DUKE UNIVERSITY LIBRARY FRANK BAKER COLLECTION OF WESLEY AN A AND JiKLlMSH METHODISM .0 SIR, Your Majesty's moft humble, moft obedient, and moft dutiful, Subjed and Servant, GEORGE ADAMS. PREFACE. THE connecSllon of agronomy with geography is fo evident, and both in conjundion are fo necelTary to a learned education, that no man will be thought to have delerved ill of the republic of letters, who has applied his endeavours to throw any new light upon fuch ufeful fciences. And as the phenomena of the earth and heavens can be adequately illu- ftrated only by the mechanical contrivance of globes ; whatever improvement is made in thefe muft deferve regard, in pioportion as it facilitates the attainment of agronomi- cal and geographical knowledge. As to maps and all projedlons of the fphere in piano, their uie is more difficult than thofe of the globe, of which indeed they are only fo many pidures ; nor can they be thoroughly underftood without more fkiU viii PREFACE. fkill in geometry than is commonly pof- CciTt'd by beginners, for vvhofe ufe the fol- lowing treatiie is principally defigned ; tho' it alio contains fome obfervations, which I hope will not be altogether unacceptable to a mere learned reader. The globes now offered to the public, arc of a conftruction new and peculiar, being contrived to folve the various phenomena of the earth and heavens, in a more eafy and natural manner than any hitherto publifhed, being fo fufpended that the ftudent may elevate the fouth pole 3 a thing impradlicable in the ufe of the common globes. That agreement too, which is here pointed out between the celeftial and terre- flrial fphere, will be found to open a large field of geographical and agronomical know- ledge ; and wiil afford both inflrudlion and amufement to every unprejudiced enquirer. This agreement arifes from, a comparifon of one globe with the other, or ot the diftances of different places on the earth's fuiface, with the relative diflances of iuch fixed liars as anfvver to them in the heavens. By Pi^EFACE. m By thefe fteps of fcience, the mind of: man may be raifed to the contemplation of the divine wifdom, whicli has ib ad- jufted the proportion of days, months, fea- fons, and years, in the different parts of the terraqueous globe, as to have diftributed with an impartial hand, though after a manner wonderfully various, an equal fhare of the fun's light to every nation under heaven. By thcfe globes, with little or no expe- rience in aftronomy, may be feen how the moon changes her place every night, by obferving her pofition with refpecl to anjr fixed ftar, and how flie proceeds reguhrly from it to the eaftward ; as the leveral planets alfo may be obferved to do, fome more flowly than others, as their orbits are more or lefs remote from the c:ntL;r oi" the fyftem; while the regularity of their motions, Aridly conformable at all times to the laws of their Creator, exhibits a flriking pattern of obedience to every rational fp^ctator. But it will be proper in this place to in^ form the reader what he is to expccl in the globes, and in the following treatife intended to accompany and explain them. The ^ PREFACE. The fuperior accuracy with which the plates are drawn and engraved, will, it is hoped, appear to competent judges at the firft fight ; for the perfeding of which no expence of time or labour hath been fpared. The celeftial globe is improved by the addi- tion of feveral thoufand ftars more than have app.ared upon any globe hitherto pub- lifhed 'j all the iateft difcoveries in geography and aftronomy are in both of them ftridly followed, and many new lines and circles are inicribed, the ufe of which will be fully explained hereafter. .,. In the treatife, we have made choice of that method of finding the times of equinox, which is the moft modern and fnnple j and which perhaps is the trueft mean length of ^ tropical year j that the young fludent may with greater eafe and pleafure be made ac- quainted with the firft principles, and from them be carried on to the more intricate branches of aftronomy. The table of the pafTage of the firfl point of aries over the meridian, is taken from an Ephemeris of La Caille, with fome little alterations j and has been carefully compared with twenty years calculations made PREFACE. ti made by the fame author. The necefTity under which I found myfelf of haftening the publication of this Treatife, and the va- rious interruptions and avocations from which a perfon in my ftation cannot be exempt, would not allow me fufficient leifure to cal- culate an original table. To render this book as extenfively ufeful as poflible, I have endeavoured, with all the clearnefs I am mafter of, to exprcfs both my own and the fentiments of other authors on the fame fubjed ; and I think it my duty to acknowledge the afl'ftance I have received in the courfe of this work, as well from books, as from fome worthy friends j as I would not willingly incur the imputation either of plagiarifm or ingrati- tude. If there (hould appear to be any defects, to which every human work is liable, the reader, I hope, will make fome favourable allowance for the unde* taker of a tafk fo complicated and laborious, and corred: my errors for himfeif, as well as he is able. ADVER- xii PREFACE. ADVERTISE ME N T. When the reader is hereafter diredled to apply a card, or the edge of a card, to any part of the globe, it is to be underftood that he Ihould cut a card of any kind exadly in the fize and fhape of A B C D, fig. 4. for the globes of eighteen inches diameter j and of the Cze and fhape of E F G H, for thofe of tvvefve inches diameter ; then, if the arch B C, or F G, are applied to the furface of their refpeftive globes, the lines A B, or C D, E F, and G H, will become radii from the center of the globe. It is frequently required to know what point upon the ftrong brafs meridian, or broad paper circle, exadly an- fwers to a given point upon the globe, and as this cannot be well known by inlpedion, on account of the necefiary diltance of thefe two circles from the furface, if the corner B or F b'i applied to the given point upon the globe, the edge of the card will exactly mark the de- gree br part of the d.-gree required. For elevating the pole exa6lly, the card is to be laid upon the broad paper circle, and its edge applied to the ftrong brafs meridian, by which means the degree, and parts of a degree, may be afcertained with fufiicient accuracy. The PREFACE. xiii The explanation of the letters to the figures i and 2. Fig. I. reprsfents the new terrt-ftrial, and fig 2. the new celeilial globe, with their im- proved apparatus. N ^ R Z N. The ftrong brafs meridian. N H S. The thin brafs ftrmi circle, or move- able meridian, upon the terreftrial, but upon the celfftial globe it is a moveable circle o[' decli^ nation ; on the firfl: of thele is placed H a flidinw- circle, which is hereafter called an artificiai horizon i the little Aiding circle upon the ce- Jeltial globe, is called an artificial fun. -Si I Q^ The equator, o"cr which in either figure is reprefented about half of the femi- circular wire F I M^ which carries the horary indices, one of them is feen at I. E L. The ecliptic Z A. The brafs quadrant of altitude fcrewcJ fall to Z, the zenith point of the ftron.o- brafs meridian, its other end, A, going a little faelov.? the plane of B A C. The broad-paper circle upon the ■furface of the wooden frame. T W Y. The wire circle, rcprefcntinp- the boundaries of twylight. N C 5. xir PREFACE. N C S. A filk firing, fig. 2. fixed occafionally to the north and fouth poles of the celeltial globe, which is hereafter defcribed, and called an artificial moon j it may alfo reprefent the place of any planet. M. The mariner's compafs, with a magnetic needle. THE THE N T E N T S. Page ARtificial globes, terreftrial and celcflial, what r The broad-paper circle on the i'urface of the wooden frame defcribed 6 Problem I. To find the fun's place 7 The fhong brafs circle, or meridian ^ The horary circle Jl The motion of the terreftrial globe I J of the celeflial globe 13 Thin brafs femi-circle l j The brafs quadrant of altitude 14 The feveral circles defcribed on each globe 14 The equator 15 Prob. II. To find the latitude of a place 17 III. To find all thofe places which have the fame latitude with any given place 17 IV. To find the difference of latitude between any two places ^^ 18 V. To find the declination of die fun or any ftar / iS VI. To find what ftars pafs over or nearly over the zenith of any place 20 Cclcftial and terreftrial meridians, what^ 21 Pros. xvi The CONTENTS. Page Prob. VII. To find the longitude of a place 23 VIII. To find what places have mid-day^ or the fun upon their meridian, at any given hour of the day, in any place propofed 25 IX. To find viliat hour it is at any place propofed when it is noon at any given place 28 X. At any given time of the day at the place where you are to find the hour at any other place propofed 29 XI. The latlrude and longitude of any place being known, to find that place upon the globe ; or if it be not infer ted, to find its place, and fix the artificial horizon thereto 30 The ecliptic defcribed 31 , The celeftial figns and conftellations 34. General phenomena arifing from the earth's diurnal motion 36 Parallels of latitude, declination, tropics, and pokr-circlcs 37 The colurcs 43 Arctic and antardlic circles 45 The caufe of the daily change in the declina- tion of the fun 48 To fupply the want of a tellarium 53 Pjiob. XII. To re6iify either globe to the lati- tude and horizon of any place 57 To reftify for the fun's place 58 for the zenith of any place 58 Xlil. To find the moon's mean place, her age and dzy of the month be- -ing known 5/) Prob. The CONTENTS. xvii Page pROB. XIV. To reprefent the apparent diurnal motion of the fun, moon, and ftars, on the celeftial globe 62 Their time of rifing, oblique afcenfion, right afcenfion, declination, oblique defcenfion, afcenfional difference, &c. from art. 182 to 198. Parallels of altitude, what 66 Prob. XV. To find the fun's altitude 68 Azimuth or vertical circles, what 69 Proc. XVI. To find the azimuth of the fun or any flar jo To find the angle of pofition and bearing of one place from another yi A parallel fphere --2 A right fphere 73 An oblique fphere y^ Of the twilight 7-5 To reprefent the earth's enlightened difk by the terreftrial globe 7^ Prob. XV^II. To redify the terreftrial globe that the enlightened half may be apparent for any time of the year 78 XVIII. The times of equinox 80 XIX. The fummer-folftice 83 XX. The wintcr-folflicc 85 The tcrreflrial horizon 86 pRGB. XXI. The fun's altitude as obferved with a terreftfial horizon 87 XXII. The fun's meridian altitude at three different feafons 88 XXIII. To find the fun's meridional alti- tude univerfally 90 XXIV. The fun's azimuth compared with the vifible horizon 9 1 b Pros. xviii The CONTENTS. Page PROB. XXV. The Afcii 94, XXVI. Amphifcii, Heterofcii, Perifcii, Ancaeci, Periaeci, Antipodes 96 XXVII. To find all thofe places on the globe over whofe zenith the fun will pafs on any given day 99 XXVIII. To find the fun's declination, and thence the parallel of latitude cor- refponding therewith, upon the terreltrial globe lOi XXIX. To find thofe two days on which the fun will be vertical to any place between the tropics loi XXX. The day and hour at any place being given, to find where the fun IS vertical at that time lOZ XXXI. The time of the day being given, to find all thofe places where the fun is then rifing and fetting on the meridian; vcitical alfo, mid- night, twilight, darknight, &c. at the fame inftant 103 XXXII. To find the time of the fun's rifing and fetting, length of day and night, &c. in any place be- tv/een the polar-circles j and alfo to find the climate 105 XXXIII. To find thofe places within the polar-circles on which the fun begins to fhine, the time he ftiines, when he begins to difap- pear, length of his abfence, and the firft and laft day of his ap- pearance 108 Pp.os. The CONTENTS. x\x ^'jf.l Page Prob. XXXIV. To find the length of any day in the year in any latitude IIO XXXV. To find ihe length of the longeft and ftiortefl days in any latitude ill XXXVI. To find the latitude of a place in which its longeft day may be - of any given length between twelve and twenty-four hours II2 XXXVII. To find the diftance between any two places Ii2 XXXVIII. To find all thofe places which are at the fame diftance from a given place 113 XXXIX. To (hew at one view upon the terreftrial- globe for any place the fun's meridian altitude, bis amplitude, or point of thecom- pafs on which he rifes and fets every day in the year 113 XL. To fhew at one view upon the terreftrial globe the length of the days and nights at any par- ticular place for all times of the year 113 XLI. To find what conftellation any remarkable ftar, [c:n in the fir- mament, belongs to iig XLII. To find at whiit hour any known ftar pafles tiiC meridian any day in the year I2Q 'XLTII. To find on what day of the year - ■ any ftar panes the meridian at ^ny propofed hour of uie ni^.'it 121 X3f the CONTENTS, Page Proe.XLIV. To trace the circles of the fphere in the ftarry firmament 121 To find the time of the fun's entry into the firft point of libra or aries, and thence that point in the equator to which the fun is vertical at either of thofe times 126 To reduce hours, minutes, and fcconds of time, into dcg;ees, minutes, and feconds of the equator 142 The contrary 143 Prob. XLV. To find all thofe places where it is noon at the time of an equinox, as well as that point upon the equator to which the fun is ver- tical at that time 144 Of the natural agreement between the celeftial and terreftrial fpheres ; or. How to gain a perfedl idea of the fituation and diflance of all places upon the earth by the fun and ftars 148 Prob. XLVI. To find the folar correfpodence to a fixed point upon the earth, when the fun is feen by an ob- ferver fituated upon any other point of its furface 151 Of the celeftial correfpondents 160 Of the pafTage or tranfit of the firft point of aries over the meridian 162 Prob. XL.VII. To find the time of the right afcenfion of the firft point of aries upon aqy meridian 168 XLVIII. To find the time of the right afcen- fion of any ftar upon, any par- ticular meridian on any day in the year 174 Prob. The CONTENTS. xxi Prob. XLIX. To reaify the celeflial globe for "^ any time in the evening of any day in the year by the know- ledge of the time when theiirft point of aries (hall pafs the nje- ridian that day jy^ The correfpondcncy of the fixed ftars i^q Prob. L. To find all thofe places to which any ftar is a correfpondent l8o A general defcription of the paiVage of the ftar y in the head of the conftellation draco, over the parallel of London 182 Prob, LI, To find a fignal or warning-ftar that /hall be upon or near the meridian of an obferver at the time any known ftar is perpendicular to any place en its correfponding parallel iSc LIL The phenomena of the harvcft moon 198 LIIL To find the time of the year in which a ftar rifes or fets cofmically or achronically 2Cl LIV. To find the time of the heliacal rifin.o- and fetting of a ftar 205 The manazil al kamer of the Arabian aftronomers 206 Prob. LV. To find a meridian-line 211 LVL Of the equation of time 214. LVIL To obferve the fun's altitude by the terreftrial globe when he ftiincs bright, or when he can but juft be difcerned through a cloud 219 LVin. To place the terreftrial globe In the fun's rays that it may rcprefcnt the patuial pofition of the earth, cither by a meridian-line, or without it 222 Prob. xxU The CONTENTS. Page Prob. LIX, To find naturally the fun's decli- nation, diurnal parallel, and his place thereon 225 LX. To find the fian's azimuth natu- rally 226 LXI. To fhew that in fome places of the earth's furface the fun will be twice on the fame azimuth in the morn- ing, and twice on the fame azi- muth in the afternoon. 228 LXII. To obferve the hour of the day in the moft natural manner when the terreftrial globe is properly placed in the fun-fhine 229 Method to redlify the terreftrial globe to the fun's rays 234 A Table of retroceffion and autumnal equi- noxes 236 Of months 237 Of week-days 237 Of the horary difference in the mo- tion of the firft point of aries, at the time of a vernal equinox 238 Of the difference of the pafTage of the firft point of aries over the meridian, for every day in the year 239 T H b; -K- J^ront fij. The New^ Celestial Globe, As Impro red and Constructed by GE OiAdAMS InYlc^i Street LONDON. THE DESCRIPTION and USE OF THE NEW CELESTIAL and TERRESTRIAL GLOBES. 'F a femi-circle be turned round its diameter as an axis, it will ge- nerate the furface of a globe or iphere, and the center of the fe- mi-circle will be the center of the globe : it therefore follows, that as all the points in the circumference of the femi-circle, are at an equal diftance from its center, fo all the points of a globe, thus generated, mufl be the fame. B 2. Any 2 Description and Use of the 2. Any ftrait line pafling through the center of a globe, being terminated by its furface, is called a diameter j and that dia- meter about which the globe turns, is called its axis J the extremities of which are called the poles of the globe. 3. There are two artificial globes. That on which the furface of the earth is repre- fented, is called the terrejlrial globe. 