1398 48 4.7098 47 6.2697 46 43 18 48 1.5696 43 91 39 87 35 82 30 42 19 46 92 38 84 30 76 22 68 14 41 20 44 88 33 77 21 65 09 54 7.0598 40 21 4:) 22 41 23 3 c 24 37 25 3U 27 32 28:3 C 29 28 30 26 ~T 24 32 23 33 2 1 84 1 9 35 1 7 Y6 1 5 37 13 88 12 89 1 0 40 08 -T4- 06 42 04 48 03 44 01 45 0.7799 T6 97 47 95 48 93 49 92 50 90 Cl 88 62 86 68 84 64 82 55 81 C6 79 67 77 68 75 69 7 60 0.7772 I185 81 77 74 71 67 63 59 56 52 49Q 45 41 38 34 30 27 23 20 16 12 09 05 01 1.5598 94 91 87 83 79 76 72 I69 65 58 54 50 47 1.6543 — 2F - 27 22 16 11 05 00 2.3495 89 84 78 7I3 68 62) 56 51 46 40 35 29 24 18 131 08 02 2.33196 91 86 80 75 69 64 58 53 47 41 36 31 25 20 2.8815 8 70 62 55 481 40 33 26 19 12 04 3. 1297 90 82 75 68 61 54 46 39 32 24 17 10 03 3.1195 88 81 74 66 59 52 44 37 30 22 15 08 00 3.109 3. 1086 4 I 12 3.9103 94 85 76 671 58 49 40 31 221 1 3 03 3.9094 85 76 67 58 49 40 31 22 13 04 3.8994 85 76 67 58 49 40 31 22 12 03 94 85 76 3.8867 3.8858 5 I 54 43 3,2 21 1 1 00 44.6989 78 67 57 46 35 24 1 3 02 4.6891 80 70 59 47 37 26 1 5 04 4.6 793 82 7 1 60 5(1 38 27 1 7 06 4.6694 84 78 61 51 40 4.6629 6 5.4897 84 71 46 38 21 08 5.4795 83 70 58 44 32 19 06 5.4694 81 69 55 43 30 18 05 5.4592 79 66 54 41 28 15 03 I 5.4490i 77 6 4 52 388 26 183 5.4401 39 24 10 6.2595 11 81 66 52 38 23 09 1 6.2494 80 65 501 36 22 07 6.2393 78 63 49 84 20 06 6.2290 76 62 47 03 18 03 6.2189 74 59 45 30 15 01 86 6.2172 8 82 48 32 16 * 00 7.0484 67 51 35 19 03 7.0385 69 53 37 21 04 7.0288 711 55 39~ 23 06 7.01 89 73 67 o41 24 07 7.0091 75 59 42 25 09 6.9992 76 60 6.9944 39 38 37 36 35 33 32 31 30 28 27 26 25 23 -22 21 20 18 17 16 15 13 12 11 10 8 7 6 5 8 2 1~ 0'i 11 DEPAUTURI 51 DKGREES. 11 DEPARTURE 38 DEGREES. 1'51 '-, I 1...2.8. 4 6 7 8 9 0.0157.2 313 I.8470 2.4626 3.07838 8.6940 4.3096 4.9253 5.540960 1 59 18 77 36 95 53 4.3112 71 3059 2 61 22 84 45 3.0806 67 28 90 5158 3 64 27 91 54 18 81 454.9308 72 57 4 66 32 97 63 29 95 61 26 9256 5 68 36 1.8504 72 41 3.7009 77 45 5.5513 55 6 -- 70 41 11 82 52 22. 983 63 83454 7 73 45 18 90 63 36 4.3208 81 5353 8 75 50 25 2.4700 75 49 24 4.9400 7452 9 77 54 32 09 86 63 40 18 9551 10 80 59 39 18 98 77 57 36 5.5616050 11 82 64 45 27 3.0909 91 738 54 36 49 12 84 68 52 36 213.7105 89 73 57 48 13 86 73 59 46 32 18 4.3305 91 7847 14 89 77 66 55 44 32 21 4.9510 98 46 15 91 ' 82 73 64 56 45 36 27 5.5718 45 16 93 86 80 73 66 59 52 46' 3944 17 96 91 87 82 78 73 69 64 6043 18 98 96 93 91 89 87 85 82 8042 19 0.6200 1.2400 1.8600 2.4800 3.1001 3.7201 4.3401 4.9601 5.5801 41 20 02 05 07 10 12 14 17 19 2240 21 05 09 14 18 23 28 32 37 41 39 22 07 14 21 28 35 41 48 55 6238 23 09 18 28 37 46 55 64 74 83 37 24 12 23 35 46 58 69 81 92 5.5904 36 25 14 28 41 55 69 83 97 4.9710 2435 26 1- P 32 48 64 80 964.3512 28 4434 27 18 37 55 73 92 3.7310 28 46 6533 28 21 41 62 82 3.1103 24 44 65 8532 29 23 `46 69 92 15 37 60 83 5.6006 31 30 25 50 75 2.4900 26 51 __76 4.9801 26830 31 27 -55 82 10 37 64 92 19 4729 32 30 59 89 19 49 78 4.3608 38 67 28 33 32 64 96 28 60 92 24 56 88 27 34 34 68 1.8703 37 71 3.7405 39 74 5.6108 26 35 37 73 10 46 83 19 56 92 29 25 -36 39 78 16 55 941 3388 72 4.9910 49124 37 41 82 23 64 3.1206 47 88 29 70 23 38 43 87 30 73 17 60 4.3703 46 9022 39 46 91 37 82 28 74 19 65 5.6210 21 40 48 96 44 92 40 87 35 83 31 20 T41] -50 1.25o0 6 51 2.5001 51 3.7501 51 5 6.0002 52 19 42 52 05 57 10 62 14 67 19 72 18 43 55 09 64 19 74 28 83 38 9217 44 57 14 71 28 85 42 99 56 5.6313 16 45 59 18 78 37 96 55 4.3814 74 3315 46 62- 283 85 46 3.1308 69 31 92 5414 47 64 28 91 55 19 83 47 5.0110 74 13 48 66 32 98 64 30 96 62 28 9412 49 68 37 05 73 42 3.7610 78 46 5.6415 11 50 71 41 1.8812 82 53 24 94 65 35810 1 7 46 18 -- 91 65 87 4.3910 82 55 9 52 * 75 50 25 2.5100 76 51 26 5.0201 76 8 53 77 55 32 10 87 64 42 19 97 7 54 80 59 39 18 98 78 57 37 5.6516 6 55 82 64 46 28'3.1410 91 73 55 37 5 56 - 84 - 68 53 37.. 21 3.7705 89 74 58 4 57 86 73 659 46 32 18 4.4005 91 78 8 58 89 77 66 665 44 32 21 5.0310 98 2 69 91 82 73 64 55 45 36 27 5.6618 1 60 0.6293 1.2586 1.8880 2.5178 3.1446 3.7769 4.4062 6.0346 5.6639 0 ""~ F Y",,' 4, 66 - 7 81 9D LATITUDE 51 DEGREES. _ x I I I I I I, 152 ~~~~LATITUDE 39 DEGREES., 0 0.7177 1.55643 2.833 115 -3.1086 3.85-8 4.695.4401 6.T21 72 '6.9-9 44 C 1 70 39 09 7 8 48 1 8 87 57 26 59 2 68 8 6 08 7 1 39 07 5.4375 42. 10 58 8 6 6 32 2.3298 64 30 4.6596 62 28 6.9894567 4 64 28 92 56 2 1 85 59 1 3,7756 S 62 25, 8 7 4 9 1 2 74 36 6.2098 '61 55 8 9 10 it 12 13 14 15 17 18 19 20 22 23 24 25 61 59 57 55 53 51 49 48 46 44 42 40l 38 35 38 31 29 27 26, 2 1 17 14 10 06 03 1.6499 95 92 88 84 80 77 73 69 66 62 59 55 51 I 6 5, 56C 54 48 43 37 32 26 21 1 5 10 04 2.3199 93 88 82 77 11 I 0 1 I I I I 42 34 27 20 12 05 3.0998 90 83 76 68 61 54 46 39 32 24 17 09 02 3.8793 84 75 66 77 47 38 29 20 11 01 3.8692 83 74 65 55 i46 37 28 I I I F 6:i 52 41 36 16 08 4.6496 86 75 63 53 41 30 20 Q8 4.6397 86 ~ 75 64 53 II II I I I I I I I 24 10 5.4298 85 72 59 46 33 21 07 5.4195 81 69 56 43 30 17 04 5.4091 79 65 53 39 27 13 01 5.398S 75 62 49 84 69 54 40 25 10 6.1995 81 66 M1 37 22 07 6. 1898 78 63 48 34 18i 04 6 79 6744 59 * 45 30 15 00 6. 1685 70 566 I4b 27 11 6.9795 78 62 45 28 12 6.9695 79 62 46 29 12 6.9596 79 63 46 30 12 6.9496 79 I63 46 30 13 6.9396 79' 631 I I I I I I I I 1 4 1 i I II 54 53 52 51 50 48 47 46 45 43 42 41 40 39 38 37 36 86 88 82 81 80 27 28 29 30 Ft 32 88 84 85 I Z4 22 20 18 16 14 18 11 09 07 I 44 4C 3( 32 26 25 21 18 14 I 1 I'I II I I 71 65 60 54 49 43 38 82 26 21 3iub894 87 80 72 65 58 50 43 35 28 7 I I I it 0 C Of 3.8591 81 72 63 54 44 35 I i I II I 42 31 16Cl 09 4.6297 86 75 64 53' 42 I I 1, 86 05 10 lS 20 26 31 36 41 46 24 37 03 07 10 13 16 20 23 26 30 28 38 01 03 04 06 07 08 10 11 13 22 89 00 1.5399 2.8099 3.0798 3.8498 4.6198 5.3897 6.1597 6.9266 21 40 0.7698 95 93 91 89 86 84 82 7.920 41 96 92 88 84 80 75 71 67 6319 42 94 88 82 76 70 64 58 52 46 18 43 92 84 76 68 61 53 45 87 29 17 44 90 81 71 61 52 42 32 22 13 16 45 88 77 65 54 42 30 19 07 6.9196 16 46 8 7 7-3 60 46 38 20 06 6.1493 7914 47 85 69 54 39 24 08 5.3793 78 6213 48 83 66 48 31 14 4.6097 80 62 45 12 49 81 62 48 24 05 86 67 48 2911 60 79 58 37 16 96 75 54 33 12 10 51 77 54 32 09 3.8386 68 41 186.90959 52 75 51 26 02 77 52 28 03 79 8 53 74 47 21 2.0694 68 41 15 6.1388 62 7 54 72 43 15 87 59 30 02 74 45. 6 55 70 40 09 79 49 19 5.8689 58 28 5 56 68 36'i~~~4 72 40 07 75 43 114 57 66 32 98 64 81 4.56997 63 29 6.8995 3 58 64 28 93 67 21 85 49 14 78 2 59 62 26 87 49 12 74 36 6.1298 61 1 60 0.7660 1.6321 2.2981 3.0642 3.8802 4.5962 5.3623 6.1283 16.8944 0 1 2 8 ~ 4 T9 7~ DEPARTURE 50 DEGREES. A N I I I II I 0I 11 f r I i I I I T 3 7 3 5 1.3 2 1 D:r_ I i 1~ 11 1-1 1T eWAWI Tt t I JJ fl1 - - S. il n1m'wATtIrTM'W H4. DIGREMS. TWiY298 12561.8880 2.5173 3.14663.-7-769 -4.4-062 -6.04 -666389 1 96 91 87 82 78 73 69 64 6969 2 98 95 93 91 89 86 84 82 796 3 0.6300 1.2600 1. 8900 2.5200 3.1600 3.7800 4.4100 6.0400 6.67 00657 4 02 04 07 09 11 13 16 18 2066 6 06 09 14 18 23 27 32 36 "P4-166 T —1 H~7~ 14 200 - 27-34 ~41 ~ 48 54 6154 7 09 18 27 36 45 64 63 72 81653 8 11 28 34 46 67 68 79 90 6.6802652 9 14 27 41 64 68 81 95 5.0508 22 61 10 16 82 47 63 79 95 4.4211 26 42650 TI 18 36 5 2 90 3.7908 2 4 64 12 20 41 61 81 3.1602 22 42 62 83 48 13 23 46 68 90 13 35 68 8056.6903 47 14 26 60 74 99 24 49 74 98 23 46 16 27 64 81 2.5308 36 63- 90 65.0617 44 46 1-6 29 6 88 171 47 764.4305 34 64 44 17 32 63 96 26 68 90 21 63 84 18 34 68 1,9001 35 69 3.8003 37 70 6.7004 42 19 36 72 08 44 81 17 63 89 25 41 20 38 77 15 63 92 30 6865.0706 46 40 21 41 81 22 62 3.1703 44 84 26 6639 22 43, 86 28 71 14 57 4.4400 42 86 38 23 46 90 36 80 26 71 16 61 6.7106 37 24 47 95 42 89 37 84 31 78 26386 26 60 99 49 98 48 98 47 97 46 36 26 52 1.2704 65 2.5407 69 3.8111 63 5.0814 66 34 27 64 08 62 1 6 70 24 78 32 86 83 28 66 13 69 26 82 38 94 60 6.7207 32 29 69 17 76 34 93 61 4.4610 68 27 31 30 61 22 82 43 3.1804 66 26 86 47 30 31 ~63 26 89 62 16 78 41 5.0904 62 82 66 31 96 61 27 92 67 22 88 28 33 68 35 1.9103 70 38 3.8205 73 40 6.7308 27 34 70 40 09 79 49 19 89 68 28 26 35 72 44 16 88 60 32 4.4604 76 48 26 36 74 48 23 97 71 46 19 94 68 2 37 77 63 30 2.6606 83 69 3665.1012 89 23 38, 79 67 36 16 94 72 61 80 6.7408 22 39 81 62 43 24 3.1906 86 67 48 29 21 40 83 66 60 33 16 99 82 66 49 20 41 867~1 66 42 273.8312 9 8 8 3 6919 42 88 756 6 3 6 1 3 9 26 4.4714 6.1102 89 18 43 90 80 70 60 60 3 9 2 9 19 8.7609 17 44 92 84 7 7 69 6 1 6 3 46 3 8 3016 46 94 89 8 3 7 8 7 2 6 6 6 1 6 6 60 15 4 0 7 98 90 86 ~83 80 R 76 73 69i4 47 99 98 9 96 95 93 92 91 90 18 48 0.6401 1.2802 1.9203 2.6604 3.2006 3.8407 4.4808 6.1209 6.7610 12 49 03 07 10 13 17 20 23 26 3011 60 06 11 17 22 28 34 39 46 60 10 61 08 16 23 31 3 4 55 6 70 52 10 20 30 40 60 60 70 80 90 e 53 12 26 37 49 62 74 86 9865.7711 7 64 16 29 44 68 73 87 4.4902 6.1316 31 E 56 17 33 50 67 814 3.8600 17 34 50I 56 19 38 67 7 5 4 3 2 V 57 21 42 64 86 3.2006 27 48 70 91 58 23 47 70 94 17 40 64 87 5.7811 59 26 51 77 2.5702 28 54 79 5.1406 80 60 0.6428 1.2856 1.928412.671213.2140 3.8667 4.499565.1423 5.7851I T 2 U.. ~4 1 5 6 7 8 9 LATITUDE 50 DEGREES. K I,; I 154 - -LATITUDI 40 DiGim~s. ______ 5~ ~ 6 - 9 p~ 0 0.7660 1.5321 2 2981 3.0642R3.8302 4T 62 5.3628 6.1288 6.894460 1 59 17 76 34 3.8293 52 10 69 27659 2 57 13 70 27 84 40 5.3597 54 10568 8 55 10 64 19 74 29 84 3886.8893 57 4 63 06 59 12 65 18 71 24 77566 5 51 02 53 04 56 07 58 09 60 55 6 49 1.5298 48 3.0597 46 4.56-895 44 6.1194 43564 7 47 95 42 89 37 84 31 78 26653 8 46 91 37 82 28 73 19 64 10562 9 44 87 31 74 18 62 05 49 6.8792 51 10 42 83 25 67 09 50 5.3492 34 75 50 11 40 80 19 5983.8199 39 79 18 68 49 12 38 76 14 52 90 28 66 04 42 48 13 36 72 08 44 81 17 53 6.1089 25 47 14 34 68 03 37 71 05 39 74 08 46 16 32 65 2.2897 29 62 4.5794 26 58 6.8691 45 16 30 61 91 22 52 82 13 43 7 44 17 29 57 86 14 43 72 00 29 57 43 18 27 53 80 07 84 60 5.3387 14 4042 19 25 50 74 3.0499 24 49 74 6.0998 23 41 20 23 46 69 92 15 37 60 83 06 40 1 ~210 42 63 84P 0b5 26N 47 68[ 6.859039 22 19 38 58 77 3.8096 15 34 54 73 38 23 17 85 52 69 87 04 21 88 56837 244 15 31 46 62 77 4.5692 08 28 39 36 25 14 27 41 54 68 81 5.3295 08 22 35 26 12 23 35 46 58 70 81 6.0893 0434 27 10 19 29 39 49 58 68 78 6.8487 33 28 08 16 23 31, 39 47 55 62 70 32 29 06 12 18 24 30 35 41 47 53 31' 30 04 08 12 16 21 25 29 83 8730 81 02 04 07 09 11 13 15 18 20 29 82 00 01 01 01 02 02 02 02 08 28 33 0.7598 1.5197 2.2795 3.0394 3.7992 4.5590 5.8189 6.0787 6.8386 27 34 97 93 90 86 83 79 76 72 69 26 35 95 89 84 78 73 68 62 57 5125 86 93 85 78 71 64 56 49 42 34 24 37 91 82 72 93 54 45 86 26 17 23 88 89 78 67 56 45 83 22 11 00 22 89 87 74 61 48 85 22 09 7.0696 6.8283 21 40 85 70 55 40 26 11 6.3096 81 66 20 41 83 66 50 33 16 4.5499 82 66 49 19 42 81 63 44 25 07 88 69 50 32 18 43 79 59 38 18 3.7897 76 56 35 1517 44 78 65 33 10 88 65 43 20 6.8198 16 45 76 51 27 02 78 54 29 05 8015 -4- ~74 48 21 3.0295 69 43 17 6.0590 641 4 -47 72 44 16 88 60 31 08 75 47113 48 70 40 10 80 50 19 5.2989 69 29 12 49 68 86 04 72 40 08 76 44 1211 50 66 32 2.2698 64 31 4.5897 63 29 6.8095 10 51 64 28 93 S7 21 85 49 14 78 9 62 62 25 87 49 12 74 86 6.0498 61 8 53 60 21 81 42 02 62 28 88 44 7 64 69 17 76 34 3.7793 51 10 68 27 6 66 67 13 70 26 83 40 5.2896 63 09 6 55 09 64 19 74 28 83 3886.79924 57 58 06 68 11 64 17 70 22 75, 8 58 61) 251 6302 04 55 05 66 07 68 2 69 49 1.5098 47 3.0196 45 4.5294 43 6.0892 41 1 80 0.7547 1.6094 2.2641 3.0188 8.7736 4.6283 5.2830 6.0877 6.7924 0 1 I l 4 6 6 7 8 1 DEPAUTURS 49 DEGBEES. I I r I 3 DEPARTURE 40 DEGREES. 15 ' ' ' ------ -j -- - - - _ — ^^ on A.. j^ ^ r->^-^.~*>';-ir~r o Q~ar A AGeNt - ' 7I A 61 I 1 I 1 l I I I I I I ], 4 4 II I II I c 1 2 4 I 6 7 8 9 LO L1 [l L2 13 L4 15 16 17 18 19 20 0.6428 80 82 35 87 39 41 44 46 48 50 52 55 57 59 61,64 66 68 7C 72. 1.2856 60 65 69 74 78 82 87 91 96 1.2900 05 * 09 14 18 22 27 81 86 40 45 2.9284 90 97 1.9304 10 17 24 81 37 44 50 57 64 70 77 84 91 97 1.9404 10 17 2.l571 20 29 38 47 56 65 74 83 92 2.5800 10 18 27 36 45 54 63 72 80 89 I I II I I 51 62 73 84 95 8.2206 18 29 40 51 62 73 84 95 8.2306 18 29 40 51 62 6.0001 81 94 8.8608 21 84 47 61 74 87 3.8701 14 28 41 54 67 81 94 3.8807 21 84 4.5011 26 42 58 73 88 4.5105 20 35 51 67 82 98 4.5213 28 45 6C 75 91 4.580( I I I I I 0 O. 9z'O 41 58 77 94 5.1512 30 48 66 83 5.1601 19 37 54 72 90 5.1708 26 43 61 78 71 91 5.7911 81 51 71 92 5.8011 81 51 72 91 5.8111 31 51 72 91 5.8211 31 ivv 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 I.1 - 2' 21 21 2i 24 2' 2( 28 2~ 8 8 3 3 3 3 8 3 3 8 4 4 4 4 4 1 2 3 5 6 7 8 9 0 - - - 751 77 79 81 83 86 88 90 92 95 4y 54 58 62 67 71 76 80 85 89 I.1 24 80 87 44 51 57 63 70 77 84 98 2.5907 16 25 34 42 51 60 69 78 I 73 84 95 3.2406 17 28 89 51 62 73 I I II 48 61 74 87 3.8900 14 28 41 64 67 1 -, 1 2 3 4 5 8 19:0 L1:2:3 =4 I5 I 97 99 0.6501 03 06 08 10 12 14 17 19 21 23 25 28! - I I 93 98 1.3002 07 11 15 20 24 29 33 38 42 46 51 65 i 90 97 1.9503 10 17 23 30 37 43 65 53 63 7C 7~ 83 I I II I II II. 87 96 2.6004 13 22 31 40 49 58 66 75 84 93 2.6102 10, I 84 95 3.2506 17 28 39 50 61 72 83 94 3.2605 16 27 88.! - - 01 93 3.9007 20 33 46 59 73 86 3.9100 13 26 39 52 66 22 38 53 68 84 99 4.5415 31 46 62 77 92 4.5508 23 83 54 63 85;4.5601 10 32 47 62 7E 94 0I - 5.1814 32 50 67 85 5.1902 5.831., 74 91 5.2009 26 44 62 79 98 5.2115 33 51 68 86 5.2203 21 5.85 5.861( 8( 41 61 81 5.8701 46 0 60 89 - 9 499 794.5709 38 47 82 64 96 28 60 92 24 56 48 84 68 1.9603 37 71 3.9205 39 74 5.8, 49 36 73 09 46 82 18 55 91 50 39 77 16 54 93 32 70 5.2309 w~~~~~~6 8.2 __W~ anaIt 40 00. t i 5 I 52 54 i6 56 57 58 59 O..,8 41 48 45 47 60 52 64 66 68 0.6561 I — I t1 82 86 9C 95 93 I )I i; I 1I I 1.8104 08 12 17 1.8121. 2 \ l 22 29 36 42 49 66 62 69 75 1.9682 8 I I I I 68 72 81 90 98 I I I I,I - I -I 2.6207 59 16 70 / 25 81 1 84 92 2.6242 3.2808 3.27U4 I c 20 15 26 87 4E ) I F q 40 58 71 84 98 'i I O0 4.6801 16 I It 3.9311 24 37 50 3.9864 t0 93 4.6909 4.5924 4 5 LATITUDB 49 4 I;.;;;: ---- - T~ --- --- T-i e q I -. - - - - I 156 ~~~~LATITUDS '41 DEGRZES. 1 2 8 -47 6 7 W T 0 0-.7547 1.5094 2.26~41 3.0188 8.7736 4.5283 5.2830 6.0877 6.7924 60 1 45 90 36 81 26 71 16 62 07569 2, 48 8 7 30 78 17 60 08 46 6.7890568 8 41, 83 24 66 08 48 5.2790 81 78567 4 40 79 19 5883.7698 87 77 16 56 56 38 75 18 50 88 25 68 00 38 55 6 36 71 0M7 42 78 14 49 6.0285 204 7 34 67 01 35 69 02 86 70 08 53 8 82 64 2.2595 27 59 4.5191 28 54 6.7786 52 9 30 60 90 20 50 79 09 89 69 51 10 28 56 84 12 40 6856.2696 24 52 50 1-1 26 52 -— 78 04 31 57 88 09 35 49 -12 24 48 72 3.0096 21 45 69 6.0W83 17 48 18 22 44 67 89 11 88 55 78 0047 14 20 41 61 81 02 22 42 62 6.7688 46 15 18 87 55 7483.7592 10 29 47 66 45 16; 17 88 50 66 88 4.5099 16 82 49 44 17 15 29 44 58 78 88 02 17 81 48 18 13 2.5 88 50 68 76 5.2588 01 18 42 19 11 21 82 48 54 64 75 6.0086 6.7596 41 20 09 18 26 85 44 53 62 70 79 40 21 07 ~14 21 2 8 86 41 48 55 62839 22 05 10 15 20 25 80 85 40 45388 28 03 06 09 12 15 1 8 21 24 27837 24 01 02 03 04 06 07 88 09 10836 25 0.7499 1.4998 2.2498 2.9997 3.7496 4.4995 5.2494 5. 9994 6.7498 85 26 97 95 92 89 87 84 i 78 63 27 95 91 86 81 77 72 67 62 58883 28 98 87 80 74 67 60 54 47 41832 29 92 88 75, 66 58 49 41 82 24831 390 90 79 69 58 48 38 27 17 06830 81 88 75 63 50 38 26 1 01X6.7388 29 32 86 71 57 48 29 14 00 5.9886 71 28 88 84 68 51 85 19 03 5.2387 70 54 27 84 82 64 45 27 09 91 73 54 86 26 85 80 60 40 20 00 4.4879 59 89 19 25 36 78i 56 84 1283.7390 68 46 24 02 24 0171 1 Pt A 9.. M lit An RP ~9 OR 6.7284 23 48 44 41 22 17 11 2.9896 89 81 71 61 52 4-9L 3 E 2 19 05 5.2292 5.9798 78 62 50 88 22 21 20 68 87 06 78 42 10 78 46 15 19 66 88 2.2899 66 82 4.4798 65 81 6.7198 18,64 29 93 58 24 86 51 15 8017 68 26 88 50 18 75 88 00 68 16 61 21 82 42 08 64 2456.9685 45 15 5 17 76 84 3.7293 52 10 69 27 14 57 18 70 27 84 4056.2197 54 1013 55 10 64 19 74 29 84 38 6.7098 12 58 06 58 11 64 17 70 22 75 11 51 02.53 04 55 05 56 07 5810............:J 1.48% 94 90 86 82 78 75 71 1167 1.48a3 2 47 41 86 29 24 18 12 06 00 2294 88 80 72 65 57 41 2.9726 85 26 16 06 8.7196 87 77 67 3. 71 57 6 4.46W~ 82 71 59 47 85 24 12 00 4.4588 6 29 16 02 5.2088 7 4 61 47 84 5.2020 7 76 28 61 06 45 6.6988 30 71 5.9498 36 82 18 67 01 6.9451 6.6888 8 7 6 5 ~2 0 DzPAUTuBJx 48 DRGREI98. DBPAXTUnE 41 DERE.167 p 1 2 3 4 5. 6 7 8 9 7).~6561 1.3121 1.9682 2.6242 3.2803 3.9364 4.592 5.2485.046 1 63 26 88 51 14 77 40 5.2602 65569 2 65 30 95 60 25 90 55 20 85568 3 67 34 1.9702 69 86 3.9403 70 38 5.9106557 4 69 3 9 08 78 47 1 6 86 55 25566 1 72 43 1 5 86 58 30 4.6001 73 44 65 ~6 74 8 21 95 69 43 17 90 646 7 76 52 28 2.6304 80 55 31 5.2607 83538 8 78 56 34 12 91 68 47 25 5.9203562 9 80 61 41 21 3.2902 82 62 42 23 51 10 83 65 48 30 13 95 78 60 43 50 11 85 69 54 ~~39 2.9 50 8 93 78 64 12 87 74 61 48 35 21 4.6108 95 82 48 18 89 78 67 56 46 35 24 5.2713 5.9302 47 14 91 83 74 65 57 48 39 30 22 46 15 94 87 81 74 68 61 55 48 42 45 I 6 96 ' 9 87 82 7 8 74 69 65 60O44 17 98 96 913 91 89 87 ~85 82 8043 18 0.6600 1.3200 1.9800 2.6400 3.3000 3.9600 4.6200 5.2800 5.9400 42 19 02 04 07 09 11 13 15 18 20 41 20 04 09 13 18 22 26 31 35 4040 21 07 13 20 26 -33 40 46 53 59 39 22 09 18 26 35 44 53 62 70 79 38 23 11 22 33 44 55 65 76 87.98 37 24 13 26 39 52 66 79 92 5.2905 5.9518386 25 15 31 46 61 77 92 4.6307 202 38;5 26 18 3 5T3 70 88 3.9705 23 40 5834 27 20 39 59 79 99 18 38 58 77 33 28 22 44 65 87 3. 3109 31 53 74 96 32 29 24 48 72 96 20 44 68 9256.961631l 30 26 52 79 2.6505 31 57 83 5.3090 3630 i 31 32 34 35 37 38 39 40 31 37 by~ 61 65 70 74 36 41 44 46 48 79 83 87 92 96 41 42 43 44 45 47 48 49 60 5c 52 56 57 56 61 68 66 68 76 1.3300 05 I 09 13 18 22 26 31 35 39 92 98 1.9905 11 18 24 31 37 44 50 57 64 70 76 83 90 96 2.0003 0 6. 1 6 22 ~29 35 42 48 54 6 1 67 2.0074 31 48 66 74 83 92 53 64 75 86 97 3.3207 18 29 40 51 62 73 83 94 3.3305 16 27 38 49 2.f66UU 06 18 26 36 44 61 7( 76, 84 96 3.9809 23 36 48 62 75 88 3.9901 14 27 40 53 66 79 92 4.0005 18 31 44 57.70 83 96 4.0109 22 35 4.0148 6 4.6414 26 44 66 75 96 4.6505 21 36 51 66 82 96 4.6612 27 42 57 73 88 5.3201 18 36 53 70 88 5.3306 22 40 58 74 92 5.3410 26 44 Ae' 45 62 80 97 5.3114 49 66 84 75 94 5.9714 34 54 73 92 5.9812 32 51 28 27 26 25 24 23.22 21 I I I 51 62 53 64 656 67 68 69 60 72 74 76 78 81 85 87.% 89 0.,6691 44 48 52 57 61 65 70l I 74 78 1.13383 87 96 2.6706 18 22 31 36 48 56 2.6765 5 9 70 81 92 3.3403 14 24 35 46 3.3457 5 4.IY(Ub 18 38 48 64 46 9 86 7 6.01056 256 44 4 688 83 6.02021 6. 022 0 IO LATIT-UDE 48 DEGaREES. I~ I 168 LATITUDE 42 DEGREES. 2 8 4 6 6 7 8 9 9 00.7481 1.4863 2.2294 2.9726 3.7157 4.4588 5.2020 5.9451 6.6883 60 1 20 69 89 18 48 7 7 07 36 66569 2 28 55 83 10 38 66 5.1993 21 48 58 3 26 51 77 02 28 54 79 05 30567 4 24 47 71 2.9695 19 42 66 5.9390 13 56 56 22 43 65 87 09 30 52 74 6.6795 65 6 20 40 59 79 3.7099 20 39 58 78514 7 18 36 53 71 89 07 25 42 60 53 8 16 32 48 64 80 4.4495 11 27 43 52 9 14 28 42 56 70 83 5.189 7 11 25 51 10 12 24 36 48 60 72 84 5.9296 08 50 11 10 30 40 50 60 70 80 6.6690 49 12 08 16 24 32 40 48 56 64 72 48 13 06 12 18 24 30 37 43 49 65547 14 04 08 12 16 21 25 29 33 37 46 1 5 02 04 07 09 11 13 15 18 20 45 16 00 00 01 01 01 01 01 02 0244 17 6.7398 1.4797 2.2195 2.9593 3.6992 9.4390 5.1788 5.9186 6.6585 43 18 96 93 89 85 82 78 74 70 6742 19 94 89 83 78 72 66 61 55 50 41 20 92 8 5 77 70 62 54 47 39 32 40 2 1 90 81 71 62 52 42 33 23 14 39 22 89 77 66 54 43 31 20 08 6.6497 38 23 87 73 60, 46 33 19 06 5.9092 79 37 24 85 69 54 38 23 08 5.1692 77 61 36,2 33 65 48 30 13 4.4296 78 61 43 35 26 81 61 42 22 03 84 64 45 2534 27 79 57 36 1583.6894 72 51 30 08 33 28 77 53 20 07 84 60 37 14 6.6390 32 29 75 49 24 2.9499 74 48 23 5.8998 72 31 30 73 46 18 91 64 37 10 82 65530 31 71 42 12 83 54 25 5.1596 66 37 29 32 69 38 06 75 44 13 82 50 19 28 33 67 34 01 68 35 01 68 35 02 27 34 65 30 2.2095 60 25 4.4189 54 19 6.6284 26 35 63 26 89 52 15 77 40 03 66 25 36 61 22 83 44 05 66 27 5.8888 4924 37 59 18 77 36 3.6795 54 13 72 31 23 38 57 14 71 28 85 42 5.1499 56 13 22 39 55 10 65 30 76 31 86 41 6.6196 21 -40 53 06 59 12 66 19 72 25 78 20 41 5 02M 53 04 6 07 58 09 59 19 42 49 1.4698 47 2.9396 46 95 44 5.8793 42 18 48 47 94 42 89 36 83 30 78 25 17 44 45 90 36 81 26 71 16 62 07 16 45 43 86 20 73 1 659 02 42 6.6089 15 I i 46 47 48 49 60 62 Aft I I 41 82 39 79 37 75 85 71 33 67 31 63 29 59 27 55 26 61 I 23 47 22 43 20 39 18 35 16 31 0.7314 1.4627 24 18 12 06 06 2.1994 88 82 76 70 65 59 53 47 2.1941 65 5 7 49 41 33 26 18 10 - 02 2.9294 86 78 70 62 2.9254 06 2.6697 87 77 67 67 47 37 27 17 08 2.6598 88 78 3.6568 47 36 24 12 06 4.3988 76 64 52 46 29 17 05 4.3898 4.3881 16.1388 75 61 47 33 20 06 5.1292 78 51 37 23 09 5.1195 80 14 5.8698 82 66 61 85 19 03 5.8587 72 66 40 24 5.8508 71 54 36 18 06 6.598'd 47 26 11 6.fi894 76 6E 6.5822.1 t 1. I I I1 I1 I I I II I 3 2 1 D B 7 5 3 2 ) 2 8 4.I I 5 6 1 7 1 8 9 DBPARTURV 47 DEGREES. i_: dh DEPARTURE 42 DEGRES 9,e r 1 4 1 a __I2 4 & 6 7 8 9 7 o 69 1.3383L 2.0074 2.67656 3.34574.0148 4.6839 5.3530 6.0222 1 94 87 81 74 68 61 55 48 42 2 96 91 87 82 78 74 69 65 6058 3 98 96 93 91 89 87 85 82 80 57 4 0.6700 1.3400 2.0100 00 3.3500 99 99 99 996 5 02 04 06 2.6808 11 4.0213 4.6915 5.3617 6_030955 6 04 09 13 17 22 26 30 34 3954 7 06 13 19 26 32 38 45 51. 5853 8 09 17 26 34 43 52 60 69 77 52 9 11 21 32 43 54 64 75 86 96,51 10 13 26 39 52 65 77 90 5.3703 6.0416 50 111 15 30N 45 60 76 91 4.7006 21 36 49 12 17 34 52 69 86 4.0303 20 38 5548 1 3 19 39 58 78 97 16 36 55 75 47 14 22 43 65 863.3608 29 51 72 94 46 15 24 47 71 95 19 42 66 90 6.0513 45 16 26 526 77 2.6903 - 29 55 815.3806 32 44 17 28 56 84 12 40 68 96 24 52413 18 30 60 90 20 51 81 4.1111 41 7142 19 32 65 97 29 62 94 26 68 9141 20 34 69 03 38 72 4.0406 41 75 6.0610 40 21 37 73 2.0210 46 83 20 56 93 2939 22 39 77 16 55 94 32 7 1 5.3910 4838 23 4-1 32 22 64 3.3705 45 86 27 68 37 24 43 86 29 72 15 58 4.7201 44 87 36 25 45 90 36 81 26, 71 16 62 6.0707 35 26 47 95 42 89 37 84 31 78 2634 27 50 99 49 98 48 97 47 96 4633 28 52 1.3503 55 2.7006 58 4.0510 61 5.4013 6432 29 54 08 6 1 15 69 23 77 30 84 31 30 56 12 68 24 80 35 91 47 6.0803 30 31 58 16 74 32 90 48 4.7306 64 229 32 60 20 81 41 3.3801 61 21 82 4228 33 62 25 87 49 12 74 36 98 61 27 34 65 29 94 58 23 87 52 5.41 F 8126 35 67 33 2.0300 66 33 4.0600 66 33 9926 366 69 38 06 75 44 13 82 506.0919 24 37 71 42 13 84 55 25 96 67 38 28 s8 73 46 19 92 65 38 4.7411 84 6722 39 75 50 26 2.7101 76 51 26 5.4202 77 21 40 77 55 32 09 87 64 41 18 96 20 41 80R 59 39 s18 98R 7577 57 3616.10161-9 42 82 63 45 26 3.3908 90 71 53 34 18 43 84 67 51 35 19 4.0702 86 70 5317 44 86 72 58 44 30 15 4.7501 87 78 16 45 88 76 64 52 40 28 16 5.4304 9215 461 90 80 70 60 51 41 31 21 6.111114 47 92 85 77 69 62 53 46 38 8118 48 94 89 83 78 72 66 61 55 5012: 49 97 93 90 86 83 79 76 72 6911, 50 99 97 96 95 94 92 91 90 8810 61 0.6801 1.360 22.0402 272023 3.4004 4.0805 4.7606 5.4406 6.1207 9 52 03 06 09 12 15 17 20 23 26M8 53 05 10 15 20 26 31 36 41 467: f 64 07 14 22 29 86 43 50 58 650 55 09 19 28 37 47 56 65 74 845 562l~ i~l 23 *35 46 68 69 8 1 9213 57 14 27 41 54 68 82 95 5.4509 22 8 58 16 81 47 63 79 94 4.7710 26 4 59 18 36 54 72 90 4.0907 25 43 61 1 60 0.6820 1.3640 2.0460 2.7280 3.4100 4.0920 4.774015.4560 6.,18-80 LATITUDE 47 DEGREES. 160 L~~~~AnTITDE 48 DEGREES. ~~ 1 2 8 4 ~~~~~~ 6 6 7 8 07341.4627.1941i 2.9254 3.6568- 4831 619.58652 $ 1 12 23 85 46 68 70 81 5.8498 04 59 2 10 19 29 88 48 58 67.77 6.5786568 8 08 15 23 80 88 46' 53 41 68 57 4 06 11 17 22 28 84 89 45 50 56 5 04 07 11 14 18 22 25 29 82 55 6 0 03 0N5 06 08R 10 11 13 14564 7 00 1.4599 2.1899 2.9198 3.6498 4.3798 5.1097 5.8397 06 58 8 0.7298 95 93 90 88 86 83 81 6.5678 52 9 96 91 87 83 79 74 70 66 61 51 10 94 87 81 75 69 62 56 50 43 50 1-1 ~ 92 8 3 7N5 67 59 50 42 34 2549 12 90 79 69 59 49 38 28 18 07 48 13 88 75 63 51 39 26 14 01 6.5589 47 14 86 71 57 43 29 14 00 5.8286 71 46 15 84 67 51 85 19 02 5.0986 70 53.45 16 82 ~63 4R5 27 09 4.3-690 72~54 ~ 354 4 17 80 59 39 19 3.6399 78 58 38 17 43 18 78 55 33 11 89 66 44 22 6.5499 42 19 76 51 27 03 79 54 30 06 81 41 20 74 47 21 2.9095 69 42 16 5.8190 63 40 21 72 43 1U5 ~87 5Vbl ~30 -02 74 45 39 22 70 89 09 79 49 18 5.0888 58 27388 23 68 35 03 71 39 06 74 42 09 37 24 66 31 2.1797 63 29 4.3594 60 26 6.5391 36 25 64 27 91 55 19 82 46 10 73 35 26 62 23 85 47 09 70 32 5.80945534 27 60 1 9 7 9 39 3.6299 5 8 1 8 7I8 37 33 28 58 15 73 31 89 46 04 62 19 32 29 56 11 67 23 79 34 5.0790 46 01 31 30 54 07 61.15 69 22 76 30 6.5283 30 81 2 03 5 0 7 5 9 10 6 2 1 4 652W9 82 50 1.4499 49 2.8999 49 4.3498 48 5.7998 47 28 83 48 95 43 91 39 86 34 82 29 27 84 46 91 37 83 29 74 20 66 11 26 35 44 87 31 75 19 62 06 50 6.5193 25 T6 42 83 ~ 25 670 09 50M5. 06 92 34 75 24 87 40 79 19 59 3.6199 38 78 18 57 23 88 88 75 13 51 89 26 64 02 39 22 89 86 71 07 43 79 14 60 5.7886 21 21 40 84 67 01 35 69 02 36 70 03 20 11 82 ~63 ~2.1795 207 59- 4.3 390 22 546.5. 