4. The other on which the face of the ftarry fphere is delineated, is called the ce- lejiial glok. 5. In the life of the terreftrial globe ^ we are to confider ourfelves ftanding upon fome ■part of its furface, and that its motion re- prefents the real diurnal motion of the earthy which is from 'wejl to eajl. 6. In the ife of the celeflial globe ^ we are to fuppofe ourfelves at the center^ and that its motion reprefents the apparent diurnal motions of the heavens^ which is from eafi to imfi, 7. Note, The ftars being delineated upon ihe cohvex furface of the celeftial globe^ we muft fuppofe ourfelves at the ce?2ter : becaufe under fuch a fuppofition they would appear CeJeJlial arid Terrejirial Globes. 3 appear as they naturally do in the concave iurface of the heavens. 8. Several circles are defcribed upon the furface of each globe. Thofe whofe planes pafs through the center of the globe, are called great circles j fome of which are gra- duated into 360 degrees, 90 of which make a quadrant. 9. Thofe circles whofe planes do not pafs through the center of the globe, are called lefer circles. 10. Our new terreftrial and cclejlial globes are each of them fufpended at their poles in a ftrong brafs circle, and turn therein upon two iron pins, which are the axes of the globe. They have each a thin brafs femi'Circle moveable about the poles, with a fmall thin Aiding circle thereon. 11. On the terreftrial globe this femi- circle is a moveable meridian^ and its fmall Aiding circle, the vifible horixon of any par- ticular place to which it is fet. But, 12. On theceleftial globe this femi-circlc Is a moveable circle of declination^ and its fmall circle an artifcial fun or phmet. 1 3 . Each globe hath a brafs wire circle, placed at the limits of the crepufctdum^ or B 2 twilight. Description and Vse of the twilight, which, together with the globe, is fet in a wooden frame, the upper part of which is covered with a broad paper-circle, whofe plane divides the globe into two he- mifpheres, and the whole is fupported upon a neat pillar and claw, with a magnetic needle in a compafs box. 14. On our new terreftrial globes, the delineation of the face of the earth into land and water, is accurately laid down from the latefl: and befl agronomical, geographi- cal, and nautical difcoveries. There are alfo many additional circles, as well as the rhomb-lines, for the greater eafe and conve- nience in folving all the neccfTary geogra- phical and nautical problems. 15. On the furface of our new celeftial globes, all the fouthern conjlellations, lately obferved at the Cape of Good-Hope byM. de la Caille, and all the ftars in Mr. Flam/led's Britifh Catalogue, are accurately laid down, and marked with Greek and Roman letters of reference, in imitation of Bayer. Upon each fide of the ecliptic are drawn eight- parallel-circles at the diftance of one degree from each other, including a fpace of lix- teen degrees, called the zodiac i thefe are crolTed Cekjlial and Terrejlrial Globes. 5 crofled at right angles, with fegments of great circles at every fifth degree of the ecliptic, for the readier noting the place of the moon or any planet upon the globe. 16. We have alfo inierted from TJlugh Beigby printed at Oxford, A. D. 1665, the manazil al kamer^ i. e. the manfions of the moon of the Arabian Allronomers j which are fo called, becaufe they obferved the moon to be in or n^ar one of thefe every night during her monthly courfe round the earth, to each of which the Arabian cha- raders are affixed. They may be of very great ufe to beginners to teach them the names of the ftars, as well as to mariners for the fame purpofe ; who may have occa- fion to obferve the diftance of the moon from a fixed ftar, in the new method of difcovering the longitude at fea. They will likewife ferve to flicw, how the moon palTes from ftar to fl:ar in the courfe of one or feveral nights, which is a very curious and ufeful amufement ; and as they are a divi- iion of the heavens different from any thing the Greeks were acquainted with, and therefore not borrowed from them, and as we do not know they ^vere ever inferted B 3 on 6 Description and Use of the on any globe before, we hope we have with propriety placed them on our new celeftial globe. The broad paper-circle on the fur- face of the wooden frame 17. Contains four concentric circular fpaces. The innermoft of which is di- vided into 360 degrees, and numbered in- to four quadrants, beginning at the eaft and weft points, and proceeding each way to 90 degrees at the north and fouth points; thefe are the four cardinal pcnnts of the horizon. The fecond circular fpace contains, at equal diftances, the thirty-two points of the mariner's compafs. Another circular fpace is divided into twelve equal parts, reprefenting the twelve figns of the zodiac ; thefe are again fubdivided into 30 degrees each, between which are en- graved their names and characters. This fpace is connected with a fourth, which contains the kalendar of months and days ; each day, on the new eighteen inch globes, being divided into four parts, which exprefs the four cardinal points of the day, ac- cording Celeftial and Terreftrial Globes. 7 cording to the Julian reckoning ; by which means the fun's place is very nearly ob- tained for the three common years after biilextile, and the intercalary day inferted without confufion. Whence we derive the following Problem I. To find the fun's place any day in the year on tlie broad paper- circle. 18. Confider whether the year in which you feek the fun's place, is biffextile, or the firft, fecond, or third year after. 19. If it be the firft year after biilextile, thofe divifions to which the numbers for the days of the month are affixed, are the refpedive days for each month of that year at noon i oppofite to which, in the circle of twelve figns, is the fun's place. 20. If it be the fecond year after bKTex- tile, the firft quarter of a day backwards, or towards the left hand, is the day of the month for that year, againft which, as be- fore, is the fun's place. 21. If 8 Description and Use of the 21. If it be the third year after biflextiie, half a day backwards is the day of the month for that year, oppofite to which is the fun's place. 22. If the year in which you feek the fun's place is bifTextile, then three quarters of a day backwards is the day of the month from the winter-folftice to the 28th day of February incluiive. The intercalary or 29th day, is three fourths of a day to the left hand from the ifl: of March -, and the I ft of March itfelf is one quarter of a day forward, from the diviiion marked i ; and fo for every day in the remaining part of the leap-year ; againft each of which is had the fun's place. In this manner the intercalary day is very well introduced every fourth year into the kalendar, and the fun's place very nearly obtained according to the Julian reckoning. Thus : A. D. Sun's place, April 25. 1759. firft year after bifTextile b : 5° : 21' 1770. fecond -------- 0:5°: 06' ijyi. third t5:4°: c^c^' 1772. bifiextile ^ ' 5^ '■ 35' 22. One Celeflial and Terrejirial Globes. 9 22. One ufe of the broad paper-circle is to diftinguifh the points of the horizon ; in which cafe it reprefents the real horizon of any particular place. 23. Another ufe we fliall make of this circle is to reprefent the circle of illumina- tion^ or that circle which feparates day from night. 24. A third ufe to which this circle may be applied, is to reprefent the plane of the ecliptic. All of which fliall be illuftrated in their proper places. 25. In all politions of the celeftial globe this broad paper-furface is the plane of the horizon, and diflinguiflies the viiible from the invifible part of the heavens. 26. The north-fide of the wooden frame ought to be placed diredly towards the fiorth-lide of the heavens, which is readily done by the mariner's compafs under our new globes. The flrong brafs circle, or meri- dian. 27. There are two notches in the broad wooden circle, upon the plane of which the broad lo Description a?2il Use of the broad paper-circle is placed, which receive the ftrong brafs circle : the body of the globe being fufpended at two oppofite points in this circle, turns round therein on its iron poles, one of which reprefents the north and the other the fouth-pole. 28. One fide of this ftrong brafs circle is graduated into four quadrants, each con- taining 90 degrees. The numbers on two of thefe quadrants increafe from the equa- tor towards the poles ; the numbers on the other two increafe from tlie poles towards the equator. 29. The ftrong brafs circle of the celeftial globe is called the meridian^ becaufe the ftin's center is diredlly oppofite thereto at noon. 30. On the ftrong brafs circle of our new terreftrial globe, and about 23I de- grees on each fide of the north- pole, the days of each month are laid down accord- ing to the fun's declination ; and this brafs ■circle is fo contrived, that the globe may be placed in the pofition of a dired: or right fphere, ( which is, when the north and fouth- poles are placed in the plane of the broad paper-circle) and alfo that the fouth- pole ' Cekjiial and T'errejirial Globe s. 1 1 pole may be elevated above the plane of the broad paper-furface, with as much eafe as the north-pole. A circumftance which we thought not unworthy of our attention in the conftrudlion of our new globes. 31. The graduated fide of the ftrong brafs circle, encompafling our new terreftrial globe, faces the weft. 32. But that which furrounds the cele- ftial globe, faces the caft. 33. In all inclinations of either globe, their north-poles fhould be dired:ed towards the north-point of the heavens, which the mariner's compafs placed under each of the globes, will enable us to do with the greater readinefs. The horary circle. 34. We ufe no other circle to meafure the hours and minutes of time, but the equator upon the furface of either globe; it not only being the moft natural, but the largeft circle that can poflibly be applied for that purpofe. This is done by a femi-circular wire placed in the plane of the equator, carrying two indices -, one 12 Description ajjd Use of the one of which is occaiionally to be ufed to point out the time. As the firfl: meridian in our new globes palTes through London, it therefore becomes the XII o'clock hour-circle j and this falls upon the interfedion of the equator and ecliptic at the firfl point of aries j the other Xllth hour-circle pafles through the oppofite interfedion at the firft point of libra. , Alfo remember, when the globe fliall be hereafter re(flified for London, or any other place, on the fame meridian with it, that then the graduated fide of the ftrong brafs meridian is the horary index itfelf. Likewife it may happen, the globe fhall be fo rectified -as that the two points of XII o'clock will fall in or fo near the eafi: and weft-points of the broad paper-circle that neither of the Lorary indices can be applied thereto ; therefore either of thefe points themfelves will then be the horary index in fuch a cafe. 35, The hours and minutes are graduated below the degrees of the equator on either globe ; and as 36. The C^lejiial and Terrejlrial Globes. i^ 36. The motion of the terreftrial globe is from weft to eaft, the horary numbers increafe according to the direction of that motion. 37. The motion of the celeftlal globe being from eaft to weft, the horary num- bers increafe in that dire(^ion. The thin brafs femi-clrcle. 38.' This turns upon the poles of the globe, and may be called a proper or a moveable ineridian. It is graduated each way to 90 degrees from the equator to either pole. 39. To this femi-clrcle on the new ce- leftial globe is fitted a fmall thin brafs cir- cle about half an inch diameter, which Hides from pole to pole j when we confider the fun's apparent diurnal motion, we call it an artificial fun. 40. But to the thin femi-circle applied to the new terreftrial globe, is fitted a fmall thin circle about two inches diameter, that Aides from pole to pole ; which is divided into a few of the points of the mariner's compafs. 14 Description and Use of the compafs, and is called a terreftrial or 'vifibk horizon. The brafs quadrant of altitude 41 . Is a thin narrow flexible flip of brafs, that will bend to the furface of the globe ; it has a nut with a fiducial line upon it, which may be readily applied to the diviflons on the flrong brafs meridian of either globe ; one of its edges is graduated into 90 degrees. Upon the terrefl:rial globe its ufe is to fliew the difl:ance of places j and when applied to the celefliial globe, it fhews the difl:ance between two ftars. Upon both globes it becomes occaflonally a fecondary to the ho- rizon ; and has other ufes, which will be hereafter fhewn. Of the feveral circles defcribed upon the furface of each globe. 42. We may imagine as many as we pleafe upon the furface of the earth, and conceive them to be extended to the fphere of the heavens, marking thereon concentric circles. 43. Great Cdejlial and ^errefirial Globes. 15 43. Great circles pafs through the center, and divide the globe into two equal hemi- Ipheres : all circles are fuppofed to be di- vided into 360 degrees. We fhall begin with the defcription of the equator, this being the moil eminent great circle on either globe. The EQUATOR 44. Is 90 degrees diftance from the two poles of the globe ; and is io called, becaufe when the fun appears to pafs ver- tically over this circle, the days and nights are of an equal length to all the inhabitants of the earth. 45. The plane of the equator pafles through the middle of the globe at right angles to the polar-axis. On our new globes it is graduated into 360 degrees j upon the terreftrial globe the numbers increafe from the meridian of London weilward, and proceed quite round to 360. 46. They are alfo numbei'cd from the fame meridian eaftward by an upper row of figures, for the eafe of thole who ufc the 76 Description and Use of the the Englifli tables of the latitude and longi- tude of places. 47. On our new celeftial globes the equa- torial degrees are numbered from the firfl point of aries eaftward to 360 degrees. 48. Clofe under the degrees, on either globe, is graduated a circle of hours and minutes. 49. On the celeflial globe the hours in- creafe eaftward from aries to XII at libra, where they begin again in the fame direc- tion and proceed to XII at aries. 50. But the horary numbers under the equator of the terreftrial globe increafe by twice twelve hours weftwards, from the meridian of London to the fame again. 51. In every pofition of the globe, ex- cept that of a parallel-fphere, the plane of the equator cuts the eaftern and weftern points of the broad paper-circle, when con- fidered either as an horizon, the ecliptic, or circle of illumination. And as the globe is turned about, it al- ways keeps to one point of the ftrong brafs circle, in which, as hath been obferved, the degrees are numbered both ways from the equator, that the diftance of latitude north or Celejlial and Herrejlrial Globes. 17 or fouth of any point on the furface of the globe may be more eafily computed. Whence arifes the following Problem II. To find the latitude of a place. 52. Bring the place to the graduated fide of the ftrong brafs meridian, the degree it then cuts fhews its diftance from the equa- tor, which on the terreftrial globe is called latitude. Thus London has 5ideg. 32 min. of north latitude J Conftantinople 41 deg. of north latitude ; Quebec, in Canada, 46 deg. 55 min. of north latitude •, and the Cape of Good Hope 34 deg. fouth latitude. Problem III. To find all thofe places which have the fame latitude with any given place. 53. Suppofe the given place London; turn the globe round, and all thofe places which C pafs iS Dr.scRiPTioN and Use of the pafs under the fame point of the ftrong brafs meridian, are in the fame latitude. Problem IV. To find the difference of latitude between any two places. 54. Suppofc London and Rome, iind the latitude of each place by problem ii. art. 52. Their difference is the anfwer. Problem V. To find the declination of the fun or ^ny fear. 55. Firft, On either globe for the fun's decli?intion Iind his place in the ecliptic by problem i. art. 1 8. Then bring that point of the ecliptic line upon the globe under the graduated fide of the ftrong brafs meridian, and the degree which it cuts is the funs declination for that day. Or, Upon the terreftrial globe, that parallel which pafles through the point of the ecliptic anfwering to the day of the month, will fliew Celcftml and ^crrejirial Gloees. \<^ (hew th^ Jitns declination^ counting the num- ber of jiarallcls from the equator. Alfo, Oil the ccleftial globe, feek the day of the month clofc iincki' the ecli|)tic line itfelf, ngainft which is the fun's place, hring that point under the gnidiiateci fide (jf the ftrong braC- meridian, and the degree that (lands over it is ihcfuns declination for that day. Thus on the 20th of May the fun's declination will he about 23 deg. 10 min. and upon the 23d of Auguft it will he 1 1 (Xq'^. 13 min. For die declination of any liar. Secondly, uring the flar to the graduated fide of the ftrong brafs meridian on the ccleftial idobe, and the de;);ree it ftands under is its diftance from the equator, and this diftance is called \\\Q.Jl(ir$ dccUnaiioJiy which may he either north or fouth, according to the fide of the equator on which the liar is fituated. Thus the declination of the ftar Ardurus, marked a in the C(.nftellation Bootes, has about 20 (leg. 30 min. north declination, and that of Syrius in Canis major, or the C 2 doe-ftar. 20 Description and Use of the dog-ftar, marked a, is about i6 deg. 3omin. fouth declination. 