08519 42 30 59 89 19 49 78 08 38 67 18 48 28 55 83 11 39 66 5.0594 22 49 17 44~ 26 51 77 08 29 54 80 06 31 16 45 24 47 71 2.8894 18 42 65 5.7789 12 15 4- 22 43 65 ~ 86 0 8 3 0 5 1 736.4 9-9414 47 2 0 8 9 5 9 78 8.6098 1 8 3 7 5 7 76 18 48 1 8 85 5 3 7 0 88 0 6 2 3 4 1 5812 491 1 6 8 1 47 62 78 4.8294 0 9 2 5 40 11 50 1 4 2 7 41 5 4 6 8 82 5.0495 09 22 10 T 12 -- 35 46 58 70i 857693 04 -9 52 10 '19 29 88 48 57 67 76 6.488-6 8 68 08 15 23 30 38 45 53 60 68 7 54 06 11 17 22 28 83 39 44 50 6 55 04 07 11 14 1s 21 25 28 3256 7F602 08 05 06 08 09'iI 12 144 67 0 1.4899 2.1699 2.8798 8.5997 4.8197 5.0897 5.7596 6.4796 8 ~:68 0.%7197 95 82 90 87 84 82 79 77 2 59 95 91 86 82 77 72 68 63 59 1 600.7198 1.4887 2.1580 2.8774 8.5967 4.8160 5.0854 5.754716.4741 0 T 2 3 4 ~6 ~6 ~ 7 ~ DEPARTURE 46DEGREES. I DEPARTURE 43 DEGREES. 161 _ 1 2 3 4 6 7 8 9 0 0.6820 1.3640 2.0460 2.7280 3.4100 4.0920 4.7740 5.4560 6.1880 1 22 44 66 88 11 33 55 77 9959 2 24 48 7.3 97 21 45 69 946.141858 3 26 53 792.7306 32 58 855.4611 3857 4 29 57 86 14 43 714.7800 28 5756 31 61 92 22 53 84 14 45 7555 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 83 35 37 39 41 48 46 48 5C 52 6 54 56 58 60 62 65 67 69 71 73 75 77 79 81 84 86 88 90 92 94 96 98 0.6900 03 05 )1 I,I 6b 70 74 78 82 87 91 95 99 1.3704 08 12 16 21 25 29 33 38 42 46 50 54 59 63 67 71 76 80 84 89 92 97 1.3801 05 09 98 2.0505 11 17 24 30 37 43 49 55 62 68 75 81 87 94 2.0600 06 13 19 25 32 38 44 51 57 63 70 76 83 89 95 2.0701 07 14 31 40 48 56 65 73 82 90 99 2.7407 16 24 33 41 50 58 66 75 84 92 2.7500 09 17 26 34 43 51 60 68 78 85 93 2.7602 10 18 64 75 85 96 3.4206 17 28 38 49 59 70 81 91 3.4302 12 23 33 44 55 65 76 86 97 3.4407 18 29 39 50 60 72 81 92 3.4502 13 23 96 4.1009 22 35 47 60 73 86 98 4.1111 23 37 49 62 74 87 4.1200 13 25 38 51 63 76 88 4.1301 14 27 39 52 66 77 90 4.1402 15 28 44 5 74 88 4.7903 19 33 48 6 77 93 4.8007 22 37 52 66 82 96 4.8111 26 40 55 70 85 4.8200 15 29 44 61 73 88 4.8303 18 32 I I E I I I fz 79 96 5.4713 30 46 64 81 ' 98 5.4814 31 49 66 82 99 5.4916 33 50 67 84 5.5001 18 24 51 68 86 5.5102 19 36 35 70 86 5.5203 20 4 A4 6.1514 53 3352 52 51 71 50 90 49 6.161048 2847 47 46 6645 8544 6.1705 43 2442 4341 6240 81 39 9938 6.181937 3836 57 35 7634 9533 6.191432 3331 5230 7129 9028 6.2009 27 2826 50 25 66 24 8523 6.2104 22 2321 - 7. 41 42 43 44 45 47 48 49 50 51 52 53 54 55 58 59 s0 07 09 11 13 15 17 19 21 24 26 28 30 32 34 36 38 40 42 44 0.6947 16 18 22 26 30 34 38 43 47 51 55 60 64 68 72 76 80 85 89 1.3893 2u 26 33 39 45 52 58 64 71 77 83 89 96 2.0802 08 15 21 27 34 2.0840 27 35 44 52 60 69 77 86 94 2.7702 11 19 28 36 44 63 61 70 78 2 7786 I - 34 44 55 65 76 86 97 3.4607 18 28 3 49 60 70 81 91 3.4702 12 23 3 4733 I - 40 53 65 78 91 4.1508 16 28 41 54 66 79 91 4.1604 17 29 42 54 67 4.1680 I - 47 62 76 91 4.8406 20 35 50 65 79 94 4.8509 23 38 53 67 82 97 4.8612 6.8626 I A I~3 [ 5 I I I: Il --- --- 1 - 8 - 1 4 1 6 1| 6 { 7 |1 8 9 '...L. ATITUtE 46 DEGREES. i,_==.......,,,,, L 44 DzGUEElS..w I U 1 2 a 4 5 6 7 8 9 10 TI 12 13 14 15 17 18 120 U ol 85 83 81 79 772 75 73 7 1 69 671 65 63 6 1 59 57 55 53 i 28.1580.83 74 79 68 75 62 71 56 67 50U 63 44 58 38 54 32 50 26 46 20 42 13 38 07 34 01 20 2.1495 26, 8K I 4 2. 8774 166 58 49 41.33 25 17 09 01 2.8693 84 76~ 68 60 52 3.5967 57 47 27 17 07 3.5896 86 76 66 56 46 36 25 15 Ii I I I 4.3160 48 36 24 12 00 4.3088 75 63 51 39 27 15 03 4.2990 78 I I I 5. 035 4 40 26 1 1 97 5.0283 ~ 69 5 4 40 2 6 1 2 6. 0 1-9 8 84~ 7 0 5 5 4 1 8 5.7547 31 15 5,7498 82 66 50 34 18 i02 5.7386 69 53 37 20 04 5.7288 72 55 39 23 6.4 7-4 1 60 23 59 05 58 6.4686 57' 68566 50 55 32 54 13 53 6.4595 52 77 51 59 50 40 49 22 48 04 47 6.4485 46 67 45 49 44 31 43 12 42 6.4394 41 76140 II 22 18 14 10 06 I I II 83~ 77 71' 65 59 -44 36 28 20 12 Of) 3.5795 85 75 65 Ut' 54 41 21 17 13 5.0098 84 70 5j~ 1 0~2 - 52 03 54 05 5 6 5 3 22 49 1.4298 46 2.8595 44 4.2893 42 90 39 38 23 47 94 40 87 34 81 28 5.7174 21 37 24 45 89 34 79 24 68 13 58 02 36 25 43 85 28 71 14 56 4.9999 42 6.4284 35 'JO ~ 1 a4 A0 I 26 27 28 29 30 32 33 34 35 37 38 39 140 ~4I 42 43 44 45 41 Z51 39 77 37 73 35 69 33 65 31 61 28 57 26 53 24 49 22 45 20 41 18 36 16 32 14 28 12 24 10R 20 08 1 6 06 1 2 04 08 02 04 16 10 04 2.1398 92 85 79 73 67 61 55 49 42 36 30 24 18 12 06 54 46 38 30 22 14 06 2.8497 89 81 73 65 56 48 40 32 24 0 8I 3.5693 83 73 63 42 32 22 12 3.5591 81 71 61 I501 40 30 1020 1, 10 32 20 07 4.27951 83 70 58 46 34 22 09 14.2697 85 73 60 48 35 23 11 70 56 42 28 14 4.9899 85 70 56 42 27 13 4.9799 185 70 56 41 27 09 5.7093 76 60 43 27 11 5.6994 78 62 46 30 13 5.6897 80 64 47 31 il 15 47 29 11 6.4193 74 56 37 19 01 6.4083 64 46 27 09 6.3990 7IT2 53 3 5 1 7 33 32 31 30 ~29 28 27 26 25 23 22 21 20 18 17 16 15 I I I I 0.1 I i 11 r 1. 00 00 00 2.8399 3.5499 4.2599 4.9699 5.6798 2.3898 14 0.7098 1.4196 2.1293 91 89 87 85 82 8013 96 91 87 83 79 74 70 66 61 12 94 87 81 75 69 62 56 49 43 11 92 83 75 66 58 50 41, 33 24 10 90o 79 69 58 48 38 27 ~17 0~6 9 88 75 63 50 38 25 13 00 6.8788 8 86 71 57 42 28 13 4.9599 5.6684 70 7 83 67 50 34 17 00 84 67 61 6 81 63 44 25 07 4.2488 69 50 32 6 ~79 59 38 17 3.53-97 762 6 55 3 144 7 7 54 32 09 86 63 40 18 6.3695 3 76 50 2 6 01 7 6 5 1 26 02 77 2 73 46 19 2.8292 66 39 12 5.6586 58 1 0.7071 1.4142 2.1213 2.828 3.536 64.2427 4948 56 69 63 4 T 2 ~~~ 4 6 ~~6 7~ 8 DEPARTURs 45 PSGREES. L I r -: 7: e;; I j I? I!! ~ I!'I): I I:! ~:!: 1;.; 1 ~~~.: ~:::: I~: 4 " % ~-~:~-: I a 'tEPARTURB 44 DEOaGEB. *, Iv -:- — i ---2 — ^..^ ^ ^-^~^ —1 8 4 6 7 T0. —457 1.3898 2.0840 2.7786 3.4733 4.1680 4.8626 5.6572 6.251960 1 49 97 46 95 44 92 41 90 8859 2 6511.3902 52 2.7803 644.1705 66 5.6606 6758 8 63 06 69 12 65 17 70 23 76576 4 65 10 65 20 75 29 84 39 9456 6 57 14 71 28 85 42 99 6 566.261355 -- -69 18 77 86 96 554.8714 73 8254 7 61 22 84 452.4806 67 28 90 5158 8 63 27 90 53 17 80 435.5706 7052 9 65 31 96 62 27 92 68 23 8951 10 68 352.0903 70 384.1805 73 40 6.270860 11 -- 70 -- 39 09 78 48 18 87 67 2649 1 72 43 15 87 59 304.8802 74 4548 13 74 47 21 95 69 42 16 90 6347 14 76 52 27 2.7903 79 55 31 5.5806 8246 15 78 * 56 34 12 90 67 46 23 6.2801 45 16 80 60 -- 40 20 2.4900 80 60 40 2044 17 82 64 46 28 11 93 75 57 3948 18 84 68 53 37 21 4.1905 89 74 6842 19 86 72 59 45 31 174.8903 90 7641 20 88 77 65 53 42 30 18 5.5906 95'40 21 90 81i 71 -- 62 52 42 33 286.2914 39 22 93 85 78 70 63 55 48 40 3338 23 95 89 84 78 73 68 62 57 5137 24 97 93 90 86 83 80 76 73 6936 25 99 97 96 95 94 92 91 90 88385 26 0.7001 1.4002 2.1002 2.80 2.004 4.20054.9006 5.6006 6.8007 27 03 06 09 12 15 17 20 23 26183 28 05 10 15 20 25 29 34 39 4432 29 07 14 21 28 35 42 49 56 6331 30 09 18 27 36 46 55 64 73 8230 831 11! 22 34 45 56 67 78 90 6.310129 32 13 26 40 53 66 79 925.6106 1928 833 15 31 46 61 77 924.9107 22 8827 34 17 35 52 70 874.2104 22 39 672*6 35 20 39 59 78 98 17 37 56 76i25 3-6 22. 43D 65 -862.5108 29 51 72 9424 87 24 47 71 94 18 42 65 89 6.321223 38 26 51 772.8103 29 54 805.6206 81 22 89 28 55 83 11 39 66 94 22 4921 40 30 60 89 19 49 794.9209 38 6820 41 32 64 96 28 60 92 23 55 8719 42 34 682.1102 36 704.2203 87 716.330518 48 36 72 08 44 80 16 52 88 2417 44 88 76 14 52 91 29 67 5.6805 4816 45 40 80 20 60 2.5201 41 81 21 6115 6 42 84 279 — 11 53 95 88 80 7 44 89 83 77 22 664.9310 54 9918 48 46 93 89 85 82 78 24 706.8417 12 49 48 97 45 94 42 90 89 87 8611 50 51 1.4101 52 2.8202 53 4.2303 54 5.6404 55 16 5"1 5 — 05- 58 —10 —! 63 15 68 20 739 52 55 09 64 18 73 28 82 87 91 8 658 57 18 70 27 84 40- 97 54 6.8510 7 54 69 17 76 85 94 524.9411 70 28 55 61 22 82 48 2.5804 65 26 86 47 f 56 3.6 26- 88 51 14 77 405.6502 66 57, 65 80 95 60 25 89 54 19 84 68 67 842.1201 68 854.2402 69 86 6.8608! 69 69 88 07 76 45 14 83 52 21 1 600.7071 1.4142 2.1218 2.8284 3.6350 4.2427 4.9498 5.6569 6,8640 LATITUDE 45 DEGREES. i I ~ i EXPLANATION OF THE TRAVERSE TABLE. Latitude is the distance made in a north or south direction on a given meridian, by running a line at any bearing less than 90 degrees from that meridian; or it is the distance on any line parallel to a given meridian. When the given meridian is assumed at true north and south, the distance made in running on a course in a northerly direction is termed north latitude, or northing; and if ran southerly, the distance south is termed south latitude, or southing. Departure is the distance perpendicular to the given meridian that is made by running on a given course. East departure, or easting, is when the line is run east of the meridian. West departure, or westing, is when the line is run west of the meridian. M Example. Let M N represent the meridian, such as any line (generally assumed north and south); let the B point M = north, and the point N = south; let thebearing of the line N C = N. 440, 1 7/ E., and the distance N C == 9,74 chains = 9 chains and 74 links. Here N B is the latitude made, and B C is the departure perpendicular to the meridian or base line N M; consequently, N B is north latitude or northing, and B C is the east departure or easting. Or, latitude N B = cosine of the < C N B X by the distance N C. And departure B C = sine of the < C N B X by the distance N C. N The degrees are at the top and bottom, and the minutes in the outer columns. The distances 2, 3, etc., to 9, at top and bottom, may be used as chains, tenths of a chain, or links. Example. Lat. N C for 440 17', and distance 9 chains = 6,4431 Lat. N C for 440 17', and distance 90 chains, remove the decimal point one place to the right = 64,431 Lat. N C for 440 17/, and distance 900 chains, remove the, point two places to the right = 644,31 Lat. N C for 440 17', and distance 90 links, or,9 chains, remove the point one place to the left = 0,64431 Lat. N C for 440 17/, and distance 9 links, or,09 chains, remove the point two places to the left = 0,064431 Application. Given the course N 440 17/ E., and distance N C = 97,48 chains, to find the latitude N B and departure B C. Take a piece of card paper, two inches wide, and as long as the width of the page; have it ruled, and numbered 1, 2, 3, etc., to 9, similar to the tables. Lay this across, from 17/ to 23', under latitude 44~ Lay a small weight on the guide paper; then under the edge of the paper you will have the required numbers to be taken out. Under 9 chains we have 6,4431.'. for,90 chains we have 64,4310 Under 7 chains we have 6,0113 Under 4 chains we have 2,8636.~. for,4 chains we have 0,2864 Under 8 chains we have 5,7272.. for,08 chains we have 0,0573 Latitude N B = 69,7860 chains. Let the distance be 9748'links. Under 9 we have 6,4431.-. 9000, remove the point 3 places = 6443,1 Under 7 we have 5,0113.-. 700, remove the point 2 places = 501,13 Under 4 we have 2,8636.. 40, remove the point 1 place 28,636 Under 8 we have 5,7272.. 8, = 5,723 6975,589 Latitude N C = 6978o links. TABLE Il-E~xpansion ~of Solids in Direction of their Lengths fro W2 to 2120 (Change of Temperature 1800). Name of Substance. Platinum. do. do. do. Mean of the four. Glass, white barometer tube. "flint. "tube, without lead (4 sorts). " " with lead. Steel, not tempered. 4 tempered yellow at 1490. cc rod. 94blistered. cctempered. tron wire. "cast (prism). "bar. forged. Copper, mean of three specimens. cc hammered. cceight parts, tin 1. Brass, cast. 4.wire. Hamburgh. English angular. English round rod. mean of three specimens. Antimony. Bismuth. Lead. Tin, fine. 4Cgrain. Zinc. Pine, white, Norway. Authority. Troughton. Dulong & Petit. Borda. Hasler. Smeatonl. Brunner. Lavoisier & Laplace. Brunner. Lavoisier & Laplace. do. Major General Roy. Smeaton. do. Troughton. Brunner. Smeaton. Major General Roy. Smeaton. H asler. Lavoisier & Laplace. do. Tronghton. Smeaton. Brunner. Smeaton. do. do. Roy. do. do. Lavoisier & Laplace. Smeaton. do. do. do. do. do. Captain Kater. Vulgar fractiounF 1 in 1008 1 inl 1131 1 in 1167 1 in 1082 1 in 1094 1 in 1175 1 in 1248 1 in 1115 1 in 1142 1 in 927 1 in 807 1 in 847 1 in 870 1 in 816 1 in 840 1 in 812 1 in 795 1 in 901 1 in 795 1 in 797 1 in 819 I in 582 1 in 521 1 in 588 1 in 581 1 in 550 1 in 533 1 in 517 1 in 539 1 in 528 1 in 528 1 in 532 1 in 923 1 in 719 1 in 349 1 in 438 1 in 403 1 in 340 Dec. frac. con-orex. 1800 ch. in O00eh. 0.000991860.0O05I 0 0008242 0.00004,58 0.00085660 04 00476 0.0009242 0 0000512 0.0009142 0.0000508 0.0008510 0.0000472 0 0008012 O 0000445 0.00089690 0000492 0.0008757 0.0000486 0.0010788 0.0000599 o 001239610.0000699 0.0011807 0.0006656 0.0011500 0.0000682 0.001258306.0000699 0.0011899 0 0000661 0.00123.50 0 0000685 0.-001215 83 0.0000699 0 0011100 0.0000617 0 0012583 0.0000699 0.0012534 0.0000696 0.0012205 0.000f 678 0.0017122 0 00009-11 0 00l9188 0.000l066 0.001700010.0000944 0 0017211 0.00009,56 3.0018167 0.0001009 1.0018750 0.00(1042 1 001983330.0(01074 1.0018555 0.(001031 1.0018945 0.0001052' 1 0018930 0.t 001052 1.0018797 0 001044 1 00108330.0000602 1.0013917 0.0000772 0.0028667 0.0001592 0.0022833 0.0001257 ).00248#30.00Rl229 0.002941710.0001634 0.0604083.0 0000227 Example. A surveyor had adjusted his chain at a temperature of 600, the standard chain of 66 feet or 100 links being cut in the floor of a public hall. During the time that he measured a line of 8000 links, the mean temperature had been 1050 Required the true length of the line, the chain being of iron wire. From col. 100 correction for 10 0,00000685 450 to be added, 1 1 +c- 1,00030825 here = c correction. 8000 8002,466 links true length. (1 + c) L = true length, when chain or box expanded. (1 - c) L true length, when chain contracted. Here L measured length, and c — tabular correction for change of temperature. The above correction 2,466 links would be subtracted if the mean temperature was 150 above zero (Fahrenheit). NTlote 1. If the above line had been measured by a Norway pine pole or rod, 15 feet long (see measuring of Iase lines), the correction would only be 0,82 link, nearly eight tenths of a link in a mile. Note 2. It appears from this table that there is no sensible or practi..4 cal benefit to be derived in using a steel chain, in reference to expansion, or contraction. However, steel chains are to' be preferred, as they are not liable to bend like the iron wire chain. I f 166 - TABLE III.-To ReduceLink* to Feet. ___ ______ 6% 6W070 0 ~ T I k I I 11 1 2'~ 2~ 21 21 2 8 3, 8 3 3 3 3 3 3 4 4 4' 4' 4' 4' 54 45 JFeet. WUK D 0.00 66.00 1 0 66 66.66 2 1.32 67.32 a 1.98 67-98 4 2.64 68.64 5 3.30 69.30 6 3.96 69.66 74. 62 70.62 8 5.28 71.28 9 5.94 71.94 0 6.60 72.60 1 7.26 73.26 2 7.92 73.92 3 8.68 74.58 4 9.24 75.24 5 9.90 75.90 610.56 76.66 7 11.22 77.22 8 11.88 7I7.88 9 12.54 78.64 0 13.20 79.20 1 13.86 79.86 2 14.52 80.52 3 15.18 81.18 4 15.84 81.84 5 16.50 82.50 6 17.16 83.16 7 17.82 83.82 8 18.48 84.48 9 19.14 86.14 0 19.80 85.80 1 20.46 86.46 2 21.12 87.12 3 21.78 87.78 4 22.44 88.44 5 23.10 89.10 6 23 76 89.76 7 24.42 90.42 8 25.08 91.08 9 25.74 91.74 0206.40 92.40 1 27.06 93.06 2 27.72 93.72 3 28.38 94.38 4 29.04 95.04 5 29.70 95.70 6 30.36 96.36 7831.02 97.02 8 31.68 97.68 9 32.34 98.34' D933.00 99.00 1 38.66 99.66 2 24.32 100.32' 3 34.98 100.98, 4 35.64 101.64' 5 36.30 102.30i B 36.96 102.96' 7387.62 103.62i 8 38.28 104.281 D 88.94 104.941 )139.601 105. 601 132.66 133.32 133.9E 134.64 135.3( 135.96 136.62 137.2~ 137.94 138.66 139 26 139.92 1 40. 5~ 141.24 141.96 142.5( 143.22 143.8E 144.54 145.26 145.864 146.52 147.l1 147.84 148.56 1.49.16 149.82 150.48 151.14 151.86 152.46 153. 12 153.7E 154.44 155.16 155. 76 156.42 157.08 157.74 158.46 159.06 159.72 160.38 161.04 161.7C 162.36 163.02 163.68 164.34 165.00 165.66 166.32 166.98 167.64 168.30 168.96 169.62 170.28 170.94 171.60 I U6.01 198.66 199.32 199.98 200.64 201.30 201.96 202.62 203.28 203.94 204.60 205.26 205.92 206 58 20 7.24 2071. 90 208.56 209.22 209.88 210.54 211.20 211.86 212.52 213.18 213.84 214.50 215.16 215.82 216.48 217.14 217.80 218.46 219.12 219.78 220.44 221.10 221.76 222.42 1223.08 1223.74 ~224.40 225.06 225.72 226.38 227.04 227.70 228.46 229.12 229.78 230.34 231.00 231.66 232.32 232.98 233.64 234.30 234.96 235.62 236.28 236.94 237.60 2T 64. 06 264.66 265.32 265 98 266.64 267.30 2967.96 568.62 269.28 269.94 270.60 271.26 271.92 272.58 273.24 273.90 274.56 275.22 2-75.88 276.54 277.20 277.86 278.52 279.18 279.84 280.50 281.16 281.82 282.48 283.14, 283.80 284.46' 285.12' 285.78 286.44 287.10' 287.76 288.42 289.08& 289.74' 290.40' 291.06 291.72~ 292.381 293.04 293.70 294.36 295.'02 295.68 296.34 297.00 297.66 298 32 298.98 299.64 300.30 300. 96 301.62 302.28 302.94 303.60 '; MOUo,330.66 '331.32 331.98 332.64 133.30 333.96, 334.62 335.28, 335.94' 336 60! 337. 261.337 92 338.58 339.24 339.90 340.56 341.22,341.88 342.54 343.20.343.86 344.521.345.18 345.84 '346.50 347.16 347.82 348.48 '349.14 349.80 350.46 351.12 351.78 352.44 353.10 353.76 354.42 355.08 355.74 3.56.40 357.06 357.72 358.38 359.04 1359.70 360.36 361.02 361.68 362.34 363.00 363.66 364.32 364.98 365.64 366.30 366.96 367.62 368.28 368.94 369.60 8'6.U0 462,.00 396~66 462.66,397.32 463.32 39. 8463.98 398.64 464.64 399.30 465.30,399,96 465.96 400.62 466.62 401.28 4fi7.28 401.94 467.94 402.60 468.60 403.26 469.26 403.92 469.92 404 58 470.58 1405.24 471.241 405.90 471.90 406.56 472.56' 407.22 473.22' 407.88 473.88~1 408.54 474.54 409.20 47,5.20 409.86 475.86 410.52 476.'52 411.18 477.18 411.84 477.84 412.50 478.50 413.16 479.16 413.82 479.82 414.48 480.48 415.14 481.14 415.80 481.80 416.46 482.'46 417.12 483.12 417.78 483.78 418.44 484.44 419.10 485.10 419. 76 485.76 420.42 486.42 421.08 487.08 421.74 487.74 422.40 488.40 423.06 489.00 423.72 489.72 424.38 490.38 425-04 491.04 425.70 491.70 426.36 492.36 427.02 493.02 427.68 493.68 428.34 494.34 429.00 495.00 429.66 495.46 430.32 496.32 430.98 496.98 431.64 497.64 432.30 498.30 432.96 498.96 433.62 499.62 434.28 500.28 434.94 500.94 435.60 501.60 0:48.00 528.66 529.32; 529.981 530.64 531.30 531.9 532.62 533.28 533.94 534.60 535.26 535.92 536.58 53 7.24.537.90 538.56.539.22 539.88 540.54 541.20 541.84.542-52 543.18 543.84 544.50 -545.16 545:82 546.48 547.14 547.80 548.46 549.12.549.78 550.44 5051.10 551.76 552.42 553.08 553.74 554.40 555.06.555. 72 556.38 557.04 557.70 558.36 559.02 559.68 560.34, 561.00 561.66' 562.32' 562.'98, 563.64 564.30' 564.96' 565.62' 566.28' 566.94' 567.60 094.00 594.66 595.32 595.98 596.64 597.30 1597.96 598.62.5 99.28 599.94 600.60 601.26, 601.92 602.58 603.24 603.90 604.56 605.22 605.88 606.54 607.20 607.86 608.52 609.18 609.84 610.50 611.16 611.82 612.48 613.14 613.80 614.46 615.12 615.78 616.44 617.10 618.476 618.42 619.08 619.74 620. 40 621.06 621.72 622.38 623.04 623.70 624.36 625.02 625.68 626.34 627.00 627.66 S28.32 628.98 629.64 630.30 630.96 681.62 632.28 632.94 633.60, 4 I ri TABLE I111-To Reduce Links to Feet. l: t 1 k. Feet. 100 200 300 400 500 600 700 80 900 61 40.26 106.26 172.26 238.26 304.26 370.26 436.26 502.26 568.26 634.26 62 40.92 106.92 172.92 238.92 304.92 370.92 436.92 502.92 568.92 634.90 63 41.58 107.58 173.58 239.58 305.58 371.58 437.58 503.58 569.58 635.68 64 42.24 108.24 174.24 240.24 306.24 372.24 438.24 504.24 570.24 686.24 65 42.90 108.90 174.90 240.90 306.90 372.90 438.90 504.90 570.90 636.90 66 43.56 109.56 175.56 241.56 307.56 373.56 439.56 505.56 571.56 637.66 67 44.22 110.22 176.22242.22 22308.22374.22440.22506.22572 228.2 68 44.88110.88 176.88 242.88 308.88 374.88 440.88 506.88 572.88 638 88 69 45.54111.54 177.54243.54 309.54 375.54441.54 507.54 573.54 639.54 70 46.20 112.20 178.20 244.20 310.20 376.20 442.20 508.20 574.20 640.20 71 46.86 112.86 178.86 244.86 310.86 376.86 442.86 508.86 574.86 640.86 72 47.52 113.52 179.52 245.52 311.52 377.52 443.52 509.52 575.52 641.62 73 48 18 114.18 180.18 246.18 312.18 378.18 444.18 510.18 576.18 642.18 74 48.84 114.84 180.84 246.84 312.84 378.84 444.84 510.84 576.84 642.80 75 49.50 115.50 181.50 247.50 313.50 379.50 445.50 511.50 577.50 643.60 76 50.16 116.16 182.16 248.16 314.16 380.16 446.16 512.16 578.16 644.16 77 50.82 116.82 183.82 248.82 314.82 380.82 446.82 512.82 578.83 644.82 78 51.48 117.48 183.48 249.48 315.48 381.48 447.48 513.48 579.48 645.48 79 62.14 118.14 188.14 250.14 316.14 382.14 448.14 514.14 580.14 646.14 80 52.80 118.80 184.80 250.80 316.80 382.80 448.80 514.80 580.80 646.80 81 53.46 119.46 185.46 251.46 317.46 383.46 449.46 515.46 581.46 647.46 82 54.12 120.12 186.12 252.12 318.12 384.12 450.12 516.12 582.12 648.12 83 54.78 120.78 186.78 252.78 318.78 384.78 450.78 516.78 582.78 648-78 84 55.44 121.44 187.44 253.44 319.44 385.44 451.44 517.44 583.44 649.44 85 56.10 122.10 188.10 254.10 320.10 386.10 452.10 518 10 584.10 650.10 86 56.76 123.76 188.76 254.76 320.76 386 76452.76 518.76 584.76 650.76 87 57.42 123.42 189.42 265.42 321.42 387.42 453.42 519.42 585.42 651.42 88 58.08 124.08 190.08 256.08 322.08 3.0808454.08 520.08 586.(8 652.08 89 58.74 124.74 190.74 256.74 322.74 388.74 454.74 520. 74 586.74 653.74 90 59.40 125.40 191.40 257.40 323.40 389.40 455.40 521.40 587.40 653.40 91 60.06 126.06 192.06 258.06 324.06 390.06 456.06 522.06 588.06 654.06 92 60.72 126.72 192.72 258.72 324.72 390.72 456.72 522.72 588.72 654 72 93 61.38 127.38 193.38 259.38 325.38 391.38 457.38 323.38689.38 655.38 94 62.04 128.04 194.04 260.04 326.04 392.045804 524. 04 656.04 95 62.70 128.70 164.70 260.70 326.70 392.70 458.70 524.70 590.70 656.70 96 63.36 129.36 195.36 261.36 327.36 393.36 459 36 525.36 591.36 657.36 ~11 I II 97 64.02 130.02 196.02 262.02 328.02 394.02 460.02 526.02 592.02 658.02 ~'{[I [[68 64.68 130.68 196.68 262.68 328.68 394.68 460.68 526.68 592.68 658.68 9965.34 131.34 197.34 263.34 329.34 395.34 461.34527.34|593.34 659.34 ~~) ~ Lks. 1000 2000 3000 4000 5 000 6000 7000 80C 90 000 660 132U0 980 2640 3300 3960 4620 5280 5940 ~ll)! 1t 100 726 1386 2046 2706 3366 4026 4686 5346 6006 ill! 1t 1200 792 1452 2112 2772 3432 4092 4752 541216072,31 8[ {I 1300 858 1518 2178 2838 3498 4158 4818 547816138 ~1 1 il 1400 924 1584 2244 2904 3564 4224 4884 5544 6204 0{{ 6 [[ ~ [500 990 1650 2310 2970 3630 4290 4950 5610 6270 6 600 1056 1716 2376 3036 3696 4356 5016 567616336 2 700 1122 1782 2442 3102 3762 4422 5082 5742 6402 8 800 1188 1848 2508 3168 3828 4488 5148 5808 6468 4 [00 1254 1914 2574 3234 3894 4554 52145 6874165341 6 Example. Reduce 9664 links to feet. 8 From the bottom table, under 9000 at top, and opposite 600 in the 4 left hand column, we find 6336 0 l I Opposite 64, in upper table, and under 0 = 42,24 2 6378,24 feet. i I i I r ,- j'i I I I I I t8 TABLE IV.-To Reduce Feet to Links. I 6 TALEIV.To edce eettoLincs FtL. 1 2 3 4 5 6 7 8 9 16 11 12 1~3 14 1r 114 21 24A 2i 3z 31 3' 3 4 4 4 4 3 3 4 4 4 S litaik s 0.94J 1.515 3.03 4. 55I 6.0( 7.5E 9.0( 10.61 12. 1' l13.64 115.151 16.611 18.1E 19.7( 21.21 22.7t~ 324.2. 25.741 i 27.2' )28.71 )30.34 131.8! 2 33.3 3 34.8. 13b.31 5 37.8 1 39.3 7 40.9 B 42.4 9 43.9 o 45.4 1 46.9 2 48.4 3 50.0 4 51.5 5 53.0 6 54.5 7 -56.6 8 57.5, 9.59 C.0 60.41:1 62.1.2 63A 4 66.( 5 68.1 6 69.( 17 71.', [8 72., i9 74.1 M 75.,.100200300 4005500 600 700 1561.5239u3.03~ 454.55 4506.06 75i7.o8 909.,09 1060.60 12 153.03 304.155 5.07 7.58 9.10 910.61 2.12 154.55 6.06 7.58 9.09 760.61 2.12 3.63 6.07 7.58 9.10 610.61 2.13 3.64 5.15 7.58 9.09 460.61 2.12 3.64 5.15 6.66 9.10 310.61 2.13 4.64 5.16 6.67 8.18 4160.61 2.12 3.64 5.15 6.67 8.18.9.69 12 2.13 3.64 5.16 6.67 8.19 9.70 1071.21 3.64 5.15 6.67 8.18 9.70921.21 2.72 1 5.16 6.67 8.19 9.70 771.22 2.73 4.24 i6.67 8.18 9.70 621.21 2.73 4.24 5.75 8.19 9.70 471.22 2.73 4.25 5.76 7.27 i9.70 321. 21 2.73 4.24 5.76 7.27 8.78 1 )171.22 2.73 4.25 5.76 7.28 8.79 1080.30 1 2.73 4.24 5.76 7.27 8.79 930.30 1.81 3 4.25 5.76 7.28 8.79 780.31.1.82 3.33 1 5.76 7.27 8.79 630.30 1.82 3.33 4.84 1 7.28 8.79 480.31 1.82 3.34 4.85 6.36 7 8.719 330.30 1.82 3.33 4.85 6.36 7.87 3 180.31 1.82 3.34 4.85 6.37 7.88 9. 39 J, 141.82 3.33 4.85 6.36 7.88 9.39 1090.90 2 3.34 4.85 6.37 7.85 9.40 940.91 2.42 3 4.85 6.36 7.88 8.39 790.91 2.42 3.93.5 6.37 7.88 9.40 640.91 2.43 3.94 5.95 6 7.88 9.39 490.91 2.42 3.91. 5.45 6.96 8 9.40 340.91 2.43 3.94 5.46 6.97 8.451I 9 190.91 2.42 3.94 5.45 6.97 8.48 9.99 1 2.43 3.94 5.56 6.97 8.49 950.00 1101.51 3 3.95 5.46 6.98 8.49 800.01 1.52 3.03 4 4.46 6.97 8.49 650.00 1.52 3.03 4.54 6 6.98 8.49 500.01 1.52 3.04 4.55 6.06 7 8.49 350.00 1.52 3.03 4.55 6.06 7.57 8 200.00 1.51, 3.03 4.54 6.06 7.57 9.08 1 10 1.52 3.03 4.55 6.06 7.58 9.09 1110.60,2 3.04 4.55 6.07 7.58 9.10 960.61 2.12 13 4.55 6.06 7.58 9.09 810.61 2.12 3.63 4 6.06 7.58 9.09 660.60 2.12 3.63 5.14 46 7.58 9.09 510.61 2.12 3.64 5.15 6.66 7 9.09 360.60 2.12 3.63 5.15 6.66 8.17 49 210.61 2.12 3.64 5.15 6.67 8.18 9.691 3)0 2.12 3.63 5.15 6.66 8.18 9.69 1121.20 L2 3.64 5.15 6.67 8.18 9:70 971.21 2.72 53~ 5.15 6.66 8.18 9.69 821.21 2.72 4.23 [5 6.17 8.18 9.70 521.21 2.73 4.24 5.75 3)6 8.18 9.69 521.21 2.72 4.24 5.75 7.26 18 9.70 371.21 2.73 4.24 5.76 7.27 8.78 1 1 9 221.21 2.72 4.24 5.75 7.27 8.78 1130.29 21 2.73 4.24 5.76 7.27 8.79 8. 0 1 1 73 4,256 5.76 7.28 8.79 830.31.2 33 24 5.76 7.27 8.79 680.30 1.82 3.33 4.84 77 7.29 8.80 530.32 1.83 3.35 4.86 6.37 27 8.79 380.30 1.82 3.33 4.85 6.36 7.87 79 230.31 1.82 3.34 4.85 6.37 7.88 9.38'.30 1.82 3.33 4.85 6.36 7.88 9.39 1140.9.0 S1 3.33 4.84 6.36 7.87 9.39990.90 2.41 33 4.85 6.36 7.88 9.39 840.91 2.42 3.93 85 6.37 7.88 9.40 690.91 2.43 3.94 5.45 36 7 88 9.39 540.91 2.43 3.94 5.45 6.96 88 9.40 390.91 2.43 4.94 5.46 6.97 8.48 29 240.91 2.42 3.'94 5.45 6.97 8.48 9.96 91 2.43 3.9 546 6. 97 18.49 1000.001151.51 800 90 12.12 1363.64 3.64 5.16 5.15 6.67 6.671 8.19 8.18 9.70 9.70 1371.22:21.21 2.73 2.73 4.25 4.24 6.76 5.76 7.28 7.27 8.79 8.79 1380.31 )430.30 1.82 1.82 3.34 3.33 4.85 4.85 6.37 6.36 7.88 7.88 9.40 9.39 139$3.91 240.91 2.43 2.42 3.94 4.09 5.46 5.45 6.97 6.97 8.49, 8.48 1400'.00 250.00 1.52 1.51 3.03 3.03 4.5 5 4.54 6.07 6.06 7.58 7.58 9.10 9.09 1410.61 260 60 2.12 2.12 3.64 3.64 5.16 5.15 6.6 7 6.66 8.18 8.1 8 1420.70I 9.69 1.21.271.22 2.73 2.72 4.24 4.24 5.76 5.75 7.27 7.27 8.79 8.78 1430.30.280.30 1.82 1.81 3.33 3.33 4.85 4.85 6.37 6.36 7.88 7.89 9.41 9.39 1440.91 1290.91 2,43 2.42 3.94 3.93 5.45 5.4.5 6.97 6.97 8.49 8.48 1450.00 1300.00 1.52 1.51 3.03 3.03 4.55 j I -1 -4~ 4c It i. II.- 5:0 1? TABLE IV. —To Reduce Feet to Links. 169 ft. Links 10 200 800 400 500 600 700 800 900 61 92.42 243.94 39m.45 546.97 698.48 850.00 1001.51 115302 1304.54 1456.06 62 93.94 5.46 697 8.49 70000 1.52 3.03 4.54 6.06 7.58 63 95.05 6 97 8.48 9.60 1.51 3.03 4.14 6.06 7.57 9.09 64 96.57 248.99 400.00 551.52 708.03 854.55 1006.06 1157.57 1309.09 1460.61 65 98.08 250.00 401.51 3.03 4.55 6.06 758 59.08 1310.61 '2.13 66 100.00 251.52 3.03 4.55 6.06 7.58 9 09 1160.60 2.12 3.64 67 101.52 3.04 4.55 6.07 7.58 9.09 1010 61 2.12 3.64 5.16 68 103.03 4.55 6.06 7.58 9.09 860.61 2.12 3.63 5.15 6.67 69 104.55 6.07 7.58 9.10 710.61 2.12 3.64 5.15 6.67 8.19 70 106.06 7.58 9.09 660.61 2.12 3.64 1015.15 6.66 8.18 9.70 71 107.58 9.10 410.61 2.13 3.64 5.16 6.67 8.18 9.70 1471.22 72 109.09 260.61 2.12 3.64 5.16 6 67 8.18 9.69 1321.21 2.73 73 110.61 2.13 3.64 516 6.67 8 19 9.70 1171.21 2.73 425 74 112.12 3.64 5.15 6.67 8.18 9.70 1021 21 2.72 4.24 5.76 75 113.64 3.16 6.67 8.19 9.70 871.22 2.73 4.24 5.76 7.28 76 115.15 6.67 8.18 9.70 721.21 2.73 4.24 5.75 7.27 8.79 77 116.67 8.19 9.70 571.22 2.73 4.25 5.76 7.27 8.79 1480.31 78 118.18 9.70 421.21 2.73 4.24 576 7.27 8.75 1380.30 1.82 79 119.70 271.22 2.73 4.25 5.76 7.28 8.79 1180.30 1.82 3.33 80 121.21 2.73 4.24 5.76 7.27 8.79 1030.30 1.81 333 4.85 81 122.73 4.25 5.76 7.28 8.79 880.31 1.82 '3.33 4.85 6 37 82 124.24 5.76 7.27 8.79 730.30 1.82 3.33 4.85 6.36 7.88 83 125.76 7.28 8.79 580.31 1 82 3.34 4.85 6.36 7.88 9 40 84 127.27 8.79 430 30 1.82 3.33 4.85 6.36 7.87 9.39 1490.91 85 128.79 28031 1.82 334 4.85 6.37 7.88 9.39 1340.91 2.43 86 13030 281.82 3.33 4.85 636 7.88 9.39 1190.90 2.42 3.94 87 131.82 3.34 4.85 6.37 7.88 9.40 1040.91 2.42 4.00 5.52 88 133 33 4.85 6.36 7.88 9.39 890.91 2.42 3.93 5.45 6.97 89 134.85 6.37 7.88 9.40 740.91 2.43 3.95 5.45 6.97 8.49 90 136.36 7.88 9.39 590.91 2.42 3.94 5.45 696 8.48 1500.00 91 137.88 9.40 440.91 2.42 3.94 5.46 6.97 8.48 1350.00 1.52 92 139.39 290.91 2.42 393 5.45 6.97 8.48 9.99 1.51 8.03 93 140.91 1.43 3.94 5.45 6.97 8.49 1050.00 1201.51 3.03 4.55 94 142.42 3.96 5.45 6.96 8.48 900.00 1.51 3 02 4.54 6.06 95 143.94 5.46 6.97 8 48 750.00 1.62 3.03 4.54 6.06 7.68 96 145.46 6.98 8.49 600.00 1.52 3.03 4.55 6.06 7.58 9.10 97 146.97 8.49 450.00 1.52 3.03 4.55 6.06 7.57 9.00 1510.61 98 148.48 300.00 1.51 3 03 4.54 6.06 7.58 9.08 1360.60 2.12 99 150.00 301.52 3.03 4.55 6.05 7.58 9.09 1210.60 2.12 3.64 Ft. 1000 2000 3000 4000 5000 6000 7000 8000 9000 0 1515.15 3030.30 4545.45 6060.61 7575.76 9090.91 10606.06 12121.21 13636.36 100 1666.67 3131.82 4696.97 6212.13 7727.27 9242 42 10757.58 12272.73 13787.88 200 1818.18 3333.33 4848.48 6368.64 7878.79 9393.94 10909.09 12424.24 1393989 300 1969.70 3484.85 5000.00 6515.15 8030.30 9545.45 11060.61 12575.76 14090.91 400 2121.21 3636 36 5151.51 6666.66 8181.82 9696.97 11212.12 12727.27 14242.42 500 2272.73 3787.88 5303.03 6818.18 8333.33 9848.48 11363.64 12878.79 14393.94 600 2424.24 3939.29 5454.55 6969.70 8484.85 10000 00 11515.15 13030 30 14545.45 700 2575.76 4040.91 5606.06 7121.21 8636.36 10151.52 11666.67 13181.82 14696.97 800 2727.27 4242.42 5757.58 7272.78 8787.88 10803.03 11818.18 18833.33 14848.48 900 2878.79 4393.94 5909.09 7424.24 8939.39 10454 55 11969.70 13484.85 15000.00 inches. Feet. Links. inches. Feet. Links. inches. Feet. Links.; 1 0.083 0.126 5 0.416 0.631 9 0.750 1.126 2 0.1760.253 6 0.5000.757 10 0.8331.262 3 0.250 0.379 7 0.583 0.883 11 0.9471.388 4 0.333 0.505 8 0.667 1.010 12 1.0001.515 Example. Reduce 9874 feet to links. From the bottom table we find 9800 feet - 14848,48 links. From the upper table, 74 links = 112,12 I - 14960,60 links. i I M ae 1. W 8 0.052360~ 40.069813 50.087267 60.104720 7 0.122173 8 0.189626 9 0.157080, 10 0.174688 11 0.191986 12 0.209439 18 0.2268921 14 0.244345 16 0.261799 16 0.2792521 17 0.296705 18 0.814158 19 0.881611 20 0.849066 21 0.866519 220.3838972 28 0.401425 24 0.418878 25 0.486382 260.458785 27 0.4712388 280.488691 29 0.506144 300.528599 81 0.541052 82 0.558506 88 0.575958 84 0.598411 85 0 610865 86 60t38818 87 0.65577 1 3880.673224 89 0.690677 40 0.698182 41 0.715585 42 0.78830388 48 0.750491 44 0.767944 45 0.785898 46 0.802851 47 0.820304 A QA A7 71;7 4 65 6 7 8 9 70 1.4C 4 7 8( 2 4 85 7 8 90 1 2 3q 4 9 IF 7 8 6 100 4 1.117011 1.134464 1. 151917 1. 169371 1.186824 1.204277 1.221731 1.239184 1.256687 1.27409C 1.291543 1.308997 1.82645C 1.343903 1.361356 1.37880 1.896268 1.4187 16 1.43116 1.448622 1.466075 1.488526 1.500982 1.518435 1.535888 1.553341 1.570796 1.588246 1.605702 1.6281 55 1.640608 1.658062 1.675515 1.692968 1.710421 1. 727 874 1.745326 1.762782 1.780235 1.797688 1.815141 1.832595 1.850048 1.867501 1.884954 1.902407 1.919862 1.937315 1.954768 1.972221 1.989674 2.007128 2.024581 2.042034 2.059487 2W.076940 2.09489E 7 8 180 1 2 8 135 7 8 6 140 I 2 8 4 145 6 7 8 6 150 1 2 8 4 155 6 7 8 6 160 1 2 8 4 11 65I 1. 164208 1.181662 1. 199115 1.216568 1.234021 1.251475 1.268928 1.286381 1.803834 1.821287 1.838740 1.856194 1.873647 1.391100 1.408553 1.426006 2.443461 2.460914 2.478367 2.495820 2.513273 2.530727 2.648180 2.565633 2.583086 2.600539 2.617994 2.635447 2.652900 2.670353 2.687806 2.705260 2.722713 2.740165 2.757618 2.775071 2.792527 2.809980 2.827483 ~2.844886 2.862339 2.879793 2.897246 2.914699 2.932152 2.949605 2.967060 2.984518 3.001966 8.019416 8.036872 8.054326 3.071776 8.089282 8.106686 8.124138 3.141598 2 4 S 6 1 1 12 18 1 4 156 16 1 7 18 16 20 21 22 23 24 25 26 27 28 29 80 31 32 33 34 85 36 3 7 38 39 40 41 42 48 44 45 46 47 48 46 50 51 562 58 54 55 56 57 58 56 60 Are. 582 878 1164 1454 1745 2086 2827 2618 2909 8120 3491 3782 4072 4863 4654 4945 5235 5526 5818 6109 6400 6690 6981 7272 7563 7854 81 45 8436 87127 9018 9308 9599 9890 10181 10471 10762 110-53 11344 11636 11926~ 12217 12508 1279.9 13090 13381 13672 13968 14254 14544 14885 15126 15417 15708 15999 16290 16581 ~16872 17162 17458 S. 1 2 8 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 241 25' 26 27 28 29 30 31 32 33 34 Are. 10 15 19 24 29 34 89 44 49 52 58 68 68 73 78 83 87 92 971 102 1071 1121 116 121 126 131 136i 141 145 1501 155~ 160' 165~ cS; 0 0 0 o 4 0 0 0 0 0 ', #4.4.4. 0 - 1.. 0 0 0 '0,0 0 0 + 0 0 #4;. '0 P4 0 0 0 4 0,0; 0 #4.4 0 - 0 To 0 0 P4 '0 cia 0 0 0 0 0:4:4 0 0 0 0 0 #4.4 0 0 0 0 bO,0 p ci 0 0 0.. +4 0 -4 c.i, ,0 1051 6 7 10 65 110 '18 1 '71 2 124 8 177 4 831 115 84 6 187 7 190 8 '43 9 98120 7 170 4 7 180 35i 36' 37~ 38 39 t0 41 42 43 44 45 46 47 48 49 50 51 52 58 54 55 56 57 58 59 50 170 175 179 184 189i 194 199, 204 208 213 218 223 228 238 238 242 247 252 257 262 267 272 277 281 286 291 Here M = minutes, S = seconds. TABLE VI.I -Length.b ~.100 1.0265.14 1 70 2 75 8 81 4 86.105 91.1' 6 97 7 1.0808 8 08 9 14.110 20.1 1 85 2 81 8 37 4 48.115 49.1 6 55 7 61 *8 67 9 78 -.120 80.1 1 86 2 92 8 99 4 1.0405.125 12.1 6 18 7 25 8 81 9 88.180 45. 1 52 2 58 8 65 4 72.135 79:' 6 86 7 98 8 1.0500 9 08.140 15. 1 22 2 29 8 87 4 44.145 52. 6 9 7 67 8 74 9 82.150 90. 1 97 2 1.0605 ~8 18 4 21.155 29. 6 87 7 45 8 58 9 61.160 1.6069 -Lengths of Circular Arcs obtained by having the Chord or~ i Base, and Haight or Vrersed S ine g itven. B1)C '1 ( 714.8 [8 L9 2.21 Length.1.0669.2j' 78 86 94 1.0708 11.2! 19 28 87 45 54.2 1 62 71 3 80 1 89 -5 98.2 B 1.0807 7 16 B 25 9 84 0 48.2 1 52 2 61 8 70 4 80 S 89. 6 98 7 1.0908 8 17 9 27 ~0 862A 1 46 2 56 8 65 4 75 15 852, 9 95 7 1.1005 8 15 9 25 )0 85. 1 45 2 55 8 65 4 75 )5 85. 6 96 7 1.1106 8 17 9 27 10 87. 1 48 2 58 8 69 4 80 15 90 6 1.1201 7 12 8 28 9 88 20 1.1245 1 2 8 4 C 1 C 81 14 24 2.2 3.2 h Length. - Le b 1.1245.280 1. 56 i 66 21. 77 8 89 4 11.1800 285 11 6 22 7 88 8 44 9 56.290 1. 67 1 79 2 3 90 8 t1.1402 4 i 14.295 B 25 6 7 86 71 3 48 8 D 60 9 D 71.300 1 88 1 2 95 2 831.1507 8 4 19 41 5 81.805 6 48 6 7 55 7 8 67 8 9 79 9 0 91.810 1 1.1608 1 1 2 16 2 8 28 8 4 40 4 65 58.815 6 65 6 7 77 7 8 90 8 1 9 1.1702 9 1)0 15.820 1 28 1 2 40 2 8 513 8 4 66 4 BS 78.825 6 91 6 7 1.1804 7 8 16 8 9 29 9 70 483.380 1 566 1 2 69 2 8 82 8 4 97 4 75 1.1908.885 6 21 6 7 84 7 8 48 8 9 61 9 180 1.1974.840 ingth. 1974.8 89 2001 15 28 42.80 56 70 88 97,2110.3 24 88 52 66 79. 98.2206 20 85 50 64 78 92.2806 21. 85 49 64 78 98.~..2407 22 86 51 65. 80 95 L.2510 24 89. 54 69 84 99 1.2614. 29 44 59 74 89 1.2704 20 85 50 66 81 96 1.2812 27 11.2848~ b 40 1 2 8 4 45 6 7 8 9 SC I I 16( 81.4', Length. - Length. b 1.2848.400 1.8882 68 1 50 74 2 67 90 8 85 1.2905 4 1.8902 21.405 20 87 6 87 52 7 55 68 8 72 84 9 90 1.8000.410 1.4008 16 1 26 82 2 48 47 8 61 68 4 79 i79.416 97 95 6 1.41 15 r1.8112 7 82 28 8 50 44 9 68 60.420 86 76 1 1.4204 2 92 2 22 3 1.8209 8 40 1 25 58 5 41.425 76 B 58 6 9S 7 74 7 1.4818 8 91 8' 81 9 1.8807 9 49 0 28.480 67 1 40 1 86 2 66 2 1.440-41 8 78 8 22 4 90 4 41 5 1.8406.485 59 5 28 6 77 7 40 P7 96 8 56 8 1.4514 9 78 9 388 0O 90.440 51 I 1.8507 1 7C 2 24 2 88 8 41 831.4601 4 58 4 2C ~5 74.4465 44 6 91 6 bf 7 1.8608 7 82, 8 25 8 1.470( 9 48 9 11 )0 60.450 8t 1 177 1 fij 2 94 2 7 83183711 8 94 4 28 41.4811 DS 46.455 8 6 683 7 80 7 7 8 97 8 8 9 15 9 1.4900 00 1.8882.4601.2 I I I I 0 1 k I I 11 ------ TABLE VI. —Lengths of Circular Arcs obtained by having the Chord or Base, and Height or Versed Sine given. = h h h h h h - Length. - Length. - Length. - Length. - Length. - Length, b b b b b b.460 1.4927.467 1.5061.474 1.5196.481 1.5332.488 1.5470.495 1.5608 1 46 8 80 51.5215 2 52 9 89 1 28 2 65 9 99 6 35 3 71.490 1.5509 2 48 3 84.470 1.5119 7 54 4 91 1 29 3 68 4 1.5003 1 38 8 74.485 1.5411 2 49 4 88.465 22 2 67 9 93 6 30 3 69.500 1.5708 6 42 3 76.480 1.5313 7 50 4 85 7 1.5061 4 1.5196 1 1.5332 8 1.5470.595 1.5608 II I I I I i Example. Given the chord =-12,16 feet, and the height 3,48 feet, to find the length of the arc. Here h - 3,48, and b = 12,16, h 3,48 and - = - = tabular height =,2862 nearly. b 12,16 Tabular arc corresponding to 286 = 1,2056 = 1,2056 Tabular arc corresponding to 287 1,2070 difference, 14 multiplied by,2, 0002,8 1,2058,8 12,16 Length of the curve = 14,6635 feet nearly. Rele. To the tabular arc corresponding to the first three figures, add the product of the fourth decimal, if any, by the difference of the tabular heights, of the one less and the other greater than the given tabular number. The sum will be the required tabular length to the nearest ten thousandth part, which sum multiplied by the given chord, will give the required length. Example 2. Let chord b = 40,20 feet, and height h = 5,16 feet. h 5,16 Here - =,1277 = tabular height. b 40,2,127 = 1,0425 = 1,0425,128 = 1,0431 difference =,0006, multiplied by 7 = 4,2 1,0429,2 Base or chord = 40,2 The required length of the curve = 41,92 feet. I - 3 3 3 I rI LI -r TABLE VII.-Areas of Segments of a Circle whose Diameter is Unity. Tab. Tab. Tab. Tab. Tab. h'ight Area seg. h'ight Area seg. h'ght Area seg. h'ght Area Beg. h'gh Area eg..001.000042.063.020681.125.056663.187.101553 249.152680 2 119 4 1168 6 7326 8 2334.250 3546 3 219 5 1659 7 7991 9 3116 1 4412 4 337 6 2154 8 8658.190 3900 2 5280 5 470 7 2652 9 9327 1 4685 3 6149 6 618 8 3154.130 9999 2 5472 4 7019 7 779 9 3659 1.060672 83 6261 5 7890 8 951.070 4168 2 1348 4 7051 6 8762 9.001135 1 4680 3 2026 5 7842 7 9636.010 1329 2 5195 4 2707 6 8636 8.160510 1 1533 3 5714 5 3389 7 9430 9 1386 2 1746 4 6236 6 4074 8.110226.260 2263 3 1968 5 6761 7 4760 9 1024 1 3140 4 2199 6 7289 8 5449.200 1823 2 4019.5 2438 7 7821 9 6140 1 2624 2 4899 6 2685 8 8356.140 6833 2 3426 4 5780 7 2940 9 8894 1 7528 3 4230 6 6663 8 3202.080 9435 2 8225 4 5035 6 7546 9 3471 1 9979 3 8924 5 5842 7 8430.020 3748 2.030526 4 9625 6 6650 8 9315 1 4031 3 1076 5.070328 7 7460 9.170202 2 4322 4 1629 6 1033 8 8271.270 1089 3 4618 5 2180 7 1741 9 9083 1 1978 4 4921 6 2745 8 2450.210 9897 2 2867 5 5230 7 3307 9 3161 1.120712 3 3758 6 5546 8 3872.150 3874 2 1529 4 4649 7 5867 9 4441 1 4589 3 2347 5 5542 8 6194.090 5011 2 5306 4 3167 6 6435 9 6527 1 5585 3 6026 5 3988 7 7330.030 6865 2 6162 4 6747 6 4810 8 8225 1 7209 3 6741 5 7469 7 5634 9 9122 2 7558 4 7323 6 8194 8 6459.280.180019 3 7913 5 7909 7 8921 9 7285 1 09181 4 8273 6 8496 8 9649.220 8113 2 1817 5 8438 7 9087 9.080380 1 8942 3 2718 6 9008 8 9680.160 1112 2 9773 4 8619 7 9383 9.040276 1 1846 3.130605 5 45211 8 9763.100 0875 2 2582 4 1438 6 6425 9.010148 1 1476 3 3320 5 2272 7 6329.040 0537 2 2080 4 4059 6 3108 8 7234 1 0931 3 2687 5 4801 7 3945 9 8140 2 1330 4 3296 6 5544 8 4784.290 9047 8 1734 5 3908 7 6289 9 5624 1 9955 4 2142 6 5522 8 7036.230 6465 ' 2.190864 5 2554 7 5139 9 7785 1 7307 3 1775 6 2971 8 5759.170 8535 2 8150 4 2684 7 8392 9 6381 1 9287 3 8995 5 3596 8 8818.110 7005 2,.090041 4 9841 6 4509 9 4247 1 7632 3 0797 5.140688 7 5422.050 4681 2 8262 4 1554 6 1537 8 6337 1 5119 3 8894 5 2313 7 2387 9 7252i 2 5561 4 9528 6 3074 8 8238.300 8168 83 6007 5.050165 7 3836 9 4091 1 9086 4 6457 6 0804 8 4601.240 4944 2.200008 5 6911 7 1446 9 5366 1 6799 8 0922 6 7369 8 2090.180 6134 2. 6655 4 1841 7 7831 9 2736 1 6903 3 7512 6 2761 8 8296.120 8385 2 7674 4 8371 6 8683 9 8766 1 4036 8 8447 5 9230 7 4606i5.060 9239 2 4689 4 9221 6.150091 8 5527 1 9716 3 5345 6 9997 7 0953 6451 2.020196 4 6003 6.100774 8 1861.310 7376i -i — ~; I, - `:~ --- L Il - -- -- ----- -- -_ -~I 11 BLE VIL-Areat of Segments of a Circle whose Diameter is Uity. I I Tab Tab. h'ght Area seg. h'ght.811.208301.373 2 9227 4 8.210154 5 4 1082 6 I Tabh I I I h 6 7 E.32C 1 2 8 I I I II II 4 S 6 7 8 9.330 1 2 8 4 5 6 7 8 9.840 1 2 8 4 E 2011 2940 8871 4802 5733 6666 7599 8533 9468.220404 1344 2277 3215 4154 5093 6033 6974 7915 8858 9801.230745 1689 2634 8580 4526 6473 6421 7369 8318 9268.240218 1169 2121 3074 4026 4980 5934 6889 7845 8801 9757 5.250716 1673 2631 859C 5 661( ) A71 I 7 8 9.380 1 2 8 4 5 6 7 8 9.390 1 2 8 6 7 8 9.400 1 2 3 4 5 6 7 8 9.410 1 2 8 3 4 7.42( 1 I 4 )1 t i L.48( [ 4J If I I L Area seg..267078 8045 9013 9982.270951 1920 2890 8861 4832 5803 6775 7748 8721 9694.280668 1642 2617 8592 4568 5544 6521 7498 8476 9453.290432 1411 2390 3369 4349 5330 6311 7292, 8273 9255.300238 1220 2208 3187 4171 6155 6140 7125 8116 9095.310081 1068 2054 8041 402.9 5016 6004 1 6992 i 7981 8970 r 996C 3.320940 193 292E L 8913 1 4906 3 590( i689% h'ght.435 6 7 8 9.440 I 2 3 4 5 6 7 8 9.450 1 2 8 4 5 6 7 8 9.460 1 2 3 4 5 6 7 8 9.470 1 2 8 4 5 6 7 8 9.480 1 2 8 4 C 7 IC.49( 1 4 I Area seg..327882 8874 9866.330858 1850 2848 383& 4829 5822 6816 7810 8804 9798.340793 1787 2782 8777 4772 5768 6764 7759 8755 9752.350748 1745 2742 3739 4736 5732 6736 7727 8726 9723.360721 1716 2717 371t 4413 571M 671( 7706 8703 9707j.37070( 170t 2764 8703 4702 5702 670r 7701 8701 970(.38070( 1691 2691 3691 4691 5691, 6691 7691 5 8691 Tab. Area seg. To find the Tabular Versed.497.389699 Sine. 8.890699 9.391699 Rule. Divide.500.392699 the height of the given segment by the diameter of the circle of which it is a segment. The quotient will be the required tabularheight. And because the areas of circles are to one another as the squares of their diameters, multiply the tabular areas in this table by the square of the diameter of the- circle of which a segment is given. The product will be the area of the required segment. TExample. (See fig. II.) Let the chord A B.- 42, versed sine D C = 7. By Euclid III, prop. 3 and 35, the diameter cuts the chord of the are at right angles, consequently making the rectangle contained by the versed sine, and the remaining part of the diameter, equal to the square of half the chord..~.212 divided by 7 =V D = 63; therefore the diameter V C = 63 + 7 = 70, and 7 divided by 70 =,100 = tabular versed sine, whose corresponding area =,040876,which multiplied by the square of the diameter = 4900, gives the required area =200,2876. Example 2. Let the tabular versed sine =-,3466, which is not to be found in the table. Tab. versed sine 346, T area segment =,240218 Tab. versed sine 847, area segment =,241169 difference, 951 ) As10:951::6: 670,6, nearly 671,.' 240218 more 571,240789 = the re)I quired area of segment. I 7 8 6 L.850 I _:~ 4 I ( 7.86( I 61 3 I.A I r175! Rule. Take out the areas corresponding to the nearest tabular versed sine,-one greater and the other less than the given tabular versed sine; take the difference of the area segments; multiply this difference by the fourth decimal figure of the given tabular versed sine; cut off one figure to the right, and add the remainder to the lesser area segment. The sum will be the required area segment. -(See the last example.) Note. When the tabular versed sine is greater than,500, the segment is greater than a semicircle; in which case subtract it from 1, find the area seg. of the difference, which take from,785398. Multiply this difference by the square of the diameter. The product will be the required area. Example. Let tabular versed sine =,867, and let 60 = diameter of the circle. From 1,000 Area circle,785398 take tabular versed sine 0,867 difference,,133 Area segment,062026 Correct area of segment =,723372 Square of 60 (the diameter) = 3600 Required area of the segment = 2604,039200 TABLE VIII.-To Reduce Square Feet to Acres, and Vice Versa. Ac. Sq. feet. Acre. Sq. feet. Acres. Sq. feet. Acres. Sq. feet. Acres. Sq. feet. 1 43560 11 479160 21 914760 31 1350360 41 1785960 2 87120 12 522720 22 958320 32 1393920 42 1829520 3 130680 13 566280 23 1001880 3311437480 43 1873080 4 174240 14 609849 24 1045440 3411481040 44 1916640 5 217800 15 653400 25 1089000 35 1524600 45 1960200 6 261360 16 696960 26 1132560 361568160 46 2003760 7 304920 17 740520 27 1176120 37 1611720 47 2047320 8 348480 18 784080 28 1219680 38 1655280 482090880 9 492040 19 827640 29 1263240 3911698840 49 2134440 10 435600 20 871200 30 1306800 40 17424001 5012178000 0.1 4356.01 435.6 0.001 43.560.001 4.360.00001 0.44.2 8712.02 871.2.002 87.12.0002 8.71.00002 0.87.3 13068.03 1306.8.003 130.68.0003 13.07.00003 1.31.4 17424.04 1742.4.004 174.24.0004 17.42.00004 1.74.5 21780.05 2178.0.005 217.80.0005 21.78.00005 2.18.6 26136.06 2613.6.006 261.36.0006 26.14.00006 2.61.7 80492.07 3049.2.907 304.92.0007 30.49.00007 3.06.8 34848.08 3484.8.008 348.48.0008 34.85.00003 3.49 0.9 39204 0.09 3920.4 0.009 392.04 0.0009 39.20 0.00009 3.92 Ex=ample. Reduce 1283446 square feet to acres. From the first part, 1263240 = 29 20206 From the second part, 17424 =,4 2782 2613,6 =,06 168,4 130,68 =,003 87,72 34,85 =,0008 2,61 =,00006 -0,26 =,000006 nearly;.'. 29,46385 = Answer. This example, being one of the most difficult that can occur, is sufcient to show the application. i 7, I i I - -- I I V I 176 TABLE VIIVa.-Properties of Polygons whose Sides are= Unity. TAS '0; Name of polygon _ _ 8 4 6 6 7 E 9 L1 L2 Trigon. Tetragon. Pentagon. Hexagon. Heptagon. Octagon. Nonagon. Decagon. Undecagon. Dodecagon. Area of polygon. 0.4320127 1.0000000 1.7204774 2.5980762 3.6339124 4.8284271 6.1818242 7.6942088 9.3656404 11.1961524 Angle made Angle at the by two of centre. itssides. 0 f it 0 / 120,00,00 60,00,00 90,00,00 90,00,00 72,00,00 108,00,00 60,00,00 120,00,00 51,25,42P 128,34,17 45,00,00 135,00,00 40,00,00 140,00,00 36,00,00 144,00,00 32,00,16A 147 16,21h 30,00,00 '150,00,00 Sid, Radius of yga the inscrib'd ed i circle. whc 0.2886751 0.5000000 0 6881910 0.8660254 0.0382617 1.2071068 1 3737887 1.5388418 1.7028437 1.8660254 1. 1. 1. 1. 0. 0. 0. 0. 0. 0. aL V1I1b1 c of a po a inscribe,n a circe we diane er = 1 732051 414214 175571 000000 867768 765367 684040 618034 563366 517i638 1__1_ _ I, TABLE IX-Properties of the Five Regular Bodies. rLn 4 6 8 10 22 Area of regular polygon c-Tame of polygon whose side is =__1. Tetrwdron. 1.732051 Ilexaidron. 6.000000 Octuedron. 3.464102 Dodecasdron. 20.645729 Icosaidron. 8.660254 Solidity of regular polygon whose side is = 1. 0.117851 1.000000 0.471405 7.663119 I2.181695 Side of a poi. Ins-in sphere whose diameter - 1. 0.117851 1.000000 0.471405 7.663119 i 2.181695 Side of poly, circ'mscrib'g sphere whose dism. = 1. 0.816497 0.577350 0.707107 0.525731 0.356822 Side of a pol == a sphere whose diam. eter = 1. 2.44948 1.00000 1.22474 0.66158 0.44903 TABLE X.-To Reduce Square Links to Acres, Roods and Perches.?erch. 160 120 80 40 39 38 37 36 35 34 33 32 31 30 Sq. links. 100000 75000 50000 25000 24375 23750 23125 22500 21875 21250 20625 20000 19375 18760 Per. 29 28 27 26 25 24 23 22 21 20 19 18 17 16 Sq. links, 18125 17500 16875 16250 15625 15000 14375 13750 13125 12500 11875 11250 10625 10000 Per. Sq. links Perches Sq. links. Perches. 15 9375 1.0 625 0.05 14 8750 0.1 62.5 0.06 13 8125 0.2 125.0 0.07 12 7500 0.3 187.5 0.08 11 6875 0.4 250.0 0.09 10 6250 0.5 312.5 0.001 9 5625 0.6 375.0 0.002 8 5000 0.7 437.5 0.003 7 4375 0.8 500.0 0.004 6 3750 0.9 562.5 0.005 6 3125 0.01 6.25 0.006 4 2500 0.02 12.50 0.007 3 1875 0.03 18.75 0.008 2 1250 0.04 25.00 0.009 Sq. links. 31.25 37.50 43.75 50.00 66.25 0.63 1.25 1.88 2.50 3.13 3.75 4.37 5.00 5.63 Example 1. Rednce 47032854 links to Example 2. Reduce 1758 square links acres, roods and perches. to perches. 47,63285 A. R. This being less than 25000, shows that Cut off always 47,50000 47, 2 - 21,256 there are no roods in the answer. five places to -- Answer. the right. 18285 1753 square links. 21 perches = 18125 2 perches = 1260 160 603 0,2 perch = 125,8 perch = 500 0,05 perch 35 8 81,25 005 8,15 8,75 Answer, 2,805 *erches. 0,oO per* 8,75 I I. I i! 41 L::: o:: 4,? -: i?:)??i ii:! 3!i! io??:!ii: i?! fz 4i:? 0:4:?!? o: i:O::? iiii?~ i:i~: i~j~!:!ni4?: TA:BLE XL — owing te Reduion, on Eac Chain to Reduce Bypothenusal to Base or Horizontal AMeau Angle of Red. Angle of Red. Angle of Red. Angle of Red. Inolinat'n. inlk. incllnat'n. in Iks. inclinat'n. in lks. inclinat'n. in Iks. - o 0 // 2 340 8 27 29 4 26 20 5 07 35 6 4355 61645 64700 7 15 07 7 30 38 80634 8 8028 8 53 07 91455 9 8555 9 56 11 10 15 47 10 34 48 10 53 16 11 11 12 11 2842 11 45 6 12 02 26 12 18 44 12 34 41 12 50 20 13 05 88 13 20 00 13 35 37 13 49 66 14 03 12 14 18 13 14 32 02 14 45 37 14 59 01 15 12 14 15 25 14 15 38 05 15 50 45 16 03 05 16 15 06 16 27 48 16 39 52 16 51 48 17 03 35 17 15 14 17 26 45 17 35 10 17 49 27 18 00 38 18 11 42 o0.1 2C 3C 4C 5C0 6C 70 80 90 1.00 10 20 30 40 50 60 70 80 90 2.00 10 20 30 40 50 60 70 80 90 3.00 10 20 30 40 60 60 70 80 90 4.00 10 20 30 40 50 60 70 80 90 5.00 -. o / / 19 26 19 19 86 34 19 46 47 19 56 55 200656 20 16 54 20 26 46 20 36 35 20 46 19 20 556 58 21 05 331 '21 15 04 '21 24 32 21 33 54 21 48 14 21 52 30 22 01 41 22 10 50 22 19 54 22 28 55 22 37 63 22 46 47 22 65 38 53 04 26 23 13 12 23 21 52 23 30 31 23 39 07 23 47 40 23 65 59 24 04 36 24 13 00 24 21 22 24 29 40 24 37 10 24 46 10 24 54 20 25 02 30 25 10 40 256 1840 25 2640 25 34 40 25 42 40 25 0308 25 8 20 26 06 10 26 14 00 26 21 50 26 29 30 26 37 10 I - I - 6.70 80 90 6.00 10 2C 80 40 50 60 70 80 90 7.00 10 20 30 40 50 60 70 80 90 8.00 10 20 30 40 50 60 70 80 90 9.00 10 20 30 40 50 60 70 80 90 10.00 10 20 30 40 50 60 70 80 90 11.00 10 20 t - - 27 80 05 27 7 3C 7 44 50 27 52 20 27 69 40 28 06 56 28 14 12 28 21 27 28 28 41 28 36 52 28 43 02 28 50 11 28 57 18 29 04 23 29 11 27 29 18 29 29 25 30 29 32 29 29 39 27 29 46 20 29 53 18 30 30 10 30 07 02 30 13 52 30 20 42 30 27 29 30 84 15 30 41 00 30 47 44 30 54 26 31 01 07 31 07 47 31 14 25 31 21 02 31 27 38 31 34 12 31 40 46 31 47 18 31 53 49 32 00 19 32 06 47 32 13 15 32 19 41 32 26 06 32 32 30 32 38 53 32 45 15 32 51 36 32 57 55 83 04 14 33 10 81 83 16 47 33 23 03 83 29 17 83 85 32 83 41 48! - I. 11.30 40 50 60 70 80 90 12.00 10 20 30 40 50 60 70 80 90 13.00 10 20 30 40 50 60 70 80 90 14.00 10 20 80 40 50 60 70 80 90 15.00 10 20 30 40 50 60 70 80 90 16.00 10 20 80 40 50 60 70 80 0 // 33 47 54 33 63 04 34 00 14 34 06 26 34 12 30 34 18 36 34 24 41 34 30 46 34 36 50 34 42 53 34 48 54 34 54 55 35 00 55 35 06 54 35 12 52 35 18 49 35 24 45 35 30 41 85 86 36 6 42 30 85 48 22 35 4 15 86 00 06 6 05 566 46 11 46 36 17 86 36 28 23 36 29 10 86 34 57 36 40 43 36 46 27 36 2 12 36 57 55 37 03 37 37 09 20 37 15 01 37.20 41 37 26 21 37 32 00 37 37 38 37 43 16 37 48 52. 37 54 28 38 00 04 38 06 38 38 11 12 38 16 46 38 22 18 38 27 60 38 33 21 I 'I - - L16.9C 17.0C 1C 2C 80 46 60 6C 7( 80 90 18.00 10 20 30 40 50 60 70 80 90 19.00 10 20 30 40 50 60 70 80 90 20.00 10 20 80 40 50 60 70 80 60 21.00 '10 20 80 An I ) ) )1 ) I oI, Iw aB ~ 0:~ '? t! l II " Scr i Cg o a Ii I O k. G bo-. on ~c Iss 4 NiI 3r~ '1.1 aa i u.. I 182289 102644 18 88 80 2026 52 184418 802700 18 64 5 40127 07 19 05 5017 16 A: 1'1 \2722 00 'S '\:1 '\I d~t;;fS'Vff; 50 80 00 40 1C 4(1 I I 3 3 3 3 3 3 I - - - - -~ ~ v -! '- -7 177 I4is 2d1.