56. Hence we fee that the latitude of places on the earth, and the declination of the fun and ftars, &c. in the heavens, have but one idea, the meaning of which is no more than their diftance (either of places on the terreftrial, or of the luminaries in the celeftial fpheres) from the equator. ^j. The declination of a fixed ftar always continues the fame, but that of the fun, moon, and planets, vary. 58. Thofe ftars, whofe declinations are equal to the latitude of any place upon the earth, are called correfponde?its to that place j and pafs once in every 24 hours vertically to the inhabitants of fuch latitude : that is, thofe ftars appear in their zenith, or are diredtly over their heads. Hence the following Problem VI. To find what fiars pafs over or nearly over the zenith of any place. 59. Find the latitude of the place by prob. ii. art, 52, upon the terreftrial globe, which Celefiial and T!crreftrial Globes. 21 which is the diftance of that place from the equator ^ then turning the celeftial globe, all thofe ftars which pafs under the ftrong brafs meridian at the fame diftance from the equator, will pafs diredly over the heads of thofe inhabitants, and therefore become celeftial correfpondents to all thofe who live under the fame parallel of latitude. Thus the ftar marked y of the fecond magnitude in the head of the dragon is 51 deg. 32 min. diftant from the celeftial equator, fo alfo is London at the fame dif- tance from the terreftrial equator : therefore the declination of this ftar is equal to the latitude of London, and confequently it be- comes our celeftial correfpondent. The ftar marked a of the iirft magnitude in Perfeus's fide, called Algenib, paftes over the zenith of thofe inhabitants in France who live 14 min. of one degree fouth of Paris ^ it alfo pafles nearly over the zenith of St, George's Bay in Newfoundland. Celeftial and terreftrial meridians 60. Are great circles drawn upon the: globes from one pole to the other, and C 3 crofting 22 Description and Use of the crofling the equator at ri';!it angles. Upon our new terreflrial globe there arc tvvetity- fourofthefc meridians, which are alfo hour- circles, being i 5 degrees from each other. Thus 1 5 degrees on the equator is equal to one hour, and each finglc degree equal to four minutes of time. Only four meridians are drawn upon the furfacc of the cclcdial globe. 61. There are no places on the furface of the earth, or fpaces in the apparent fphere of the heavens, through which meridians may not be conceived to pafs j confcquently all points on the terreftrial or in the celeftial fpheres have their meridians. 62. This variety of meridians on the globes is fupplied by the thin brafs femi- circle, which being moveable about the poles, may be fet to every individual point of the equator. Whence we call it a move-^ able meridian, art. 38. 63. All thofe great circles, that are drawn from pole to pole, are the meridians of thofe places through which they pafs. 64. One of thcfe meridians on our new terreftrial globe palTes through London, and is called afirjl meridian , becaufe from that point where it crolTes the equator, the degrees of Celejlial and 'Xerrcfirlal Globes. 23 of longitude, aiid the hours and minutes of time, i^cLfin. Some geographers make their firft meri- dian pafs dirough the ifle of Fer or Fcrro. Problem VII. To find the longitude of a place. 65. The longitude of any place is that point or degree upon the equator which is crofled by the meridian of that [)lace, reckon- ed from a lirfl: meridian. Bring tlie graduated edge of the move- able meridian to the place, and diat degree on the equator which is cut by the fame edge, is its longitude from London, in de- grees, and minutes, or that hour and minute is its longitude cxpr^lfed in time. Or if we bring the place to tlie graduated fide of the ftrong bral's meridian, that will cut the equator in the longitude as before. Thus Bofton in New En:dand is about 70^ degrees weft of London ; Cape Comorin in the Eaft Indies 282°. weft of London, or the longitude of the firft C 4 place 24 Description and Use of the place exprefled in time is 4 h. 42 miii. of the fecond 18 h. 48 min. 66. The method of reckoning longitude always weftward from the firft meridian is moft natural, becaufe it is agreeable to the real motion of the earth ; 67. But the common method is to reckon it half round the globe eaftward, and the other half weft ward from the firft meridian, ending either way at 180 degrees. Thus Cape Comorin is 78 degrees eaft of London. Note, The numbers neareft the equator increafe weftward from the meridian of London quite round the globe to 360, over which another fet of numbers is en- graved which increafe the contrary way, by which means the longitude may be reckoned upon the equator either eaft or weft. 68. It is mid-day or noon to all places in the fame meridian at the fame time. Thus London, Oran, Cape Coaft-caftle in the Mediterranean, and Mundfort on the Gold-coaft, have their noon nearly at the fame time ; Bofton in New England about 4 h. 42 min. later ; and Cape Comorin 18 h, 48 min. later. 69. The Celejlial and 'Terrefirial Globes. 2 c 69. The difference of longitude of any two places is the quantity of an angle at the pole made by the meridians of thofe places ; which angle is meafured upon the equator. To exprefs this angle upon the globe 70. Bring the graduated edge of the move- able meridian to one of the places, and the other place under the graduated fide of the ftrong brafs circle: they then contain the required angle i the meafure or quantity of which is the number of degrees counted on the equator between thefe two brafs meridians. Problem VIII. To find what places have mid-day or the fun upon their meridian, at any given hour of the day in any place propofed. 71. Firfl:, Let the hour propofed be X o'clock in the morning at London. As 26 Description and Use of the As the real diurnal motion (jf the earth, here reprefentcd hy the teiTefirial globe, is from weft to eaft, 72. All places to the caftvvard of any particular iiicridian muft neccfilirily pafs by the fun, before the meridian cf any other place to the vveflward of that particular meridian can arrive at it. 73. And therefore as the lirfl nierldian on our ne\v terreflrial globe pafles through London, if the propofcil pKxe be London, as in this cafe, bring the given hour to the eaft of London if it be in the morning, but to the weft of Lojidon if it be in the after- noon, to the graduated fide of the flrong brafs meridian 3 and all thofe places which lie diredly under it, have noon or the fun upon their meridian when it is X o'clock at London. Thus having brought the Xth hour on the equator to the eaflward of London un- der the divided fide of the flrong brafs meridian, it v/ill be found to pafs over the eaftcrn lide of Lfipland, and the eaflern ex- tremity of the gulf of Finland, Peterlburgh in Ruflia, to crofs a part of Moldavia and the Celcjlial and T^errcftrial Globes. 27 the Blacli Sea, thence it pafTes over a part of Turky, and goes between tlie iQaj-ids of Candia and Cyprus in the Mediterranean, thence over tlic middle uf K^^ypt tlirougli theeaflern fide of Africa, and acrofs the bay of Lorenzo; all wliich places have the fun on their meridian when it is X o'clock in the morning at London. 74. Secondly, Let tlie hour propofe(! be IV o'cloci'. in the afternoon at Purt-Royal in Jamaica. Bring Port-Royal in Jamaica to the gra- duated fide of die firong brafs meridian, and fet the horary index to that XII which is moil: elevated ; then turn the globe from weft to eaft, until the horary index points to I\^ o'clock, and the ftrong brafs meridian will pafs over tlie vv^ftern ficb of the ifle Pafares in the Pacific ocean ; and the eaftern fide of the iile la Mefae, thence it crofles the equator, and palTes nearly over the illands Mendoca ajid Dominica, which places have the fun on their meridian when it is IV o'clock in the afternoon at Port-Royal in Jamaica. ^S' Thirdly, 28 Description and Use of the y^. Thirdly, Let the propofed hour be 30 min. paft V o'clock in the morning at Cape Pafaro in the ifland of Sicily. Bring Cape Pafaro to the graduated fide of the ftrong brafs meridian, fet the horary index to that XII which is moft elevated, and turn the globe weftward, becaufe the propofed time is in the morning, till the horary index points to 5 h. 30 min. and you'll find the ftrong brafs meridian to pafs over the middle of Siberia, Chinefe Tartary, the kingdom of China, Kanton in China, the middle of the illand of Borneo, 6cc. at all which places it is noon, (they having the fun upon their meridian at the fame time) when it is half an hour pafl V o'clock in the morning at Cape Pafaro in Sicily. Problem IX. To find what hour It is at any place propofed when it is noon at any given place. 76. Bring the propofed place under the graduated fide of the flrong brafs meridian, and Celeftlal and Terrejlrial Globes. 29 andfetthe horary index to XII (if the given place be London, the graduated fide of the ftrong brafs meridian is the horary index) then turning the globe, bring the given place to the meridian and the hour required will be fliewn by the horary index upon the equator. If the propofed place be to the eaftward of the given place, the anfwer will be after noon, but if to the weftward of it, the anfwer is before noon. Thus when it is noon at London, it is 49 minutes pafl XII at Rome, and 32 minutes part VII in the evening at Kanton in China, and alfo 15 minutes paft VII o'clock in the morning at Quebec in Canada, and this at one and the fame inftant of time. Problem X. At any given time of the day in the place where you are, to find the hour at any other place propofed. 77.Bringthe propofed place under the gra- duated fide of the flrong brafs meridian, and fet the horary index to the given time; then turn ^o Description a7id Use of the turn tJie glube till the place where you are is under tl\c brafs meridian, and the horary index will point to the hour and minute required. Thus fuppofe wc are at London at IX o'clock in the morning, what time of the day is it then at Kanton in China ? anfwer 3 1 minutes paft IV in the afternoon. Alfo, when it is IX in the evening at London, it is about 1 5 minutes pafl IV o'clock in the afternoon at Quebec in Canada. Problem XI. The latitude and longitude of any place being known ; to find that place upon the globe, or if it be not inferted, to find its place and fix the center of the artificial horizon thereon. 78. The latitude of Smyrna in Afia is 38 deg. 28 min. north, its longitude 27 deg. 30 min. eaft of London. Bring 27 deg. 30 min. on the equator eaft ward of our iirft meridian to the gra- duated ■Cehjiial and Tcrrcjlrial Globes. 31 duated face t»f the ftrcjng brafs circle, and under 38 deg. 2G min. o»i die nordi lide of the equator you will find Smyrna. The latitude uf Cape Lorcjizo in Peru is I deg. 2 min. loudi, and longitude 80 deg, 17 min. wcfc of London: this place is not inferted upon the glohe. Tlierefore bring the graduated edge of the moveable meridian to 80 deg. 17 min. counted weftward on die equator, and Aide the diameter of the artificial horizon to i deg. 2 min. fouth; and its center will be correctly placed on that point of the globe wliere the Cape of Lorcjizo ought to have been placed. The four lafl: problems depend entirely on the knowled.^e of the longitude and dif- fcrence of longitude of places. The ecliptic 79. Is diat graduated circle which crofles the equator in an angle of about 23^^ de- grees ; and this angle is called the obliquity of the ecliptic. 80. Tliis circle is divided into 12 equal parts, each ^)f which contains 30 degrees j the beginning of each 1 2th part is marked with 32 Description and Use of the with the ufual charaders T, tJ, n, s, f(^, Ti;e, ^, "I, /, ^> ^j ^, hy which the twelve figns are reprefented upon the ter- reftrial globe. But upon our celeftial globe, juft under the ecliptic, the months, and days of each month, are graduated, for the ready fixing the artificial fun upon its place in the ecliptic. 8i. The fun's apparent place is always in this circle ; he advances therein every day about 59 min. 8 fee. of one degree, and feems to pafs through it in a tropical year. 82. Thofe two points, where the ecliptic croffes the equator, are called equinoBial pointSy and are marked with thefe characters T and ^ at the beginning of Aries and Libra. 83. The firfl: of thefe is called the vernal ^ the fecond the autumnal equinox. 84. The beginning of cancer and Capri- corn are m.arked with the charadters © and vs, which two points are called the folftices; the firft is the fummer folftice, the fecond that of the winter, to all inhabitants upon the north fide of the equator ; but diredly contrary to thofe on the fouth fide of it. Although Cehjlial and T'erreflrial Globes.^ 3 3 Although the ecliptic does not properly belong to the earth, j'et we have placed it upon our terreftrial globe according to an- cient cuftom ; it being ufeful in fome par- ticular cafes; it is chiefly to be regarded upon the celcftial globe. 85. The longitude of the ftars and planets is reckoned upon the ecliptic; the numbers beginning at the firft point of aries T, where the ecliptic crofles the equator and increaiing according to the order of the figns. 86. The latitude of the (lars and planets is determined by their diftance from the ecliptic upon a great circle pafling through its poles, and crofting it at right angles. 87. Twenty-four of thefe circular lines, which crofs the ecliptic at right angles, being fifteen degrees from each other, are drawn upon the furface of our celeftial globe ; which being produced both ways, thofe on one fide meet in a point on the northern polar-circle, and thofe on the other meet in a point on the fouthern polar-circle. 88. The points determined by the meet- ing of thefe circles are called the poles of the ecliptic, one north, the oih^x font h. D 89. The 34 Description and Use of the 89. The longitude of the ftars hath been obferved to increafe about a degree in 72 years. The celeftial figns and conftellations 90. On the furface of the celeftial globe are reprefented by a variety of human and other figures, to which the ftars that are either in or near them, are referred. 91. The feveral fyftems of ftars, which are applied to thofe images, are called con- Jlellations, Twelve of thefe are reprefented on the ecliptic circle, and extend both northward and fouthward from it. So many of thofe ftars which fall within the limits of 8 degrees on both fides of the ecliptic circle, together with fuch parts of their images as are contained within the aforefaid bounds, conftitute a kind of broad hoop, belt, or girdle, which is called the zodiac. 92. The names and the refpedive cha- racters of the twelve figns of the ecliptic may be learned by infpedion on the furface of the broad paper circle i and the con- ftellations from the globe itfelf. 93- The Celejlial and Terrejlrial Globes. 3 5 93. The zodiac is reprefented by eight circles parallel to the ecliptic, on each fide thereof; thefe circles are one degree diftant from each other, fo that tlie whole breadth of the zodiac is 16 degrees. 94. Amongft thefe parallels, the latitude of the planets is reckoned ; and in their ap- parent motion they never exceed the limits of the zodiac. 95. On each fide of the zodiac, other conftellations are diflinguiflied ; thofe on the north fide are called northern, and thofe on the fouth fide of it, fouthern conflellations. 96. All the ftars which compofe thefe conftellations, are fuppofed to increafe their longitude continually j upon which fuppo- fition the whole flarry firmament has a How motion from wefl to eafl; infomuch that the firfl liar in the conflellation of aries, which appeared in the vernal interfedion of the equator and ecliptic in the time of Metoji the Athenian, upwards of 1900 years ago, is now removed about 30 degrees from it. 97. From the different magnitudes of the ftars, fome appear to be greater than others, or nearer to us : on our celeflial D 2 gl^he. 36 Description and Use of the globe, they are diftinguiilied into feven dif- ferent magnitudes. General phaenomena arifing from the earth's diurnal motion. 98. The daily rotation of the earth about its axis is one of the moft elTential points, which a beginner ought to have in view ; for every particular meridian thereon is fuc- cedively turned towards every point in the heavens, and as it were defcribes circles in the celeftial fphere, perpendicular to the axis of the earth, and parallel to each other; by which means the fixed flars feem to have an apparent diurnal motion. 99. Except thofe two points in the ftarry firmament, into which the earth's axis, fup- pofed to be fo far extended, would fall ; thefe two points are called the celeftial poles, which correfpond with our terreftrial north and fouth poles. 100. We have contrived our new globes fo that the real diurnal motion of the earth and the apparent diurnal motion of the heavens are reprefented by them, art. 5.6. and Celejiial and Teji-ejirial Globes. 37 and thence all problems folved as readily in fouth as in north latitudes, and in places on or near the equator : by which means we are enabled to (hew, how the viciffitudes of days and nights, their various alterations in length, the duration of the twilight, &c. are really made by the earth's daily motion, upon the principles of the Pythagorean and Copernican fyftems. 