-To.Keauce ereal Time to Mean Solar Time. I Minutes. sid.; t. Mean time. m. m. S. 1 0 59.84 2 1 59.67 8 2 59561 4 8 59.35 fir 469.18 6 5 59.02 7 65 8.85 8 7 58.69 9 8 58.53 10 9 58.36 11 10 58.20 12 11 58.03 14 12 57.87 14 18567.71 15 14 57.54 1Q 15 57.38 17 16 57.22 18 17 57.05 19 18 &6.89 20 19566.72 21 20 56.56 22 21 515.40 23 22 56.23 24 23 59.07 25 24 56.90 26 25 55.74 27 26 55.58 28 27 55.41 29 28 65.25 30 29 55.69 81 30 54.92 82 31 54. 76 88 32 54.59.84 33 54.48 85 34 54.26 86 85 54.10,37 86 63.94 88 37 53.78 89 88 53.61 40 89 53.44 41 40 53.28 42 41 53.12 48 42 62596 44 43 52.79 45 44562.63 46 45 95.46 47 4692.30 48 47 52.14 49 48-51.97 50 49 51.81 51 50 51.65 rs a, I1A Q Seconds. sid. t.. mean t... 1 0.997 2 1.995 8 2.992 4 3 989 5 4.986 6 5.984 7 6.98 8 7.98 9 8.98 10 9.97 11 10.97 12 11.97 13 12.97 14 13.96 156 14.96 16 15.96 17 19.95 18 17.95 19 18.95 20 19.9.5 21 20.94 22 21.94 23 22.94 24 23.93 25 24.93 26 25.93 27 26.93 28 2-7.9.2 29 28.92 80 29.92 31 30.92 32 31.91 33 32.91 34 33.91 35 34.90 36 35.90 37 36.90 88 37.90 39 38.89 40 39.89 41 40.89 42 41.89 43 42.88 44 43.88 45 44 8.8 46 45.87 47 46.87 48 37.87 49 48.87 50 49.86 51 50.86 52 51.86 53 52.86 54 53.85 65 54.85 56 55.-8 57 66.84 68, 58.84 59 58.84 I I I I I hours mean time. 1 2 3 4 S 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hours of sidereal time. h.m. S. 1 0 9.86 2 0 19.71 3 0 29.57 4 0 39.43 5 0 49.28 6 0 59.14 7 1 9.00 8 1 18.85 9 1 28.71 10 1 38.56 11 1 48.42 12 1 58.28 13 2.8.13 14 2 17.99 15 2 87.85 16 2 37.70 17 2 47.56 18 2 57.42 19 3 7.27 20 3 17.13 21 2.6.99 22 3 38.84 23 3 46 70 24 8 56.56 I i I TABLE XIIH —To Reduce Mean Solar Time to Sidereal Time. Min. mean time. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 66 57 58 59 eq'ival'nts in sidereal time. m. S. 1 0.16 2 0.33 3 0.49 4 0.66 5 0.82 6 0.99 7 1.15 8 1.31 9 1.48 10 1.64 11 1.81 12 1.97 13 2.14 14 2.30 15 2.46 16 2.63 172.719 1,8 2.96 19 3.12 20 3.29 21 3.45 22 3.61 23 3.78 24 3.94 25 4.11 26 4.27 27 4.44 28 4 60 29 4.76 30 4.93 31 5.09 32 5.26 33 5.42 34 5.59 35 5.75 36 5.91 37 6.08 38 6.24 39 6.41 40 6.57 41 6.74 42 6.90 43 7.06 44 7.23 45 7.a9 48 7.89 49 8.05 50.8.21 51 8.38 52 8.54 53 8.71 54 8.87 55.9.04 56 9.20 57 9.36 58 9.&3 59 9.69 See. mean time. 1 2 3 4 S 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 83 34 85 36 87 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 63 64 55 66 67 58 TABLE XII. Continued. sours Hours of afid. time: mean time. h. h m. 1 0 59 50.17 2 1 59 40.34 3 2 59 30.51 4 3 59 20.68 5 4 59 10.85 6 559 1.02.7 6 58 51.19 8 7 5.8 41.36 9 8 58 31.53 10 9 5,821.70 11 10 58 11.88 12 11 58 2.05 13 12 57 52.22 14 13 5,7 42.39 15 14 57 32.56 16 15 57 22.73 17 16 5,7 12.,90 18 17 57 3.07 19 18 56 53.24 20 19 56 48.41 21 20 56 83.58 22 21966 23.75 28 22 56 13.92) 24 23 56 4.09 S. 1.00 2.01 3.01 4.01 5.01 6.02 7.02 8.02 9.02 10.03 11.03 12.03 13.04 14.04 15.04 16.04 17.05 18.05 19.05 20.05 21.06 63.06 24.07 25.07 26.07 27.07 28.08 29.08 30.08 31.08 32.09 33.09 34.09 35.10 36.10 37.10 k38.10 39.11 40.11 41.11 42.12 43.12 44.12 4G.12 46.13 47.13 48.13 49.13 50.14 51.14 52.14 53.15 64.15 55.15 56.15 57.16 58.16 5l9.16 i As of sconds agree to two places of decimals for mean and sidereal. 178 i i I TABLE XIV.-7To R educe Sidereal Time to Longitude.or Degrees. 11' — e II Hour -T 2 8 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 1. I Degrees. 15 80 45 60 4 75 90 105 120 135 150 165 180 195 210 225 240 255 27 0 285 i 300 315 330 345 360 i Time. Min. Sec. 2 3 4 S 6 7 8 9 10 11!12 13 14 15 16 17 118 '9 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 38 49 50 51 52 53 54 55 56 57 58 59 Arc. Deg. Min Min. Sec 0 15 0 30 0 45 1 00 1 15 1 30 1 45 2 00 2 15 2 30 2 45 3 00 3 15 3 30 3 45 4 00 4 15 4 30 4 45 5 00 5 15 5 30 5645 6 00 6 15 6- 30 6 45 7 00 7 15 7 30 7 45 8 00 8 15 8 30 8 45 9 00 9 15 9 30 9 45 10 00 10 15 10 30 10 45 11 00 11 15 11 30 11 45 12~ 00 12 15 12 30 12 45 13 00 13 15 13 30 13 45 14 00 14 15 14 30 14 45 115 00 I I I TABLE XV. To Reduce Longitude or Degrees to Sid. Time. Arc. Time. Deg. Hr. Min. Min. Min. Sec. Sec. Sec. Tb. 1 04 20 8 3 0 12 4 0 16 5 0 20 6 0 24 7 0 28 8 0 32 9 0 36 10 0 40 11 0 44 12 0 48 13 0562 14 0 56 15 1 00 16 1 04 17 1 08 13 1 12 19 1 16 20 1 20 21 1 24 22 1 28 23 1 32 24 1 36 25 1 40 26 1 44 27 1 48 28 1 52 29 1 56 30 2 00 31 2 04 32 2 08 33 2 12 34 2 16 35 2 20 36 2 24 37 2 28 o8 2 32 39 2 36 40 2 40 41 2 44 42 2 48 43 2562 44 2 56 45 3 00 46 3 04 47 3 08 48 3 12 49 3 16 50 3 20 21 3 24 52 8 28 53 3832 54 3 36 55 2 40 566 3 44 57 3 48 58 3562 59 35'66 60 4 00 Height Dip in are. in feet. 1 058 2 122 3 140 4 155 5 209 6 2~2. 7 233 -8 244 9 254 10 303 11 312 -12 321 13 329 14 33-7 15 345 16 353 17 401 18 408 19 415 20 422 21 428 22 434 23 440 24 446 25 452 26 458 28 510 30 521 32 631 34 540 36 550, 38 600 40 610 42 619r 44 628 46 637 48 645 50 653 55 711 60 72,9 65 7 47 70 805 75 823 80 8 44 85 857 90 914 95 930 100 946 105 10 01 110 10 16 115 10 30 120 10 43 125 10 566 130 11 09 135 11 22. 140 11 3& 145 11 47 150 11 59 155 12 11 160 12 28 I TABLE 3 Showing the Dip ei ofthe, Horizon, 4 tance at Sea in A ponding to gizen r I I.VI Depression,nd the Die'Wes, CJorresHeights. Dist. seen at sea in miles. 1.32 1.87 2.29, 2.65 2.96, 3.24 3.50 3.74 3..97 4.18 4.39 4.58 4. 77 4.95 5.12 5.29 5.45 5.61 5.77 5.92 6.~06 6.21 6.34 6.48 6.61 6;75 7.00, 7.25 7.48 7.71 7.94 8.16 8.37 8.57 8.78 8.97 9.17 9.35 9.81 10.25 10.6 7 11.07 11.46 11.83 12.20 12.65 12.89 13.23 13.56 13.88 14.19 I 179 1, " % -, -4 - i: i - - - -,. - - q, - - -. I - - - - - - r TABLE XVII.-Correction of the Apparent Attitude for Refractirn (Subtractive). _____________ Ap ea or. In Ap Mean cor.ApMenor ApMancr altitude. refract. 1 uni.attd ref. 1 un. altit'de ref. 1 un. tt'e rf 1Un 0 /// 1/ 0 f/ /10 /,1/0 1/ / 4 00 11 47 19.9 12 00 4 28 6.9 20 00 2 89 4.1 40 00 1 101. 10 26 19.2 10 25 6.8 20 86 4.0 41 00 7 1.7 20 6 18.5 20 21 6.8 40 84 8.9 42 00 5 1.7 80 10 46 18.0 80 18 6.7 21 00 81 3.9 4800 8 1.6 40 28 17.5 40 14 6.6 20 29 3.8 44 00 0 1.5 50 11 16.9 50 11 6.4 40 26 8.7 46 00 0 58 1.6 5 00 9 54 16.4 13 00 8 6.4 22 00 2483.7 46 00 5661.4 10 88 16.0 10 6 6.4 20 21 8.7 7 00 54 1.4 20 28 15.6 20 2 6.2 40 19 3.5 48 00 53 1.4 80 9 15.1 8085 9 6.2 28 00 17 8.5 4900 51 1.3 40 8565 14.7 40 5666.0.20 1583.5 5000 49 12 50 421. 0 58 6.0 40 18 8.5 51 00 47 1. 6 00 80 13.914 00 50 6.0 24 00 1183.852 00 46 1.1 10 18 18.5 10 47 5.9 20 09 8.3 58 00 44 1.1 20 7 18.8 20 45 5.8 40 07 8.8 54 00 42 1.0 30 7 56 12.9 80 4256.7 25 00 0583.8 5500 41 1.0 40 45 12.6 40 40 5.6 20 03 2.2 56 00 839 1.0 60 86 12.8 50 87 5.6 40 01 8.1 57 00 88 0.9 7 00 25 12.0 15 00 8556.5 26 00 15983.1 58 00 86.9 10 16 11.8 10 82 5.4 20 58 8.0 59 00 85.9 20 7 11.6 20 80 5.4 40 56 2.9 60 00 84.8 80 6 69 11.8 80 2856.8 27 90 54 2.9 6100 32.8 40 50 11.0 40 26 5.2 20 63 2.9 62 00 31.8 50 42 10.8 50 28 5.2 40 51 2.9 68 00 80.8 8 00.85 10.6 16 00 21 5.2 28 00 49 2.9 6400 28.7 10 27 10.4 10 19 6.2 20 48 2.8 66 00 27.6 20 20 10.2 20 17 S.1 40 46 2.7 66 00 26.6 80 18 10.0 80 1S 5.0 29 00 46 2.7 67 00 26.6 40 7 9.8 40 186.0 80 44 2.7 68 00 24.6 50 0 9.6 50 11 4.9 40 42 2.7 69 00 22.6 9 00 5 44 9.4 17 00 9 4.9 80 00 41 2.7 70 00 21.5 10 48 9.2 10 7 4.8 20 89 2.6 71 00 20.5 20 42 9.1 20 6 4.8 40 3882.6 72 00 19.4 80 86 8.9 80 8 4.7 31 00 87 2.5 78 00 18.4 40 81 8.7 50 1 4.7 20 86 2.6 74 00 17.4 50 26 8.4 50 0 4.7 40 84 2.4 75 00 16.4 10 00 20 8.6 18 00 2 68 4.6 32 00 88 2.8 76 00 $15.4 10 15 8.8 10 66 4.6 20 32 2.8 77 00 a13.8 20 10 8.1 20 6564.6 40 81 2.2 78 00 12.8 80 6 8.0 80 58 4.6 88 00 80 2.2 79 00 11.3 40 1 8.0 40 61 4.4 20 28 2.2 80 00 10.3~ 50 4 56 7.8 50 60 4.8 40 27 2.1 91 00 9.2' 11 00 62 7.7 19 00 48 4.8 34 00 26 2.1 82 00 8.2 10 48 7.6 10 47 4.8 36 00 28 2.1 88 00 7.1 20 44 7.6 20 46 4.2 36 00 20 2.1 8400 6.1 80 40 7.4 80 44 4.2 ~W00 17 2.0 800 4.0 40 86 7.8 40 42 4.2 38 00 16 1.9 88 00 2.0 60 82 7.1 50 41 4.1 39 001 12 1'.8 90 001 0.0 I I i I 11 I r Td3IZ GxYIIL TABLE X1X.-Parallaz Atit of t Iun's P XY PLANETS' IHoRIZONTrm PABALLAX. (From fa t. 4m..) I < sule8 Parallax in.; - Altitude. Ap. 1" 3" 7" " 113" 17 19" |21" " 2 27 2 0 Alt. Sun's alt. Parallax in degreeS. in seconds. 10 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 30: O _ 15 1 '3 5 7 9 11 13 115 (17 19 21 23 25 26 28:0 29 a 10 9 20 13 5 79 10 2 14 16 18 20 2224 27 2 20 8 25 135610 12 14 15 1, 19 2 12324 26 27 30 8 30134 68 10 11 13 15 16 18 20a 1222 25 2 40 7 33 112468 911 13 14116118 19 121123 124 125 50 6 36 112 467 1 9 12 14 15 17 19 120 122 123 263 65 5 39a1p124e 15 7 910 112 13 15 16 18 1912 12324 60 4 42 112 14 5 17 81l 111311411617 1191202223 65 4 145 112m4566 8 911 1213 5 16 9 1819 212 7e0 8 th 48 123561 7 910 11 13 4 15 17 1819 20, 75 2 516 121346 7 8 911112 13 14 16117 18 19 80 2 54123185 6 8 91011 112 14 15 116 17 18 85 1 57112131315 6 7 8 911011112114115 1617 90 0 6002131315 6 7 8 910111 12 13 14115l4 6201234 5 6 7 810101112131414 Parallax istobe 64011234 5 6 7 8 9 10o 11 12113 13 added to apparent 6601 234 4 5 6 7 8 9 9f1111 12112 altitude, or it may 6801233 4 5 5 6 7 8 9 91 01111 be added afterthe 7001223 4 575 6 7 7 8 9 911010 corrections,fordip 7201222 3 45 6 6678 88 9 9 and refraction are 7401122 33 34 45 5 6 6 7 7 7 taken fromtheap. 76011 22 3 3 4 4 4 4 5 6 6 6 alt., or it may be 78g0 1111 2 3 3 3 3 3 4 4 5 taken fromthesum 81 00111 2 2 2 2 2 2 2 3 3 3 ofthedipandref., 8410011 1 11 22 2 2 2 3 3 3 3 and the difference 8700000 1 1 1 1 1 1 1 11 22 taken fromap. alt. 900 _0000 o o o o 0: 00l TABLE XX.-Reduction of the Time of the Moon's Passage over the Meridian at Greenwich to that over any other Meridian. DAILY VARIATION OF THR MOON'S MERIDIAN PA8SAGE. In 40' 42' 44' 46' 48' 5|0 52' 64' 66' 58' 60' 62' 64 66 lo deg. 1 1 1 7 7l 1 1 10 2 12 2 3 3 3 3 3 3 4 4 0 3 3 44 4 4 4 4 4 5 5 5 6 40 4 4 65 56 5l 6 6 666 6 7 7 7 50 5 6 6 6 6 7 7 7 7 8 8a 8 9 9 60 6 7 7 8 8 8 9 1 91010101111i D 70 8 8 9 9 9 s o 10 11 11 12 12 12 13 0 80 9 9 10 10 11 11 12 12 12 13 13 14 14 15 0 90 10 10 11 11 12 12 13 13 14 14 15 15 16 16d 100 11 12 12 13 13 14 14 16 16 16 17 17 181 - I 110 12 13 13 14 15 15 16 16 17 18 18 19 20 i 20 120 1314 15151617 17 18 19 19 20 21 21 22;I0 14- 15 6 1 l 1 17 18 19 19 20 21 22 22 23 24 140 16 16 17 18 19 19 20 21 22 23 23 24 26 26 150 17 17 18 19 20 21 22 22 23 24 25 26 27 2 160 18 19 20 20 21 22 23 24 265 26 27 28 28 2 16. 170 19 20 21 22 23 24 25 25 26 27 28 29 30;180 20 21 22 23 24 26 26 27 28 29 30 31 82 8 No te. In this table, longitude means the moon's longitude, o: tix R:in ar, from her meridian passage. The corrections are in..;~~ -;-18 -- 181 TABLE XXI.-Best Timefor Obtaining Apparent Time. ' 1....Declination of the same name with the Latitude.:at. 20 40 6 8~- 100 120~ 140 16~ 180 200 220 1246. m.h. m h'. h. mm h.. m. h. m h. ni. h. m. h. m.. m h. m h. m 0 6 06 0 6 0 6 06 06 06 6 06 0 6 06 06 0 1 4 05 2 5 225 31 5 375 415 44 5 465 48 5 495 505 51 2 004 0 4 425 25 14 5 225 28 5 325 355 38 5 405 42 8 3 13 2 464 04 32 4 51 5 35 115 18 5 23 5 27 5 305 33 44 40 0 3 13 4 4-27 4 43 4 555 4 5 10 5 16 5 205 24 5 4 262 282 15 3 26 4 14 23 4 384 494 58 5 45 105 15 6 4 42 3 130 0 2 46 3 344 1 4 204 344 45 4 53 5 05 5 7 4 54 3 41 2 5 1 568 3 3 394 24 194 31 4 41 49 4 56 8 5 24 1 2 4600 2 293 143 43 4 34 1714 29 4 394 46 95 9 4 15 3 14 1 501 44 2 47 3 22 3 46 4 3 4 174 284 37 10 5 14 4 27 3 4 2 29 0 02 163 03 28 3 49 4 44 16 4 27 11 5 19 4 363 9 2551 40 1352 35 8 93 333 51 4 5416 12 5 22 4 43 4 1 3 14 2 16 0 02 6 2 493 173 373 53 4 6 13 5254 494 123 30 2 41 1 321 292 26 2 593 23 3 41 3 55 14 5 28 4 55 4 20 3 43 3 02 60 01 58 2 40 3 73 283 44 15 5 30 4 59 4 28 3 53 3 15 2 30 1 26 1 23 2 18 2 503 143 32 16 5 32 5 4 4 344 3 3 282 491 58 0 0 1 52 2 32 2 593 20 17 5 345 7 4 40 4 11 3 39 3 4 2 21 1 211 1 9 2 11 2 433 7 18 5 35 5 10 4 45 4 17 3 49 3 17 2 40 1 52 0 0 1 472 262 53 19 5 37 5 13 4 49 4 24 3 57 3 282 54 2 14 1 17 1 162 6 2 37 I.................. I i i 20 21 22 23 24 25 26 27 28 29 30 31 22 33 34 35 36 37 38 5 38 5 39 5 40 5 41 5 42 5 43 5 44 5 44 5 45 5 46 5 46 5 47 5 47 5 48 5 48 5 49 6 49 5 49 5 50 5 50 5 50 56 1 5 51 5 51 6 52 5 16 5 18 5 20 5 22 5 24 5 26 5 27 5 28 5 30 5 31 5 32 5 33 5 34 5 35 5 36 5 37 5 38 5 39 2 39 5 40 5 41 5 42 5 42 5 43 5 43 0 I 4 5, 4 54 54 5 5 i 3 6 3 3 5 5 8 5 10 5 12 5 14 5 16 5 18 5 20 5 21 5 28 5 24 5 25 5 27 5 28 5 29 5 30 5 31 5 32 5 33 5 34 4 29 4 34 4 39 4 43 446 4 50 4 53 4 56 4 59 5 1 5 4 5 6 5 8 5 10 5 12 5 14 5 15 5 17 5 19 5 20 5 21 5 23 5 24 5 25 5 27 i 4 41 41 4 2 4 2 43 4 3( 4 3. 4 41 4 44 4 41 4 5' 4 5, 4 5' 4 54 5 ' 4 1 6 2 7 1 5 9 3 5 2 1 7 i 3 0 3 37 3 46 3 53 4 0 4 6 4 12 4 17 4 21 4 26 4 30 4 34 4 37 4 40 4 44 4 47 4 49 4 52 4 54 4 57 4 59 3 7 3 18 3 28 3 36 3 44 3 51 3 57 4 3 4 8 4 13 4 18 4 22 4 26 4 30 4 33 4 37 4 40 4 43 4 46 4 48 _ m 2 32 2 47 2 59 3 I0 3 20 3 28 3 36 3 43 3 49 3 55 4 1 4 6 4 11 4 15 4 19 4 23 4 27 4 31 4 34 4 37 II I I I 1 47 2 9 2 26 2 40 2 53 3 3 3 13 3 22 3 29 3 36 3 43 3 49 3 55 4 0 4 5 4 9 4 14 4 18 4 22 4 25 i 0 0 1 14 1 43 2 4 2 21 2 35 2 47 3 0 3 8 3 16 3 24 3 31 3 38 3 44 3 49 4 55 4 0 4 4 4 9 4 13 1 43 1 13 0 0 111 1 39 2 0 2 16 2 30 2 42 2 53 3 2 3 11 3 19 3 26 3 33 3 39 3 45 3 50 3 55 4 0 i 2 21 2 2 1 39 1 10 0 0 1 9 1 36 1 56 2 13 2 26 2,38 2 49 2 58 3 7 3 15 3 22 3 29 3 35 3 41 3 47 r r IL r f r I 5 5 i ) ( 1C - 40 41 44 45 46 47:48 5 62 Ig 52 52 53 35 53 I. 5 44 5 45 5 45 5 46 5 46 5 35 5 36 5 37 5 38 5 38 5 39 I5 5 5 i5 l5 11 j 2E, 26 i 3C 31 32 53 54 5 47 5 47 5 48 5 S >!.5 5 3 r 5 40 5 33 5 41 5 35 6 42 5 37 5 44 5 38 6 45 5 40 5 46 5 41 5 47 5 43 5 48 5 44 5 49 5 46 5 50 5 47 5 61 5 48!; I I 5 26 5 28 5 31 5 33 5 35 5 37 5 38 5 40 5 42 5 44 6 45 3 I I 5 11 5 13 5 15 5 16 5 18 5 19 5 21 5 22 5 23 5 25 I 5 19 5 22 5 24 5 27 5 29 5 32 5 34 5 36 5 38 5 40 5 42 5 1 5 3 5 5 5 7 5 '9 5 1i 5 13 5 14 5 16 5 17.I 4 51 4 54 4 56 4 58 5- 0 5 A 5 4 5 6 5 8 5 10 5 12 5 15 5 18 5 21 5 24 5 27 5 30 6 32 5 35 5 37 5 39 I - i 5 4 5 8 i 12 5 15 5 19 5 22 5 25 5 28 5 31 5 33 6 36 4 4C 4 43 4 46 4 48 4 51 4 53 4 56 4 58 5 0 5 2 ) I! 4 29 4 32 4 35 4 38 4 41 4 44 4 47 4 49 4 52 4 54 4 5 5 67 M 5 5 9 5 13 5 17 5 20 6 24 5 27 5 80 5 30 5 83 I -- 4 4c 4 54 4 59 5 3 5 7 5 11 5 15 5 19 5 23 5 26 5 30 4 17 4 21 4 25 4 28 4 31 4 35 4 38 4 41 4 43 4 46 -I I; ~1 I I 4 4 1, 4 18 4 21 4 21 4 2E 4 31 4 38 4 38 5 3 I ~ i l 31 3 3 4 41 4. 46 4 52 4 67 5 2 5' 6 5 10 5 15 5 19 5 22 5 26 I I I I I i I 2 52 257 41 4 6 410 414 418 422 425 4 29 4 32 4 39 4 45 4 50 655 5 0 5 5 10 5 14 519 5 23,i:: __; --- —-- ~ ~ ~ ~ e. 182 —:-~" " "''....Declination of the same name with the Latitude. Lat. - o o -' ---- '22-~~ Lat. 20 40 60 1O 1oO 120 140 1G6 180 200 220 24~ - O-" --- ~O. "- O -0 o 0 '""0 o O O O O: 0 0 0 0 0 0 0 0? 0 0 07 0 0 0 0 0 0 0 0 0 0 1 30 01429 937 712 546 449 4 8 338 314 255 240 228 2 90 030 1193014311136 940 818 716 629 551 521 455 8 4149483730 322 51732143512301057 945 848 8 2 724 4 30 190 0415230 5234119361645144013 31146 1044 953 6 23 3653 10156 30 38 46 30 8244721 7182616231446 13271222 6 19 30 41 5290 0484137 1 30 1] 25 3622 17 19 46 17 48 16 12 1453 7 16 38 34 55 59 461 7 44 34 35 53 3015 2614 2314 20 5218 5917 26 8 143130 5484190 0531642 1 35 7130202646 24 1 214920 1 9 12 53 26 29 41 56 62 50 64 16 48 48 4017 34 35 30 25 27 13 24 41 22 37 10 11 361 23 41 37 1l 53 6 90 0 56 38 45 5239 3 34 1130 3127 3725 16 11 10 32212733 1346 50 65 3166 36 52 443 4838 8 33 5530 3727 59 12 9401936301142 1563890 05915485842173726334330 4 13 85618 427413813503267336825A5442464341 836543335 14 8181645253635 74552591590 06122513245 140143630 15 7 45 15 38 23 49 32 32 42 8 53 27 69 11 69 53 56 93 49 11 43 42 39 31 16 71614402217 302039 34858612290 063 7 53 42 47 22 42 4 17 6 51 13 48 20 57 28 26 36 26 45 20 55 50 70 31 71 758 44 5118 45 57 18 629123 319 46 26 46 34114217 5132 63 790 0643755354927 19 6 91222184425 18 3214394148 057 51 71 3972 9 60 21 53 1 20 55111 46174824 13031 37 2645 1534264 3790 065 555714 21 5 3511 13 16 58 22 51 28 59 35 28 42 28 50 17 59 34 72 38 73 4 61 47 22 6 2110 4416 12 21 4927 333 4340 1447 2255 3.65 55 90 067 23 5 7 1017 15 31 20 52 26 23 32 9 38 15 44 52 5216 61 5 73 29 73 53 24 455 953145320 125163045363042404927571467 5 90 0 25 444 9301419191424 16292834554043465954 162257416 26 4'34 9 913 4818 3123 20 2819:3 30 3858 4449 5117 58 43 68 6 27 4 25 8 50 13 19 17 51 22 29 2715 32 12 37 23 42 54 48 53 5536 63 37 28 416 8 33 12 521715 2142 2617 31 1355741104646525660 8 29 4 8 8 16 12 27 16 41 20 59 25 24 29 56 3439 3936 4452 50 36 57 2 30 4 0 8 112 41610201924342856332738104310 4831 5426 31 353 747114315411942234928 1322136524137146405210 32 347 7341123151419 823 62710312135404012445950 9 33 340 72211 4144818362226262230243434385443274818 34 335 7101046142518 52150253829323333374242 44639 35 329 659103014 3173721152457284332 3636340474511 36 324 6 49 10 16 13 42 17 11 2043 2418 27 58 31 43 35 35 39 36 4346 37 319 63910 0132216462013234227163054343838304231 38 315 681 94713 41623194423 8263630 8334537294120 39 3 11 622 934124716 1191822362559 2925325536324016 40 3 7 614 922 12 301540185222 72524 284432 9 35393915 41 3 3 6 6 9101215152118292138245128 63125344913818 42 259 559 85912 015 218 6211224202730304434 337 2 43 256 552 84911471445174520472350265730 6 3319 36 86 44 253 546 8391133142917252023232332625293032383549 45 250 540 8301121141317. 620 022 57 255528 56 31 5935 6 46 247 534 821 11 9 13 5S 16 4819 39 22 32 25 2628 2331 21534 26 47 244 528 813105813 4416 31191922 825 027 53304933 47 48 242 5 23 8 5104813 31161519 02146 24 342724 30163 12 49 2 39 418 7 58 10 3813 18 15 59 18 42 21 25 2410 26 57 29 46 32 86 50 237 513 7511028113 615 45182521 5 2247 26 312917 32 4 52 232 5 7371010 124415181753202823 5254328 2331: 54 228 457 725 9541224145417241955222725 127353801 56 225 450 715 94012 514311658192521 5324222652292 58 222 443 7 5 9271149141116 351858 212223 47 2613 28 60 219 4 37 656 9 1511 34 13 53 16 13 18 342054 23 1625 3828 62 216 431 647 8 3111913 37155418122029224825 6272 64 214 427 641 85411 81323153717 5220 8222224882664 66 211 423 634 846105713 91521 17 4 19 46 2158 2418 26 68 2 9 419 628 8381048125715 71718192821392350'2.1 70 2 8 415 6 23 8 31 10 3912 47 14 55 1 3 19 12 21 21 23 0 _ _ _,-: 5; 183 i i 8 7 10 11 12 13 14 15 16 17 18 19 20 21 22 ~ 23 24 25 I 40 00 02 03 06 09 13 17 24 30 37 45 54 41 03 14 25 37 50 42 03 18 34 51 59 43 09 18 27 37 47 57 44 08 19 45 '00 02 03 06 10 14 20 26 33 41 50 46 00 11 23 35 49 47 03 18 35 53 48 12 22 32 41 53 49 04 15 27 39 51 0 50 00 02 04 07 11 16 23 29 37 46 56 51 07 19 32 46 52 01 17 34 53 53 12 33 45 56 54 07 19 32 44 57 55 10 24 6 5/ 0 / 0 55 ( ( ( 56 ( 1 1 01 t frutan. (The numbers at top denote poar dt Alpha in Ursaminoris (Polaris). 10 1~ 5 1 10 1 1~ 15t 1~ 20' ' 0 / //0 / / 0 / // 0 / / of )01 0 11 5 00 1 10 011 15 011 20 01 )2 2 02 03 08 08 )4 5 05 05 06 06 )8 9 09 10 11 12 13 14 15 16 14 18 18 20 22 23 25a 26 25 27 29 32 34 36 33 35 38 41 45 47 41 45 49 52 66 21 00 51 56 6 01 05 16 09 14 02i 1 7 13 19 24 30 14 20 27 34 41 47 27 35 43 51 58 22 06 11 50 59 12 08 17 17 27 56 2 7 7 18 28 39 49 L3 25 37 49 18 02 23 13 31 46 58 13 12 26 39 50 3 05 8 21 36 52 24 07 LO 27 45 14 02 19 19 37 32 51 910 30 49 2508 55 4 16 38 59 2020 42 )7 29 52 1514 37 59 [9 43 1006 30 53 2617 32 57 21 46 21 11 35 15 5 11 37 16 03 29 55 58 26 53 20 47 27 14 [2 41 11 09 37 22 06 34 26 56 26 56 26 55 11 6 12 43 14 45 28 16 56 29 12 01 17 33 23 06 38 I ___1- -- 30 42 54 45 06 18 31 44 657 46 11 25 50 04 17 30 44 58 51 12 27 42 57 52 13 38 52 56 07 22 3E 54 57 16 27 44 58 02 1 12 27 44 2 00 17 35 53 3 12 31 50 45 7 03 2C 39 57 8 16 3t 56 9 17 38 38 57 13 17 37 56 14 19 41 15 03 26 18 13 34 56 19 17 39 20 02 26 5C 21 15 27 48 24 11 34 57 25 21 45 26 1C 36 27 03 2d VI 24 47 30 11 36 31 02 28 55 3223 51 I1 40 j 55 t247 10 26 3 41 i 67 4 48 16 832 k::fb au 46 53 04 21 39 67 54 17 42 56 46 38 59 58 17 37 58 1 0 19 4C 1 02 26 4 10 30 50 5 13 35 57 6 20 44 7 09 33 10 0O 22 46 11 09 32 57 12 22 48 13 15 42 5C 16 14 37 17 04 31 57 18 2 65 19 21 51 4C 22 06 33 23 OC 2E 57 24 26 57 2527 69 3C 5E 28 26 56 29 26 57 30 28 31 01 83 820 33 20 50 34 20 51 35 23 56 36 30 87 04 40 5 87 59 ~6 20 43 j7 06 80: fto 64;8 29 48 2 12 86 8 02 27 " 58 4 20 48 5 16 45 59 14 10 20 21 26 82 42 8 25 38 52 27 05 33 1 50 15 08 21 23 29 6 9 20 38 66 28 14 3432 48 16 09 22 29 60 35 11 10 17 40 23 03 29 27 C 46 17 12 39 0 04 36 8 11 17 46 2415 43 37 12 48 18 20 61 8123 54 112 191 18 551 2 291 32 0418 88 89 40 41 42 48 44 1 45 184 TABLE XXII.-Azimuths or Bearings of Certain Stars when at th: Greatest Elongationsfrom the Meridian. (The numbers at top denote polar dist.) Polaris. UrsaMinoris. Ursa Minoris. 10 25' 10 30' 30 20/ 30 23/ 70 450 70 50' 1 70 55' 8~ 00 0o -77 / // 0 /7// o o // ooO / / / /, 1 25 01 1 3000 32002 323557 45 04 7 50 04 7 55 05 8 004 03 03 08 2401 4517 5017 5518 018 07 08 17 2410 45 39 50 39 55 39 0 40 12 13 29 2423 4608 5110 5610 111 20 21 46 2440 46 47 51 49 56 50 151 28 30 2106 2500 47 35 52 36 57 38 1 33 38 40 2130 2525 48 31 5333 58 35 3 38 50 53 2158 25 53 49 36 54 39 59 42 4 45 2603 3107 2230 2626 5050 5554 8 058 602 19 23 2306 2702 5213 5718 223 727. 36 41 2345 2742 5346 5851 3 57 9 03 54 3201 24 29 28 2 55 27 8 034 541 10 48 2714 22 2516 2915 57 19 227 734 1251 36 45 2608 3008 5920 429 938 14 48 2800 33 10 2704 3105 8 131 641 1152 1703 26 38 2804 32 06 352 904 1461 19 29 53 3407 2909 3315 623 11 37 1651 2205 2929 38 3018 3423 905 1421 19 37 24 53 54 3511 3132 3539 1158 1716 2234 27 51 3027 47 3251 3659 15 03 2022 2542 31 02 31 03 3624 3415 3825 18) 9 2340 2902 34 24 22 44 3459 3909 2001 2524 3047 36 10 41. 3704 8544 3955 2146 2711 3234 3758 3200 25 36 30 40 42 23 35 2900 34 25 39 51 20 46 3718 41 31 2526 30 53 36 20 41 46 42 3809 3807 4221 2721 3249 3816 4344 3303 31 3857 4312 2919 3448 4017 45 46 25 54 39 49 44 05 3120 36 61 42 21 47 51 47 3919 4042 4459 33 25 3857 4428 50 00 3411 43 4137 4555 3533 4106 4639 2 12 34 4008 42 33 4652 3744 43 19 4853 54 28 59 34 43o1 4751 3959 4535 5111 5648 3524 4101 4430 4852 4217 4755 5333 59 11 50 28 45 31 49 54 44 33 5019 55 58 9 1 38 36 16 56 46 33 50 57 47 06 52 47 5828 4 08 2 44 42 27 47 37 52 02 49 36 5526 9 101 6 43 3712 55 4842 5309 5210 5754 338 922 40 43 25 4950 5418 5447 9 033 619 1205 3809 55 50 59 5528 5729 432 904 1452 39 4427 5210 5641 9 015 605 1154 1743 s3 910 4500 5 5322 554 305 857 1448 20 39 42 38 5437 5910 600 11583 1746 2339 4015 4608 5553 4 029 859 1454 2049 26 44 47 43 5712 1,18 1202 17 59 2356 29 53 4121 4719 5832 310 1510 2109 2709 33 08 56 56 59 54 434 1823 2424 3026 3627 4232 4829 4 118 559 2141 27 44 3348 39 27 4309 4913 245 728 2504 3109. 3715 43 21 48 52 413 858 2831 3439 4047 46 55 4425 50 33 544 1030 32 04 3815 4425 6035 45 07~ 5115 717 0 1205 8542 4155 4808 4 20 45 5158 853 1 45 3926 4542 51 57 5812 4626 5242 1031 1522 4317 4934 5551 10 152 4709 5327 12 11 1705 4711 5331 5952 6 12 52 5413 1353 1850 5113 5735 10 3 58 1021 4837 5500 1538 2037 5520 10146 811 14.37 1, 4923 5549 1727 2227 5933 602 1230 1859 5010 56 39 1918 2420 10 53 10 25 1656 52 27 58 5730 2111 2616 8 20 1454 2129 28 08 5147 5822 2308 2814 1254 1931 2608 32 45 0 185 j k;,l ',,1. ~~~~1;;~ ~'-::::i::;~I;~1~ ~~S_!:l: —~~_,~ I.0 11 vt BLE -Azimuths or Bearings of Certain Stars when at their Irettet Elongations from the Meridian. (The numbers at top denote polar dist., a Sigma in Octantis. Alpha in Ursa Minoris (Polaris). pAd 40' 451 50' 55 10o 10 5/ 10 10' 10 15' 10 20' lat0 6/o - / ff0 /O f0 f0 1 / 0/o 41 0 53 00 0 59 38 1 6 15 1 1253119301 2608132451392314601 53 24 1 0 43 6 46 1326 2007 26 48 3328 4009 4650 42 53 50 0 23 7 17 14 01 20 44 27 28 3412 4056 4740 4 5415 1.02 749 1436 2128 2810 34 57 4144 4831 43 54 42 1 31 8 22 15 11 22 03 28 53 3544 4234 4924 4 5509 2L 02 856 1550 2243 2937 3631 4324 5018 44 55 37 2 34 9 31 16 28 23 25 30 22 3719 4416 51 13 4 56 05 305 1006 17 07 24 08 3109 3809 4511 5210 45 56 34 3 39 10 43 17 47 24 52 31 56 3900 4604 5309 57 04 4 12 11 20 18 28 25 36 32 44 39 53 47 01 5409 i I I 4i 47 48 49 4i 50 i 4 51 52 53 1 54 54 i~ 55 4 56 4 4 ii 58 4 '59 4 60 61 62 4 63 4 64 4 65 4 11 57 38 58 07 58 39 59 12 59 47 1 0 22 0 58 1 36 2 14 i 253 3 34 4 16 4 58 5 43 6 28 7 15 8 03 8 53 9 44 10 37 11 32 12 28 13 37 14 27 15 49 16 34 17 40 18 49 20 00 21 14 22 31 23 50 25 12 26 38 28 07 29 39 31 15 32 55 34 39 36 28 38 Z1 40 19 42 23 44 32 6 468 49 09 51 38 54 14 1 5658 I I I I I I I 4 47 5 23 5 59 6 37 7 15 7 55 8 36 9 17 10 01 1 10 45 11 31 12 17 13 06 13 55 14 47 15 39 16 34 17 30 18 28 19 27 20 29 21 32 22 38 23 46 24 56 2608 27 23' 28 40 30 001 31 231 32 50U 34 19 35 52 37 28 3908 4051 42 40 44 33 46 29 48 31 50 39 52 52 55 11 57 37 2 0 09 2 48 5 35 8 32 11 36 11 59 12 38 13 19 14 01 14 54 16 28 16 13 1 700 17 47 1 18 37 19 27 20 19 21 13 22 08 23 28 24 05 25 04 26 06 27 11 28 29 29 25 30 36 32 01 33 04 34 22 35 42 37 05 38 30 40 02 14133 43 09 44 48 46 31 48 18 50 09 52 04 54 05 56 09 58 20 2 035 2 57 5 25 8 00 10 41 13 30 16 27 19 33 22 48 22614 193 11 19 58 20 39 21 28 22 12 23 0( 23 50 24 42 25 34 1 26 28 27 24 28 21 29 20 30 21 31 24 32 28 33 35 34 36 35 54 1 37 20 38 22 39 39 41 14 42 23 43 48 45 16 46 47 48 23 50 01 1 51 42 54 26 55 17 57'10 59 07 2 1 10 3 17 5 29 7 47 10 10 12 39 15 115 17 68 20 48 23 46 26 52 3006 33 31 37 0& 2 40515 I I I I I II 26 23 27 10 t27 59 28 49 29 40 30 33 31 28 32 24 33 21 84 20 35 211 36 23 37 28 38 34 39 42 4053 42 05 43 20 44 37 45 56 47 19 48 43 50 20 51 41 53 14 5451 56 31 58 13 2 011 1 52 3 52 5 46 7 49 9 58 12 11 14 30 16 54 19 24 22 00 24 43 2733 30 30 33 36 36 50 4013 43 57 47 29 51 25 2 55 30 83 38 34 29 35 19 36 1q 37 09 38 09 39 08 4009C 41 08 1 42 12 43 09 44 26 45 35 46 47 48 01 49 17 50 35 51 57 53 20 55 02 56 15 57 57 59 38 2 059 2 41 4 26 6 13 8 05 10 02 2 12 01 14 0 6 16 15 18 29 20 48 23 12 25 42 28 19 31 11 33 51 36 47 3952 43 04 46 25 49 55 53 35 57 25 3 1 27 5 41 3 10 08 40 47 4142 42 39 43 28 44 37 45 39 46 42 47 28 48 55 1 50 04 51 15 52 28 53 43 54 00 56 20 57 42 59 06 2 034 2 03 3 53 512 651 8 50 1018 12 07 1400 15 56 17 57 20 02 222 11 24 25 26 44 29 18 31 38 3414 36 56 3944 42 39 45 41 48 51 52 10 55 36 59 13 3 300 6 57 1104 15 25 19 59 3 24 47 47 55 48 58 49 59 51 01 52 06 53 12 54 20 55 30 56 41 1 57 56 59 11 2 030 1 50 3 11 4 &8 6 06 7 37 910 10 47 12 45 14 08 15 54 18 03 19 37 21 34 23 34 25 39 27 48 30 02,2 32 21 3444 37 13 39 48 42 28 45 15 4808 5109 54 16 57 32 3 056 428 810 12 02 16 04 2018 24 25 29 24 3417 3 39 25 55 1 5614 5719 58 29 59 34 2 048 157 312 428 5 47 7 09 832 9 58 1129 12 57 14 31 16 08 17 47 19 30 21 10 23 06 24 58 26 15 28 55 31 00 33 09 35 22 37 40 40 03 42 31 45 04 47 43 50 27 53 19 5617 59 22 3 234 5 54 9 22 1300 16 46 20 45 24 51 29 09 33 41 38 25 43 22 48 35 3854 04. 1 I I I I I I I I I I I,, I I 186 I.: ',;.... " fil -: "~./'.':: N:-: —::! /' I '::; 'i: A, I;-f I II i - f t I D 'TABLE XXIII.Z —Azimuths or Bearings of Certain Stars when the. Greatest Elongationsfrom the Meridian. (The numbers at top denote polar dist. lioa.t~. R; _ Polaris. d Ursa Minoris. 1 '25 1~ 30/ 3~ 20' 30 23' 0D ff o / // O // 1 52 381 59 16 42507 4 3016 53 302 0 11 27 09 32 21 54 23 1 07 29 00 34 2c 55 18 2 05 31 15 36 14 56 14 3 04 33 24 38 5 57 12 4 05 35 52 41 1 58 11 5 08 38 45 44s1 59 11 6 12 40 30 46 01 2 0 13 7 18 43 00 48 3C 1 17 8 25 45 31 51 04 2 23 9 35 48 05 53 41 3 30 10 46 50 43 56 23 4 39 11 59 53 27 59 09 5 50 13 14 56 145 2-00 7 00 14 31 59 06 4 55 8 18 15 50 5 2 03 7 55 9 35 17 12 505 11 01 10 52 18 36 812 14 11 12 16 20 02 11 24 17 27 13 39 21 13 14 42 20 49 15 05 23 02 18 05 24 16 16 34 24 36 21 34 27 49 18 05 26 13 25 09 31 29 19 39 27 52 28 51 3518 21 16 29 35 32 40 39 08 22 56 31 20 36 35 43 08 24 38 33 09 40 38 47 15 26 24 35 01 44 48 51 30 28 14 36 57 49 06 55 53 30 06 38 56 53 32 6 024 32 02 40 59 58 06 505 34 03 43 06 6 2 50 9 54 36 07 45 41 7 44 14 52 38 14 47 33 12 45 19 59 40 27 49 53 17 58 25 20 42 44 52 15 23 21 30 49 45 05 54 48 28 56 36 30 47 31 57'23 34 42 42 24 50 033 0 04 40 41 48 29 52 40 2 50 46 52 54 48 65 23 5 42 53 187 1 21 58 12 8 14 59 57 8 10 3 1 08 11 47 7 652 15 11 4 09 15 00 14 03 22 30 7 18 18 20 21 30 30 10 10 34 21 48 3018 38 02 13 59 25 24 37 19 46 15 17 32 29 10 45 43 '54 51 21 13 33 04 54 29 8 3 45 25 04 37 09 8 3 36 1313 29 05 41 24 1208 2246 33 17 45 51 23 05 32 54 37 40 50 29 33 28 43 31 42 15 55 20 44 22 54 37 47 034 0 25 55 46 9 614 52 05 45 9 7 42 18 25 57 08 11 20 20 15 31 13 4 2 64 17 12 33 25 44 39 8 43 23 02 47 17 58 48..~~~~~~~~~~~~~~~~~~ I e Ursa Minoris. _f.; 70 45/ 0 / /I 10 17 0E 22 22 27 17 32 2( 36 3 42 5( 48 1U 53 54 59 4( 11 5 4 11 37 17 51 24 15 30 5C 37 3( 44 2E 51 42 59 08 12 636 14 23 22 24 30 39 39 09 47 53 56 55 13 610 15 47 25 41 35 52 46 24 57 16 14 831 20 09 32 07 44 33 57 24 15 10 43 24 30 38 50 53 37 16 6 43 29 04 43 34 58 49 17 16 47 35 28 54 57 18 15 16 36 27 58 36 19 21 45 45 59 20 11 17 37 59 21 556 35 20 22 615 38 05 23 13 16 7~ 50/ 7055/ 1 80 00( 0 o /"/ o o / // 10 24 06 10 30 55 10 37 36 29 06 35 49 42 33 7 34 04 40 51 47 38 ) 38 26 46 01 52 51 3 44 25 51 18 58 12 5118 56 44 11 3 42 55 18 11 219 920 11 058 803 15 07 ) 68 20 13 57 21 04 12 36 19 58 27 10 18 53 26 10 33 26 25 12 32 32 39 53 31 40 39 05 46 30 38 19 45 48 53 18 45 09 52 44 12 0 17 52 11 59 50 7 28 59 24 12 7 07 14 51 12 6 51 14 29 22 27 14 30 22 222 30 16 22 21 30 20 38 19 30 27 38 31 48 33 38 48 46 57 55 07 47 33 55 38 13 03 54 56 03 13 4 26 12 56 13 5 21 13 46 22 16 14 45 23 18 31 52 24 27 33 07 41 47 34 26 43 12 52 00 44 45 53 39 14 2 33 55 25 14 424 13 20 14 6 24 1533 24 41 17 46 27 02 36 18 29 34 38 54 48 18 41 39 51 12 15 0 44 54 13 15 354 13 34 15 7 13 17 03 26 52 20 44 30 39 40 38 34 38 44 46 54 48 49 05 59 22 16 9 41 16 405 16 14 33 25 02 19 37 27 57 40 57 38 10 46 38 55 04 55 00 17 3 37 17 14 39 17 10 03 21 17 32 31 28 13 39 39 51 06 47 40 58 47 18 13 04 18 6 50 18 18 43 30 38 27 23 39 31 51 40 48 50 19 49 13 19 13 37 19 11 14 23 53 36 56 34 40 47 36 20 0 38 59 04 20 12 25 25 40 20 24 53 38 28 51 56 51 51 21 541 21 19 84 21 20 08 34 28 48883 49 53 22 427 221902 22 21 11 36 09 51 07 5411 23 934 232457 23 29 02 44 50 24 040 I I I I -- I — -~ ~~ -; — --- nn lot n', ', 11 ~~~1R"~~~~~~~~B;_,;~~~~~~~ P- ~ -7 ' If:;lyS S 1'^":.: "t, ~t, " I,I,; -0Ti1 iX XIII.-Azimnm Gr: eatest Elongations fro Star. *f Chamaeleontis. P.D. 11 30 110 35' Lat. o / //-o / 1 11 30 06 11 35 06 2 ' 30 26 35 26 3 30 58 35 58 4 31 42 36 43 5 32 40 37 42 6 33 51 38 53 7 35 15 40 18 8 36 53 41 56 9 38 43 43 27 10 4 48 45 53 11 43 06 48 12 12 45 38 5045 13 48 24 53 33 14 51 36 56 35 15 54 41 59 53 16 58 13 12 325 17 12 1 56 7 14 18 5 31 1 18 19 10 21 15 27 20 14 57 20 17 21 19 50 25 12 4 22 23 27 48 22 25 01 30 26 4 27 44 33 10 23 30 30 35 58 4 33 23 38 51 24 36 20 41 49 39 21 44 52 25 42 29 48 00 45 40 51 14 26 48 57 54 32 1 52 19 57 56 27 55 47 13 1 26 59 19 5 01 28 13 2 37 8 32 i 6 44 12 28 29 10 12 16 12 4i 14 31 20 18 30 18 34 24 23 22 43 28 34 31 26 58 32 57 31 21 37 25 32 35 45 41 46 40 13 46 23 3 45 07 50 56 4 49 57 5600 34 5454 14 0 59 4 5 558 6 06 85 14 5 11 11 21 10 32 16 44:86 15 59 22 13 21 36 28 06 87 27 21 33 42 3315 3939 8 39 19 45 43 47 36 5200 39 63 59 58 25 68 25 15 500 40 16 6 07 1145 11 69 18 40 7 tths or Bearinqs of Certain Stars when at their m the Meridian. (The numbers at top denote polar dist. I f Hydri and C Ursa Minoris. 11650/ 1W55'VIU IJ 11~ 40/ 11~ 45/ 0o / / o / // 11 40 06 11 45 07 40 26 45 26 40 59 45 59 41 44 46 45 42 43 47 45 43 55 4856 45 19 50 22 46 59 52 02 48 51 53 55 50 57 56 02 53 18 58 23 55 52 12 0 59 58 41 3 49 12 1 45 6 55 504 10 15 8 38 13 51 12 28 17 42 16 34 21 51 21 08 26 15 25 37 30 57 30 35 35 57 33 10 38 34 35 51 41 16 38 36 44 02 41 25 46 52 44 20 49 48 47 19 52 49 50 23 55 55 53 33 57 16 56 48 13 8 32 13 008 5 21 3 33 9 10 7 04 12 43 10 41 16 21 14 23 20 05 18 11 23 55 22 05 27 51 26 05 32 06 30 12 36 01 34 25 40 15 38 44 44 37 43 10 49 05 47 42 53 39 52 22 58 21 57 09 14 3 11 14 2 03 8 06 6 29 13 14 12 14 18 20 17 31 23 41 22 56 29 09 28 29 3444 34 01 40 29 40 02 46 22 46 01 52 24 52 10 58 22 58 28 15 4 46 15 4 56 11 28 11 34 18 09 18 22 25 00 25 32 32 02 11~ 50/ 110 55/ 0 / / o / // 11 50 07 11 55 07 50 26 55 27 50 59 56 00 51 46 56 46 52 43 57 47 53 58 59 00 55 25 12 0 27 57 05 2 08 58 59 4 03 12 1 07 612 3 29 835 606 11 13 8 51 14 06 12 04 17 14 15 26 20 37 19 03 24 16 22 57 28 11 27 07 32 23 31 33 36 52 36 18 41 38 41 20 46 42 43 58 49 21 46 40 52 05 49 27 54 55 52 20 57 47 55 17 13 0 45 58 19 3 49 13 1 26 6 57 427 10 11 7 54 13 30 11 19 1654 14 47 20 24 1822. 2400 21 54 27 41 25 47 31 29 29 38 35 22 33 24 39 21 37 40 43 27 41 50 47 39 46 06 5 57 50 29 56 22 54 48 14 9 54 59 36 5 33 14 420 10 19 9 11 15 12 14 09 20 13 19 15 25 21 24 29 30 37 29 29 36 02 35 21 41 34 4100 47 15 46 34 52 04 52 30 59 03 58 41 15 5 11 15 502 11 28 11 26 17 55 18 00 24 31 24 43 31 18 31 24 38 16 38 43 46 24 12~ 00O, / // 12 007 0 27 1 00 1 47 248 402 529 7 11 907 1117 1340 1620 19 14 2223 2548 2828 31 40 36 39 4210 4709 52 04 5501 57 30 13 019 3 14 6 14 9 18 12 28 1543 1904 22 30 2602 29 39 3322 37 11 41 06 4507 49 14 53 28 5748 14 2 15 649 11 30 16 18 21 13 2616 31 37 3645 4217 4747 53 30 5922 15 524 11 34 17 54 2424 31 03 3753 4464 52 05 I,A [ 1' g k 0 * f - - -cc --- —---— 5 rrr\ - 1 l -i6 ~~?i: — It TABLE XXIII.-Azimuths or Bearings of Certain Stars wh a Greatest Elongations from the Meridian. (The numbers at top denote poir st.. -~~~~~~~~~Tl cntbr -tpcea~~ 9;J4.i:-:I Star. P.D. 41 1 44 45 43 47 1 1 49 50 51 49 i 52 1 53 1 51 55 4 56( 5' 58 59 60 60 /3 Chamaeleontis. /3 Hydri and ( Ursa Minoris. 110 30/ 110 35/ 110 40/ / 1 46 110 50/ 1is5s o / / 0o / 0 /o 7 0 / f 0 / / O 15 19 03 15 26 00 15 32 30 15 39 50 15 45 59 15 52 4 26 17 33 17 39 57 46 391 53 26 16 0 1 33 42 40 33 45 10 52 00 16 1 05 7 41 20 48 14 55 08 16 2 03 8 57 15 49 10 56 07 16 3 05 1Q 02 17 01 23 5 5711 16 412 1114 -1816 2518 32 2 16 506 1213 19 57 2642 3349 40 5 13 54 21 03 28 12 35 22! 42 32 49 4 22 36 29 49 37 03 44 16 51 16 58 4 31 32 3849 4607 5356 17 04317 80 40 13 48 05 55 27 17 2 49 10 11 17 3 5009[175700/17 502 12 28 19 57 272 59 51 7 22 14 53 22 24 29 55 37 2 17 9 49 17 25 25 00 32 37 40 12 47 4 20 04 27 44 35 25 43 06 50 47 58 2 30 37 38 23 46 08 53 54 18 1 4018 9 2 41 25 49 19 57 09/18 501 12 52 204 52 38 18 0 35 18 8 30 16 27 24 23 32 2 18 4 08 12 10 20 11 28 12 36 14 44 1 15 58 24 05 32 12 40 20 48 27 56 3 28 -10 36 23 44 36 56 ub 19 1 02 19 9 1 40 44 49 02 57 21 19 5 41 14 00 22 2 53 40 19 2 05 19 10 30 18 56 27 21 35 4 19 7 01 15 19 24 05 32 36 41 08 49 4! 20 47 29 25 38 03 4642 552020 4 0 34 59 43 40 52 28 20 1 14 20 10 00 19 04 49 38 58 35 20 7 02 16 15 25 07 34 0 20 5 52 20 13 44 22 45 31 44 40 47 49 4i 20 23 29 30 38 29 47 45 56 53 21 6 0( 3631 4547 55 02' 21 3211 21 13 39 22 5: 53 14 21 2 37 221 12 00 21 24 30 48 40 15 21 1029 20 01 2933 3905 48 38 58 11 31 28 41 10 5053 22 0 35 2 10 18 22 16 4 46 50 56 40 22 6 30 16 20 26 24 36 1 22 6 00 22 15 59 25 58 35 58 46 00 56 0( 25 51 36 00 46 10 56 19 23 6 30 23 16 4 46 26 56 47 23 7 05 23 1726 27.47 38 0 23 7 47 23 18 17 28 48 39 19 49 50 24 0 24 29 27 40 39 51 20 24 2 03 24 13 21 23 31 52 59 24 3 52 24 14 46 25 41 36 37 47 38 * nd 1200' 0/ o13 15 59 27.4 16 7 02 )7 14 48 0 22 46;9 30 58!0 39 22 4 48 00:2 56 02 L4 17 5 58 1 15 19 4 24 56 2 34 49 7 44 58 9 55 25 818 5 34 6 17 12 3 28 18 0 4016 6 52 19 5 19 443 6 17 30 0 30 22 7 4413 0 58 13 O 20 12 39 0 2732 1 42 5 6 58 46 3 21 15 10 32 07 3 49 38 122 745 7 26 30 1 45 56 )23 602 26 53 48 31 24 10 58 34 15 58 27 25 23 41 49 54 26 17 12 4540 27 15 20 46 21 28 18 46 4357 29 28 08 30 622 4431 X 31 26 37 32 863 54 31 33 4242 348338 35 27 48 36 2 08, 372614 I i - _f_ 61 24 16-56 28 0 41 29 53 09 62 25 746 251918 i 34 47 46 34 63 26 2 58 26 15 00 32 22 44 40 64 27 3 06 27 15 39 35 04 48 05 65 28 8 52 28 22 02 4 43 27 57 36 66 2921 05 29 34 56 i 5956 30 14 08 67 30 40 48 5525 i 11 23 42 31 38 53 68 32 917 32 2445 57 17 33 13 15 69 33 4807 34 436 134 42 02 59 16 70 35 39 21 35 57 00 V -- — ~~~~~I II I 39 07 50 15 25 4 28 25 15 49 30 52 42 25 58 21 26 10 17 26 27 02 39 05 56 55 27 917 27 28 14 40 51 28 0 57 28 13 51 35 12 48 24 29 11 06 29 24 39 48 47 30 2 40 30 28 22 42 38 31 10 02 31 24 41 53 56 32 9 01 32 40 16 55 49 33 29 14 33 45 17 34 21 07 3437 45 35 16 10 35 33 19 86 15 43 36 33 30 25 1 42 25 12 32 27 09 38 32 54 00 26 5 36 26 21 58 33 48 51 09 27 3 15 27 21 37 34 00 53 27 28 6 06 28 26 46 39 42 29 1 39 29 1454 38 12 5148 30 16 36 30 30 33 56 56 31 11 15 31 39 23 54 07 32 24 08 32 39 18 33 11 24 33 27 02 34 1 22 341730 64 19 35 11 00 35 50 32 36 7 48 36 50 82 37 816 I 189 11. TABE:; X~TII.-Aimuths or Beari n Great~ e ongcati'on bfrom the Meridian. I I I i I 4 i i star. P. D. Lat. 1 2 3 4 5 6 7 8 9 10 -T 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 -27 28 29 1 82 33 34 84 35 36 87 '88 120 05', 0 /1 12 507 i 5 27 6 01 6 48 7 49 9 03 10 32 12 14 14 11 16 21 18 48 21 27 24 24 27 33 30 59 34 41 38 40 42 55 47 28 52 18 57 27 13 008 2 54 5 45 8 41 11 51 14 48 18 00 21 15 24 38 28 06 31 50 35 07 39 02 42 53 46 49 50 52 55 01 59 17 14 339 8608 12 44 17 27 22 17 27 14 32 20 37 32 42 53 48 22 54 00 59 46 15 Z540 11 44 17 47 24,21 30, 52 37 35 44 14 51 32 58 46 12040/ 0 // [2 40 07 40 28 41 36 41 53 42 57 44 16 45 48 47 36 49 38 51 55 54 28 57 16 13 015 3 40 7 17 11 10 15 21 19 49 24 35 29 40 35 04 37 54 40 48 43 48 46 53 50 02 53 18 56 39 14 0 06 3 37 7 15 10 59 14 49 18 45 02 48 26 56 31 11 35 32 40 01 44 37 49 19 54 09 59 06 15 4 12 9 24 14 44 20 14 25 51 31 37 37 31 48 35 49 48 56 10 16 2 48 9 25 16 18 23 21 30 35 38 00 45 35 120)451' 12" [ 6/0 4// 0 / 12 45 07 12 5( 45 29 5( 46 04 5* 46657 5* 47 58 51 49 17 5' 50 51 5& 52 39 5 54 42 5, 57 00 13 59 34 13 223 529 1 850 1 12 10 1 16 23 2 20 35 2 25 05 3 29 54 3 35 01 4 40 25 4 43 17 4 46 13 5 49 14 5 52 20 5 55 31 14 58 48 14 2 10 538 1 912 1 12 51 1 16 37 20 28 24 25 28 30 32 40 36 57 41 21 4 45 51 50 28 55 1 15 15 0 05 504 1 1011 I 15 26 20 49 26 20 32 00 37 47 43 45 49 51 56 06 16 16 240 906 1 15 52 22 47 29 53 37 11 44 39 52 20 of certain Starga whenattheir (The numbers at top denote po ar dist.) y Cephi. 0' 220 55/ 13V000' 130 05, 0 / //o / 1/ 0 /1/ ) 07 12 55 07 13 0 07 13 5 7 ) 29 55 29 0 29 5 29 1 05 56 05 1 05 606 1 55 56 56 1 56 6 57 3 00 58 01 3 02 803 4 19 59231 4 21 924.553 13 0 55 5 58 11 00 7 42 2 45 7 48 12 51 9 46 4 50 9 54 14 58 2 05 7 10 12 15 17 20 4 40 946 1452 19 58 7 31 12 28 17 52 22 52 0 37- 15 45 20 33 2602 4 07 19 09 24 19 29 29 7 39 22 49 28 02 33 13 1 35 26 48 32 01 37 14 550 31 04 36 19 41 03 0 22 35 38 40 54 46 10 5 12 40 30 45 48 51 07 0 21 45 41 51 02 56 22.5491i4 51 17 56 3514 1 57:8 41 54 09 59 29 4 53 4138 57 03 14 2 28 7 53 440 14 006 5 33 10 59.7 48 315 8 42 1410 1 00 6 29 11 58 17 20 4 18 9 49 15 18 20 46 7 42 13 13 18 45 24 19.1 11 16 44 22 17 27 56.4 46 20 21 25 55 31 30.8 27 24 403 293939515,2 14 27 52 33 29 39 07 '6 07 31 46 37 00 43 04 O 07 35 47 41 58 37 03 [4 12 39 54 45 36 51 19 [8 24 44 08 49 52 55 36 [2 43 48 28 54 04 15000 [7 08 52 43 58 43 4 31 A440 57 36 15 3 19 9 09 i6 15 1-5 211 8 02 13 54 1115 6 59 12 53 18 46 6 00 11 55 17 51 23 46 [1 01 16 29 22 56 28 53 [6 10 22 10 28 10 34 09!1 27 27 29 33 31 39 33 )6 53 32 57 39 01 45 05 [2 26 38 32 44 39 50 45 [8 07 44 00 50 45 56 34 13 58 50 10 56 34 2 32 19 58 56 12 16 232 839 07 16 2 23 8 39 1455 225 8 44 14 55 21 21 8 53 15 14 21 21 27 57 15 31 21 54 27 57 34 43!2 18 28 46 34 43 41 39 )9 17 35 47 41 39 48 47 W626 42 59 48 47 56 05 13 47 50 23 56 05 3 34 418 5S 7 57717 3341 11 16 i9 02117 5 241 11 16 19 09 ~':-::i —i::::i —;~l-~~::: i: -i- 6A: 4* 190 IL TABLEg XXII.-Azimuths or Bearings of Certain Stars when at t Greatest Elongations from the Meridian. (The numbers at top dnote polar dst.) Star. y Cephi. P.D. 120 05/ 120 40 12 45/ 12 125 1 55 1 13~ 00t/ 13~ 05' L o O O / / o f 0 / ff0. 41 16 612 165327 17 012 17 6571171343 1720291172714 13 50 17 1 28 8 17 15 06 22 23 28 44 36 3388 42 21 39 9 42 16 34 23 27 30 19 37 12 44 05 29 41 18 09 25 05 32 01 38 57 45 53 52 50 43 37 56 26 50 33 49 40 49 47 49 54 49 18 1 49 46 24 35 44 4248 49 51 5655 18 359 11 08 44 55 06 44 53 52 01 59 14 18 6 16 13 23 20 31 17 4 02 5417 18 1 29 18 840 15 52 2303 3015 45 1313 18 3 56 11 12 18 28 25 43 33 00 40 16 1 22 38 13 52 21 11 28 31 35 51 43 11 50 32 46 d319 243 1 3128 38 52 -4616 5 4119 106 42 16 34 33 42 00 49 13 56 59 19 4 28 11 57 47 5 5250 45 19 2 52119 025 19 759 15 83 23 07 1 18 3 01 5623 19 401 1139 1918 2655 3436 48 13 51 19 747 15 30 23 13 30 57 38 40 46 25 24 59 19 30 27 18 34 50 42 55 50 44 58 33 49 36 26 31 34 39 27 47 21 55 15 20 3 09120 11 04 48 13 43 59 51 58 59 57 20 757 15 57 23 56 50 19 0 38 56 46 20 4 57 20 12 55 21 01 29 03 37 11 12 21 20 9 56 18 07 26 17 34 28 42 39 50 51 51 25 44 23 30 40 0 48 20 56 3721 4 55 39 00 37 29 45 52 54 14 21 2 38 21 11 01 19 25 52 52 40 51 54 21 0 22 21 8 52 17 29 25 52 34 22 20 647 21 646 15 22 23 58 '2 24 41 lo 49 47 53 21 00 22 06 30 48 39 31 48 14 56 58 22 5 42 36 19 37 55 46 45 55 35 22 425 221301 22 07 54 51 48 54 16 22 3 13 22 12 10 21 08 30 06 39 04 21 7 48 22 1108 2013 2918 3823 47 29 5635 55 24 18 28 35 3747 4700 56 13 23 52723 1441 _ 41 24 46 36 55 57 23 518 23 14 29 24 02 33 24 56 59 0 23 5 14 3 14 43 24 13 317 43 04 51 45 22 17 19 24 32 3410 43 48 53 28 24 3 072412 48 57 36 13 44 30 54 17 24 4 05 24 13 54 23 43 33 32 55 48 24 5 11 24 15 08 25 06 35 03 45 02 55 02 58 23 16 04 26 37 32 05 46 51 57 00 25 7 08125 17 18 37 06 48 50 59 07 25 9 26 25 19 45 30 04 4024 59 58 4 25 11 54 25 22 22 31 43 43 21 53 52 26 4 23 ] 24 21 32 35 50 46 30 57 10 26 7 52 26 18 34 29 17 60 4502 26 043 261134 262227 33 20 44 15 5510 ] 25 927 26 34 37 38 4844 59 50 27 10 57 27 22 05 61 34 52 53 30 274 461 27 16 14 27 27 24 38 45 50 06 / 26 1 18 27 21 29 33 01 44 32 56 06 28 7 40128 19 15 62 28 50 50 41 28 2 261 28 14122826 01 37 50 49 46 57 32 28 21 07 33 08 45 10 57 13 29 9 1729 21 28 6327 27 29 52 54 29 5 11 29 17 29 29 29 49 42 13 54 31 54 33 29 26 07 38 41 51 16 30 3 52 30 16 3030 24 80 64 28 27 09 30 0 51 30 13 43 30 26 36 39 30 51 26131 56241 ] 29 439 37 14 50 24 31 3 36 31 16 56 31 30 57 43 2 65 41 29 31 15 20 31 28 51 42 24 55 59 32 9 34132 23 13 i 3018 41 55 22 32 14322308 32 87 59 51 18 38 5 08 66 58 31 32 37 25 53 28 33 5 58 33 20 17 33 34 39 49 33 31 40 00 33 21 41 33 36 20 51 03 34 5 47 34 20 3434 35 23 67 32 23 40 34 8 20 34 23 26 34 38 43 53 46 35 9 0035 24 6 i j 33 9 46 57 36 35 13 10 35 28 47 35 44 28 36 0 1036 15 66 68 58 25 35 49 42 36 5 47 36 21 55 36 88 07 54 21 37 10 38 i 34 49 55 36 44 55 37 1 33 37 18 14 3; 35 00 37 51 48138 8 40 69 35 44 30 37 43 33 38 0 50 38 18 05 38 35 27 38 52 5339 10 28 86 42 31 38 45 57 39 3 51 39 29 49 39 89 52 39 57 59 40 1610 70 7 44 17 39 59 11 40 11 11 40 29 53 40 48 40 41 7 2841 24 29 0 417 9 5. ^ ^ _19 1.. 0 1 1 ;!: ']. _ ' L;i -, i, fr: Ie B I ns from the Meri /3 (Kocha:Sar. 1875 1895 1915 PD. 150~ 20/ 15 25' IO5 30/ Lat. --- / // - 0 — / 1520 1520 125 19 15 3009 2 20 35 2535 30 35 3 21 18 26 18 31 19 4 22 18 27 19 32 20 5 23 36 28 38 33 29 6 25 12 30 14 35 15. 7 27 05 32 07 37 10 8 29 16 34 19 39 22 9 31 45 36 49 41 53 10 34 33 39 38 44 43 11 37 39 42 45 47 52 12 41 05 46 12 51 19 13 44 49 49 58 55 06 14 48 54 54 04 59 13 15 53 18 58 291 6 3 41 16 58 03 16 3 16 829 17 16 3 09 8 24 13 38 18 8 37 13 53 19 10 19 1426 1945 2513 20 20 39 2600 31 21 21 -27 15 3238 38 01 30 42 36 06 41 31 22 3415 39 41 45 06 37 55 43 22 48 47 23 41 41 47 09 52 37 45 33 51 03 56 32 24 49 32 55 03 17 0 34 53 38 59 10 4 43 25 57 50 17 3 24 8 58 4 17 210 729 1321 26 6 37 12 14 17 50 4 11 11 16 49 22 27 27 15 52 21 32 27 12 20 41 26 22 32 04 28 25 37 31 21 37 04 4 3042 36 27 4212 29 35 54 4141 47 28 41 15 47 04 5252 30 46 44 5234 5825 4 62 21 5814 18 407 31 58 U7 18 4 02 9 57 18 4 03 10 00 16 02 32 10 07 16 07 22 05 i 1621 2222 2824: 33 22 45 28 48 34 52 29 18 35 24 41 30 34 3601 4210 4818 42 55 4906 55 17: 49 18 56 1319 226 571519 331 947;36 19 442 11 00 17 19 12 20 18 41 25 02 37 20 10 26 34 32 58 4 2812 34 39 41 06 38 36 26 42 56 49 20 44 64 5127 * 5800 89 5335 20 011 20 646:20 2 29 908 1547 11 37 1820 25 0,, X 0,< i t 2?, _ _-~~~~~~~~~~~~~~~~~~ _: f _:~~~~~~~~~~~~~~ rings of Certain Stars when at their diamn. (The numbers at top denote polar dist.) b) Ursa Minoris. 1935, 1955 1975 [ 1995 150~ y' |b0V 40/ 15 45' 15050/ 0 / o/ U /// // o / // 15 35 10 15 40 09 15 45 23 15 50 09 35 36 40 36 45 36 50 36 36 20 41 20 46 20 51 19 37 20 42 21 47 22 52 23 38 40 43 41 48 43 53 44 40 17 45 19 50 21 55 23 42 12 47 15 52 17 57 19 44 26 49 29 54 32 59 35 46 57 52 01 57 06116 210 49 48 54 53 59 58 5 03 52 57 580416 3 10 816 56 26 16 1 34 6 41 11 48 16 0 15 5 23 10 32 15 40 4 23 9 33 14 43 19 53 8 52 14 04 19 15 24 27 13 42 18 55 24 08 29 21 18 53 24 07 29 23 34 38 24 27 29 43 35 00 40 17 30 22 35 41 41 00 46 19 36 41 42 17 47 23 52 44 43 24 48 47 54 11 59 34 46 55 52 20 57 47 17 3 08 50 36 55 5817 1 23 6 49 54 15 59 48 5 09 10 36 5808117 3 34 9 02 14 03 17 202 7 31 13 01 18 30 6 05 11 36 17 07 22 38 10 15 15 47 21 20 26 23 14 32 20 06 25 40 31 14 18 57 24 32 30 07 35 42 23 27 29 04 3441 40 17 28 06 33 44 39 23 45 02 32 52 38 32 44 12 49 53 37 46 43 28 49 10 54 52 42 48 48 31 54 15 59 58 47 57 53 43 59 28 18 5 13 53 15 59 0318 4 50 10 37 58 411 18 4-31 10 20 16 09 18 4 16 10 07 15 58 21 49 10 00 15 52 21 46 27 39 15 54 21 47 27 42 33 37 22 12 27 51 33 09 39 46 28 05 34 04 40 03 46 03 34 25 40 27 46 28 52 30 40 55 47 00 53 03 59 07 47 36 53 42 59 4819 5 55 54 26119 0 35 19 6 59 12 52 19 1 29 7 39 13 50 20 00 8 41 14 53 21 07 27 20 16 03 22 19 28 30 34 51 23 37 29 56 36 15 42 34 31 24 37 45 44 07 50 28 39 221 45 46 52 11 58 35 47 33 54 00 5952120 634 55 5620 226120 857 15 27?20 4 341 11 06 17 41 24 12 13 17 19 59 26 36 33 12 22 27 29 06 35 46 42 26 31 45 38 28 45 11 1 124I 192 f am...II- --- —----- ii!~i~~ i15! I - TABLE XXIII. -Azimuths or Bearings of Certain Stars when at their Greatest Elongations fromz the AIer-edian. (The nurmbers at top denote polar dist.) Star. (Kochab) /3 Ursa Minoris. -- 1875 1895 1915 1935 1955 1975 1995. 5 20' 15 25' 15~ 30' 155~ 35" 15~ 40' 15~ 45' 5~ 5' fat.,,, O- w / - - O,, -, - o O, O, - 41' 20 30 38 20 37 27 20 46 17 20 51 6 20 54 54 21 4 46 21 14 36 ] 20 41 47 24 54 47 21 1 10 21 8 4 14 57 21 51 42 50 4 57 36121 4 33 11 30 182 25 25 3222 1 21 1 5 21 8 6 15 6 22 8 29 8 36 9 43 10 43 11 48 18 52 25 57 33 1 40 1 47 11 54 10 1 22 49 29 56 37 4 44 15 51 22 58 31 22 24 41 44 34 6 41 18 48 31 55 44 22 2 57 22 10 10 19 24 45 42 54 59 22 16 22 7 38 14 50 22 8 29 26 45 57 38 22 5 6 2121 19 42 27 4 34 26 41 48 i 22 9 54 17 19 24 45 31 14 39 38 47 5 54 32 46 22 30 302 37 31 45 3 52 34 23 0 5 23737 1 35 29 43 4 50 39 58 15 23 5 2 10 4 21 4 47 48 49 56 3123 4 10 23 11 51 19 32 22 14 3455 2323 223 23 10 18 S 18 4 25 50 30 37 41 23 48 10 48 16 40 24 31 32 22 40 14 48 5 55 57 24 3 50 1 31 13 39 10 47 6 55 3 24 3 00 24 10 58 18 58 49 46 12 54 14 24 2 16 24 10 19 18 22 26 23 34 29 1 24 1 38 24 9 46 17 54 26 2 34 11 42 20 5030 50 17 31 25 45 - 34 42 14 50 29 58 45 25 7 0 1 33 54 42 14 50 35 58 56 25 7 17 25 15 39 24 1 51 50 48 59 15 25 7 42125 15 9 24 37 33 6 25 41 34 1 25 8 12 25 16 47 25 21 33 56 42 30 42 30 59 40 52 26 3 343 34 53 5143 51 126 0 46 26 9 40 25 18 22 ~ 44 46 53 33 26 2 22 26 11 10 20 00 28 51 37 41 53 26 3 55 26 12 50 21 47 30 43 39 40 48 43 57 35 2 23 44 32 46 41 5050 54 27 0 2 27 9 4 27 18 10 54 44 10 53 2227 2 34127 11 45 21 0 30 14 3936 2 27 5 21 27 14 40 24 33 16 42 43 52 4 28 1 37 55 27 13 36 41 46 16 55 40128 5 10 14 42 24 I3 2 49 52 59 20 28 9 8 28 18 50 28 27 38 7 47 48 56 28 13 18 2 23 6 32 52 42 443 52 48 29 2 23 29 1213 2 87 376 47 39 57 28 29 7 3129 17 31 27 32 37 32 57 29 2 48 29 12 56 29 23 5 33 4 43 14 53 36 30 3 48 28 56 39 13 49 35 59 55 30 10 23 30 20 51 31 2 58 56 4 30 6 34 30 17 57 30 27 38 38 11 48 40 59 48,- 30 24 15 34 58 45 41 56 25 31 7 10 31 17 57 31 28 44 59 58 17 31 4 28 31 15 21 31 26 21 37 21 48 22 59 18 / 31 24 1 35 10i 46 19 57 3032 8 43 32 15.8 32 31 4 60 55 45 32 7 7132 18 31 32 29 55 41 23 52 49 33 413 A 32 28 43 40 25 52 4 33 3 43 33 15 23 33 27 9 38 48 61 33 3 17 33 15 10 33 24 4 39 50 55 34 2 54 34 14 53 2 39 317 51 2 34 3 37 34 15 48 34 28 2 40 17 52 33 62 34 16 5313 29 20 41 49 54 19 35 6 50 35 19 22 35 31 56 1 56 14 35 9 35 21 4(; 35 34 35 47 25 36 0 17 36 13 28 63 35 37 27 50 38 36 3 3936 16 47 36 30 2 43 10 56 26 ~ 36 20 40 36 34 6 47 34 37 1 437 14 37 3728 11 37 41 48 64 37 6 4 37 19 52 37 33 42 47 38 38 1 30 38 15 29 38 29 29 53 47 3 8 38 22 1135 3 32 36 3 S 5 52 39 5 15 39 19 40 65) 38 44 2 38 58 40139 13 23 39 28. 3 1213 59 42 4 57 4440 12 48 39 43 38 40 7 21 40 7 21 40 22 3340 37 51 40 53 10 41 833 66 40 34 29 40 48 45) 41 641;4l 20 10141 36 0141 51 50 42 746 - 41 32 2941 48 4042 4 55 42 21 1442 37 36 42 54 243 10 32 67 42 35 301422 1843 9 9 43 26 4 43 43 844 0 11 44 17 21 2 43 42 34144 0 3144 17 3544 35 13 4- 53 545 10 4345 28 36 68 44 54 8 45 12 19 45 38 4:3;i5 49 3 46 7 33146 33 40 46 44 50 2 46 10 46 46 29 34 46 40 34147 8 13 47 27 37 47 47 7 48 6 42 69 47 33 5147 53 5148 13 13 43 3 28148 53 5049 14 2049 35 7 549 1 57493 4944 1450 5 34 50 27 7150 48 47 50 13 35 70 50 38 17 51 23 35 51 23 5151 45 43152 8 41 52 31 37152 54 50 i I t I TABLE XXIV. Showing the Azimuths of Polaris when on the same vertical plane with y (Gamma) in Casiopew at its under transit. All the Azimuths or bearings are North-zest. I The column headings are the years or dates. 