1 01. In fig. 3. ^ N Q^ R reprefent s the apparent concave fphere of the fixed ftars, a? n q s a^ the globe of the earthy whofe axis n s is fuppofed to be extended to N S, in the fphere of the fixed ftarsj all the ftars feem to revolve upon thefe two points as poles, 102. If the plane of the earth's equator JE z q c 33, is conceived to be extended to the ftarry firmament, it will point out the celeftial equator /E ^ Q^Y /E. 103. N reprefents the celeftial, and n the terreftrial north pole, S and s the fouth pole. Parallels of latitude, declination, tropics and polar- circles. 104. Fig. 3. That circle which any flar feems to defcribe in twenty-four hours, is D 3 called 38 Description and Use of the called its parallel : thus, fuppofe a right line drawn from C the center of the earth, through any point d of its furface, and ex- tended to D in the ftarry firmament, by means of the earth's daily rotative motion, the extremity D of the line C D will de- fcribe the celeftial parallel G x D x G, correfponding to the terreftrial parallel g d, of the point d. If D C be fuppofed to be extended to H, the oppofite fide of the ftarry firmament, it will defcribe another parallel equal to the former. 105. Thofe circular lines upon the ter- reftrial globe, which are defcribed from the poles, on either fide of the equator, are parallel to it, and are called parallels of latitude, but on the celeftial globe they are C2L\\e.d parallels of declination, 106. There are four principal lefier cir- cles parallel to the equator, which divide the globe into five unequal parts called zo?2es ; thefe are the two tropics, and the two polar- circles. 107. We have already ftieWn, that the diftance of any parallel from the equator, meafured in the arch of a great circle on the terreftrial Celeftial and ^errefirial Globes. 39 terreftrial fphere, is its latitude ; and on the celeftial fphere, its declination, art. 56. 108. If the fun, moon, a fixed ftar, or planet, is fituated in any parallel between the equator iE Qjjig. 3. and the north pole N, it is faid to have north declination, but if towards the fouth pole S, fouth declination. 1 09. Thus the two parallels G D, and H I, have the fame declination : becaufe they are equally diftant from M. Q^he equator ; the firft hath north, the laft fouth declination. no. Hence we muft obferve, that a celeftial parallel G X D, and its corref- pondent g x d upon the earth, are two parallel-circles, being fimilar elements of a cone whofe axis is that of the earth, and apex C the center of the earth. Therefore the plane of a terreftrial parallel cannot be the fame with its correfpondent celeftial parallel j only the plane of the celeftial equa- tor ^ :c: Q^V &, is the fame wath that of the terreftrial equator as z q, becaufe thefe two planes are produced by the fame radius C Q^ perpendicular to the axis N S on which the earth or the heavens are fuppofed to turn. D 4 III. If 40 Description and Use of the 111. If by the earth's daily rotative mo- tion, a ftar D pafles over the zenith d of any inhabitant of the earth, that ftar is in the celeftial parallel, which correfponds to the terreftrial parallel of the obferver j for the di- ftance of the celeftial pai'allel G D contains the fame number of degrees from JE Q^the ce- leftial equator, as that of the inhabitant's paral- lel g d does from ae q the terreftrial equator. 112. Therefore the meafure of the arch of any inhabitant's diftance from the ter- reftrial equator, which is called the latitude of the place, is fimilar and equal in the number of degrees, to that fixed ftar's decli- nation^ which pafles over his zenith. 113. If the inhabitant changes his fitua- tion either north or fouth, the different declinations of thofe ftars which pafs over his zenith, at the feveral places of his re- moval, will fiiew his advance to, or regrefs from the equator. 114. Whence any place upon the earth may be reprefented by its correfponding zenith point, in the apparent concavity of the ftarry fphere j as fliall be hereafter lliewn. 115. Upon our new terreftrial globe, there are twenty-three parallels drawn at the diftance Cekfiial and Terrejlrial Globes. 41 diftance of one degree from each other, on both fides the equator; which, with two other parallels at 234 degrees diftance, in- clude the ecliptic circle j thele two are called the tropics. That on the north fide of the equator is called the tropic of cancer : and the other, which is on the fouth fide of it, the tropic of Capricorn, 116. The fpace between thefe two tro- pics, which contains about 47 degrees, was called by the ancients, the torrid zone. 117. The two polar-circles are placed at the fame diftance from the poles, as the two tropics are from the equator. One of thefe is called the northern^ the other xhc fouthern polar-circle. 118. Thefe include 231- degrees on each fide of their refpedive poles, and confe- quently contain 47 degrees, equal to the number of degrees included between the tropics. 119. The fpace contained within the northern polar-circle, was by the ancients called the north frigid zone, and that within the fouthern polar-circle thtjouth frigid zo?ie. 120. The fpaces between either polar-cir- cle, and its neareft tropic, which contain about 42 Description and Use of the about 43 degrees, were by the ancients called the two temperate zones. ' 121. Wherever any parallel pafles through two places on the terreftrial globe, thofe places have the fame latitude. 122. Alfo all thofe ftars which are in the fame parallel upon the celeftial globe, have the fame declination. 123. And as the ecliptic is inclined to the equator in an angle of 23! degrees, and 3S included between the two tropics, every parallel in the torrid zone niuft necelTarily •crofs the ecliptic in two places ; which two points fhew the fun's place, when he is vertical to the inhabitants of that parallel ^ and the days of the month upon the broad paper-circle anfwering to thofe points of the ecliptic, are the days on which the fun palTes diredtly over their heads at noon, and are called their two midfummer days: whence the inhabitants of the torrid zone have two fummers and two winters every year. 124. Hence as the earth's progreflive, or rather apparent annual motion, feems to be in the celeftial ecliptic, the fun's declination is thereby changed gradually every day. Therefore Celejlial and Jerrejlrial Globes. 43 Therefore on our new terreftrial globe, as mentioned in art. 115. we have drawn parallels through the whole fpace of the tor- rid zone, and the two fpaces within the polar-circles, to give a general and clear idea of the fun's apparent paflage from one tropic to the other. The colures 125. Are circular lines drawn on the celeftial globe from pole to pole, (as meri- dians are upon the terreftrial globe) crofting the equator at right angles. 126. There are four colures, which form two great circles of the fphere. 127. That colure or celeftial meridian, which goes through the firft point of aries T , and tliat which paftes through the firft point of libra ^ , making together one great circle, is reprefented by the circle B T K ^ in fig. 3. and is called the equmoBial colure. The points marked y and ^ are called the equinoxes y or equinodial points. 128. The two celeftial meridians repre- fented by the circle N iE S Q^, paffing through the folftitial points (marked ^ and vs) 44 Description and Use of the '^) of cancer and Capricorn, are called the foljiitial cohires. 1 29. Thefe colures cut each other at right angles in the poles of the world, and divide the celeftial equator, ecliptic, and zodiac into four equal parts. 130. The equino6tial colure only pafles through the poles of the world at N and S. But, 131. The folftitial colure pafles through the poles of the world at N and S, and alfo through the poles of the ecliptic at B and K. Fig. 3- 132. Whence it happens In every daily rotation of the earth about its axis, that the folftitial and equinoctial colures are twice blended with every meridian upon the fur- face of the earth : confequently, each pole of the ecliptic appears to pafs, once every day, over all the meridians of the terreftrial iphere. 133. All thofe circular lines that are or may be fuppofed drawn on the celeftial globe, which pafs through the poles, cutting ■the equator at right angles, are called circles of declination J becaufe the declination of thofe points or ftars through which they pafs. Celejlial and Terrejinal Globes. 45 pa(s, or the diftance of thofe ftars from the equator, is meafu red upon thefe circles: and this is done by bringing the divided edge of the moveable meridian to any flar. 134. Hence the thin brafs femi-circle, art. 38. which we call the moveable meri- dian, is alfo a moveable circle of declination. ArSiic and antardlic circles, or circles of perpetual apparition and occultation. 135. The largeil: parallel of latitude on the terreftrial globe, as well as the largeft circle of declination on the celeftial, that appears entire above the horizon of any place in north latitude, is called by the ancients the ar^ic circle or circle of perpe- tual apparition. 136. Between the ardic circle and the north pole in the celeflial fphere, are con- tained all thofe ftars which never fet at that place, and feem to us, by the rotative mo- tion of the earth, to be perpetually carried round above our horizon in circles parallel to the equator. 137. The 46 Description and Use of the 137. The largeft parallel of latitude on the terreftrial, and the largeft parallel of declination on the celeftial globe, which is entirely hid below the horizon of any place, is by the ancients called the antarBic circle y or circle of perpetual occultation. 138. This circle includes all the ftars which never rife in that place to an inha- bitant of the northern hemifphere, but are perpetually below the horizon. 139. Hence all ard:ic circles touch their horizons in the north point, and all antarc- tic circles touch their horizons in the Ibuth point; which point, in the terreftrial and celeftial fpheres, is the interfedion of the meridian and horizon. 140. If the elevation of the pole be 45 degrees, the moft elevated part, either of the ardic or antardic circle, will be in the zenith of the place. 141. If the pole's elevation be lefs than 45 degrees, the zenith point of thofe places will fall without its ardic or antardic circle. If greater, it will fall within. 142. Therefore the nearer any place is to the equator, the lefler will its ardic and antardic circles be ; and on the contrary, the Celejiial and Terrejlrial Globes. 47 the farther any place is from the equator, the greater they are. So that, ;m 143. At the poles, the equator may be confidered as both ardic and antardic circle, becaufe its plane is coincident with that of the horizon. 144. But at the equator (that is, in a right fphere) there is neither ar<5tic nor antardic ■circle. 145. They who live under the northern polar-circle, have the tropic of cancer for their ardic, and that of Capricorn for their antardic circle. 146. And they who live on either tropic, have one of the polar-circles for tlieir ardic, and the other for their antardic circle. 147. Hence whether thefe circles fall within or without the tropics, their diftance from the zenith of any place is ever equal to the difference between the pole's eleva- tion, and that of the equator above the horizon of that place. 148. From what has been laid it is plain, there may be as many ardic and antardic circles, as there are individual points upon any one meridian, between the north and fouth poles of the earth. 149. Many 48 Description and Use of the 149. Many authors have miPcaken thefe mutable circles, and have given their names to the immutable polar-circles, which laft are arctic and antardic circles, in one parti- cular cafe only, as has been fliewn. The caufe ot the daily change in the declination of the fun 150. Arifes from the earth's annual mo- tion, in the ecliptic, the inclination of her axis, and its always moving parallel to itfclf. 151. Imagine the plane of the earth's orbit extended as far as the fixed ftars, it will there mark out the circle S, ^, vs, T, s, which we call the celeftial ecliptic j fee 152. From this comparifon of the earth's orbit with the celeftial ecliptic, is derived the ancient rule to find the fun's place, if we firft find the earth's place, either by obfer- vation or calculation j fix figns added to or fubftracted from it gives the fun's true place in the ecliptic. Confequently it is the fame thins:, when we confider the daily motion of Cek/iial mid Terre/lrtal Globes. 49 of the earth about her equatorial axis, re- prefented by the terreftrlal globe, whether we fuppofe the earth) or the fun, to have an annual motion. 153. It is alfo the fame thing in the ule of the celeflial globe, whether we fuppofe the earth to turn upon her equatorial axis, or the ftarry fphcre to revolve upon the extremities of the fame axis extended to the heavens : the refult in either cafe will be the fame, provided we conceive ourfclves at the center of the globe. 154. Hence we Ihall fuppofe tlie fan's apparent annual motion to be in the plane of the celeflial ecliptic, and in his pafTage through it, defer ibing by a ray conncdling the centers of the earth and fun, a different circle of declination, parallel to the equator every day. Whereby all thofe people who inhabit any of thofe places on the earth which are lituated between the terreftrial tropic of cancer reprefented in fig. 3. by G, e, and the terreftrial tropic of Capricorn reprefented by h, vs, have the fun at the time he is defcribing their parallel in their zenith ; or diretflly' vertical, or over their heads, which happens twice every year. E 155. 50 Description and Use of the 155. Whence the inhabitants of thofe places, as well as mariners who pafs be- tween the tropics, have a correfponding zenith-point, where their latitude is equal to the fun's parallel of declination, from the lun by day, and from the ftars by night. 156. Hence it is eafily conceived, thar if the planes of the equator and ecliptic were united in one continued plane, a central folar ray connedling the centers of the earth and fun, would by the earth's diurnal motion defcribe the equator every day; but, as we have before obferved, the fun does apparently defcribe a different parallel every day : wherefore the ecliptic and equator are inclined to each other in an angle confirmed by obfervation of about 23 deg. 29 min. 157. Let the fun's apparent annual mo- tion be reprefented by the circle ©, a, y, ®, fig. 3. which bifeds the celeftial equator J£j ^ Qjf My in the points ^ and T; the iirfl of thefe is called the autumnal, the fecond the vernal equinodlial point. 158. When the fun is in :=:, he appears to defcribe the equator, at which time he has no declination -, and as he proceeds gradually Celefiial and 7errejinal Globes. 51 gradually from ^ towards vs, his fouthern declination continually increafes, and he defcribes lefs and lefs parallels, till he ap- pears in vs, and then defcribes the tropic of Capricorn ; being then at his grcateft fouthern declination, and at his ereateil: diftance from the equator foutherly, and alfo in the winter-folflice. 159. It pafling from vs to Y, his decli- natioji decreafes, and the parallels he de- fcribes are greater and greater, until he comes to aries or the vernal equinox, and again has no declination, defcribing the equator as before. 160. As he advances from thence to- wards G5, the declination increafes, and the parallels defcribed are lefs and lefs, until he arrives at £j or the fummer-folitice -, being then at his greateft north declination, de- fcribing the tropic of cancer. 161. Thence proceeding forwards to- wards ^, the declination continually de- creafes, and the parallels defcribed increafe till the fun's arrival at the next fucceeding autumnal equinox ; where he again de- fcribes the equator, having nO declination ; and compleats the length of a mean folar E 2 tropical 52 Description and Use of the tropical year, containing 365 d. 5 h. 49 min. 162. What v/c have faid with refped to fummer and winter-folftices, is to be under- ftood with relation to thofe places which lie between the equator and the north polej but to the places between the equator and louth pole the contrary happens. 163. The two equinoxes are the fame to all the inhabitants of the earth. 164. We have been thus particular in our defcription of the fun's apparent annual motion, for the ufe of beginners ; and we hope this confideration will plead in our behalf, if we ihould appear tedious or trifling to thofe who are mailers of the fubjed:. 165. But what has been faid, might yet be more clearly illuftrated by an orrery or a tellarium, which (hews the annual and diurnal motions of the earth and parallelifm of its axis, &c. which by the different poli- tions of the earth's axis, with relpedl to her enlightened dife, will appear to the eye ai it is really underftood by aftronomers, and then we may with more propriety repair to the ufe of the globe itfelf. To h Celejiial mid Terr eft rial Globes. 