1870 1880 1890 1900 1910 1920 1930 1940 2 8 6 8 46 9 24 10 02 10 38 11 12 11 41 12 10 4 7 47 26 04 40 14 43 12 6 9 49 28 06 42 16 45 15 8 12 52 41 09 45 19 49 18 10 15 55 34 13 49 23 53 23 12 19 59 38 18 54 28 5S 28 14 23 9 04 44 23 11 00 35 12 05 35 16 28 10 50 30 07 42 12 42 18 34 16 57 37 14 50 20 51 20 8 41 23 10 04 45 23 59 30 13 01 22 48 32 13 54 33 12 9 41 12 24 57 41 23 11 05 44 21 53 25 26 9 06 51 34 16 56 33 13 05 38 28 17 10 02 46 29 12 09 48 21 54 30 28 15 59 43 25 13 04 37 14 14 32 41 28 11 4 59 41 21 55 29 34 55 44 30 12 16 59 40 14 15 51 36 10 11 1 11 48 35 13 19 14 01 37 13 38 28 18 12 8 56 42 24 15 02 15 3 40 47 39 30 13 19 14 06 50 28 16 06 41 57 -49 41 22 20 15 04 43 21 42 11 7 12 01 54 45 33 18 58 37 43 19 14 13 07 59 48 34 16 14 54 44 32 27 20 14 14 15 03 50 31 17 12 45 43 401 35 29 20 16 08 49 30 46 56 54 50 45 37 26 17 08 49 47 12 11 13 09 14 06 15 03 55 44 28 18 10 48 25 25 23 21 16 14 17 05 48 32 49 41 42 41 40 35 26 18 10 55 50 57 14 0 15 00 16 00 56 48 34 19 19 51 1315 19 21 22 17 19 18 12 59 45 52 33 39 42 44 43 37 19 25 20 12 53 53 15 0 16 05 17 09 18 08 19 04 53 41 54 14 14 23 29 34 36 33 20 22 21 12 55 36 47 54 18 01 19 05 20 03 54 45 56 15 0 16 12 17 22 31 35 35 21 28 22 19 57 25 40 51 19 02 20 08 21 10 22 05 57 58 53 17 09 18 22 35 43 46 42 23 3( 59 16 22 40 56 20 11 21 21 22 26 23 23 24 19 60 53 18 14 19 32 49 22 01 23 08 24 07 25 0 61 17 26 50 20 11 21 20 45 23 54 54 25 54 62 18 03 19 29 53 22 14 23 32 24 43 25 45 26 47 63 42 20 11 21 38 23 03 24 22 25 36 26 41 27 44 64 19 24 58 22 27 55 25 17 26 34 27 40 28 40 65 20 11 21 47 23 20 24 52 26 17 27 36 28 45 29 54 66 21 02 22 2 24 18 25 53 27 22 28 45 29 56 31 0 67 57 23 41 25 21 27 01 28 33 29 56 31 14 32 2 68 22 57 24 47 26 32 28 15 29 52 31 22 32 39 33 50 69 24 05 25 59 27 49 29 37 31 18 32 52 34 13 35 33 70 25 20 27 19 29 15 31 09 32 54 34 23 35 32 37 22 t _~~~~~~~. i I I I I I I I I I I I i i IS i. i, Cog t I l 194 TABLE XXV. Showoing t/i Azinmuths of Polaris, zo/hin vertical w0it/i Alioth in Ur-sa Mllojoris (t its under tronsit. All the Azinuthls or beezrhivs are Aorthz-east. (The tot. coltza;o is years, beginninitg 2ani. s.) North 1870 1880 1890 1900 1910 1920 1930 1940 Lat. 2 801 8 411 930 10 03 10 30 1115 11 47 12 18 4 02 43 32 04 35 17 49 19 6 03 45 34 05 40 19 52 26 8 05 47 37 07 45 22 55 24 10 07 50 39 11 _ 50 24 58 28 12 11 54 42 15 54 31 12 03 33 14 15 58 48 20 59 36 09 40 16 19 9 04 53 26 11 06 431 16 46 18 25 10 58 34 13 49 23 54 20 31 1-6 10 06 41 21 57 32 1303 22 38 23 14 49 30 12 07 42 14 24 45 31 23 59 40 19 54 26 26 53 40i 34 11 09 52 31 13 06 39 28 9 02 50 45 20 12 05 45 21 54 30 13 10 02 59 33 18 13 00 36 14 11 32 24 16 11 12 50 34 13 16 544 28 34 38 30 28 12 06 51 35 14 12 49 36 53 45 44 24 13 11 55 34 1510 38 10 08 11 03 12 01 44 32 14 18 57 34 40 25 22 23 13 06 55 41 15 22 16 01 41 34 32 34 18 1407 561 36 16 42 44 42 46 30 21 15 10 51 31 43 53 53 58 43 35 23 16 07 55 44 11 04 12 06 13 11 56 50 39 22 17,04 45 15 19 24 14 11 15 05 56 40 21 46 29 33 38 26 21 16 11 57 40 47 42 51 52 42 37 31 17 16 18 00 48 55 13 08 14 07 59 55 50 36 20 49 12 09 16 25 15 17 16 15 17 12 58 42 50 24 32 43 35 35 38 1S 20 19 05 51 40 49 15 04 56 57 18 01 43 30 52 56 14 11 25 16 16 17 19 26 19 08 56 53 13 14 29 48 40 43 50 34 20 24 54 34 48 16 11 17 04 18 08 19 10 20 02 53 55 52 15 10 34 28 35 40 33 21 23 56 14 14 33 58 56 19 04 20 11 21 04 54 57 38 58 17 26 18'25 37 45 38 22 28 58 15 01 16 25 54 56 20 07 21 17 22 14 32 59 27 54 1826 19 28 42 52 35 23 10 60 55 17 24 58 20 03 21 19 22 33 23 21 50 61 16 24 57 19 57 41 59 23 16 24 10 24 33 62 56 1832 20 16 21 21 22 42 59 25 03 25 18 63 17 30 19 10 58 22 05 23 28 24 51 25'56 26 02 64 18 06 - 51 21 41 22 52 24 19 25 46 26 55 27 00 65 18 47 20 35 22 33 23 43 25 13 26 48 27 51 28 02 66 67 68 69 70 19 30 21 23 23 27 24 39 26 13 27 46 28 51 30 10 20 17 22 15 24 20 25 39 27 17 28 58 30 15 31 21 21 10 23 13 25 14 26 45 28 27 30 19 31 28 32 46 22 04 24 16 2631 3 27 58 29 44 31 35 32 46 34 14 23 05 25 26 27 49 2918 31 09 33 00 34 22 35 55 1 i i I TABLE XXVI. Mean places of Commna, (C~asiof)anEpio (Aith), Ursa M17ajoris, at Greenwich. Mean noon for tre first day of Yaanuary of eack y'ear, from sSpo to 19.5o. Gamma in Cassiopw. Alioth in Ursa Majoris., Right Asce'n. N. Polar Dist. Right Ascenon. N. Polar Dist.~ 1870 0 48 52.6 29 59 15.6 12 48 18.2 33 20 3.8 o 1 56. 58 56.0 20.9 2 02 3. 5 -M- "J 2 59.7 58 36.4 230.5I 20 43.2 a 3 49 3.3 58 16.8 26.2 21 2.9 Z 4 0 49 6.8 58 57.2 28. 9 21el22.5 ~ 5 10.4 5 737.9 31.5 21 42.2 6 14.0 57 18.0 34.2 22 1.8 a 7.17.5 57 58.3 36.8 22 21.6 S. 8 21.1 56 38.7 039.5 2 2 41. 2 9 24.7 56 4.1 42.2 123 0.9 F.: 1880 28. 2 55 59.5 12 48 44.8 3)323 20.5 aO 1 0 49 31.8 55 39.9 47.5 23 40.2 2 350.4 55 20.3 50.1 23 5 9. 9 3 38.9 55 0.7 52.8 24 19.5 vv 4 42.5 54 41.1 55.5 24 39.2 a 5 46.1 54 21.4 48 58.12 24 58.9 6 49.7 54 1.9 49 0. 8 25 18.5 a 7 53.2 53 42.3 3.4 25 38.2 r 8 0 49 56.7 53 22.7 6.1 25 57.8 S 9 0 50 0.3 53 3.9 8.7 29 17.5 1890 4.0 5 2431.5 12 4911.4 33 26 37.2 1 7.5 52 23.9 14.1 29 56.8 0. 2 11.1 52 4.3 16.7 27 16.5 3 14.7 51 44.7 19.4 2-736.2 a 4 18.3 51 25.1 22.0 27 55.8 5 21.8 51 5.5 24.7 28 15.4 6 25.4 50 45.9 27.3 28 25.1 a 7 29.0 50 26.3 30.0 28 54.8 U' 8 32.6 58 6.7 32.6 29 14.4 c 9 36.2 49 47.1 35.3 26 34.1 b 1900 0 58 39.7 49 27.6 12 49 37.9 29 53.7 <u 1 43.3 49 8.0 40.6 30 13.5 0. 2 46.9 48 48.4 43.2 30 33.0 ~ a 3 50.5 48 28.8 45.9 30 52.7 > 4 54.1 48 9.2 48.5 31 12.3 4- anC 5 57. 47 49.6 51.2 30 32.0 C6 6 0 51 01.2 47 30.0 53.9 31 51.6 7 04.8 47 10.4 56.5 32 11.3 6O. 8 08.4 46 50.8 59.2 32 30.9 Z a 9 12.0 46 31.7 01.9 32 50.6. 1910 0 51 15.6 29 43 11.6 1250 ) 04.5 33 33 10. C0 191 051. 45 12.4 12 50 07.2 - 9.8 12 5 1 221.8 44 52.8 9.8 49.5 0 13 26.4 44 33.2 12.5 34 09.1 5c C 14 30.0 29 44 53.2 15.12 28.7 U 0: 15 33.6 44 33.6 17.8 48.0 a~' VO 16 37.2 44 14.0 20.5 35 O8. 0,or ad to 17 40.8 43 54.4 23.12 27.9 a n18 44.4 43 34.8 25.8 47.3 ~. 19 48.0 43204.2 28.1 36 06.0 > 12 051 51.5 4258 12 5030.7 36 26.6 30 52 27.6 39 40.2 57.4 39 42.9 w I 40 53 03.7 36 24.7 51 23.8 42 59.1 50 53 32.8 29 23 9.6 50.2 34 43 15.6 M j TABLE XXVII. Showing the Azimuth or bearing of Alp/ha in the foot of the Southern Cross (Crucis), when on the same vertical plane with Beta in Hydri, or in the tail of the Serpent. Bearings are all South-east when Alipha Crucis is at its under transit, and for the Ist of January of the years given at lto. Lat. 1850 1900 1950 2000 2050 2100 2150 "I!-I -- ~ ' I ' ". 2 15 12 1 12 1 14 1 19 1 43 15 2 58 3 53 13 12 14 19 43 16 58 54 14 12 14 20 43 16 58 56 15 12 15 21 44 17 59 57 16 13 105 2 44 17 301 58 17 13 16 23 45 17 03 59 18 14 16 24 46 18 3 06 4 00 19 14 17 24 47 19 07 01 20 14 17 25 48 20 3 09 02 21 1 15 18 1 25 1 49 2 21 3 10 4 05 2 -2 15 18 26 150 22 10 06 23 16 19 27 50 23 11 07 24 16 19 28 51 24 12 09 25 17 20 28 52 25 13 11 26 17 20 29 52 26 14 13 27 18 21 29 53 27 15 15 28 19 22 30 1 54 29 17 18 29 20 22 31 55 30 19 20 30 21 23 32 56 32 3 21 23 31 1 22 1 24 134 157 2 34 3 23 4 26 - — 32 22 2-35' 58 36 325 29 33 23 26 36 59 37 27 32 34 24 27 37 201 39 30 35 35 25 28 38 02 41 32 38 36 26 29 39 03 43 35 42 37 28 30 40 05 45 38 45 38 29 31 42 07 48 41 49 39 30 32 43 09 50 45 53 40 31 34 44 11 53 48 58 41 132 1 35 1 46 2 255 3 51 5 02 42 34 37 48 15 57 58 07 43 36 39 50 17 59 59 11 44 37 41 51 20 3 03 403 16 45 39 43 53 22 06 07 22 46 41 44 55 25 10 12 28 47 43 46 57 28 13 17 34 48 45 48 2 00 2 31 17 22 40 49 47 50 02 33 21 28 47 50 49 52 05 36 26 34 54 51 151 1 54 07 38 3 30 437 6 02 52 5 57 10 40 34 43 12 53 57 2 00 13 45 39 49 17 54 59 02 16 51 44 55 27 55 2 02 06 19 53 50 502 39 56 05 09 23 3 01 56 10 51 57 08 13 27 05 4 01 18 7 01 58 12 16 32 09 09 27 11 59 16 19 36 14 16 36 23 60 -20 24 40 20 24 44 36 61 24 29 4 26 32 604 7 50 62 29 34 51 33 41 612 801 63 34 38 56 40 50 20 23 64 40 43 302 4 5 00 27 41 65 2 45 2 47 09 3 56 5 10 6 35 9 01 19u 11111 III - ', -. " N 11 TABLE XXVIII. ALTITUDES AND GREATEST AZIMUTHS FOR IST JAN., 1867, (SIDERIAL TIME.) FOR CHICAGO-LAT. 41' 50' 30", LONG. 87 34' 7" W.; AND BUENOS AYRES-LAT. 34' 36' 40" S., LONG. 58' 24' 3" W. British Up. Meredian Time to Time of Time of Greatest Alt. at Associati. NAME OF STAR AND CONSTELLATION. Mag. Pol. dist. R. A. Passage. Gt. Az. G. E. Az. G. W. Az. Azimuth. G. Az. Cat 'logue of Stars. h. m. s. h. m. s. h. m. s. h. m. s. h. m. s. 360 a (Polaris) Ursa Minoris............. 2 1 24 1 10 17 6 26 38 5 55 0 0 31 38 12 21 38 1 52 46 11 51 25 6281 a Ursa Minoris...................... 4.5 3 23 44 18 15 15 23 31 36 5 47 51 17 43 45 5 19 20 4 33 36 44 55 34 5780.............. 4.5 7 44 55 16 59 42 22 16 03 5 32 9 16 43 54 3 48 12 10 24 9 42 18 58 5285..... 4.5 11 47 52 15 48 52 21 5 13 5 16 59 15 48 14 2 22 12 15 55 44 42 57 31 4936 ft (Kochab)............. ' 2 15 18 5 14 51 7 20 7 28 5 3 21 15 4 7 1 10 49 20 44 46 43 45 22 8238 yCephi........................... 3.4 13 6 35 23 33 55 4 5016 5 12 5 23 38 11 10 02 21 17 43 32 43 13 47 169 a Cassiope....................... var. 34 11 333 0 32 59 49 20 3430356 2 1824 20 16 48 58 0 53 45 9 3242 9pUrsa Majoris..................... 3 37 43 7 9 23 56 14 40 7 3 5 13 10 34 54 17 15 20 55 14 9 57 29 27 o 3777 r (Dubhe).. 2 27 31 55 10 55 30 16 11 51 4 9 17 12 2 34 20 21 08 38 21 11 48 47 14 4017 Y........3 35 33 57 11 46 49 17 3 10 3 21 12 13 41 58 20 24 22 51 19 39 55 5 27 5937 /JDraconis..................... 3.2 37 35 57 17 27 26 22 43 47 3 6 8 19 37 39 1 49 55 54 58 59 57 20 48 6091 r y............ 2.3 38 29 40 17 53 31 23 09 52 2 58 57 20 10 55 2 8 49 56 28 2 58 27 48 7416 a Ceplhi......................... 3.2 27 58 39 211524 2 31 45 4 6 41 22 25 04 6 38 26 39 1 42 49 3 22 5959 6 Octantis........7................. 6 0 43 17 18 0 55 23 17 51 5 58 0 17 19 51 5 17 51 0 53 48 34 36 51 88 /JIHydri............................. 3 11 59 45 0 18 43 5 35 39 5 26 21 0 9 18 11 02 00 14 39 21 35 2) 58 4131 /J Chamranieontis...................... z 5 11 25 34 12 10 36 17 27 32 5 27 55 11 59 37 22 55 27 13 55 20 35 24 52 5578 a Trianguli Australis................. 2 21 13 18 16 34 37 21 51 33 4 57 47 16 53 46 2 49 20 26 4 50 37 32 27 507 a Eridani (Acherner)............... 1 32 5 13 1 32 45 6 49 41 4 17 29 2 32 12 11 07 10 40 10 43 42 5 56 2096 a Argus (Canopus).................. 1 37 22 33 6 21 0 11 37 56 3 53 4 7 44 52 15 31 0 47 29 59 45 37 27 3186............................ 2 31 16 58 9 13 32 14 30 28 4 20 50 10 9 38 18 51 18 39 5 57 41 39 14 4187 c Crucis............'I.....1..... I 1 27 38 22 12 19 13 17 36 9 4 35 28 13 0 41 22 11 37 34 17 37 39 52 45 4669 3Centauri.......................... 1 30 16 13 13 54 28 19 11 24 4 24 59 14 46 25 0 33 23 57 45 2 41 7 21 7004 aPavonis........................... 2 32 50 11 20 14 57 1 31 53 4 14 12 21 17 41 5 46 05 41 11 29 42 31 59 II i Il TABLE XXVIIIA. TABLE OF EQUAL ALTITUDES. Intervl Log. A. Log. B. Int'rval. Log. A. Log.. B.Int'val. Log. A. Log. B. h. m. h. m. h. m. -2. 0 7.7297 7.7146 4. 2 7.7451 7.6815 6. 0 7.7703 7.6198 2 98 43 4 54 07 2 08 84 4 7300 39 6 58 800 4 13 70 6 02 36 8 61 792 6 19 56 8 04 32 10 64 84 8 24 42 10 05 28 12 68 76 10 29 27 12 07 25 14 72 68 12 35 13 14 09 21 16 75 59 14 40.6098 16 11 17 18 79 51 16 45 82 18 13 13 ___ ___18 51 68 20 15 09 20 82 43 20 56 53 22 17 05 22 86 34 22 62 38 24 19 7.7101 24 90 26 24 67 23 26 21 7.7097 26 94 17 26 73 07 28 23 92 28 97 08 8 79.5991 30 25 88 30.7501.6700 30 84 75 32 27 83 32 05.6691 32 90 59 34 29 79 34 09 82 34 96 43 36 31 75 36 13 73 36.7801 27 38 33 70 38 7.7517 7. 663 38 07 10 40 36" 65 40 7.7521 7.6654 -40 13.5894 42 38 61 42 25 45 42 19 77 44 40 56 44 29 35 44 25 60 46 42 51 46 33 26 46 31 43 48 45 46 48 37 16 48 36 25 50 47 41 50 41.6606 50 42 08 52 49 36 52 45.6597 52 48.5790 54 52 31 54 49 87 4 54 72 56 54 26 56 53 77 56 60 54 58 57 21 58 5 7.6567 5_58 67 36 3.00 59 lo- 5. 00 2 5 7. 00 73 17 2 62 10 2 66 46 2 79.5699 4 64 7.7005 4 70 36 4 85 80 6 67 7.6999 6 75 25 6 91 61 8 69 93 8 79 14 8 98 41 10 72 88 10 83.6504 10.7904 22 12 74 82 12 88.6493 12 10 02 14 77 76 14 92 82 14 16.5582 16 80 70 16 97 71 16 23 62 20 7.7386 7.6958 20 06 | 48 20 -36 22 22 88 52 22 10 37 22 42 01 24 91 46 24 15 25 24 49.5480 26 94 40 [ 26 20 14 26 55 59 28 97 34 28 24.6402 28 62 37 30.7400 2 7 30 29.6390 30 69 16 32 03 21 32 34 78 32 75.5394 34 06 14 34 38 66 34 82 72 36 1 09 1 08 36 43 54 36 89 50 38 12.6901 38 48 42 38 95 27 40 15.6894 40 53 30 40.8002 04 421 18 88 42 58 17 42 09.5281 44 21 81 44 G63.6304 44 16 58 46 24 74 46 (68.6291 46 23 34 42 18 48 28< 7 - 818 1 73 78 48 30 11 0 31 | 5 ' ||50 | 78 65 50 37.5186 "2 34 52 5'2 83 52 52 44 62 54 37 45 54 88 39 54 51 37 56 41 38 56 93 25 56 58 12 58 44 30 58 7.7698.6212 58 65.5087 4.00 47 23 6.00 7.7703.6199 8.00 7.8072 72 199 _i TABLE XXVIIIB. 11 TABLE XXVIIIc. Showing t/e Ie;ntIh of a Degree of Lat. and Long. in Metres and Miles. To Convert Lat. Metres into Stat. Miles. o 1 Metres. Miles. 2 10.006 3 20.012 4 30.019 5 40.025 6 50.031 7 60.037 8 70.044 9 80.050 10 90.056 11 100.062 12 200.124 13 300.186 14 400.249 15 500.311 16 600.373 700.435 800.497 900.559 51 1000.621 52 2000 1.243 53 3000 1.864 54 4000 2.485 55 5000 3.107 56 6000 3.728 57 7000 4.319 58 8000 4.971 59 9000 5.592 60 10000 6.213 61 14000 12.427 62.12000 18.640 63 13000 24.8054 64 14000 31.067 65 15000 37.281 66 16000, 43.494 67 Statute Miles. 69.7I 69.06 69.08 68.07 68.90 68.81 68.62 68.48 68.31 69.15 67.95 67.73' 67.481 67.21 66.95 66.65 69.31 43.43 42.48 41.53 40.56 39.58 38.58 37.58 36.57 35.54 34.50 33.45 32.40 31.33 30.24 29.15 28.06 26.96.1 In I Lat. 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 I Length of a Length of a )egree of Lat I Degree of Lon in Metres. in Metres. Length of a D. of Lon. inStat.Miles I 11.658.4 106.473.4 66.157 11.669.5 105.892.6 66.796 11.681.1 106.279.7 65.415 693.3 104.634.8 65.015 706.0 103.958.7 64.594 719.2 103.250.0 64.154 732.9 102.510.0 63.695 747.1 101739.7 63.216 761.7 100.938.2 62.718 776.7 100-105.9 62.200 90.43 (51.6 792.2 808.3 824.4 841.9 858.0 875.2 110.892.8 910.7 928.8 947.2 995.8 98 4.6 111.003.5 022.6 041.8 061.1 080.5 100.0 119.4 138.9 158.4 177.8 197.2 216.4 90. 243. 2 61.664j 98.350.2 61.109 97.427.4 60.536 96. 474.8 59.944 95.492.9 59.334 94.481.9 58.706 93442.1 58.060 92373.8 57.396 91.277.3 56.715 90.152.9 56.016 89001.0 55.300 87-821.6 54.568 86.616.0 53. 819 85.383.9 53.053 84.125.1 52.271 82.840.8 51.473 81.531.1 50.659 80.196.5 49.830 78 837.3 48.986 77.453.9 48.126 79.0465.8 47.251 74.612.3 46.362 73.162.9 45.460 71-687.0 44.543.H I That part of Table C, from Lat. i.7 to 50', is calculated according to Bessel's formula, as given in the United States Coast Survey of 1853, page 100. Tables C and 1. arc from the same volume, pp. 103 and 106, excepting that showing the length of a dcgree of Longitude, from Latitudes 0 to 17, and 50 to 90 degrees, which is tak-en from Keith on the Globe, p. 193. Those having occasion to project a nssp on ant extensive scale, will find, in the albove volume, tables from pp. 107 to 163 which have been calculated for tile United Stat s Coast Survey, undler the superintendence of the late A. 1). BAC 1E. To find tile le an-th of a dogs ee of Ion-tfude in any degree of Lat. Rad. is to //ge iengt 7 of a (1e cc oil 1/i Equator-as 1/ic Cosiiie J ture given Latituide is to 1/ic icgt/ of a ol<~-'c'cc of Lougitwde in 1/sot Lot. Length of a (iegr-ee on th-, 1iquator is 3635144 feet. Rladius of the Equator 2 09-`21150. IPolr Se-niaxis = 20853180. NOTE,-There has been nothiig printed to fill from page 2oo to 249. 200 i TABLE xxiX.-To Reduce French Litres T I to Cubic Feet and Imperial Gallons. 1 Litre -0.0353166 Cubic Feet, or 0.2200967 F Imperial Gallons. ne' d) Cubic Egih Cubic E1nglish or 3Mi or Imper Litre. Imprial Ce Feet Gallons. Fe. Gallons. De 1 0.03.54 0,2201 60.71190 _13.205~8 M( 2.070. 4401 61.1543.4258 ji( 3.1059.6603 62.1896.6460 Iii 4.1413.8804 63 2.2249 13.8661 F 5.1766 1.1005 64.2603 14.0862 6.2 119.3206 65.2956.3063 ST 7.2472.5 407 66.3309.5264 F" 8.2825.7608 67.83662.7465 K-A 9.31 78.9809 68.4015.9666 Li 10-.5032 2.2010 66'.4368 15.1867 TL 11.3885.4211 70.4722.4068 S( 12.4238.6412 71.5075.6268 s( 13.4591.8613 72.5428.8470 -14.4944 3.0814 73.5-781 16.0671 15.5297.3014 74.6134.2872 E 16.5651.521 75.6487.5073A 17.6004.4716 76.6841.727 1, 18.6357.9617 77.7194.9474 IN 19.6710 4.1818 78.7547 17.1675 ~ 20.7083.4019 79.7900.3876 21.7416.6220 80.82"'5 3.6077 i 22.7770.8421 81.8606.8278 23.8 12 '3 5.0622 82.8960 18.047 9 24.8476.2825 83.93131.268 25.8829.5024 84.9666.4881 26.9182.7225 85 3.0019.7082 27.9535.,9426 86.0372.9283 28.9889 6.1 6207 87.07125 19.1484 29 1.0242.3828 881. 10719.3685 30.0595.6029 89.1932.5886 31.0948.8230 90.1785.8087 1 32.1301 7.0431 91.2138 20.0288 33.1654.2631 92.2491.2489 34.2008.4832 93.1844.4690 35.2361.7034 94.3198.6891 36.2714.9235 95.3551.9092 37.3067 8.1436 96.3904 21.1293 38.3 4 2.0.3637 97.4257.3494 39.3773.5838 98.4610.5695 40.4127.8039 99.4963.7896 41.4480 9.0240 100 3.5317 22.0097 42.4833.2441 200 7.0633 44.0193 43.5186.4642 300 10.5950 166.0290 44.5539.6843 400 14.1266 188.0387 45.5892.9044 500 17.6583 110.0484 46.6246 10.1244 600 21.1900 132,0580 47.6599.3445 700 24.72,16 154.0677 48 U652.5646 800 28.2533 176.07714 49.7305.7848 900 31.7849 198.0871 50.7658 11.0048 1000 35.3166 220.0967' 51.8011.2249 2000 70.6332 440.019 52.8365.4450 3000 105.950 660.029 53.8718.6651 4000 141.266 880.039 54.9071.8852 5000 176.583 1100.48 55.9424 12.1053 6000 211.901 1320.58 156.9777.32-54 7000 247.216 1540.68 57 2.0130.5455 8000 282.5633 1760.77 58.0484.7656 9000 317.849 1980.87.59,.0837 -~9857110000 353.166 12200.97 ~BLE XXX.-Foreign Weights and Measures. 'rench, English VV System. inches. Ilimetre equals 0.039871 Dtimetre 0.393708 ~cimetre 3.9370(i9 4re " 39.37079!cametre " 393.7079 ~ctometre 3937.079 l1ometre " 393-0.79 yriametre " 3937107.9 )ot (Pied de Roi) =12.7926 )anish foot =11.034- inches -ench " = 12.7925 " vedish " = 11.690 " ustrian" = 12.448 Isbon " = 12.96 " )ise, or 6 ft. Fr. = 76.735 in. 1. metre = 1550.85 sq, in. 1. metre = 10.7698 sq. feet Measure. ISqy.ds. ugland Acre 480 msterdam Moyen 9722.Lamhnrgh Moyen 11545 r-eland Acre 7840 aples Moggia 3998 ~ortugal (3eira 6970 russia Morgen 3053,ome Pizza 3158 'Ussia Dessitina 13066.6 p a idn, Fanegade 5500 vede Tunneland 5900 ~cotland Acre, 6150 SURFACE. French, id system. English. ',quare inch =1.1364 inches krpent (Paris) = 900 sq.- toises (woodland) = 1-00 sq. royal perches I Are = 10(1 sq. metres Are = 1076.98 sq. feet (Centare 1 sq.- metre Decare = 10 ares Hlecatare = 100 ares CAPACITY. Litre taken as a standard. IMyrialitre =10000 litres Kilolitre = 10 H ectol itre = 10 Decalitre 10 " Litre = 1 " Decilitre = 0.1 " Centilitre = 0 01 Millilitre = 0.001" Litre =cubic centimetre Troy grains. Milligramme =.0154 Centigramme =.1544 Decigramme = 1.5444 Gramme = 15.4440 Decagramme = 164.4402 Hlectogramme = 1544.4023 Kilogramnme = 15444.0234 Milligrammne =154440.2344 For a valuable collection of tables of weights and measures, see Oliver Byrne's Dictionary of Mechanics and Engineering. 249 TABLE Cor Veloc'y per sec. 10 C Diam. Area of ilgt Metre section. 100 n 0.01 0.0001 0.31 2 03 11 3 07! 4 13 5 20: 6 28 7 38 8 50 9 64 10 79 11 95_ 12 113 13 133 4 14 154 15 177 16 201 17 227 18 254 19 284 20 314 21 846 22 380 23 415 24 452 25 491 26 531 27 573 28 616 29 661 30.0707.1 31 755 32 804 33 855 34 908 35 962 36 1018 37 1075 38 1134 39 1195 40 1257 41 1320 42 1385 43 1452 44 1521 45 1590 46 1662 47 1735 48 1810 49 1886 50 1964 65 2376 60 2827 65 3318 70 3848 75 4418 ~80 5027 85 65675 90 6362 96 7088 1.00.7854 XXXI.-Discharge of Water through New Pipes. ipiled from Henry Darcy's French Tables of 1857. q tentillmetres.. in lisch'ge net. in litres. 302 0.008 154 031 326 071 115 126 306 196 241 283 198 385 168 503 145 636 127 785 114 950 102 1.131 093 327 86 539 79 767 73 2.011 69 270 64 545 61 835 57 3.142 54 4i4 51 801 49 4.155 47 524 45 909 43 5.309 41 726 40 6.158 38 605 037 7.069 35 548 34 8.043 33 553 32 9.079 31 621 30 10.179 29 752 28 11.341 28 946 27 12.566 26 13.203 26 855 25 14.522 24 15.205 24 904 23 16.619 23 17.350 22 18.090 22 85E 21 19.635 19 23.75E 18 28.274 16 33.18& 15 38.48i 14 44.17c 13 50.26( 12 56.74f 12 63.611 11 70.88' 1010 78.54(.[. 12 Centiimetres. ilgt. in Disch'ge 100 met. in litres. 0.5187 0.009 1662 038 0901 085 598 151 441 236 347 389 285 462 241 603 208 763 183 943 164 1.140 148 357 134 593 123 847 114 2.121 106 413 99 724 93 3.054 87 402 82 770 78 4.156 74 562 71 980 67 5.429 64 6.091 62 371 59 871 57 7.389 55 926.0153 8.482 51 9.057 49 651 48 10.264 46 895 45 11.545 43 12.215 42 903 41 13.609 40 14.335 39 15.080 38 843 37 16.625 36 17.427 35 18.246 34 19.085 34 943 33 20.819 32 21.715 31 22.629 31 23.562 28 28.510 25 33.929 23 39.820 22 46.182 20 53.015 19 60.319 18 68.994 17 76.341 16 85.059.0115 94.248 14 Centimetres. 16 Centimetres. 11gt- in Disch'ge Rgt. iD Disebarge 100 met. in litres 100met. in 11tres. 0.7060 0.011 0.9221 0.013 2262 44 2954 050 1226 99 1601 113 0811 176 1063 201 600 275 0784 314 472 39 61-1 452 387 539 506 616 328 704 428 804 283 891 370 1.018 249 1.100 326 257 22 83 2.91 521 201 5 88 262 810 183 858 23.9 2.124 168 2.155 219 463 155 474 208 827 144 815 188 3.217 134 3.178 1 76 632 126 563 165 4.072 119 969 155 536 112 4.398 146 5.027 1 (P6 8 49 1 3bt 4 542 101 5.822 182 6.082 096 81 7 125 648 92 6.338 120 7.238 88 8 7 2 114 854 84 7-.-4 3-8 1 RO 8. TF5 81 8.016 105 9.161 77 621 101 852 75 9.247 097 10.568.001-2 9.896.0094 11.310 69 0.56-1 91 12.076 67 11.259 88 868 65 974 85 13.685 63 12.711 82 14.527 61 13.470 80 15.394 5',) f 4. 2 5 (5 77 16.286 5 7 15.053 75 17.203 56 078 73 18.146 54 16.724 7 1 19.113 53 17.593 69 20.106 5 1 18.484 67 21.124 50 19.396 66 22.167 49 20.331 64 23.235 48 21.287 62 24.328 47 22.266 60 25.446 46 2 . 2-6 7 UO -6.-59 1 45 24.289 5 8 27.759 44 25.334 57 28.953 43 26.401 56 30.172 42 27.489 5 5 81.416 38 33.26 49 C8 0-1 6 35 39.584 45 45.239 82 46.456 42 63.093 29 53.878 38 61.575 27 '61.850 36 70.686 26 70.372 38 80.4'25 24 79.443 31 90.792 23 89.064 30 101.788 21 99.235 28 113.412.0020 109.956.0016 125.664 14 Centimetres. Hgt. in Disch'ge 100 met. in litres 0.7060 0.011( 2262 44 1226 99 0811 176 600 275 472 396 387 539 328 704 283 891 249 1.100 223 330 201 583 183 858 168 2.155 155 474 144 815 134 3.178 126 563 119 969 112 4.398 106 849 101 5.322 096 817 92 6.333 88 872 84 7.433 81 8.016 77 621 75 9.247.0072 9.896 69 10.567 67 11.259 65 974 63 12.711 61 13.470 59 14.250 57 15.053 56 078 54 16.724 53 17.593 51 18.484 50 19.396 49 20.331 48 21.287 47 22.266 46 23.267 45 24.289 44 25.334 43 26.401 42 27.489 38 33.262 35 39.584 32 46.456 29 53.878 27 61.850 26 70.372 24 79.443 23 89.064 21 99.235.0020 109.956 16 Centimetres. [Igt. iD Disebarge LOOmet. in 11tres. ).9.221 0.013 2954 050 1601 113 1063 201 0784 314 61-1 452 506 616 428 804 370 1.018 326 257 2.91 521 262 810 23.9 2.124 219 463 2 08 827 188 3.217 1 76 632 165 4.072 155 536 146 5.027 13tJ 542 182 6.082 125 648 120 7.238 114 854 110 8.4 5 105 9.161 101 852 097 10.568.0094 11.310 9 1 12.076 88 868 85 13.685 82 14.527 80 15.394 7 77 16.286 75 17.203 73 18.146 7 1 19-113 69 20.106 6 21.124 66 22.167 64 23.235 62 24.328 60 25.446 60 - -6.-59 1 58 27.759 57 28.953 56 30.172 55 81.416 P -— -8 0-1 6 45 45.239 42 63.093 38 61.575 36 70.686 38 R 425 31 90.792 30 101.788 28 113.412.0016 125.664 16 Centimetres. Hgt. iD Discharge L00 met. in litres. ).9221 0.013 2954 050 1601 113 1(63 201 0784 314 617 452 506 616 428 804 370 1.018 326 257 291 521 262 810 239 2.124 219 463 203 827 188 3.217 176 632 165 4.072 155 536 146 5.027 139 542 132 6.082 125 648 120 7.238 114 854 110 8.495 105 9.161 101 852 097 10.568.0094 11.310 9l 12.076 88 868 85 13.685 82 14.527 80 15.394 77 16.286 75 17.203 73 18.146 71 19.113 69 20.106 67 21.124 66 22.167 64 23.235 62 24.328 60 25.446 60 26.591 58 27.759 57 28.953 56 30.172 55 31.416 49 38.01l 45 45.239 42 63.093 38 61.575 36 70.686 38 80.425 31 90.792 30 101.788 28 113.412.0016 125.664 I I 250 I I TABLE XXXI. - Discharge of Water through New Pipes. Compiled from Henry Darcy's French Tables of 1867. I.1 i& Centimetres. 20 Centimetres. 22 Centimetres 24 Centimetres. 26 Centimetres. 7i gin Iushg [lgt. it. Diseh'ge lHgt. in DI sehir. Hgt. in Dischir. 1-igt. in IDiseh'r, 100 m~et. I n I tres 100 met. in litres. 100 met.1in litres, 100 met. in litres 100 met.. -in litres I - --- - I - I I 1.1670 9.3739 2027 1345 992 780 640 542 469 412 368 3 32 -302 277 256 238 222 208 196 185 175 1 67 159 151 145 1 39, 133 128 123.0119 0.014 057 127 226 353 509 693 905 1.145 414 7 ~ J 2.036 389 7 71 3.181 619 4.086 580 5.104 I655 -6. 2-35 842 7.479 8.143 836 9.557 10.306 11.084 889 12. 723 1.4408 4616 2502 2661 1225 0.096 4 791 669 579 509 454 410 373 343 319 294 274 257 242 229 219 209 199 187 179c 171 164 15E 152.01,47 0.016 063 141 251 393 566 770 1.005 272 571 901 2.262 655 3.079 534 4.021 540 5.089 671 6.283 927 9.048 818 1T0-. 6-19 11.451 12.315 13.210 14.137 I 1.71434 0. 5585 3028 2010 1483 1166 957 809 700 616 550 496 452 414 383 356 332 311 293 377 262 2 49 237 229, 216 2077 199 191 184.0178 I 0.017 069 155 277 432 622 847 1.106 400 728 09 1 488 920 387 888 4.423 999 5.588 6.238 912 7.620 8.863 9.140 953 10. 799 11.680 12.596 13.547 14. 531 15.551 2.0748 0.6647 3603 2392 1764 1388 1139 963 833 733 I654 590 537 493 456 4213 395 370 349 329 312 1296 82 69 57 471 37 28 19.1211 0.019 75 17-0 302 471 679 924 1.206 527 885 281 714 3.186 6951 4.241 RZo 5.448 6.107 805 7.540 8. 