53 To fiipply the want of a tellarium, Defcribe a circle with chalk upon the floor, as large as the room will admit of, that the globe may be moved round upon it : divide this circle into twelve parts, and mark them witli the characters of the twelve figns, as they are engraved upon the broad paper circle ; placing S at the north, vs at the fouth, T in the eaft, and •^ in the weft : the mariners compafs under the globe will dired: the iituation of thefe points, if the variation of the magnetic needle be attended to. Note, At London the variation is be- tween 19 and 20 degrees from the north weft ward. Elevate the north pole of the globe that 66-^ degrees on the ftrong brafs meridian may coincide with the furface of the broad paper circle, and this circle will then repre- fcnt the plane of the ecliptic, as mentioned in article 24. Set a fmall table or a ftool over the center of the chalked circle to reprefent the fun, E 3 and 54 Description aiid Use of the and place the terreftrial globe upon its cir- cumference over the point marked vs^ with the north pole facing the imaginary fun, and the north end of the needle pointing to the variation : this is the poUtion of the earth with refpedt to the fun at the time of the fummer-folftice about the 21 ft of June: and the earth's axis, by this redification of the globe, is inclined to the plane of the large chalked circle, as well as to the plane of the broad paper circle, in an angle of 23!- degrees j a line or firing paffing from the center of the imaginary fun to that of the globe, will reprefent a central folar ray con- ncdingj the centers of the earth and fun: this ray will fall upon the firft point of cancer, and defcribe that circle, iTiewing it to be the fun's place upon the terreftrial ecliptic, which is the fame as if the fun's place, by extending the ftring, was referred to the oppofite fide of the chalked circle, here reprefenting the earth's path in the heavens. If we conceive a plane to pafs through the axis of the globe, it will alfo pafs through the fun's center, and the points of cancer and Capricorn in the terreftrial and celeftial ecliptic; Celefiial and Tcrrefirial Globes. 55 ecliptic; the central folar ray in this pofi- tion of the earth is alfo in that plane ; this can never happen but at the times of the folftice. If another plane be conceived to pafs through the center of the globe at right angles to the central folar ray, it will divide CD ' the globe into two hemifpheres ; that next the center of the chalked circle will repre- fent the earth's illuminated dific, the con- trary fide of the fame plane will at the fame time ihew the obfcure hemiiphere. The intellig:ent reader for the ufe of his pupils, may realize this fecond plane by cut- ting away a femi-circle from a rtieet of card pafte-board, with a radius of about \\ tenths of an inch greater than that of the globe itfelf J if this plane be applied to 66t de- grees upon the firongbrafs meridian, it will be in the pole of the ecliptic ; and in every fituation of the globe round the circum- fcrence of the chalked circle, it will afford a lively and lading idea of the annual and diurnal motion of the earth, of the various phenomena arifing from the parallelifm of the earth's axis, and in particular the daily E 4 change 56 Description and Use of the change of the fun's declination, and the parallels thereby described. Let the globe be removed from vs to x::, and the needle pointing to the variation as before will preferve the parallelifm of the earth's axis; then it will be plain, the itring or central folar ray will fall upon the firft point of leo, fix figns diflant from, but oppofite to the fign x:^ upon which the globe ftands : the central folar ray will now de- fcribe the 20th parallel of north declination, which will be about the 23d of July. If the globe be moved in this manner from point to point round the circumference of the chalked circle, and care be taken at every removal that the north end of the magnetic needle, when fettled, points to the degree of the variation, the north pole of the globe will be obferved to recede from* the line connedling the centers of the earth and fun, until the globe is placed upon the point cancer: after which, it will at every removal tend more and more to- wards the faid line, till it comes to Capri- corn again. Problem Cekftial and ^erreftrial Globes. 57 Problem XII. To rectify either globe to the lati- tude and horizon of any place. 166. If the place be in north latitude, raife the north pole, if in fouth latitude, raife the fouth pole, until the degree of the given latitude, reckoned on the ftrong brafs meridian under the elevated pole, cuts the plane of the broad paper circle ; then this circle will reprefent the horizon of that place. To rectify for the fan's place. 167. After the former redlfication bring -the degrees of the fun's pkce in the ecliptic line upon the globe to the ftrong brafs meridian, and fet the horary index to that Xllth hour upon the equator which is mod elevated. 168. Or, if the fun's place is to be fetained, to anfwer various conclufions, bring the graduated edge of the move- able meridian to the degree of the fuii's place 58 Description and Use of the place in the ecliptic, upon the celeftiai globe, and Hide the wire which erodes the center of the artificial fun thereto, then bring its center which is the interfedion of the aforefaid wire, and graduated edge of the moveable meridian, under the ftrong brafs meridian as before, and fet the horary index to that XII on the equator which is moft elevated. To redlify for the zenith of any- place. 169. After the firil redlification fcrew the nut of the quadrant of altitude fo many de- grees from the equator reckoned on the ftrong brafs meridian towards the elevated pole, as that pole is raifed above the plane of the broad paper circle, and that point will reprefent the zenith of the place. Thus London having 51^ degrees north latitude, move the globe till the plane of the horizon on the north fide cuts the ftrong brafs meridian in that point. 170. If you are doubtful, whether the proper point of the brafs meridian is cor- red:ly cut, when fet by the eye, apply a card cut Cekfiial and T^erreftrtal Globes. 59 cut in the fhape of fig. 4. to the place flat upon the broad paper circle, and it will be truly adjufted. If, when the globe is in this ftate, we look on the oppofite lide of the globe, the plane of the horizon will cut the llrono: brafs meridian at 381 degrees, the complement of the latitude. Problem XIII. To find the moon's mean place upon the celeftial globe, her age and day of the month being known. 172. The moon increafes her longitude in the ecliptic every day about 13 deg. 10 min. by which means fhe crofTes the meri- dian of any place about 50 minutes later than (lie did the preceding day. Thus if her place be in the 12th degree of Taurus any day at noon, it will be 25 deg. 10 min. in Taurus on the fucceeding noon. 173. It is new moon when the fun and moon have the fame longitude, or are in or near the fame point of the ecliptic. 174. When 6o Description and Use of the rv-174. When they have oppofite longi- tudes, or are in oppofite points of the ecliptic, it IS full 7110071. 175. To perform this problem tolerably near the truth, without having recourfe ta an ephemeris, which may not always be at hand, 176. Find the day of the new moon next preceding, the given day of the month in any common almanack, the number of days elapfed is the moon's age. 177. The equator on our new celeftial globe is divided by large dots into 29^ equal parts, each of which is direded by a fliort dotted line, to a number marked in Roman .figures, exprefling the feveral days oi the moon's age. The rule. 178. Elevate the north pole of the ce- kftial globe to 90 degrees, and then the equator will be in the plane of the broad paper circle ; bring the firft point of aries, marked r on the globe, to the day of the month on the faid broad paper circle, which anfwers to the fun's place for that day ; and the Cekftial and 'Terrejlrial Globes. 6 1 the day of the moon's age will ftand againft the lign and degree of the moon's mean place J to which fet the artificial moon upon the ecliptic on the globe. 179. But if you are provided with an ephemeris, that will give the moon's latitude and place in the ecliptic j firft note her place in the ecliptic upon the globe, and then counting fo many degrees amongfl the parallels in the zodiac, either above or below the ecliptic, as her latitude is north or fouth upon the given day, and that will be the point which reprefents the true place of the moon for that time, to which apply the artificial moon. 1 80. Note, The artificial moon is a fmall thin piece of brafs in form of a crefcent, having two holes a and b, fig. 5. through which a fmall firing of filk twift is put, that it may flip backwards or forwards upon it. 181. To one end c of this filk firing is tied a fmall piece of brafs dec with three holes, at d e c. The manner of putting it upon the globe is thus : firfl having put the crefcent a b, on the firing and the piece of brafs, by pafling the ftring through the two holes d. 62 Description and Use of the d, e, the ftiing being as yet left free. The two ends of the firing being loofe, pafs the end F round the north pole of the globe, in a grove made for that purpofe, and tie it into a loofe loop like F g, then put the other end of the ftring G c round the fouth pole and tie it faft to the hole at c, then by pulling the piece dec upwards, the ftring may be tightned on any part of the globe, and pufhing it downwards will flacken it, that it may be removed to any other place and then tightned again. Problem XIV. To reprefent the apparent diurnal motion of the fun^ moon, and jftarsj on the celeftial globe. 182. Find the fun's place by problem i. art. 52. and thereto fet the center of the artificial fun. Alfo, 183. Find the moon's place by problem xiii. art. 171. and fet the center of the arti- ficial moon upon it. Redifv Cekjlial and T'errejlrial Globes. 63 Redlfy the globe to the latitude, horizon, fun's place, and zenith, by problem xii. art. 166, 167, and 169. 184. The globe being turned round its axis from eall: to weft, will reprefent the apparent motion of the fun, moon, and ftars, for that day. 185. When the center of the artificial fun is in the plane of the horizon on the eaftern fide, the horary index fhews upon the equator the time oij'un rifing. 186. All thofe ftars which are then in tlie plane of the horizon on the eaftern fide, are at the fame inftant of time rifing with xhtfun, and thofe on the weftern fide of the horizon are then fetting. 187. And when the center of the arti- ficial moon comes to the horizon on the eaftern fide, the horary index will point to the hour and minute of her rifing. And thofe ftars on the eaft edge of the horizon are then rifing with her, whilft- at the fame time all thofe ftars, cut by the weftern edge, are fetting. 188. That degree and minute of the equator which is cut by the plane of the ' horizon, at the fame time, that the center of the 64 Description and Use of the the artificial fun, moon, or any ftar, is alKb cut by the laid plane, is the very point of the equator, which rifes with either of them, and is called the fun, moon, or flars oblique afcenfion. 189. As xh^ Jim afcends in the heavens till it culminates, or comes under the gra- duated fide of the ftrong brafs meridian, the horary index will fuccelTively point to the hours before noon; but when he is under the divided fide of the brafs meridian, the horary index points at XII o'clock, and that degree and minute on the equator, which is cut by the graduated face of the ftrong brafs meridian, is called the funs right afcenfion. 190. At the fame time, that degree of the brafs meridian, which is diredly over the artificial fun, is his declination^ art. t^^» for that day. 1 92. The fame is to be obferved of the moon or any flar as they afcend in the heavens, till they culminate or come under the meridian, the horary index conftantly pointing to the hour of the day or night ; their ri^ht afcenfion and declination are alfo fhewn in the fame manner as that of the fun. 193. Whilft Celcjlial and Terrejlrial Globes. 65 193. Whilft the fun defcends from the meridian weftward, the horary index fuc- ceflively fliews the hours after noon. 194. And when the center of the arti- ficial fun is in the plane of the horizon on the weftern fide, the horary index Ihews the time of fun fetting j and that point of the equator which is then cut by the plane of the horizon, is the point which fets with the fun, and is called his oblique dc~ fcenfion. 195. The number of degrees on the equator contained between the points of his oblique afcenfion, and right afcenlion, or between the points of his right alceniion and oblique delcenlion, is called his afccji^ fional difference. 196. Obferve the fame with reipe(ft to the moon or any flar : as they defcend from the meridian weftward, the horary index will fucceffively iliew the time of their arrival at any given point, their fetting, oblique delcenlion and afcenfional difference in the fame manner as before deicribed in relation to the fun. 197. The rifmg, culminating, fetting, &c. of any planet may be obtained, if the place of 66 Description and Use of the- of the planet, by its longitude and latitude taken from an ephenieris, be afcertained> and ai> artificial planet fet thereto, in the manner in which we have direded the arti- ficial moon to be placed upon the globe, or this laft may occafionally reprefent a planet. 198. Thus on the i8th day of June, A. D. 1769 new ftile, being the firft year after biffextile, the fun's place will be h, 27 deg. 22 min. the moon's place >^ 18 deg. o min. her latitude north o deg. 30 min. The new moon about a ^ of an hour paft VI o'clock in the morning, to which places, if the artificial fun and moon be fet, a beginner may readily exercife himfelf in finding the proper anfwers agreeable to thefe data, by the directions in this problem. Parallels of altitude. 1 99. The globe remaining redtified as iii ihe laft problem, the uppermoft point repre- fents a point in the heavens diredly over our heads, which is called the zenith: and as the brafs quadrant is moveable about its upper end as a center, when that center is fixed Celefiial and T^errejlrial Globes. 6/ fixed to the latitude of the place upon the ftrong brafs meridian, it will be in the zenith, and the beginning of its graduations will coincide with the plane of the broad paper circle, which in thefe cafes reprefents the horizon of the place. 200. If the quadrant be moved about the globe, its firft divilion will defcribe the horizon. And, 201. At the fame time, all Its inter- mediate divifions, will defcribe circles pa- rallel to the horizon j the point marked i o defcribes a parallel of 1 o degrees, the point marked 20 a parallel of 20 degrees, and fo of any other point. 202. Thefe circles parallel to die horizon are called parallels of altitude. Therefore thefe parallels fliew the eleva- tion of the fun, moon, ftars or planets, above the plane of the horizon. And the quadrant itfelf in each cafe re- prefents a fecondary of the horizon. F 2 Problem 68 Description and Use of the Problem XV. To find the fun's altitude at any time of the day. 203. Set the center of the artificial fun to his place in the ecliptic upon the globe ; and rectify it to the latitude and zenith, by problem xii. art. 166, bring the center of the artificial fun under the graduated fide of the ftrong brafs meridian, and fet the hour-index to that XII which is moft ele- vated 5 turn the globe to the given hour, and move the graduated edge of the qua- drant to the center of the artificial fun; and that degree on the quadrant which is cut by the fun's center, is the fun's height at that time. The artificial fun being brought under the ftrong brafs meridian, and the quadrant laid upon its center, will fhew its meridian or greateft altitude for that day. If the fun be in the equator, his greateft or meridian altitude is equal to the elevation of the equator, which is always equal to the co-latitude of the place. Azimuth Celejlid mtd Terrejlrial Globes. 69 Azimuth or vertical circles. 204. An azimuth circle in aftronomy, is the very fame as a circle of poiition in geography j they being fecondaries to the horizon, or great circles paffing through the zenith of any place, and crollhig the hori- zon at ri^ht angles : either in the heavens called azimuthsj or on the earth, circles of pnjltion. 2Q>^. Any azimuth may be reprefented by the quadrant of altitude, when the center upon which it turns, is fcrewed to that point of the ftrong brafs meridian ; which anfwers to the latitude of the place, and the place brought into the zenith. Suppofe at London, if you bring the divided edge of the quadrant to 10 degrees on the inner edge of the broad paper circle, it will reprefent an azimuth of i o degrees ; if you fet it to 20, it will reprefent an azimuth of 20 degrees j and fo of any other. 206. If the quadrant of altitude be fet to o degree, that is either upon the eaft, cr weft points, of the broad paper circle, it F 3 will 70 Description iZ7zJ Use of the will then reprefent that azimuth, which is called the prime vertical. Problem XV . To find the azimuth of the fun or any flar. 207. Redify the globe to the latitude and fun's place, art. 166. 167, then turn it to the given hour, and bring the divided edge of the quadrant of altitude to the fun's place in the ecliptic, or to the center of any ftar, and it will crofs the horizon at the azimuth required. The diftance of that point of the horizon, in which the fun appears to rife or fet, counted from the prime vertical, art. 206. or eaft and weft points of the horizon, is. called the fun's amplitude. Corollary, To find the angle of pofition, and the bearing of one place from another. 208. The angle of pofition is that formed between the meridian of one of the places, and Cekjlial and Terrefirial G lo b e s . 71 «nd a great circle paffing through the other place. Redify the globe to the latitude and zenith of one of the places, art. 166. 167. fet the graduated edge of the quadrant to the other place, and the number of degrees contained between it and the ftrong brafs meridian, is the meafure of the angle fought. Thus, The angle of pofition between the meri- dian of Cape Clear in Ireland, and St. Anguftine in Florida, is about 92 degrees north wefterly, but the angle of pofition between St. Auguftine and Cape Clear, is only about 46 degrees north eafterly. Hence it is plain that the line of pofition, or azimuth, is not the fame from either place to the other, as the romb-lines are. To find the bearing of one place from another. 209. The bearing of one fea-port from another is determined by a kind of fpiral called a romb-line, pafling from one to the other, fo as to make equal angles with all the meridians it pafleth byj therefore if F 4 both 72 Description mid Use of the both places are fituated on the fame parallel of latitude, their bearing is either eaft or weft, from each other j if they are upon the fame meridian, they bear north and fouth from, one another ; if they lie upon a romb- line, their bearing is the fame with it; if they do not, obferve to which romb-line the two places are neareft parallel, and that will fhew the bearing fought. Thus the bearing of the Lizard Point from the ifland of Bermudas is nearly E N E J and that of Bermudas from the Lizard is W S W, both nearly upon the fame romb, but in contrary directions. A parallel fphere Is that pofition of the globe, where the poles are in the zenith and nadir, the equa- tor in the horizon, and confequently thofe circles which are parallel thereto, are alfo parallel to the horizon. The inhabitants of this fphere, if any there be, mull: live upon the two terreftri^l poles. A right Cek/lial and ^erre/lrial Globes. 73 A right fphere Is that where the inhabitants fee both poles in their horizon, the equator palling through their zenith and nadir, and all the circles parallel to the equino(5lial perpendi- cular to their horizon. Thefe people live upon the terreftrial equator. An oblique fphere Hath one of the poles of the globe above, the other under the horizon ; the equator in all the cafes of this fphere is half above, and half below^ the horizon, and the pa- rallel circles cut the horizon obliquely. The inhabitants of this fphere are thofe who live on all parts of the earth, except thofe at the poles and upon the equator. Of the twilight. 210. The morning-twilight or day-break begins when the fun comes within 18 de- grees of the horizon, and continues till fun- rifing. 211. The 74 Description and Use of the 21 I. The evening-twilight begins at the time of the fun fetting, and continues till it js i8 degrees below the horizon. 212. For this purpofe on our new globes, a wire-circle is fixed eighteen degrees below the furface of the broad paper circle i fo that, 213. All thofe places which are above tlie wire-circle, will have the twilight, but it will be dark to all places below it. 214. At the time of winter-folftice, when the whole fpacc within the northern polar- circle is out of the fun's light, the greater part of it enjoys the benefit of twilight 5 there being only about ^^ degrees round the pole that will be totally dark, 215. We have here only confidered the twilight refleded to us from the earth's atmofphere by the fun himfelf; befidcs which the body of the fun is always encom- pafled with a fphere of light, which being of a larger circumference than the fun, muft rife before him, and fet after him ; which confequently lengthens the twilight by illu- minating our air, when the fun is deprelTed too low to reach it with his own light; this feems to be the caufe, why the fun is preceded Celejlial and ^errefirial Globes. 7^ preceded by a luminous fegment of a circle in the eaft before his riling, different from that light refleded by the atmofphere from the body of the fun ; the like to which may be obferved in the weft after fun-fet. To reprefent the earth's enlightened difk by the terreftrial globe. 216. We have already fliewn how the earth's diurnal motion is reprefented by the motion of the terreftrial globe about its axis from weft to eaft; and that the horary index will point upon the equator the 24 hours of one diurnal rotation, or any part of that time. 217. The broad paper circle, under this conlideration, will be now employed to re- prefent a plane fuppofed to pafs through the center of the earth, perpendicular to a cen- tral folar ray : or in other words, perpen- dicular to a line fuppofed to be drawn from the center of the fun to that of the earth at all times of the year. In which cafe, the broad paper-circle divides that half of the earth's furface, which IS 76 Description and Use of the is illuminated by the fun's rays, from the Other hemifphere which is not enlightened. 218. That the globe may appear to be fo enlightened, conceive a fun painted on the ceiling of the room in which you are, diredlly over the terreftrial globe, and of the fame diameter j from whence imagine an infinite number of parallel rays falling per- pendicularly downwards upon the upper furface of the globe, which here reprefents the illuminated hemilphere of the earth's enlightened difk. 219. Whence it is plain, that the central folar ray is the only one, which palTes through the centers of the fun and earth, as well as the only ray that can poffibly be perpendicular to the earth's furface 5 all other folar parallel rays will fall more and more oblique, as they are farther from the central ray, till their arrival at the edge of the enlightened difk, here reprefented by the inner edge of the broad paper-circle, where they v/ill become parallel to the horizons of all places then under the faid edge of the difk. 220. In one diurnal revolution of the ejvith, the central folar ray defcribes the parallel Celeftial and 'Terrejirial Globes. 77 parallel of the fun's declination j or rather that parallel, to the inhabitants of which the fun that day will pafs diredly vertical, or over their heads. 221. From this application of the ter- reftrial globe, we fee the natural caufe of the different altitudes of the fun at different times of the day, and at different feafons of the year j which arife from the earth's daily rotative and progreffive motion, &c. 222. When we view the globe in this pofition, wc at once fee the fituation of all places in the illuminated hemifphere, whofe inhabitants enjoy the light of the day, while at the fame time all thofe places below tlie broad paper-circle, are deprived of the fun's light and have only twilight fo far as the wire circle, and all below that, have total darknefs, when the moon does not fliine on them. 223. And by obferving the angles made by the meridians, drawn on the globe, cut- ting any parallel of latitude at the edge of the broad paper circle, with the ftrong brafs meridian, we fee the femi-diurnal arches continually decreafe from the elevated pole, till yi Description and Use of thi till they come to the oppofite part of the earth's enlightened dilk. Problem XVII. To reclify the terreflrial globe, that the enlightened half of the earth's furface may be all above the broad paper circle for any time of the year ; the fun being fup- pofed in the zenith. 225. On the backfide of the ftrongbrafs meridian, and on each fide of the north pole, are graduated in two concentric fpaces the months and days of the year. 226. Bring the day of the month to co- incide with the broad paper circle, and the terreftrial globe is redtified. 227. When the globe is thus redtified, that degree and minute upon the graduated fide of the brafs meridian, which is then cut by the plane of the broad paper circle, is the diftance of the fhade of extuberancy upon the earth's difk, reckoned from the pole. Celejlial and ^errefirial GLOBts. 79 pole, and is equal to the fun's declination for that day : and is therefore alfo equal to the latitude counted from the equator of all thofe places to whom the fun is vertical ; and this point on the brafs meridian repre- fents the central folar ray defcribing the parallel of the day. 228. If now the globe be turned from weft to eaft, all thofe places which arrive at the weftern edge of the broad paper circle, are pafiing out of the twilight into the fun's light ; the fun then appears rifing to all thofe inhabitants. 229. At the fame time, if you look upon the eaftern edge of the broad paper circle, it will cut all thofe places which are then pafTing, from the fun's light into the twi- light j whofe inhabitants will fee the fun fetting, and enjoy the twilight until they arrive at the wire circle, which is placed 18 degrees below the illuminated dill:, at which time they enter into total darknefs. 230. The graduated fide of the ftrong brafs meridian fliews, at the fame time, all thofe places which have mid-day or noon. 231. If the horary index be fct to XII, when any particular place is brought under the 8o Description and Use of the the graduated fide of the ftrong brafs meri- dian, it will fliew as you turn the globe from weft to eaft, the precife time of fun rifing, fetting, &c. at that place. 232. The horary index will alfo fliew how long a place is moving from the weft to the eaft fide of the illuminated difk, here reprefented by the broad paper circle, and thence the length of the day and night j it will alfo point out the length of the twilight by the time that the place is pafling from the twilight circle to the edge of the difk on the weflern fide, or from the edge of the difk. to that circle on the eaflern fide, and thence the length of time we enjoy a whole artificial day. We fhall proceed to exemplify thefe particulars at the times of equinox and folftice. Problem XVIII. The times of equinox. 233. The fun has no declination at the times of equinox, confequently there mufl be no elevation of the poles. 234. Bring Ceiejlial and Terrejirial Globes. St 234. Bring the day of the month on the backlide of the ftrong brafs circle, in which the fun enters the firfl: point of aries or hbra, into the plane of the broad paper circle, and then the two poles of the globe will be in that plane alfo ; and all thofe circles which arc parallel to the equator will cut the plane of that broad circle at right angles, and the globe will then reprefent a right fphere. 235. If you now turn the globe from weft to eaft, it w^ill plainly appear that all places upon its furface are twelve hours above the broad paper circle and as many below it, which Ihews the nights are equal to the days to all the inhabitants of the earth j that is, they are illuminated by the fun's rays twelve hours, whence thefe are called the times of equinox, which happens twice every year ; the firft is the autumnaly the fecond the ijcnml equinox. 236. At thefe times the fun appears to rife and fet at the fame inftant to all places in the fame meridian. 237. But their twilight is longer as their fituation is nearer to either pole, in fo much that within iS degrees of the poles, their G twilight 82 DESCRil>tioN and Use of the twilight is 1 2 hours, confequently there is no dark night in thofe places at the times of equinox : when at the fame time thofe places under the equator have only one hour and 12 minutes twilight j fo that their artificial day is about I4h. 24 min. at thcie two feafons of the year. 238. Thus if London, and Mundfort on the Gold Coaft, be brought to the Rrong brafs meridian, the graduated fide of which is the horary index ; in other cafes the hour index fet to that XII which is moft elevated, and if then they be brought to the weft fide of the broad paper circle, the index will then point to VI o'clock for fun rifing, and to VI for fun fetdng, when thefe places are brought to the eaftern fide. 239. Alfo if London be turned from the weft towards the eaft, and the hour index be fet to XII as before, then turning on till the ifland of Jamaica comes to the meridian, it fhews on the equator the hour after noon at London, when it is noon at Jamaica, or that London paffes under the meridian about 5 h. 4. min. before Jamaica arrives at it. Problem J Cekftia! and 'Terrejlrial Globe s . 8 Problem XIX. The fummer-folftice. 240. Rcdlify the globe to the extremity of the divifions for the month of June ; then that part of the earth's furface, which is within the northern polar-circle, will be all illuminated by the fun, and the inha- bitants thereof will have continual day. 241. But all that fpace which is con- tained within the fouthern polar-circle, will be at the fame time in the lliade, and have continual night. 242. In this podtion of the globe, we fee how the diurnal arches of the parallels of latitude decrcafe, as they are more and more diftant from the elevated pole. 243. If any place be brought under the graduated fide of the ftrong brafs meridian, and the horary index be fet to that XII which is moft elevated, and if that place be brought to the weftern fide of the broad paper circle, the hour index will fhew the time of fun rifino; - and when moved to the eaftcrn edge, the index points to the time of fun fetting; the length of the day is ob- G 2 tained 84 Description ajid Use of tJje tained by the time (hewn by the horary index, while the globe is turned from the call: to the weft fide of the illuminated difk, 244. Thus it will be found that at Lon- don the fun rifes about 15 minutes before IV in the morning, and fets about 15 minutes after VIII at night. 245. Alfo at the following places it will be nearly at the times exprelTed. Cape Horn Cape of Good-Hope Rio de Janario in Bra ~ zil, near the tropic of ' Capricorn ] TheiflandofSt.Thomas at the equator Cape Lucas, the fouther- moft point of Cali- ( fornia, at the tropic^ of cancer. Length Twi- Rifing. Setting. of Day. light. h. m. h. m. h, m. h. m. 8 44 3 16 6 32 2 35 7 "^9 + 51 9 42 I 43 6 42 s 19 10 38 I 23 6 6 12 I 20 5 12 6 48 13 36 ' 35 246. We alfo fee at the fame time, when the fun rifes at London, it rifes at the Ifland of Sicily in the Mediterranean, and at the Illand of Madagafcar. 247. And at the fame time, when the fun fets at London, it is fetting at the Ifland of Madeira, and at Cape Horn. 248. And Cekftial and Terreftrtal Globes. 85 248. And when it is fun-fetting at the Ifland of Borneo in the Eaft -Indies, the fun is rifino; at Florida in America. Problem XX. Winter-folfticc. 250. Redify the globe to the extremity of the divifions for the month of December, or to 23! degrees fouth declination. 251. At this feafon it will be apparent, that the whole fpace within the fouthern polar-circle is in the fun's light, and enjoys continual day, whilft that of the northern polar-circle is in the Ihade, and has con- tinual night. Then if the globe be turned as before, the horary index will fliew, that at the feveral places before mentioned, their days will be refpedtively equal to what their nights were at the time of the iiimmer- folftice. It will appear to be fun fetting at the time it was then fun riling ; and on the con- trary fun rifmg at the time it then appeared to kx, G 3 The 85 Description a?id Use of the The terreftrial horizon, 252. As has been defcrlbed art. 40. is a fmall brafs circle with one diameter that paiTes through its center ; its circumference is divided into eight parts, which are marked with the initial letters of the mariners com- pafs, the four cardinal points of the horizon being diftinguilhed from the reft ; this may be flipped from pole to pole on the move- able meridian, and by this means be fet to any place upon the globe. 253. When the center of It is fet to any particular place, the fituation of any other places are ittn with refpedt to that place ; that is, whether they be eaft, weft, north, or fouth J thus it reprefents the fenfible horizon. 254. Its ufe will fhew why the fun ap- pears at different altitudes and azimuths, although he is fuppofed to be always in the fame place. Problem "R front p.86 .D B' Tig. 4^ Celefiial and Terrcjlrial Globes. 87 Problem XXI. The fun's altitude as obferved with a terreftrial or viiible horizon. 255.. The altitude of the fun is greater or lefs, according as one of the parallel right lines or rays, coming from the fun to us, is farther from or nearer to our horizon. Apply the terreftrial horizon to London, the fun being fuppofed in the zenith, or on the ceiling dirediy over the globe. 256. If then from London a line pafs vertically upwards, the fun will be it^n from London in that line. 257. At fun rifing, when London is brought to the weft cd2;c of the broad paper circle, the fuppofed line will be pa- rallel to the tcrrefcrial horizon, and from London will be then itftVi. in the horizon. 258. As the globe is gradually turned from weft towards the eaft, the horizon will recede from the line which pailes per- pendicularly upwards ; for the line in which the fun was then fcen, fecms to glide far- ther and farther from the terreftrial horizon; that is, the fun's altitude increafes as gra- G 4 dually 88 Description and Use of the dually as that line declines from the ter- reftrial horizon. 