313 9.123 971 10.857 11. 781 112. 742 13. 741 14.778 15 853 16.965 2.4350 0.7801 4229 2807 2071 16'2-8 1336 1130 0978 860 768.693 631 57.9 535 497 464 435 409 386 366 348 331 319 302 299 2078 267 257.024E I 0.020 082 184 327 511 735 1.001 307 6654 2.042 471~ 941 3.451 4.002 595 5.228 901 6.616 7.3712 8.168 9~. 00 5 883 10.802 11.762 12.763 13.804 114.886 116.010 17. 174 18.378 i I 'I 115 13.586 142 15.09b 171 16.605 04 18.114 239 19.624 111 14.476 1 37 16.085 166 17.693 197 19.302 231 20.910 107 15.395 132 17.106 160 18.817 91 20.527 224229.238 104 16.343 128 18.158 155 t9.974 85 21.790 217 23.606 101 17.318 124 19.242 150 21.167 79 23.091 210 25.015.98 18.322 2 20.358 142.3 72.29 04645 95 19.354 1 17 21.504 142 23.655 69 25.805 198 27.956 9 2 20.414 114 22.682 138 24.951 64 27.219 93 29.487 90 21.503 111- 23.8,92 134 26.281 60 28.670 87 31.059 87 22.620) 108 25.1313 131 27.646 55 30.159 82 32.673 85 2)3. 7 6 ~105 2 6. ~4 io ~127 2 9. 04-6 513~ 1. 68-6 783 4. 32 7 83 24.938 102 27.709 124 30.480 48 33.251 73 36.022 811 26.140 100 29.044 121 31.949 4 4 34. 853 69 37.753 7 9 27.370 098 30.411 118 33.452 40 36.493 65 39.534 7 7 28.628 95 31.809 115 34.989 137 38.170 161 41.351, 75 29.914 931.T 1133T6.562 3439. 88 6 507143. 21 0 74 31.229 91 34.699 110 38.169 ~31 41.639D 54 45.109 72 32.572 89 36.191 108 39.810 2 84'3. 4299 60 47.049 71 33.944 87 37.715 105 41.487 25 45.258 47 49.030 69 35.343 85 36.270 103 43.197 23 47.124 44 51.051 63 42.765 ~77 4f7~.517 0M935~2.-268 1 i67. 020O 20 61.772 57 50.894 70 56.549 85 62.204 101 67.859 19 73.513 53 59.730 65 66.366 78 73.003 093 79.646 10 86.276 49 69.272 60 76.969 73 84.666 86 92.363 102 100.06 45 79.52-2 56 88.358 68 97.193 81 106.03 095 114.87 42) 90.478 521 00.5031 6...........73 10.-5~8 75 120.64 88 130.69 40 102.141 49 113.490 59 124.84 71 136.19 83 147.54: 38 114.511 46 127.235 566139.96 67 152.68 78 165.41' 36 127.'588 44 141.765i 53155.94 63 170.12 741184.30 34 141.3721.0042 157.080.00501172.79,.0060 188.50.o070[204.2O 251 I i I i I TABLE XXXI -Discharge of Water through New Pipes. Compiled from Henry Darcy's French Tables of 1857. Veocv ir e 30 ~Centinietres. 134 Centimetres. 38 Centimietres. 142 Cniers Metr( 0.01 2 3 4 S 6 7 8 9 10.11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 87 38 39 40 41 42 43 44 45 46 47 48 49 50 55 60 65 70 75 85 90 95 I100 of sect'n. 0.0001 03 07 13 20 28 38 50 64 79 95 113 133 154 177 201 227 254 284 314 346 380 415 452 491 531, 573 616 661.0707 755 804 855 908 962 1018 1075 1134 11,95 1257 1320 1385 1452 1521 1590 1662 1735 1810 18861 19-64 2376 2827 3318 3848 4418 5027 5675 6362 7088.78.4 100 met. 3.2418 1.0386 0.5630 3737 2757 2168 1779 1505 1302 1146 1022 0922 840 77 1 712 661 617 579 45 15 487 63 41 21 02 385 70 56 42.0330 08 298 89 80 71 64 56 49 43 341 30 25 19 14 09 05 00.0196 92 59 46 35 26 18 11 04 -99.0094 in litres 0.024 094 212 377 581, 848 508 90 -2.35C 851 3.391q 982 618 5.301 -6-.03-2 80 q 7.634 8.506 9.425 io. ~YI 11.404 12.464 13. 572 14.726 1F5.92 8 17. 17 7 18. 473 19. 816 21.206 22. 643 24. 127 25.659 27.238 28.863 30.536 32.256 34.024 35.838 37.699 39. 6-08 41.564 43. 566 45.616 47. 713 49.857 52.049 54.286 56.573 68.905 1. 2-7 5 84.823 99.550 115.45 132.54 150.80 1 70.24 190.85 212.65 I.I I I II 0 II II I I I I I I I I HRgt. in 100 met. 4.1639 1.3340 0.7231 4800 3541 2785 2285 1933 1672 1471 1313 1185 1079 0980 914 849 793 744 700 661 626 59 5 66' 40~ 1 7 495' 75' 57 40.0624 09 396 83, 7 1 59 49 391 29 201 04.296 89 82 75 69 63 57 52 46 23 04 187 74 62 5 1 42 34 27 in litres. 0.027 107 240 427 668 961 1.308.709 2.163 670 231 845 4.513 5.234 6.008 8,36 7.7 17 8.652 9.640 10. 681 11. 776 12.925 14. 126 15. 381 16.690 18.052 19.467 20 936 22.458 24.033 25. 662 27.344 29.080 30.869 32.712 134.608 36.557 38.560 40.6016 42.72(6 4~4.889 47.105 49. 375 51. 698 54.075 56.505 58. 988 61.525 64. 1 06 66. 759 80.778 96. 133 112.82 130.85 150.21 17 0.90, 119 2.9.3~ 216.301 241.001 267.041 100 met. 5.2013 1.6664 0.9033 5996 4423 3479 28054 2414 2088 1838 1640 1480' 1348 1237 11421 1064 0991 929 874 826 782 43 07 675 45 594 71 49.0530 494 78 63 49 36 23 11 00 389 79 70 61 52 44 36 28 21 14 08 279 54 34 17 02 189 77 67 58 in litres. 0.030 1.119 269 478 746 1.074 4629 910 2.417 985 3.611 4.298 5.044 850 6.715 7. 64 0 8.625 9.670 10. 774 11. 938 13. 162 14,445 15. 788 17. 191 18. 653 20-). 175 21. 757 23.393 25. 100 26. 861 28~. 6 81 30.561 32.501 34.501 36.560 398-.67-19 40. 858 43.096 45.395 47.752 50. 170 52.647 55. 184 57.780 60.436 63.153 65.928 68.763 7 1. 659 74. 613 9 0. 28 2 107.44 126.10 146.24~ 167.88~ 191.01 215.63 241.75 269.35 100 met. 6. 3539 2.0357 1. 1035 0.7325 5404 42)4 9 3487 2949 265 51 2246 200-(O3 1808~ 1646 1511i 1 395 129 121(0 1135 1068 1009 0955 907 864 825 788 755 725 697 7 1.0647 25 04 84 66 48 32 1 7 02 489 7 6 63 52 4 1 30 20 1 0 01 392 84 76 40 1 1 286 65 47 3 1 1 7 04 193 in litres. 0.033 132 297 528 825 188 1.616 2.111 672 3.299 991R 4.750 5.575 6-465 7.422 8.445 9.633 10. 688 11. 908 13. 195 1 4. 5-47 15. 966 17.450 19.000 20. 617 22.299 24.047 25.862 27.742 29. 688 31.700 33.778 35.923 38.133 40.409 42. 751 45.159 4 7.6833 50.173 52. 779 55.451 58. 189 60.993 63.862 66. 798 69.800 72.868 76.002 79.002 82.467 99- 1 78-5 118.75 139.37 161.64 186.66 2 1.12 238.33 267.19 297.71 329.87 11 235.6~ II.,0120.0is501298.451.0183 ' - - 262 TABLI ( 46 Centimetres. Hgt. in Disch'r. 100 met. in litres 7.6218 0.036 2.4419 145 1.8237 325 0.8787 578 6482 903 5097 301 4183 770 3538 2.312 3060 926 2693 613 2403 372 2168 5.202 1970 6.106 1812 7.081 1674 8.129 15-55 9.249 1452 10.441 1361 11.686 1281 13.042 1210 14.451 114 6 15.933 1088 17.486 1036 19.112 0999. 20.810 946 22.580 906 24.423 870 26.338 836 28.325 805 30.384.0776 32.516 749 34.71i9 724 36.995 700 39.344 678 41.764 58 44.257 38846.822 20 49.460 03 52.169 586 54. 951 71 57.805 5 660O:.7T-32 42 63.731 29 66.802 16 69.944 04 73.1601 492 70.648 81 79.808 71 83.2401 61 86.745 51 90.321 0 8 109.29 373 130.06 43 152.64 18 177.03 296 203.22 77 231.22 60 261.03 45 292.64 32326.06.02201361.28 E XXXI. -Discharge of Water through New Pipes. 'ompiled from Henry Darcy's French Tables of 1857. 50 Centimetres. flt. in Diseh'r. 100 met. in litres 9.0050 0.039 2.8850 157 1.5639 3 53 0381 628 0.7658 982 6~0-22 414 4942 924 4180 2.513 3616 3.181 3182 927 2839 4.752 562 5..655 333 6.637 141 7.697 1978 8 836 837 10.053 715 11.349 608 12.723 514 14.176 429 15.708 354 17.318 286 19.007 225 20.774 169 22. 620 118 24.544 07126. 547 028 28. 628 0988 30.788 951 33.0266.0917 35.343 885 397.738 855 40.212 28 42.765 02 45.396 777 48.1061 54 50.894 32 53. 761 12 56.706 693 59.730 74 62.832 57 66.013 40 69.273' 25 72.611 10 76.027 595 79.522 82 83.096 69 86. 748 56 90.478 44 94.288 33 98.175 482 118..7 9 41 141.37 05 165.92 375 192.42 50 220.89 27 251.33 07 283.73 290 318.09 274 354.41.0260 382.70,54 Ce-ntimetres. Llg t i n Diseh'r. 1t0 met. in litres 10.5030 0.042 3.3651 170 1.8241 ' 382 2109 679 0.8932 1.060 7024 527 5764 2.078 4875 714 4217 3.43.5 3712 4.241 311 5.131 2988 6.107 2721 7.167 2497 8 313 2307 9.543 2143 10.857 2000 12.257 1876 13.741 765 15.310 667 16.965 579 18.703 500 20.527 428 22.435 365 24.429 304 26.507 249 28.670 199 30.918 152 33.251 109 35.668.1070 38.170 32 40.757 998 43.429 65 46.186 35 49.027 06 51.954 0880 54.9,65 54 58.061 30 61.242 08 64.508 786 67.858 66 71.294 47 74.814 28 78.419 11 82.109 694 85.883 78 89.743 63 93.687 49 97.716 35 101.83 22 106.03 56 3 128. 30 14 152.68 47,3 179.19 38 207.82 08 238.57 381 271.43 58 306.42 38 343.53 320 382.76.03031424.12 58 Centinietres. IIgt. inI Dischir. 100 met. in litres 12.117 0.046 3.8820 182 2.1044 410 1.3969 729 0305 1.139 0.8104 640 6650 22.232 5623 915 4865 3.689 4282 4.555 3821 5.511 3448 6.559 3139 7.698 2881 8.928 2661 10.249 2472 11.661 2308 13.165 164 14.759 037 16.445 1923 18.221 822 20.089 730 22.047 648 24.097 572 26.239 503 28.471 441 30.793 383 33.208 329 35.713 280 38.310.1234 40.997 191 43.777 151 46. 646 114 49.607 079 52.659 46 55.803 15 59.037 0986 62.362 '58 65.779 32 69.286 07 72.885 884 76.575 62 80.356 40 84.228 20 88.191 801 92.245 783 96.391 65 100.63 48 104.95 32 109.37 17 113.88 649 137.80 93 163.99 545 192.46 05 223.21 470 256.24 40291.54 13 329.12 90 368.98 69 411.12.03501455.53 62 Centimetres. Ilgt. in l)isch'ge 100 met. in litres. 13.846 0.049 4.4360 195 2.4046 438 1.5962 779 1-715 1.217 0.9260 753 7599 2.386 6427 3.116 5529 944 4893 4.8691 4366 5.892 3939 7.012 3587 8.229 3292 9.544 3041 10.956 2825 12.465 2637 14.073 2472 15.777 2327 17.579 2198 19.477 2082 21.474 1978 23.568 883 25.759 797 28.048 71 U 30.434 646 32.917 580 35.498 519 38.177 462 40. 952.1410 43.825 361- 46.795 315 49.863 273 53.029 233 56.291 195 59.651 160 63.108 126 66.663 1095 70.315 65 74.065 37 77.911 10 81.856 0984 85.897 960 90.037 937 94.273 915 98.607 894 103.04 874 107.57 855 112.19 837 116.92 819 121.74 742 147.30 677 176.30 623 205.74 577 238.60 537 27&.91 503 311.65 472 351.82 445 394.43 421 439.47.0400 486.95 I 253 TABLE XXXI. -Dischargqe of Water through New Pip8 Compiled from Henry Darcy's French Tables of 1857. e8 Velecyv per see( MaijL. Area o1 Metre section 0.01 0.0001 2 03 3 07 4 13 5 20 6 28 7 38 8 50 9 64 1.0 79 C6 Centimetres. Hlgt. iu Disch'go tOt met. in litres. 15.690 0.052 5.0268 207 2.7249 467 1.8088 829 1.3343 1.296 1.0493 1.86ti 0.8611 2.540' 7283 3.3171 6300 4.1991,5544 5.1831 70 Centimetres. Hgt ill Diseh'ge 100 met, in litres. 17.650 0.055 5.6547 220 3.0652 495 2.0347 880 1.5010 1.374 1.1804 979 0.9686 2.694~ 8192 3.519 7086 4.453 6237 5.498 74 C'entimetres. llgt. in Disch'ge 100 met, in litres. 19.725 0.059 6.3193 232 3.4255 52 3 2.2739 930 1.6774 1.453' 3 1-91 2.092 0825 848 0.9155 3.719' 7919 4.707~ 6970 5.811 78 Centimetres. Hg t. in Diseh'g 100 met, in litres 21.915 0.061 7.0209 2 45 3.8050 551 2".5264 986 1.8637 1.532 4-65-6 2.205 2027 3.002 0172 921 0.8799 4.962 7744 6. 1266 11 12 13 1 4 15 16 17 1 8 19 20 21 22 23 24 2.5.26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 4.5 47 48 49 50 611 65 IC 75 8C 90 9j5 113 133 154 177 201 227 254 284 314 346 380 415 452 491 573 616 661.0707 755 804 855 908 962 1018 1075 1134 1195 1257 1320 1385 1452 1521 1590 1662 1735 1810 1886 1964 2376 2827 3318 3848 4418 5027 5675 6362 7088.7854 4941 4464 4065 3730 3446 3201 2988 802 637 490 359 241 134 036 1947 866 791 721 657.1598 542 490 442 397 354 814 276 240 207 175 144 116 088 062 037 014 0991 969 948 928 840 767 706 654 609 570 535 505 477.045OU 6.2721 7.4641 8.760' 10.159~ 11. 663 13. 270 14.981 16. 795 18. 713 20.734~ 2~ 2.859 25.089 27.421 29.857 32.397 35.041 37.789i 40.639 43.594 46.653 49.859 53.080 56.449 59.923 63.499 67.179J 70.964 74.851 78t.843j 82.938 8 7. ~13 7 91.439, 65.845 100.36 104.97 109.69 114.51 119.43 124.46 129.59 156.81 186.61 219.01 254.00 291.58 331.75 374.52 419.88 467.82 518.36 5565 5021 4572 4196 3876 601 362 152 2966 801 654 521 400 290 190 098 014 1936 864.1797 735 677 622 571 523 478 436 395 357 321 287 255 224 195 1 67 140 115 090 067 044 0945 863 794 736 685 641 602 568 537.0510 6.652 7.917 9.291 10. 776 12 370 14.074 15. 889 17.813 19.847 21. 991 24.245 26. 609 29.083 31. 667' 34.361~ 6219,5611 5110 4689 4332) 4024 3757 522 315 131 2966 817 682 560 448 345 251 164 083.2008 3 7.1 6 5 40.076 43.10Q 46.236 49.486 39.286 42.366 45.56.5 48.87h 52.307 52.834 56.297 59.8711 63.5551 67.348 71.251 75.265 79.388' 83.622 87.965 92 418 96.982 101.66 106.44' 11 1. 33'J 116.33 121.45 126.67 132.00 137.45 166.31 197.92 232.28 269.39 309.25 351.86 397.22 445.22 496.18 549. 78 7.032 8.369 9.822 11. 391 13.077 14.0719 16.796 18.831 20.981 23.2147 28. 129 30. 745 33.477 36.325 6910 6234 5677 5210 4813 471 174 3913 683 478 295 130 2980 844 720 7.412 8.821 10.353 12.007 13. 783 15. 683 17. 704 19. 849 22. 115 24.504 27. 016 29.650 32.407 35.286 3 8.2 8 8 1939 874 813 756 702 652 604. 659 517 477 439 402 368 335 304 274 246 218 192 167 056 0965 888 822 766 716 673 634 600.0569 155.853 59.514 63.292 67. 186 71.1-96 7 5. 32 3 79.565 83.925' 88.399 92.991, 97. 699 102.52 107.46 112.52 117.69 1229-,T98 128.29 133.91 139.55 145.30 1 7 5.8 1 209 23 245.56 284.79 326.92 371.97 419.91 470.77 524.53 581.20 606 41.412 501 44.659 404 48.029 315 51.521.2231 55.135 154 58. 871 082 62.731 014 66.713 1951 70.817 891 75.045 835 79.~39 4 782 83.866 733 88.461 685 93.178 641 98.017 598 10-O298 558 108.07 520 113 27 483 118.60 449 124.05 416 296. 384 135.32 354 141.15 325 107.09 297 153.15 174 8532 072 220.54 0986 258.83 913 300.18 851 344.60 7 96 748 44-2.61 705 496.22 667 552.88E.0633 612.61 111 -Ii I fC' 254 TABLE C( 82 Centimetres. Il~gt.in- Disch'ge 100 met. in litres. 24.220 0.064 7.7594 258 4.2062 580 2.7921 1.03C 2.0597 610 1.6197 2.319 3292 3.156 1242 4.121 0.9724 5.217 8558 6.440 7 7 779 8 6890 9.274 6274 10.884 5758 12.623 5319 14.491 4941 16.487 613 18.612 325 20.866 071 23.249 3844 25.761 641 28.401 459 31.171 293 34.069 143 37.096 006 40.251 2880 43.536 764 46.949 657 50.491 558 54.163.2466 57.962 81l 61.891 301 65.948 226 70.135 156 74.449 090 78.893 028 83.4 6 6 1970 88.167 915 92.997, 863 97.957 813 103.10 7677 1088.2 6 722 113.61 680 119.08 640 124.68 601 130.42 564 136.38 529 142.27 496 148.38 464 154.63 433 161.01 297 1 9-4. 8 2 185 231.85 090 2 72.10 010 315.57 0940 362.27 879 412.18 826 465.31 779 521.66 737 581.24.0699 644.03 XXXI. - Discharge of Water through New Pipea. )mpiled from Henry Darcy's French Tables in 1857. 86 CU numeires. Hgt. in Di:ch'ge 100 met. in litres. 26.640 0.068 8.5350 270 4.6266 608 3.0712 1.081 2.2655 689 1.7816 2.432 4620 3.310 2365 4.323 0696 5.471 0.9414 6.754 8400 8.173 7579 9.726 6902 11.415 6333 13.229 5859 15.197 435 17.291 078 19.520 4757 21.881 477 24.383 228 27.017 005 29.787 3804 32.691 623 35.731 457 38.205 306 42.215 168 45. 660 010 49.239 2923 52.955 814 56.805.2713 60.789 618 6C4. 910 531 69.165 448 73.555 871 78.081 299 82.741 231 87.537 167 92.468 106 97.534 049 102.74 1995 108.07 943 113.54 804 119.15 848 124.89 803 130.77 761 136.78 72 142. 92 682 149.21 646 155.62 610 162.17 572 168.86 427 204.32 203 243.16 199 285.38 110 330.97 034 379.94 967 432.28 909 488.01 857 547.11 811 609.59.0769 675.44 90;eintimtres. 94 Centietttres. Ilgt. in Disch'ge Hgt. in Disch'ge 100 met in litres. 100 met. inlitres. 29.176 0.071 81.827 0.074 9.3474 283 10.197 295 5.0670 636 5.5274 664 3.3635 1.131 3.6691 1.181 2.4812 767 2.7066 846 1.9512 2.545 2.1285 2.658 6012 3.464 1.7467 3.618 3542 4.524 4773 4.725 1714 5.726 2778 5.980 0310 7.068 1246 7.383 0.9199 8.553 035 8.9.33 8300 10.179 9054 10.631 7558 11.946 8245 12.477 6936 13.854 7567 14.470 6407 15.904 6990 16.611 5952F18.096 493 1'8.89b 557 20.428 462 21.336 210 22.902 683 23.880 4904 25.518 649 26.651 631 28.274 052 29.531 387 31.173 4785 62.557 167 34.212 545 35.732 3967 37.393 328 39.055 786 40.715 130 42.525 621 44.177 3950 46.142 469 47.58 4 3 784 4 9.907 330 51.530 632 53.820 201 55.418 492 57.881 082 59.447 362 62.089.2971 63.627.3241 66.445 868 67.929 128 A0.98t 771 72.382 023 75.599 681 76. 977 2925 80.398 597 81.713 833 85 345 518 86.590 747 90.439 443 91.609 665 95. 680 373 96.769 589 101.07 307 102.07 516 106.61 244 107.51 448 112.29 184 113.10 383 118.1 3 128 118.82 321 124.10 074 124.69 263 130.23 024 130.70 207 136.51 1975 136.85 154 142.93 929 143.14 104 149.50 885 T14 9. 57 056 156.22 842 156.15 010 163.09 802 162.86 1966 170.10 764 169.72 924 177.26 727 17.72 - 883 184.57 563 21-3.838 705 223.33 427 254.47 557 265.78 313 298 65 ' 433 311.92 216 346.37 327 361.76 132 397.61 235 415.'28 059 452.59 156 472.50 995 510.71 086 533.40 939 572.56 024 598.00 888 637.94 969 666.29.0842 706.86.0919 738.28 98 Ceiitimetres. Hgt. in Discb'ge 1(00 met. in litres 34.594 0.078 11.083 307 6.0078 693 3.9881 1.232 2.9418 924 2. 31;5 2.771 1.8985 3.771 6057 4.926 3889 6.234 2224 7.697 0907 9.313 0.9841 11.083 8962 13.007 8224 15.085 7597 17.318 7058 19.704 6589 22.244 6177 24.938 5814 27.785 491 30.787 201 33.943 4940 37.253 704 40.717 489 44.334 293 48.105 113 52.031 3948 56.110 795 60.343 654 64.731.3522 69.272 402 73.967 286 78.816 179 83.819 079 88.976 2982 94.287 897 99.752 814 105.37 735 111.14 661 117.07 590 123.15 523 129.39 460 135.77 399 142.32 342 149.01 287 -155.86 235 162.87 185 170.03 137 177.34 091 184.80 047 192.42 1853 232.83 692 277.09 557 325.20 442 377.15 343 432.95 2566 492.60 180 556.10 113 623.45 053 694.65.0999 769.69 255 TABLE XXXI. —Discharge of Water through New Pipes. Compiled from Henry Darcy's French Tables of 1857. Veoc'y per sec. Diam. Area of Metre section. 0.01 0.0001 2 03 3 07 4 13 5 20 28 7 38 8 50 9 64 10 79 11 95 12 113 13 133 14 154 15 177 16 201 17 227 18 254 19 284 20 314 21 346 22 380 23 415 24 452 25 491 26 531 27 573 28 616 29 661 30.0707 31 755 32 804 33 855 34 908 35 962 36 1018 37 1075 38 1134 39 1195 40 1257 41 1320 42 1385 43 1452 44 152] 45 1590 46 1662 47 1735 48 1810 49 1886 50 1964 55 2376 60 2827 65 3318 70 3848 75 4418 80) 5027 85 5675 90 6362 95 7088 1.00.7854, 10! ('entimetres Hgt. in Dischge 100 met. in litres. 37.475 0.080 12.006 320 6.5083 721 4.3208 1.282 3.1870 2.003 2.5062 884 0566 3.925 1.7394 5.128 5046 6.489 3242 8.011 1816 9.693 0661 11.536 9708 13.538 8909 15.702 8230 18.025 7645 20.50 -7137 23.152 6692 25.956 6298 28.920 5948 32.044 634 35.329 352 38.773 096 42.379 4863 46.144 651 50.070 456 54.155 277 58.401 111 62.807 3958 67.374.3816 72.100 683 76.987 560 82.033 444 87.241 336 92.608 234 98.136 138 103.82 048 109.67 2968 1 15.68 882 121.25 806 128.18 733 134.67 665 141.32 596 148.13 537 155.09 477 162.23 421 16-9.52 367 176.97 315 184.58 265 192.35 217 200.28 007 242.34 1833 288.40 687 338.47 562 392.54 455 450.62 361 513.71 278 578.80 205 648.90 140 723.00.1082 801.11 10U6 entimetres. Hgt. in Disch'ge 100 met. in litres. 40.472 0.083 12.966 333 7.0287 749 4.6658 1.332 3.4418 2.081 2.7066 997 2.2211 4.079 1.8785 5.327 6249 6.743 4391 8.325 2761 10.072 1514 11.988 0485 14.069 0.9621 16.318 8888 18.731 8257 21.312 7708 24.060 7227 26.973 6802 30.053 6424 33.300 6085 i6.715 5780 40.294 503 44.041 252 47.953 023 52.032 4812 56.278 619 60.691 440 66.27-0 275 70.015.4121 74.928 3978 80.206 844 85.250 720 90.661 603 96.238 493 101.98 389/ 107.89 292 113.97 200 120.22 113 126.63 030 133.20 29.52 139.95 878 146.86 807 153.93 740 161.18 676 168.59 6l4 176.1 556 183.90 600 191.81 446 199.89 395 208.13 168 251.84 1980 299.71 822 315.74 687 407.94 571 468.29 470 532.82 381 601.50 302 674.34 232 761.35.1168 832.52 11tU centimetres. ilgt.in I isch'ge 100 met. in litres. 43.584 0.086 13.964 346 7.5692 778 5.0245 1.382 3.7065 2.160 2.9148 3.110 3919 4.233 0230 5.529 1.7499 6.998 5401 8.639 3742 10.454 2399 12.441 1291 14.601 1362 16.933 0.9571 19.439 8892 22.117 8301 24.968 7783 27.992 7325 31.188 6918 34.558 553 8. 100 224 41.815 5927 45.702 656 49.763 409 53.996 182 58.402{ 4974 62.981 781 67.733 603 72.657.4438 77.755 284 83.025 140 88.467 006 94.083 880 99.071 761 105.83 650 111.97 545 118.27 446 124.75 352 131.41 263 138.23 179 145.23 098 152.40 023 159.74 2950 167.26 881 174.95 815 182.81 752 190.85 692 199.05 634 207.43 579 215.99 334 261.34 132 311.02 1962 365.01 817 423.33 692 485.97 583 552.92 487 624.20 142 699.79 326 779.71.1258 863.94 114 Centimetres. lIgt. in Disch'ge 100 met in litres. 46.812 0.090 14.997 358 8.1297 806 5.3966 1.433 3.9809 2.238 1306 3.223 2.5690 4.387 1728 5.731 1.8795 7.251 6541 8.953 4760 10.832 3317 12.892 2127 15.131 1129 17.548 0280 20.145 9550 22.920 8916 25.876 8359 29.009 7868 32.321 7430 35.814 7038 39.485 6685 43.334 6365 47.365 6075 51.571 5809 55.960 5566 60.526 5342 65.271 5135 70.196 4944 75.299.4766 80.582 4601 86.(044 4447 91.682 4302 97.505 4167 103.50 4040 109.68 3920 116.04 3807 122.57 3701 129.29 3600 136.18 3505 143.26 3414 150.51 3328 157.94 3247 165.55 3169 173.34 3095 181.31 3024 T897946 2956 197.78 2891 206.29 2830 214.98 2770 223.84 2507 270.84 2289 322.33 2107 378.29 1951 438.72 1817 503.64 1700 573.03 1597 646.89 1506 725.24 1424 808.06.1351 895.36 I1 I::~ ~ I I -— r -. - --— ^I --- 256 i 1 6 8 9 4 13 '2 j4 )-3 39 36 36 I I I TABLE XXXI.-Discharge of Water through New Pipee. Compiled from Henry Darcy's French Tables of 1857. 118 Centimetres. 122 Centimetres. 126 Centimetres. 130 Centimetres. 134 Centimetres. Hgt. in Disch'ge Hgt. in Disch'ge Hgt. in Disch'ge Hgt. in Disch'ge Hgt. in Disch'ge 10 met. in litres. 100 met. in litres. 100 met. inlitres. 100 met. inlitres. 100 met. in litres. 50.154 0.093 53.612 0.096 57.185 0.099 60.874 0.102 64.678 0.105 16.068 0.371 17.176 0.38318.321 0.396 19.503 0.40820.721 0.421 8.7102 0.834 9.3107 0.8629.9313 0.891 10.572 0.91911.232 0.947 5.7819 1.4836.1806 1.5336.5925 1.583 7.0177 1.6347.4562 1.684 4.2652 2.317 4.5593 2.395 4.8631 2.474 5.1768 2.553 5.5003 2.631 3.3542 3.336 3.5854 3.4493.8244 3.563 4.0710 3.676 4.3256 3.789 2.7524 4.541 2.9432 4.695 3.1383 4.849 3.3407 5.003 3.5594 5.157 2.3279 5.931 4884 6.1322.6543 6.333 2.8255 6.5353.0Q0 6.735 2.0137 7.5052.1525 7.7612.2960 8.015 4440 8.2702.5968 8.525 1.7722 9.2671.8944 9.5822.0207 9.895 1510 10.2102.2854 10.523 5814 11.212 6904 11.594 8031 119 1.9741.9193 12.354 0393 12.734 4268 13.344 5252 13.797 6268 14.250 7318 14.7031.8400 15.154 2993 15.661 3889 16.192 4815 16.723 5770 17.255 6755 17.785 1924 18.164 2746 18.781 3595 19.396 4472 20.012 53 76 20.626 1.1014 20.851 1.1774 21.558 1.2558 22.265 3368 22.973 1.4204 23.679 0232 23.724 0938 24.529 1666 25.332 2419 26.138 3195 26.942 0.9552 26.784 0211 27.691 0891 28.600 1594 29.507 2318 30.416 8956 30.0270.9574 31.045 0212 32.063 0870 33.081 1549 34.099 8429 33.457 9011 34.59 0.9611 35.725 0231 36.859 0870 37.993 7960 37.070 8509 38.327 9076 39.582 0.9662 40.841 0265 42.09 7540 40.871 8060 42.256 8598 43.641 9152 45.027 0.9724 46.411 7162 44.854 7656 46.376 8166 47.896 8693 49.417 9236 50.938 6820 49.025 7290 50.688 7776 52.349 8278 54.012 8795 55.673 6509 53.383 6957 55.192 7421 57.001 7899 58.811 8393 60.619 6224 57.924 6653 59.887 7097 61.851 7554 63.814 8027 65.776 5963 62.648 6375 64.773 679966.896 7238 69.021 7690 71.144 5724 67.561 6118 69.852 6526 72.141 6947 74.432 7381 76.723 5502 72.658 5881 75.122 6273 77.586 6678 80.048 7095 82.510 5297 77.941 5662 80.583 6040 83.225 6429 85.868 6831 88.509 0.5107 83.408 0.5459 86.237 0.5823 89.064 0.6198 91.892 6585 94.720 4930 89.064 -5269 92.082 5621.95.100 598983 98120 6357 101.14 4764 94.900 5093 98.117 5432 101.33 5782 104.55 6144 107.77 4609 100.93 4927 104.35 5256 107.77 5595111.19 5944 114.61 4464 107.13 4772 110.77 5090 114.40 5419 118.03 5757 121.66 4328 113.53 4627 117.38 4935 121.23 5253 125.08 5581 128.92 4200 120.11 4490 124.18 4789 128.25 5098 182.32 - 5416 ]136.39 4079 126.87 4360 131.18 4651 135.48 4951 139.78 5260 144.08 3965 133.83 4238 138.36 4521 142.90 4813 147.44 5113 151.97 3857 140.96 4123 145.74 4398 150.52 4682155.30 4974 160.08 3755 148.28 4014 153.31 4281 158.34 4558 163.3'6 4842 168.39 3658 155.79 3910 161.07 4171 166.35 4440 171.63 4717 176.92 3566 163.48 3812 169.03 4066 174.57 4328 180.11 4599 185.66 3478 171.36 3718 177.17 3966182.98 4222188.79 4486 194.59 3395 179.42 3629 185.50 3871 191.59 4121 197.67 4378 203.75 0.3316 187.67 0.3544 194.03 0.378 200.40 4024 206.76 0.4276 213.12 3240 619611 3463 202.75 3694 209.40 932 216.05 4177 222.70 3167 204.72 3386 211.66 3611 218.60 3844 225.54 4084 232.48 3098 213.53 3311 220.77 3532228.01 3760235.24 3995 242.48 3032 222.52 3241 230.06 3457 237.60 3679 245.14 3900 252.69 2968 231.69 3173 239.55 3384 247.40 3602 255.26 3827 263.11 2686 280.36 2871 289.85 3063 299.35 3260 308.86 3464 318.3 2453 333.64 2622 344.95 2797 356.26 2978 367.57 3164 378.88 2288 391.56 2413 404.84 2574418.11 2740431.38 2911 444.66 2091 454.12 2235 469.51 2384 484.91 2537 500.30 2696 515.69 1947 521.31 2081 538.98 2210 556.65 2363 574.32 2510 591.99 1821 5963.13 1947 613.24 2077 633.35 2210 653.46 2349 673.5 1711 669.59 1829 692.29 1951 714.99 2077 737.69 2206 760.38 1613 750.69 1725 776.13 1839801.58 1958827.03 2080 852.47 1526 836.41 1631 864.76 1740 893.12 1852 921.47 1968 949.81 0.1447 926.77 0.1548 958.19 0.1651 989.60 0.1757 1021.0 0.1867 1062.44 257 x 11 I I TABLE XXXI. - Discharge of Water through New Pipe8. ~Compiled from Henry Darcy's French Tables of 1867. Veloc'y per see. 138_Centimetres. 142 Centimetres. 146 Centimetres 1.50 Centimetres. Oliam. Ara0 [g.i Disch'r. Hgt. in Dischige llgt. in IDisch'r. Hgt. in IDisch'ge vetesection. 100 met. in litre. 100 met. in litres 100 met. in litres 100 met. in litres. I 0.01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 22 23 24 2.5 26 27 28 29 30 0.0001 031 071 13 20 28 38 50 64 79 95 113 133 154 177 201 227 254 284 -314 346 380 415 452 491 531 573 616 661.0707 I I I I II I I I I II 68.596 21.977 11.913 7.9080 5.8336 4.5873 3.7645 3. 1839 2.7541 2.4239 2.1628 1.9519 7771 6308 5064 3995 3065 2249 1529 0887 0313 0.9796 9328 8902 8513 8-15-6 7828 7525 7245 6985 0.108 0.434 0.975 1.734 2.710 3.9U2 5.311 6.937 8.777 10.839 13.114 15.608 18.315 21. 