259. When the horizon, and the line which goes from London vertically up- wards, are arrived at the flrong brafs meri- dian, the fun is then at his grcateft or meridian altitude for that day : then the line and horizon are at the largeft angle tliey can make that day with each other. 260. After which, the motion of the globe being continued, this angle between the terreftrial horizon and the line, which goes from London vertically upwards, con- tinually decreafes, until London arrives at the eartern edge of the broad paper circle, its horizon then becomes vertical again, and parallel to the line which goes vertically upwards, and will then appear in the hori- zon, and be feen to fet. Problem XXII. The fun's meridian-altitude at three different feafons. 261. Redtify the globe to the time of winter-folftice, art. 250. and place the center of the vifible horizon on London. When I CeJeJiial and Terrejlrial Globes. 89 When London is at the graduated edge of the ftrong brafs meridian, the line which goes vertically upwards, makes an angle of about 1 5 degrees ; this is the fun's meri- dian-altitude at that feafon to the inhabi- tants of London. 262. If the globe be redified to the time of equinox, art. 233. the horizon will be farther feparated from the line which goes vertically upwards, and makes a greater angle therewith, which will be about 3 Si- de- grees ; this is the fun's meridian-altitude at the time of equinox at London. 263. Again redlily the globe to the fum- mer-folftice, art. 240. and you will find the vifible horizon recede farther from the line which goes from London vertically upwards 3 and the angle it then makes with the hori- zon, is about 62 degrees, which lliews the fun's meridian-altitude at the time of the fummer-folftice. From hence flows the following arith- metical PfiOBLEM 90. Description ^W Use of the Problem XXIII. To find the fun's meridional alti- tude univerfally. ^64/ Add the fun's declination to the elevation of the equator, if the latitude and declination are both on the fame fide. If on contrary fides, fubftradt the decli- nation from the elevation of the equator, and you obtain the fun's meridian-altitude. o / Thus, the elevation of the equator at 5 j. „ London j^ Sun's declination May 20th 20 8 Their fum is the fun's meridian-alti-7 ,r> g tude for that day at London J^ ^ ^ain, to the elevation of the equator? ^ j, at London S W the fun's greateft declination at/ the time of the fummer-folftice S Their fum dian-alt 1 is the fun's greateft meri-7 ^ itude at London, J ^' Whence alfo flows another method. To Celeftial and T'errefirial Globes. 9 r To find the fun's greateft and lead altitude univcrfally. 265. Add the fun's declination to and fubftradl it from the elevation of the equa- tor, their fum and difference will be the fun's meridional altitudes, when he hath the fame declination either north or fouth. . o / Thus, to and from the elevation of ; _ I i-^8 28 the equator 3 ^ Add and llibllrad the fun's decIi-7 <2o 8 nation. J Their fum is the fun's meridian-alti- } ry . r tude in fummer \^ ^ Their difference his meridian-ahitude ? „ (^18 20 in winter \ having the fame declination one north, the other fouth. Problem XXIV. The fun's azimuth compared with the vifible horizon. 266. Imagine the fun, as we have done before, to be painted on the ceiling dire and alfo, which way at all times the noon and other lliadows are caft. 281. Antaeci are two oppofite nations lying in or near the fame meridian, one of them in north, the other in fouth latitude > they have both the fame longitude, and equal latitudes, but on oppofite fides of the equator. 282. Periosci are two nations fituated on oppofite fides of the globe, in the fame pa- rallel of latitude. Therefore their longitudes muft differ 180 degrees. 283. Antipodes are two nations diame- trically oppofite. 284. A fi:rait line pafling from one to the other muft confequently pafs through the center, and therefore become a diameter of the globe. Their longitudes and latitudes are both oppofite. 285. Thefe are exemplified by redifying the globe into the pofition of a right fphere, art. 233. and bringing the nations under confideration Celefilal and Terrejirial Globes. 99 confideration to the edge of the broad-paper circle. Thus, The inhabitants of the eaftern parts of Chili are Antaeci to thofe of New England ; whofe Periaeci live in the northern parts of China, who are alfo Antipodes to the inha- bitants of Chili. We fliall now proceed to exemplify the former precepts in a few particular pro- blems. Problem XX VII. To find all thofe places on the globe, over wliofe zenith the fun will pafs on any given day. 286. Redify the terreftrial globe, art. 224. by bringing the given day of the month, on the backiide of the ftrons; brafs meridian, to coincide with the plane of the broad-paper circle, and obferve the eleva- tion of the pole on the other fide, and that degree counted from the equator on the ftrong brafs meridian, towards the elevated pole, is the point over which the fun is vertical. Now turning the globe, ail thofe H 2 places 100 Description and Use of the places which pafs under this point, have the fun diredly over their heads on the given day. r^Thus bring the 1 1 th day of May, into the plane of the broad-paper circle, and the faid plane will cut 1 8 degrees for the elevation of the pole, which is equal to the fun's decli- nation for that day ^ which counted on the ftrong brafs meridian towards the elevated pole, is the point over which the fun will be vertical. Now turning the globe round, we (hall find that Amalagan, one of the Ladrone iflands, the northern part of Manilla, the middle of Siam, a great part of Africa, and St. Anthony, one of the Cape Verd Ifles, the fouthern fide of the iflands Porto- rico and Domingo, and the northern part of the ifland of Jamaica, &c. have all of them the fun in their zenith on the 1 1 th of May. Hence when the fun's declination is equal to the latitude of any place in the torrid zone, the fun will be vertical to thofe inhabitants that day. Hence alfo we derive the following Problem Celefiial and T^errejlrial Globes, roi Problem XXVIIL To find the fun's declination, and thence the parallel of latitude cor- refponding therewith, upon the terreftrial orlobe. 287. Find the fun's place upon the broad- paper circle for any given day, art. 18. and feek that place in the ecliptic line upon the globe J this will fliew the parallel of the fun's declination among the dotted lines, which is alfo the correfponding parallel of latitude 5 therefore all thofe places through which this parallel pafles, have the fun in their zenith at noon on the given day. Problem XXIX. To find thofe two days on which the fun will be vertical to any place between the tropics. 288. That parallel of declination which pailes through the given place, will cut the ^eek-da t> 7' 356. Divide the days of the tropical re- du(5tion by 7 ; if o remains, it is Thurfday^ K 3 if 134 Description and Use of the if I, Friday J 2, Saturday; and 3, Sunday; and lb on to 6, which is Wednefday, as ia the tabic of week-days. To obtain the time of the vernal equinox. 357. Firft find the autumnal equinox for the fame year in which the vernal equinox is required; and from it fubftrad: 186 d. II h. 51 min. which is the diftance in time from aries to libra ; their difference will be the time of the vernal equinox required. 358. The day of the month and week- day found as above, we obtain the literal character for that day as follows. In the table of months ftand the literal charafters, that are placed againft the firft day of each month in any common al- manack. And whatever letter ftands againfl the fiift day of any month, the 8th, 15th, 22d, and 29th days of that month are all cha- radterifed with the fame. 359- Celejiial a fid Tenrjlrial Globes, 135 359. A circle of the 7 literal or week- day charaders. The day of the month and week-day given, to find its literal charadler and dominical letter for that year. 360. A. D. 1772, the autumnal equinox will happen at Greenwich, September 22d, o h. ^$ min. on a Tuefday. QuERE, The literal charader foi' that day and dominical letters for that year, it being biiicxtile ? The literal character for the ift of Sep- tember is F, fo alio is the 2 2d, and Tuefday in the prefent qucftion. Look on the circle of week-day charaders, call F Tuefday, G Wednefday, A Thurlday, and fo on to Sunday which falls upon D, the laft of the two dominical letters for that year, and ferves from the intercalary day to the year's end. K 4 The 136 Description ami Use of the The fiifl: dominical letter for leap-years is the next in the circle, and ferves for January and February, which in this example is E. Tlierefore the two dominical letters for the bifTextile year 1772 are E D nev/ flile. In any common year, the letter firft found ferves for the whole year. 361. The dominical letter being known, to find what day of the week any day in the year falls on. QuERE, What day of the week is the 20th day of March A. D. 1772 ? The literal character for the ift of March is D, fo is the 15th, and the 20th being 5 days more, if we count from D, which happens to be the dominical letter, to E Monday the 1 6th, we {hall find B is Friday the 20th day of March, A. D. 1772 new flile. 362. If the dominical letters were re- quired for old flile, in thefe examples the firft would be the nth of September 1772, whofe literal character is thus found, F the ifl day of September, and alfo the 8th, G the 9th, A the loth, and B the nth, and by the following calculus Tuefday, therefore A C are the dominical letters old ftile, A. D. 1772. 363. Re- CelefJal mid ^errejlrial Globes. 137 363, Required the autumnal equinox at Alexandria in Egypt, in the 146th year before the Chriftian iEra. 4008 — 146 A M. 3862 or years from the radix, Od. 25, A. J.P, 706, Retroceflion. Tropical reduflion, years a radix, d. b. min. days a radix, h. min. 3000 22 22 o 1095727 2 o 800 6 2 40 292193 21 20 60 o 1 1 o 21914 13 o 2 O O 22 730 II 58 29 12 2 7)1410565 23 58 weeks zoi^oc)-\-z Saturday. d. h. min. Tropical days 565 tropical time 1410565 23 58 epoch -f- 298 retroceflion -f- 29122 863 Julian reduf^ion 1410595 12 o Julian daj's — 595 the 3d year after biflextile. 268 for Augufl: — 243 if^ Sept. 25 d. h. min. a kal. Jan. 268 23 58 fixed meridian, meridian difk -f" 1225 the fun in the firft point of ) . libra Sept. 26, J ^^9 12 23 at Alexandria. On a Sunday, dominical letter B, in the 1 46th year before the Chriflian iEra. 364. To 138 Description a?id Use of the 364. To find the time of the vernal equinox in the fame year, and at the fame place. d. h. min. From the autumnal equinox, Sept. 26, a ? ^ kal. Jan. (^9° '^ 23 fubftraft the diftance in time between T 7 or and ^ 1»S6 ,1 51 83 o 32 for February 59 the fun in the I ft point of aries at Alex- 1 andria ante Chrift 146 years, March 5 Note, According to the civil reckoning of the hours from midnight, this vernal equinox fell upon the 23d day of March, at 32 minutes paft noon at Alexandria. 365. To find the time of the autumnal equinox at Greenwich, A. D. 1768. 4007 4-1768 A.M. 5775 or years from the radix, Retroceflion. Tropical reduflion. years a radix, d. h. min. days a radix, h. min. 5C00 38 4 40 182621 1 ig 20 700 5 8 ;o 255669 15 40 70 o 12 50 25566 23 10 55 ^826 5 s o o 44 2 45 7)210^^274 15 15 weeks 301328-J-6 Wednefday. Tropical Celefiial and T!errejirial Globes. 139 Tropical days 274 tropical time 2109274 15 15 epoch -|- 298 letroccflion -\- 44 2 45 572 2109318 18 o Jul. days 4" i — 319 becaufe of the 18 h. biffextile year. 253 a kal. Jan. old ftile for new ftilc -}- i > 'iays 264 a kal. Jan. new ftilc for Augufl — 243 in £i Sept. 21 d. h. min. in the fixed meridian a kal. Jan. 264 15 15 meridian dift. -|- o lO 24 the wich fun in the ift point of libra at Green- ? r fich, Sept. 22, \ ' ^ 366. To find the time of the vernal equinox, A. D. 1768. d. h. min. From the autumnal equinox, Sept. 22, 265 i 39 fubftrad dift. 'f a ;c; 186 11 51 78 13 48 for Feb. 59 o o the fun in aries at Greenwich, A.D.I 768, Mar. 19 13 48 367. Having 140 Description ajid Use of the 367. Having found the autumnal and vernal equinoxes for the biifextile year, A. D. 1768, we obtain them for the three fol- lowing years by continually adding thereto 5 h. 49 min. thus in T d. h. min. O in ^ d. h. m. 1 768, March 19, 78 13 48 - 1768, Sept. 22, 265 i 39 + 5 49 + 5 49 1769, Mar. 19, 78 19 37 - 1769, Sept. 22, 26; 7 28 + 5 49 + 5 49 1770, Mar. 20, 79 i 26 - 1770, Sept. 22, 265 13 17 + 5 49 + 5 49 1771, Mar. 20, 79 7 15 - 1771, Sept. 22, 265 19 6 368. Required the time of the autumnal equinox at Greenwich, A. D. 1772. 4007 1772 A.D. 5779 or years from the radix. Retroceffion. Tropical reduflion. years a radix, d. h. min. days a radix h. min. 5000 38 4 40 1 82621 1 19 20 700 5 8 20 235669 15 40 Z5566 23 10 3287 4 2» 7)211073; 14 31 12 50 I 39 44 3 29 weeks 3015334-4 Monday. Tropical Celefiial and Herreflrial Globes. 141 Tropical days 735 to the tropical time 2110755 14 31 epoch -j- 298 retroceffion -\- 44 3 29 1033 21 10779 18 o Jul. days-^i — 780 becaufe of the 18 h. biflextile year. 253 a kal. Jan. old ftile for new ftile -f- 1 1 days 264 a kal. Jan. new ftile for Augufl: — 243 Qin libra Sept. 21 d. h. min. in the fixed meridian a kal. Jan. 264 14 31 meridian dift. -\- o 10 24 the fun in the firft point of libra at Green- Z^^- q wich, Sept. 22. 3 ■* On a Tuefday, dominical letters. 369. To obtain the vernal equinox, A. D. 1772. d. h. min. From the autumnal equinox, Sept, 22, 7 . a kal. Jan. ^^5 o 55 did. from aries to libra 186 11 51 78 13 4 for February 59 the fun in the 1 ft point of aries at Grcenw.Mar. 19 13 4 370. We find the two equinoxes in the three next lucceeding common years, as in the preceding example, by the continual ad- dition of 5 hours, 49 minutes. By 142 Description and \]s>^ of the By this method of calculation, we avoid any miftake that might happen with refpedt to the intercalary day j becaufe we find the autumnal equinox firft, and thence the vernal equinox, which always falls after the inter- calary day, and alfo as tropical time has no biiTextile years. To reduce hours, minutes, and feconds of time, into degrees, minutes, and feconds of the e- quator. 371. Divide the feconds of time by 4, the quotient is minutes, and remainder fo many times 15 feconds. Divide the minutes by 4, the quotient is degrees, and remainder fo many times 15 minutes. Multiply the hours by 15, the produdt is degrees. Example. Cekfttal and Terrejlrial Globes. 143 Example. Reduce 1 1 h. 35 min. 27 fee. of time into degrees, minutes, &c. of the equator. fee. min. 4)27 4)35 6' 45" 8045/ h. II 165° anfvver deg. min. 165 8 45 6 fee. 45 173 51 45 To reduce degrees, minutes, and feconds of the equator, into hours, minutes, and feconds of time. 372. Divide feconds by 15, the quotient is feconds, and remainder fo many times 4 thirds. Divide minutes by 15, the quotient is minutes, and remainder fo many times 4 feconds. Divide the degrees by 15, the quotient is hours, and remainder fo many times 4 minutes. Example, 144 Description and Use of the Example. Reduce 173 deg. 51 min. 45 fee, of the equator, into hours, minutes and feconds of time. fee. min. deg. h. h. min. fee. ^^)Vr.l" i5)5»(3' 5)'73( 1 1 11 32 AS 45 15 3 24 — ■ — — 3 Q 6—1 4" 23 ^5 \J .^~. * 1 1 35 27 anfwcr. 8=32' We are now prepared to folve the lat- ter part of the laft problem, which is as follows. Problem XLV. To find all thofe places vyhere it is noon at the time of an equinox, as well as that point upon the equator, to which the fun is ver- tical at that time. Having found the time of an equinox by the preceding or any other method of cal- culation, as in the firft example j we find the I Celefiial and 'Terr ejlrial Globes. 145 the fun entered the firft point of aries at Alexandria in Egypt, March 24th, o h. 32 min. which was March 23d. at 32 minutes pafl: noon. The 32 minutes of time reduced to the equator, are equal to 8 degrees. Therefore bring Alexandria under the graduated fide of the flrong brafs meridian, and fet the horary index to XII upon the equator, turn the globe from wefc to eaft until 32 minutes of time, or 8 degrees of the equator have paiTed under the horary index, where flop the globe ; then all thofe places under the faid graduated fide of the flrong brafs meridian will have noon, and that degree of the equator, which is then under the meridian, is the point to which the fun was at that inftant vertical, and is the interfeding point of the equator and ecliptic, or that terrefi:rial meridian which governs the palfige of the firfi: point of aries for that year. The -^3 146 Description and Use of the The vernal equinox, A. D, 177 will fall on the 19th day of March, at 13 h. 4 min. which reduced to the degrees and mi- nutes of the equator, is equal to 196 degrees. 374. Bring London to the graduated fide of the ftrong brafs meridian, and fet the horary index to XII, (in this cafe the graduated fide is the horary index) turn the globe from weft to eaft until 13 h. 4 min. of time, or 196 degrees of the equator have pafled under the horary index, where ftop the globe; the 196th degree of the equator will now be found under the graduated fide of the brafs meridian, and is that point on which the fun will be vertical at noon ; at which- inftant it will be 1 3 h. 4 min. paft noon at London or Greenwich. The meridian pafling through this pointer will be {(ten to pafs a little eaftward of Kamkatfki, through the Pacific Sea, acrofs the ifiand' Dicerta, thence eaft of the ifle Taumago, and through the weftern part of New-' Celejiial and i'erreftrial G lobes. 