242 24.387 27.746 31.324 35. 115 39. 125 43.354 4`7.797 52.458 57.335 62.429 67.740 73.268 79.011 87.974 91. 151 97.546 I I I I I I II II II II 72.631 23.269 12.613 8.3731 6. 1766 4.8573 3.9859 3.3712 2.9161 2.5665 2.2900 2.0662 1.8816 7267 5950 4818 3833 2976 2207 1528 0920 0372 0.9876 9425 9014 8636 8289 7968 7671 0.7395 0.112 446 1.004 1. 7I84 2 788 4.015 5.405 7i.138 9.033 ~11.153 13.495 16.606 18.849 21.859 25.093 28.5 oi 32.231 36. 135 40.261 44.610 49. 184 53.979 58.998 64.240 69.705 75.392 81.303 87.438 93.794 100.37 76.780 24.599 13.334 8.8516 6.5295 5.1348 4.2136 3.5638 3.0827 2. 7131 2.48(09 2. 1843 1. 9891 1.8254 1.6862 5664 46239 3711 2904 2186 1544 0965 1.0440 0.9964 9528 9129 8762 8423 810 0. 7 818Q 0.115 0.459 1.032 1.835 2.867 4.128 5.619 7.339 9.287 11.467 13.874 16.512 19.379 22.474 25.799 29.354 33.140 37. 151 41.395 45.866 50.569 55.498 60.659 66.049 71.668 77.516 83.593 89.900 96.435 ~103.20 81.045 25.965 14.075 9.3431 6.8922 5.4200 4.4477 o.7617 3.2539 2.8638 2.5553 3056 0996 1.9266 1.7798 6534 5436 4472 3621 2863 2185 1574 1020 0517 1.0058 0.9636 9249 8891 8560 0.8252 0.118 0.471 1.060 1.885 2.945 4.241 5.778 7540 9.543 11.781 14.255 16:966 19. 916 23.091 26.507 30.15 34.047 38.170 42.529 47.124 51.954 57.020 62.322 67.859 73.631 79.64C 85.884 92.363 99.07E 106.03~ I I I I I I I I I I I i I 31 32 33 34 35 36 37 38 39 140 41 42 43 44 45 46 47 48 49 50 755 804 855 908 962 1018 1075 1134 1195 1257 1.320 1385 1452 1521 1590 1662 1735 1810 1886 1964 6742 6516 6304 6106 5920 5744 5579 5423 5276 5136 5003 4877 4757 4643 4535 4431 4 332 t4237 4146 4059 104.16 110.99 118.03 125.29 132.77 140.47 148.38 156.21 164.85 173.42 182.20 191.19 200.40 209.88 219.48 229.34 239.42 249.72 260.28 270.96 7139 6899 6675 6465 6268 6082 5907 5742 5586 5438 5297 5164 5037 4916 0.4801 4692 4587 4486 4390 4298 107.18b 114.20 121.45 128.93 136.62 144.54 152.68 161.04 169.63 178.44 187.48 196.78 206.21 215.92 225.84 235.91i 246.36 256.96 267.78 278.82) 7046 7293 7056 6834 6626 6430 6245 6070 5905 5748 5600 5459 5325 5197 0.5076 4959 4849 4743 4641 4544 110U.ZU 117.42 124.87 132.56 140.47 148.61 156.98 165.58 174.41 183.47 192.76 202.28 212.02 222.00 232.20 242.64 253.30 264.20 27-5.32 286.67 7966 7698 7448 7214 6994 6787 6592 6407 6233 6068 5911 5762 5621 5486 0.5358 5235 5118 5006 4899 4796 1120.64~ 128.30 136.19~ 144.32 1i5 2. 6 9 161.28 170.12 179.19 188.50 198.04 207.82 217.83 328.08 338.57 2 4 9.2 9 260.24 271.43 282.86 294.53 I 662376 3674 327.86 3890 337.37 — 4-112 346.87 4341 356.38 60 2827 3355 390.19 3553 401.50 37566412.81 3964 424.12 65 3318 3088 457.93 3269 471.20 34566484.48 3648 497.75 70 8848 28595631.09 3027 546.48 3200 561.88 338572 75 4418 2662 609.67 2819 627.34 2904.1 3146 562.627 80 5021 249169~3.67 2637 713.77 278 87338R8 2943753.98 85 5675 2340 783.08 2478 805.78 2619 828.48 2765 851.18 90 8362 2207 877.92 23-36 903.37 2470 928.81 2607 954.26 95 17088 2087 978.17 2210 1006.53 2336 1034.9 2466 1063.24 1.00. 0.7854 0.1980 1088.9 0.2097 1115.2710,2217 1146.7 0.2340 1178.12.I 258 I TABLE XXXI. -Dischargqe of Water through New Pipes. Compiled from Henry Darcy's French Tables in 1857. 154 Centimetres. 1.58 Centimetres. 162 Centimetres. 166 Centimetres. 170 Centimetres; Hfgt in Disch'ge Hgt. in Disch'ge 1lgt. in Dlseh'ge Hgt. in Dilsch'ge Hgt. in Disch'gt 100 met. in litres. 100 met. in 1itre8. 100 met. in litres. 100 met. in litres 100 met. in litres 85.425 0.121 89.920 0.124 94.531 0.127 99.257 0.130 104.10 0.134 27.868 0.484 28.808 0.496 30.286 0.509 81.800 0.522 38.851 0.584 14.836 1.089 15.616 1.117 16.417 1.145 17.238 1.173 18.078 1.202 9.8441 1.935 10.366 1.985 10.898 2.035 11.443 2.08612.001 2.13( 7.2647 3.024 7.6470 8.102 8.0391 3.181 8.441 3.259 8.8527 8.33E 56.7-129 4. 3-54 6. 01-36 4.467 6.3219 4. 5-806.6380 4.6946.9617 4.807 4.6880 5.927 4.9347 6.081 5.1878 6.235 5.4471 6.388 5.7128 6.542 3.9650 7.741 4.1737 7.943 4.3877 8.144 4.60710 8.343 4.8317 8.5459 3.4298 9.797 3.6102 10.051 3.7953 10.306 3.9851 10.561 4.1795 10.81,r5 8.086 1 2.095 3.1774 12.409 3.3393 12.728 3.5073 13.037 3. 6784 18.352 2.6934 14.034 2.8352 15.014 2.9806 15.395 1296 15.776 3.2822 16.156 4802 17.416 5581 17.868 6883 18.322 2.8237 18.774 2.9614 19.227 2130 20.439 8295 20.971 4489 21.502 5714 22.038 6968 22.56tr 0309 23.706 137 7 24.322 2473 24. 938 3597 25.554 4748 26.17C 1.8760 27.218 1.9747 27.919 2.0760 28.627 2.1798 29.335 2.2861 30.042 7428 30.962 1.8345 31.768 1.9285 32.572 2.0250 33.376 1237 34.181 6270 34.954 7126 35.862 8004 36.771 1.8904 37.678 1.9826 38.587 5254 39.187 6057 40.207 6880 41.2"24 7724 42.241 8589 43.26( 4357 43.663 5113 44.797 5888 45.932 6682 47.065 7495 48.20( 8558 48.280 4272 49.686 5004 50.894 5754 52.150 6522 53.407 28-43 53.839 3519 54~.725 -4-2 12 5 6. 111 ~49 23 57.49 5 566-51i58. 881 2199 58.540 2841 60.060 3489 61.581 4174 63.102 4866 64.623E 1616 63.983 2227 65.645 2854 67.307 3497 68.969 4155 70.631 1086 69.667 1669 71.477 2267 78.287 2881 75.097 3509 76.90( 0601 75.594 1159 77.558 1731 79.522 2318 81.484 2919 83.449 0157 8-1.7-64 ~06~92 893~.886 1240 8-6.0-11 1802 8-8.1-34 237790.258 0.9749 88.173 1.0262 90.463 0788 92.754 1327 95.043 1886 97.33E 9371 94.826 9865 97.290 0370 99. 753 0889 102.21 1420 104.68 9022 101.72 9497 104.36 9984 107.00 0483 109.65 0994 112.29. 8698 108.86 0 9156 111.68 0 9625 114.51 1.0106 117.34 1.0599 120.17 1. I 0 1 i II 'I I i I I11 11 I II iI:1 I' I I i 0I I I II II 0 I I 11 1 )I I I I i I i I I I I I I I i I i 83961 8114 7851 76041 7373~ 7154 6948 6753 65701 6396 62 31 6074' 5925 5783 0.5647 65518 5894' 5276 5163 4179' 8845 8561 8316 2914 2748 2599 0.2466 116.23 123.8.5 131.72 139.82 148.17 156.76 165.58 174.65 183.97 193.52 203.32 218.36 223.64 284.16 244.93 2,55.93 267.18 278.67 290.41 802.38 36 5.8 8 485.43 511.02 592.66 6 80.3 5 873.88 979.71 1091.6 1209.5 8838 8541 8264 8004 7760 7530 7313 7109' 69151 67-32 6558 6393 6236i 60871 0.59441 5808~i 5678 5554 5485 5321 4816 4898 4047 3748 8490 8265 3068 2892 2786 0. 2596 119.25 127.07 13,5.14 143.45 152.01 160.82 169.88 179.19 188.75 198.55 208.60 218.90 229.45 240.24 251.29 262.58 274.12 286.00 297.95 310.23 375.38 446.74 524.80 608.06 698.03 794.20 896.57 1005.0 1120.0 1241.0 9291 897 8688 8414 8158 7916 7688 7473 727C 7077 6895 6721 6556 6399 0.6249 6106 5969 5839 5714 5594 5063 4624 4255 3946 3669 8433 8225.3041 2877 0.2729 122.27 130.29 188.56 147.08 155.86 164.90 174.18 183.73 193.52 208.58 213-.8-8 224.44 235.26 246.82 257.65 26 9.2 3 281.06 293.15,305.49 318.09 38 48 9 458.05 537.57 123.45 715.70 314.30 D19.27 1031.0 1148.0 1272.0 0.9751j 9428 9122 8835 8566 8312, 8073 7847 7633 7431 7239 8057 6884 6719 0.6562 6411 6268 6131 5999 5874 5316 4855 4468 4137 8852 8604 8386 8193 8020 0.2866 125.29 133.500 141.98 150.71 159.71 168.97 178.48 188.26 198.30 208,60 219.16 229.99 241.07 252.41 264.01 275.88 289.00 300.39 313.03 325.944 394.39 469.36 5I50,84 638.84 733.37 834.41 941.97 1056.0 1177.0 1304.0 'JZ6o1iZO.01 9888 9567 9266 8983 8717 8466 8230 8006 7794 7592 7401 7220 7047 0.6882 6724 6574 6430 6292 6160 5575 5092 4685.4390 4040 3780 3551 8348 3168 0.3005 136.721 145.40 154.85 163.56 173.04 182.79, 192.80 208.08 213.63 224.44 285.53 246.88 258.49 270.87 282.58 294.194 307.63 320.58~ 388.80 408.89I 480.671 564.111 654.241 751.041 854.52 964.67 1081.0 1205.0 I I I 259 i I II I Z: TABLE XXXI.-Discharge of Water through New Pipes. Compiled from Henry Darcy's French Tables of 1867. iii 'Jn,utnt. 0.'0 I _________ -_ I LMam. VIetre 0.01 2 8 4 S 7 8 9 10 12 18 14 15 16 17 18 19 20 22 28 24 25 27 28 29 80 81 32 88 84, 85 Area of sect'n. 0.0001 03 '07 13 20 28 88 50 64 79 95 118 138 154 177 201 227 254 284 314 346 880 415 452 491 581 578 616 661.0707 755 804 855 908 962 1018 1075 1184 1195 1257 174 Centimetres. llgt. in Disch'ge 100 met. In litres.' 109.05 0.187, 84.939 0.547 18.939 1.230 12.572 2.187 9.27141 3.416 7. 29832~ 4.920 5.9848 6.696 5.0618 8.747 4.8784 11.069 8.8535 18.665 3~. 43 85~ 16.536 3.1024 19.678 2.8252 23.095 5926 26.786 2.3949 30.74 7 2248 34.984 2.0770 89. 494 1.9474 44 277 8328 49.333 7309 54.662 6396 60.267, 5573 66.142 4829 72.293 4152 78.715 8534 85.412 2-~967 92.382 2445 99.623 1964 107.14 1518 114.93 1.1104 122.99 0718 131.33 0359 139.94 0023 149.82 0.9707 157.98 9411 167.41 9132 177.11 8870 187.09 8622 197.34 8887 207.86 8165 218.66 1I 100 met. 114.13 36.563 19.820 13.157 9.7054 7.6324 6.2631 5.2972 4.5821 4.0327 8.5984 3.2467 2.9566 2.7132 2.5063 8283 1736 2.0379 1.9181 8114 7158 6298 5519 4810 4163 3570 3024 2520 2053 1.1620 1217 0841 0489 1.0159 0.9849 9557 9282 9022 8777 8544 I Hgt. in Disch'ge Hgt. in Disclvge l)isch'ge in litres. 0.140 0.159 1.258 2.237 8.495 5.033 6.850 8.947 11.823 13.979 16.916 20.130 23.625 27.400 31.455 35.788 40.402 45.215 50.467 55.920 61.651 67.662 73.953 80.525 87.376 94.504 101'.92 117.57 125.82 134.35 143.15 152.24 161.61 171.26 18 1-.1 8 191.39 201.87 212.64 223.68 100 met. 119.31 38.225 20.721 18.755 10.147 7.'9792 6.5478 5.5379 4.7908 4.2160 3.7619 3.3943i 3.0909 2.836 2.6201, 4341 2724 1306 0053 1.8937 7938 7038 6224 5483 4807 41 86 8616 8089 2601 1.2148 1727 1338 0965 0620 1.0296 0.9991 9704 9482 91716 8988 in litres. 0.148 0.572 1.287 2.287 3.574 5.146 7.004 9.149 11.578 14.294 17.296 20.584 24.157 28.017 32.162 36.591 41.311 46.314 51.602 57.177 63.038 69.184 75.617 82.855 89.340 96.630 104. 21 112.07 120.22 128.65 137.37 146.87 155.67 165.24 175.11 185.25 195.69 206.41 217.42 228.71 100 met. 124.62 39 924 21.646 14.367 10.597 8.3338 6.8387 5.7840 5.0032 4.4034 3.9291 3.5451 8.2283 2.9626 7866 5423 3734 2253 0944 1.97791 8735 7796 6645r 6171 5465 4817 8671 8161 1.2688 2248 1837 1452 1092 0754 0435 1.0185 0.9852 9584 9380 In litres. 0.146 0.584 1.315 2.837 8.652 5.259 7.158 9.849 11.838 14.607 1 7.67 6 21.035 24.687 28.632 32.867 37.896 42.218 47.251 52.737 58.484 64.423 70.704 77.277 84.143 91.302 98.752 106.50 114.53 122.86 131.48 140.39 149.5.9 159.09 168.87 178.95 189.83 199.99 210.95 222.19 233.74 i I II 8711 I 41 42 48 44 45 47 48 49 50 60 65 70 75 85 90 95 10(1 I I I I I i I I r I 1320 1885 1452 1521 1590 '1662 1735 1810 1886 1964 2376 i2827 8818 8848 4418 5027 5675 6862 7088 0 - VAJA4.1 7754 7563 7382 0.7209 7044 6887 6736 6592 6458 5841 5334 4909 4546 42833 8960 8720 8508 8318 0A R1 49 229.73 241.07 252.68 264.57 276.74 28 9. 17 301.88 314.86 828.12 341.65 418.89 491.97 577.39 669.63 768.71 874.62 987.36 1107.0 1233.0 1867.0.1 I - - I Z53Z4 z3b.u1 8114 246.61 7915 258.49 7725 270.66 0.7544 288.10 7372 295.82 7207 308.82 7049 822.10 6898 335.66 6754 849 50 6113 422.90 5582 503.29 5187 590.66 4757 685.08 4429 786.38 4144 894.73 3898 1010.0 8671 1182.0 8472 1262.0 0.8295 1898.0 8702 240.29 8483 252.15 8275 264.80 8076 276.74 0.7887 289.46 7707 302.47 7534 815.76 7370 329.34 7212 848.21 7060 357.36 6390 432.40 58,36 514.59 5870 603.94 4973 700.42 4681 804.05 4333 914.83 4070 1038.0 38888 1158.0 8631 1290.0 0.8445 1429.0 9089 8860 8642 8485 0.82388 8940 7869 7697 7532 7374, 66741 6096 5609 5194 4887 4525 4251 4008 8792 0.8598 245.57 257.69 270.11 282.82 295.82 890 9.1 1 822.70!386.58 850.75 865.21 441.9 0 525.90 617.21 715.81 821.78 1208.0 1318.0 1461.0 II - - - - 1 — z I TABLE XXXI. — Discharge of Water through New Pipes. Compiled from Henry Darcy's French Tables of 1857. 190 entmetes.194 Centimetres. ilgt in iechge lgt. in IDisch'ge 100me~t n itrs.100 met.1in litres. 200 Centimetres. 1210 Centimetres 1220 Centimetres. 130.03 41.659 22.582 34.981 11.058 7.136 6.036 6.221 4.595 4.100 3.699 369 091 2.856 653 477 322 185 064 1.955 857 768 687 614 546 484 427 373 1.324 2 78 235 195 158 122 089 058 028! 000 0.974 948 925 902 880 0.860 940 821 803 786 769 696 636 585 642 505 444 418 396 0.875 0.149 0.597 1.343 2.388 3.731 5.372 7.312 12.087 1t.923 18.0566 21.489 25.219 29.248 33.576 38.208 43.126 48.349 63.8l11 59.690 65.809 72.225 78.941 85.954 93.266 100.88.108.79 116.99 125.50 134.30 1143.41 152.81 162.51 172.51 182.80 193.40 204.29 215.48 226.97 238.76 250.85 263.24 275.92 288.90 302.18 31 5.7 6 329.64 843.82 358.29 373.07 4-51-.41 537.21 630.48 781.21 839.40 10718.0 1209.0 1847.0 1492.0 135.56 43.432 23.543 15.628 11.529 9.066 7.440 6.292 5.443 4.790 4.274 3.857 512 229 2.9771 766 582 421 278 151 038 1.936 843 759 682 612 547 487 432 1.3803 3320 288 246 207 170 135 103 072 043 015 0.989 964 940 918 0.89C 876 850 837 81 802 720 663 610C 569 526 492 462 436 412 0.8914 0.152 O0,609 1.372 2.438 3.809 5-6.485 7.466 9.751 12.341 15.235 18.436 21.940 25.749 29.864 34.283 39.004 44.034 49. 367 55.00 60.946 67. 195 73.'746 80.601 87.763 95.230 103.00 111.08 119.46 128.14 137.13 146. 42 156.02 165.93 176.14 186.65 197.47 208.59 220.02 231.75 243.79 256.13 268.78 281.73 294.98 308.54 322.41 386.58 851.05 365.84 380.92 460.91 548.52 643.76 746.60 857.07 975.15 1101.0 1234.0 1375.0 1524.0 100 met. in litres 144.08 0.157 46.160 0.628 25.022 1.414 16.610 2.513 12.253 3.927 97.6-36 5.655 7.907 7.697 6.687 10.053 5.785 12. 723 5.091 15.708 543 19.007 099 22.620 3. 733 26.547 425 30.788 3.164 35.343 2~.939 40.212 744 45.396 573 50.894 422 56.706 287 62.832 166 69.272 058 76.027 1.959 83.095 870 90.478 788 98.175 713 106.16 644 114.51 581 123.15 522 132.10 1.467 141.37 416 150.95 361 100.85 324 171.06 282 181.68 243 192.42 2 07 2 03.-5-8 172 215.04 139 226.82 108 238.92 079 281.33 051 264.05 024 277.09 0.999 290.44 9715 304.11 0.953 318.09 ~9 21 332.3~8 910 346.99 890 361.91 871 377.15 853 392.70 772475.17 705 565.29 749 663.66 607 759.69 559 883.58 523 1005.0 492 1155.0 463 1272.0 438 1478.0 0.416j1571.0 158.85 50.891 27.587 18.313 13.509 0.169 0.660 1.484 2.636.4.123 1100 mt~et.i litres - 10.6281 5.9381 8.717 7.373 6.373 5.613 5.009 4.519 4.115 3.776 488 241 025 2.837 670 521 388 268 160 061 1.971 889 813 743 678 1.617 561 509 460 414 371 330 292 256 222 186 156 126 102 07h 1.050 026, 003 0.981 961 940 851 7 77 71E 662 617 577 542 511 483 0.45c, 8.082 10.55( 13.361 1 6.49RI 19. 957 23.751 27.874 32.327 37.116 47.666 53.430 59.541 65.974 72.786' 79. 828~ 87.250' 95.002 103.08 f 11-1.50( 120.24 129.31 138. 71 148.441 158.50 168.89 179.61 190.661 202.04 213.75~ 225.80 238.17 250.87 263.89 27 7.2 6 290.95 304.96 319.31 333.99 349.00 364.34 380.01 396.01 412.34 498.92 593.76 696.85 808.18 927.76 1056.0 1192.0 1336.0 1489.0 ~1649.0 100 met. in litres. 174.34 0.173 55.85.4 0.691 30.277 1.555 20.098 2.765 14.826 4.320 11.659 6.220 9.567 8.446 8.092 11.058 6.999 13.996 6.160 17.279 5.497 20.907 4.960 24.881 516 29.201 145 33.866 3.829 38.877 557 44.234 320 49.936 113 55.883 2.930 62.376 767 69.115 621 76.200 490 83.629 871 91.405 262 99.526 164 107.99 0713 116.81 1.990 125.96 913 185.47 841 145.92 1.775 155.51 714 166.05 656 176.94 602 188.17 552 199.74 505 211.67 460 223.93 418 236.55 378 249.51 341 262.81 305 276.46 272 290.46 240 804.86 209 319.49 180 334.52 1.158 349.89 126 365.6 101 881.69 077 398.10 054 414.87 032 481.97 0.984 522.68 858 622.04 785 780.08 727 846.66 677 971.98 638 1106.0 595 1248.0 561 1400.6 581 1559.6 0.5031 1728.6 I 261 I i i i I i i i i I TABLE XXXL -Discharge of Water through New Pipes. Compiled from Henry Darcy's French Tables of 1867. p, )8 Velocly per se( 1.1I 230 Centimetres llt nDshg. I 240 Centimetres.;1 260 Centimetres Metre section. 0.01 0.0001 2 ~03 3 07 4 13 6 20 6 28 7 38 8 50 9 64 10 791 1 1 95 12 113 13 133 14 164 16 177 16 ~201 1 7 227 1 8 254 1 9 284 20 314 2 346 22 380 23 415 24 452 25 491 26 531 2 7 673 28 616 29 661 30.0707 31 766 32 804 33 855 34 908 35 962 100 met. In litres. 190.55 0.181 61.047 0.723 33.092 1.626 21.967 2.890 16.204 4.516 12. 7-43 6.503 10.457 8.851 8.844 1 1.5611 7.650 14.632 6.733 18.064 6 ~. 008 2 1.8-58 5.421 26.012 4.936 30.529 4.530 35.406 4.185 40.644 3.887 46.244 629 52.206 403 58.428 203 65.212 024 72 257 2.865 79.663 721 87.431 591 95.560 473 104.05 365 112.90 266 122.11 175 131.69 090 141.62 013 151.92 1.940 162.68 873 173.60 810 184.98 751 196.72 696 208.82 644 221.29 100 met 2071.48 66.470 36.032 23.918 17.644 13.875 11.386 9.630 8.330 7.331 6.542 5.902 5.375 4.932 4.556 233 3.952 705 487 293 2.963 821 692 675 467 368 276 191 2.113 039 1.971 907 847 790 I Disch'ge gt.iit inlte.100 me t. Disch'g in litrei I 0.188 2 25. 12 0. 754 72.125 1.697 39.097 3.016 25.953 4.712 19.145 6-. 786 15.056 9.236 12.355 12.064 10.449 15.268 9.039.18.850 7.955 22. 8-0 87.098 27.1lf3 6.405 31.656 5.832 36.945 5.352 42.412 4.944 48.255 592 54.475 288~ 61.073 020 68.047 3.784 75.398 573 8 3.1-27 ~38~5 91.232 215 99.714 061 108.57 2.922 117.81 794 1-27.42 677 137.41 569 147.78 470 158.53 378 169.65 2.292 18 1. 15 213 193.02 138 205.27 069 217.90 004 230.91 1.943 I 0.19( 0.78r 1.76E 3.14k 4.90c, 7.06c 9.621 12.566C 15.904 19.635 23.758 28.274 33.183 38.485 44.179 50.266 56.745 63.617 70.882 78. 540 86.590 95.033 103.87 113.10 122.72 132.73 143.14 153.94 165.13 176.72 188.69 201.06V 213 83~ 226.98 240.53 Ii )iI.11 1 II I 260 Centimetrei Hgt it 100 me t. JDisch'i in litrE 243.50 78.010 42.287 28.071 20.707 16.284 13.363 11.302 9.776 8.604 7.677 6.927 6.308 5.789 5.347 4.968 638 348.092 3.8615 661 477 311 160 022 2.895 779 671 672 2.479 393 313 238 167 101 0.204 0.817 1.83E 3.267 5.105 7.-3-51 10.006 13.069 16. 541 20.420 24.70O9, 29.405 34.515 40.024 45.946 52.276 59.015 66.162 73.718 81.682 90.054 98.835 108.02 117.62 127.63 130.04 148.87 160.10 171.74 183.78 196.24 209.11 222.38 236.06 260.16 I I I I I 36 37 38 39 40 -41 42 43 44 45 47 48 49 50 60 65 i701 751 80 85 90 95 I - 1018 1075 1134 1195 1257 1320 138.5 1452 1521 1590 1735 1810 1886 1964 2376 2827 3318 3848 4418 5027 6675 6362 7088 0.7854 I - 596 550 606 465 427 390 365 322 290 1.260 231 203 177 152 128 0.024 931 858 794 740 692 660 613 5 80 0.550 234.11 247.3C 260.85~ 274.76 289.08 303.66 318.65 334. 01 349.72 366.80 382.24 399.04 416.20 433.72 451.61 546.44 650.31 763.21 885.16 1016.0 1166.0 1306.0 1463.0 1630.0 1806.0.i I I I I I - 737 687 640 696 653 613 476 439 404 1.372 340 310 282 264 228 111 01 6& 0.934 866 805 763 708 667 631 0.599 I - 244.2c 258.05 272.16 286. 70 301.59 316.86 332.61 348.63 3 64.9 3 381.70 298 86 416.39 434.29 452.58 471.24 570.20 678.69 796.40 923.63 1060.0 1206.0 1362.0 1627.0 1701.0 1885.0 886 831 780 731 686 642 601 661 624 1.488 454 422 391 361 332 206I 101 0131 0.938 874 -8-18 768 724 686 0.650 I - 254.47 268.8C 283.54 298.65 314.16 T330.07~ 346.36 363.05 380.13 397.61 415.48 f433.74 462.39 471.44 490.88 593.96 706.86 829.58 962.12 1104.0 1267.0 1419.0 1590.0 1772.0 1964.0 I I I I I 039 1.980 926 873 823 776 731 689 648 1.610 573 638 604 472 441 304 191 096 016 0.9451 884 831 783 741 0.703 I - 264.65 279.56 294.87 310.69 326.731 3t~ 43.2 7 360.22 377.68 396.34 413.61 451.09 470.49 490.30 610.51 735.13 862.76 1001.0 1149.0 11475.0 i1664.0 1843.0 2042.0 111.001 I 262 1 i i TABLE XXXI. - Discharge of Water through New Pipes& Corpiled from Henry Darcy's French Tables of 1857. 270 Centimetres. 280 Centimetres. 290 Centimetres. 300 Centimetres. iij -i-in Disehe Hgt. in Disch'gie Ligt. in Dischige Hgt.in Disch'ge 100 met. in litres 100 met. in litres. 100 met. in litres. 100 met. in litres. 262.59 0.212 282.40 0.220 302.93 0.228 324.18 0.236 81.127 0.848 90.474 0.880 97.061 0.911 103.86 0.942 46.603 1.909 49.043 1.979 52.609 2.050 56.300 2.121 30.272 3.393 32.-556 3.519 34.923 3.645 37.473 3.770 22.331 _5.301 24.015 5.498 25.762 5.694 27.569 5.891 17.561 7.634 18.886 7.917 20.259 8.200 21T.68-0 8.482 14.410 10.391 15.498 10.776 16.624 11.161 17.791 11.545 12.188 13.572 13.107 14.074 14.065 14.577 15.047 15.080 10.543 17.177 11.338 17.813 12.1621 18.449 13.016 15.459 9.279 21.206 9.979 21.991 10.704 22.777 11.455 23.562 8.2 79 25.659 8. 904 2l i6. 609 9. 551 27.560 10.221 28.510 7.470 30.536 8.034 31.667 8.618 32.798 9.222 33.929 6 803 35.838 7.316 37.165 7.848 38.492 8.398 39.820 6.248 41.563 6.714 43.103 7.202 44.642 7.707 46.182 5.767 47.713 6.202 49.486 6.653 51.247 7.119 53.015 357 64.287 5.761 56.2-970 6.180 58.308 6.614 60.319 00] 61.285 378 63.555 5.770 65.824 6.174 68.094 4.689 68.707 5.043 71.252 5.409 73.796 5.789 76.341 413 76.553 4.746 79.388 5.091 82.223 448 85.059 168 84.823 482 87.965 4.808 91.106 145 94.248 3.948 93.518 24 6 96.981 4.554 100.45 4.874 103.91 750 102.64 4.033 106.44 326 110.24 629 114.04 571 112.18 8.840 116.33 4.119 120.49 408 124.64 408 122.15 665 126 67 3.931 131.19 207 135. 712 259 132.54 505 137.45 759 142.35 023 147.26 122 143.35 3 58 148.66 602 153.97 3.85I 5 159.28 2.997 154.59 223 160.32 457 166.04 700 171.77 881 166.25 3.098 172.41 323 178.57 556 184.73 773 178.34 2.983 184.95 199 191.55 424 198.16 2.674 190.85 875 197.92 3.084 204.99 3.301 212.06 I i i TABLE X X X I I. To reduce Centim tres te English inches. English Metre inches 0.01 0.39 02 79 03 1.18 04 1.58 05 1.97 06 2.36 07 2.76 08 3.15 09 3.54 10 3.94 11 4.33 12 4.73 13 5.12 14 5.51 15 5.91 16 6.30 17 6.69 18 7.09 19 7.48 20 7.88 21 8.27 22 8.66 23 9.06 24 9.45 25 9.85 26 10.24 27 10.63 28 11.03 29 11.42 30 11.81 31 12.21 32 12.60 33 13.00 34 13.39 35 13.78 36 14.18 37 14.57 38 14.96 39 15.36 40 15.75 41 16.15 42 16.54 43 16 93 44 17.33 45 17.72 46 18.12 47 18.51 48 18.90 49 19.30 50 19.69 55 21.66 60 23.63 65 25.60 70 27.67 75 29.64 80 31.50 85 33.47 90 35.44 96 37.41 1.00 39.88 I I i i i. i i I i 1. 0t6 494 413 337 266 199 136 076 019 1.966 915 867 821 778 1.736 696 658 622 587 554 406 284 182 095 019 0,9-53 895 845 799 0.758 203.79 217.15 230.93 245.14 259.77 274.83 290.31 306.21 322.54 339.29 356.74 374.07 392.10 410.54 429.42 44-8.72 468.44 488.58 509.15 530.15 641.47 763.41 895.95 1039.0 1193.0 1357. 0 1582.0 1718.0 1914.0 2121.0 ' 776 683 595 514 437 365 297 233 172 114 060 2.008 1.959 912 867 824 783 744 707 671 513 381 271 177 096 2 11.04 225.19 239.48 254.22 269.39 285.01 301.06 317.55 334.49 351.86 369.67 387.93 406.62 425.75 445.32 465.34 485.79 506.68 528.01 549.78 665.23 791.68 929.13 1078.0 1237.0 2.9 7 7 218.8 166 226.48 878 233.23 079 241.28 784 248.04 2.979 256.59 696 263.30 886 272.37 614 279.01 798 288.64 537 29 5.19 715 305.36 464 311.81 63 7 322.56 395 328.89 563 340.24 330 346.43 493 358.38 268 364.43 427 376.99 209 382.88 3~64 396.08 154 401.78 305 415.64 101 421.14 248 435.66 051 440.95 194 456.16 2.003 461.23 2.143 477.13 1.957 481.95 094 498.57 913 503.14 047' 520.49 871 524.77 002 542.87 831 546.87 1.959 565.73 793 569.42 918 589.05 623 688.99 736 712.75 482 819.96 586 848.23 364 962.31 459 995.50 263 1116.0 351 1155.0 176 1281.0 258 1325.9 o00 1458.0 '1f71 1508.0 1.033 1646.0 106 1702.0 0.097 1845.0 043 1909.0 922 2056.0 0.986 2126.0 0.87512278.01 0.936 2352.0 1.025 1407.0 0.963 1589.0 908 1781.0 8691 1985.0 0.81612199.0 i II I 263 --- i I I L, 1ai cy compared the various formulas on the discharge of water.~e~bpipeis,- and found that the theoretical and practical dishrgsdiffered considerably. The experiments made by him on the dshrethrough 68 pipes of cast and wrought iron, lead'and bitutm-jen,.witk velocities -from 10 centimetres to, 3 metres per -se~ond, have shown, that former formulas were not correct. His being, employed by the. municipal government of Paris tci make the necessary, experiments, no pains or expenses were spared. From -these careful' experiments, he has been able to determine a formula which reconciles' theory with practice. M. Darcy's great work has been pu~blishedwith the approval of the French Academy of Sciences, and ought to have a place in every engineer's library. It is a quarto of 2.68 pages, with -a folio atlas. M. Darcy's formula is as follows: 0.00000647 11i =(0.000507~+)V 0.0000065 Or R i (0.00051+ V 0.00051 0.0000065 i + 2 ) V2 charge per~metm.' 0.0507 0.000647 100 i ( ~ V2 charge per 10& metres.. B. Let a =0.00051, b =0.0000065; then we have, by quadratics, av2 b y2 -avej R= —j-, +.)=radius of conduit or pipe. 2i i 4 i2 Example.~ Given V velocity in metres per second ==0,30 met. R = radius of pipe or conduit = 0.20 metres. To find the head, heighit or charge in 100, metres. 0.0507 0.000647 100 M. ( ~1 ) 0.09 0.02427075..2.04 Q V, that is the quantity discharged, is found by multiplying the sectional area by the velocity. The product will be cubic metres, which, if divided Iinto cubic decimetres, will give the discbarge in litres. Or, having the product S V, remove the decimal point three places to the right, for litres. Example. S =.71854 =area of pipe in metres. v= 1. =velocity per second in metres..001 1 cubic decimetre = 1 litre..001 divided into.7854 785.4 litres. From~the above, we have: 0Hi 004 V (0.000507 +.00067 in metres, in terms of its radius. D i Or V (.004+.00001294) in metresin terms of its diameter. Di (0.00809+0.00002w8 in English feet. I I I ' —4 _#264 tot" Iwl. t Z_, i, 4E Jo- i 0 W; % 0.4-P 4 014,4 ", ,:W I iJ ,i ~ ~ ~ ~ ~ ~ ~ ~ I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ h:; in~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ "-i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~