1 4}^ New Zeland, all which places will have noon at the inflant of that vernal equinox. The autumnal equinox, A. D. 177:*, will happen September 2 2d, o h. 55 min. at London, the 55 min. being equal to 13 deg. 45 min. of the equator. 375. Bring London to the graduated fide of the ftrong brafs meridian, and let the horary index to XII, turn the globe from weft to eaft, until 55 minutes of time, or 13 deg. 45 min. of the equator have palled under the horary index, where flop the globe ; here, as in the laft example, the 1 3th degree and 45th minute is that point upon the equator to which the fun is vertical, and the meridian paffing through this point, lies under the ofraduatcd fide of the (Irons brafs meridian j which palTes over the mid- dle of Greenland, and throudi the Atlantic Ocean to the eaft of TenerifFe, a httle to the weft of Afcenfion Iftand, and thence through the Ethiopic Ocean, at which places it will L 2 be I4S Description atid Use of the be noon at the time of this autumnal equinox. Here it will be proper to give the reader a {hort account Of the natural agreement between the celeftial and terreftrial fpheres ; or, How to gain a perfed idea of the Situation and diftance of all places upon the earth, by the fun and ftars. 376. That part of the firmament which is in the zenith of London, is perpendicular to half the globe of the earth j which half comprehends almoft all the habitable land of Europe, Afia, Africa, and America, with their coafts, capes, land and feasj fince under the other celeftial hemifphere, which we do not fee at the fame time, there are only very inconfiderable lands and ifles. 377. The inhabitants of Great Britain and Ireland nearly fee the fame half of the firmament adorned with ftars and planets, which at all times fupply the place of an immenfe Cekjlial and Terrejlrial Globes. 149 immenfe map of the world ; and fliew our terreftrial hemifphere by the ftars, con- veying the correfpondent marks of the two continents to our fi'^ht and mind. 378. The fun, by his apparent daily mo- tion, feems to defcribe a kind of fpiral, in paifing from one tropic to the other and back again, continually changing his decli- nation, and every day defcribing a diffl-rcnt parallel, art. 104. Forty-feven of thefc diurnal parallels are drawn on our new terreftrial globe, art.i 15. 116. between the tropics of cancer and Capri- corn, reprefenting the parallels for every de- gree of the fun's declination. 379. Before the reader proceeds, he is delired to make himfelf acquainted with the caufe of the daily change in the fun's decli- nation, beginning at article 150, and reading from thence to the i66th article. Which being premlfed, it will be eafy to conceive, that the fun being in any one of thefe parallels, muft neceffarily caft his per- pendicular rays that day upon the heads of the inhabitants of thofe places through which that parallel of declination pafles. L 3 NotCj 150 Description and Vst of the Note, Although thefe 47 parallels are here called parallels of declination, they are alfo parallels of latitude upon the terreftrial globe. 380. From thefe principles we obtain the fituation of thole places, to which the fun is vertical every day in the year ; we alfo find the time of that day at the place of any ob- ferver, from whence looking at the fun, we may pronounce him to be over the heads of the inhabitants of divers cities and ftates, during the feveral hours of that day, and io on for every day in the year. 381. The fun being perpendicularly over any one of thefe diftant cities or princi- palities, at the time of our obfervation, if a plumb-line be held up between the ob- ferver and the fun, fo as to pafs through or before the fun's center, it will cut the vifibie horizon in a point, that will fix the bearing or paflage in a right line from the obfervei* to that place, upon which the fun is then vertical. 382. A point thus noted upon the vifible horizon, may be feen at all times, and repre- fent the fame bearing, independent of the fun and ftars, and that in fuch a confpicuous manner Celefiial and Terrejlrial Globes. 151 manner as to render this knowledge always entertaining, uieful and interefting. 383. The ftars at night perform the fame more copioufly, by pointing out to our fenfes the diftance of many diftant provinces, at one and the fame inllant of time, from our own zenith. Hence we are in pofl'cflion of a moil im- menfe and extenfive field, wherein we may corred: and improve our agronomical and geographical knowledge. Examples of folar corrcfpondents. Problem XLVI. To find the folar correfpondcncc to a fixed point upon the earth, when the fun is fcen by an ob- ferver, fituated upon any other point of its furface. Example I. 384. Let the obferver be in London (or in any of the country places within thirty L 4 miles 152 Description and Use of the miles of it) upon the 1 oth day of .March, at 10 minutes pad XI o'clock in the morning. QiJERE, The place upon which the fuci will be vertical at that time ? Redify the globe by bringing the loth of March, engraved on the backfide of the flrong brafs meridian, to the plane of the broad-paper circle 3 find the fun's place, againft the day of the month in the kalen- dar, which will be about 20 deg. i o min. in pifces j feek thefe degrees and minutes in the fign pifces upon the ecliptic line on the globe, and you will find it fall upon the fourth parallel of fouth declination, to all the inhabitants on this parallel the fun will be vertical that day. Now bring 1 1 h, 10 min. on the equator to the graduated lide of the ftrong brafs meridian, and you will find it cut the fourth fouthern parallel upon the city of Loango, on the weftern coaft of Afirica. Therefore if you look at the fun 10 mi- nutes pall XI in the morning at London, you will then fee him at the inllant he is diredly over the heads of the inhabitants of the city of Loango in Africa j at the fame time, Cekftial and ^erre/Irial Glomes. 153 time, your ideas are made fenlible of the comparative dillance, which you fee in the firmament between the zenith of London under which you ftand, and the fun, which is then in the zenith of Loango j aifo if at the time of your obfervation, you caul'e a plumb-line to be held up between you and the center of the fun, and caft your eye down towards the moll diftant part of your fenfible horizon, the plumb-line will cut a point thereon, which, if remembered, will always Ihew you the true bearing or point of the compafs, in a diredl line from your fituation, to that of Loango. 385. This diftance and bearing may be nearly found by the globe ; thus. Elevate the globe to the latitude of Lon- don, that the broad-paper circle may repre- fent your horizon, fcrew the nut of the quadrant of altitude in the zenith, that is upon 51 dcg. ^2 min. counted from the equator towards the elevated pole, bring London under that point, and lay the gra- duated edge of the quadrant upon Loango, which will cut the bearing 1 5 degrees, reckoned from the fouth towards the eaft^ or between the points S S E and S b E; now feparate 154 Description and Use of the feparate the quadrant from the globe, and lay its graduated edge upon Loango and London, fo that the beginning of the gra- duation may lie upon one of the places, then the other will cut 56 degrees, which is equal to 3360 geographical miles, or 3892 Englifh miles, the diftance between London and Loango. 386. To elucidate this example, we fhall trace the fun's vertlcity over that part of this day's parallel of declination, as is included between the riiing and fetting fun at London for that day. Imagine, as we have before fuppofed, an image of the fun to be painted upon the cieling of the room, dire(flly over the ter- reftrial globe. Let the globe be rectified to the loth of March, place the center of the artificial horizon upon London, and bring it into a coincidence on the weft fide of the plane of the broad-paper circle, now reprefenting the edge of the earth's illuminated difk ; we fhall then have the pofition of the earth widi refped: to the fun for that day j when the inhabitants of London will be leaving the twilight, and paffing into the firft point of Cekjiial and Terrefirial Globes. 155 of day, or fun-rifing, at about 1 8 minutes paft VI in the morning, cut by the gra- . duated fide of the ftrong brafs meridian on the hour line under the equator; at this time the meridian will likewife crofs the fourth parallel of fouth declination, in the Indian Ocean, between the ifland of Sumatra and the Maldive Iflcs ; if we look upon the fun that morning at the inflant of his rifing, we fliall fee that his diflancc from our zenith will then be 90 degrees, he being in our horizon, which is equal to 5400 geogra- phical or 6155 Englifli miles, the diftance from London to that part of the Indian Sea ; turn the globe from weft to eaft, until 8 h. 12 min. are under the horary index, which in this cafe is the ftrong brafs meri- dian, and it will cut the iile Macarenhas, to which the fun will then be perpendicular, at \ paft- IX he will be perpendicular to the coaft of Zanguebar, his central ray pafling between Monibacca and Pemba, thence it paftes over the kingdoms of Monomugi, Macoco, Congo, &c. until he is perpendi- cular to the city of Loango, upon the weftern coaft of Africa, at 1 1 h. 10 min. the fame morning ; immediately after which his 1^6 Description and Use of the his perpendicular rays are abforbed in the Ethiopia Ocean, over which he is 3 h. 22 min. in paffing to Fort St. Lucar, on the eaftern coafl of America, at 3 2 minutes paft II in the afternoon j thence he proceeds to fend forth his perpendicular rays over the heads of the inhabitants of Brazil, acrofs the vaft country of the Amazons and Peru, in the decline of our evening, until his arrival over Cape Blanco on the weltern fide of South America, a little before he fets to the inhabitants of London, which is about 40 minutes pad V o'clock. Example II, 387. Every redlification being obferved as in the firft example, required the place upon which the fun is a correfpondent at 48 minutes paft VI in the evening of the 1 8 th of May, the fun's place being about I7deg. 40 min. in taurus, which {hews upon the globe, that the fun will be nearly vertical to the 17th parallel of north decli- nation on that day. Turn the globe from weft to eaft, until London has pafled the ftrong brafs meridian and flop, when its graduated CekjUal a?id Herrcftrial Globes, 157 graduated fide is diredly over 6 h. 48 min. afternoon, and it will cut upon the 17th parallel of north declination, the city of Acquapulco on the weflern coafi of Mexico, over which the fun will then be vertical. Example IIL 388. Let the obferver be at Cape Clear on the weflern coaft of Ireland, on the 1 6th day of July, at 54 minutes pafi: VIII in the morning. Quaere, The place upon which the fun will then be vertical? The fun's place being in the 24th degree of cancer, which on the globe falls upon the 21 ft parallel of north declination. Bring Cape Clear to the graduated fide of the ftrong brafs meridian, and fet the horai-y index to XII, turn the globe till 8 h. 54 min. amongft the morning hours are under the horary index, and you will find the gra- duated fide of the ftrong brafs meridian to cut the 2ift parallel of north declination upon Farrat in Nubia, on the weftern coaft of the Red Sea. Example 158 Description and Use of the Example IV. 389. Let the obferver be at RomCj on the 20th day of November, at 37 minutes paft X in the morning. QuERE, The place upon which the fun will be vertical at that time? The fun being about aS-i- degrees in Icorpio, which falls to the fouthward of the 20th parallel of fouth declination. Bring Rome to the graduated fide of the ftrong brafs meridian, and fet the horary index to XII, turn the globe to have i o h, 37 min. under the horary index, and the faid graduated fide will then cut under the 20th parallel of fouth declination the city of So- fala in the kingdom of Quiteri, to the fouth of Monomotapa, on the eaftern coaft of Africa. We apprehend thefe four examples are fufficient to give the reader a clear idea of the folar correfpondents to all places within the torrid zone, and to enable him to dif- cover fome thoufands more. 390. Although we can have but one folar correfpondent at the fame time, yet as in the firft example, we can trace him through his Celejiial and ferrejlrial Globes, i 59 his diurnal parallel for every hour and mi- nute of the day, and fo alfo upon every day in the year. 391. Nothing can be eafier or more in- telligible than this method of improving the mind by reprefenting to the eyes the diftance from our own zenith to the zenith of every fpot of land and fea, within the tropics j when at every lingle obfervation we have it alfo in our power to note the bearing of each of thefe places upon our vifible hori- zon, which may be referred to, at all times, when the fun is not in that parallel. 392. Let us nov/ change the fcene from that of the great globe of day, to obferve the ftars by night, which will prefent to our view a copious field of geographical know- ledge ; many of which may be {Qzn at one and the fame inftant of time, when they are in the zenith of fo many different places upon the earth, and then immediately afterwards remove from that defignation, to give place for a great number of others. Of l6o Description and \5sz of the Of the celcftial correlpondents. 393. The knowledge of the celeftial cor- fefpondents difcover a new fyftem of aftro- homical geography, an obje<5t worthy of attention. The perfed; agreement between the celeflial and terreftrial fpheres being an afTemblage of both, and it may with very little trouble be attained, in making the ftudy of one a means to arrive at the other ^ the obje(5t of this correfpondence being the con- tinual variation between the parts of the eeleflial and terreftrial fpheres. 394. Geography alone being eaCer thari aftronomy, has generally a particular place in the education of young ftudents, who feldom leave their juvenile ftudies without gaining fome idea of the four quarters of the world, a flight notion of the fituation of places with refpcifl to each other, and a fketch of the principal empires s but gene- rally without any application to the ter- reftrial, and fcarce ever a comparifon of that and the celeftial globe, and without feeling a lively curiofity of knowing thefe necelTary and Cdejlial and Tcrrcjirial Globes. 1 6 1 and improving branches of the fcience of hiftory and its peculiar events. 395. To facilitate the ftudy of geography, it has always been neceflary to lay maps and charts before a pupil, which are generally feparate plans of different countries. But what idea do thefe afford of the vaft extent of the earth, of its fpherical form, or of the proportionable diftances, real bearings, &c. of the empires, kingdoms, and flates on the habitable part of our terreftrial globe ? 396. How much more intelligible and juft are the proportionable diffances of the fixed ftars, when compared with the natural diflances of the feveral places upon the earth, over which they dart their perpen- dicular rays j thereby conftituting this nev/ fyftem of agronomical geography, by ocular demonftration. They are faithful tedimonies of the vaft extent of the univerfe, and they declare the diftance, bearing, and iituation of all places upon the earth. 397. By thefe means, together with the affiftance of maps and charts, fuch a copious and clear idea of geography will be attained, and its natural principles fo firmly eftabliih- cd^^ as never to be eraled. M 39SvThc 1 62 Description and Vs-e of the 398. The confequences to be drawn fiorri thele principle?, are entirely in favour of the harmony betv/een the ccleftial and terreftrial fpheres. Of the paiTage or traniit of the firfl: point of aries ov^er the meridian. 399. This point determines the apparent daily motion of the heavens, and fixes the continual differences in the courfe of the fun and fears. ■ It is by the knowledge of that pecuhar point on the terreftrial equator, where its interfedtion with the celeflial ecliptic happens to fall at the time of a vernal equinox, it is that place upon the earth to which the fun is vertical at that timej and from the knowledge of this we obtain the time of its paflage over any meridian upon the globe, for every day of the year. 400. The conformity of the degrees of right afcenfion, with thofe of terreftrial lon- gitude, happen but upon one moment of the 24 hours, in a natural day, when the firft: point of aries is on the meridian of London, the firft degree of right afcenfion is on this meridian Celejllal and Terrcfirial Globes. 163 meridian alfo ; and the fignal to confirm this is, when a ftar of the fecond magnitude marked y near the extremity of the wing of Pegafus, is upon the meridian, at that inftant the equinodtial colure will be upon the meridian aUb, for this colure palles through the firfl point of aries and that (lar. 401. This is the moment when each of the 360 degrees of right afcenfion in the celeftial fphere, is perpendicular to every like degree of terreflrial longitude; at which time there is a perfed; parallelifin and per- pendicular correfpcndence of all the circles, points, and lines, in both fpheres. 402. To this we have paid a particular regard, in the conftrudion of our new globes, by numbering the degrees on the equator of the terreftrial globe, with an upper row of figures in the fame diredion, as thofe of ridit afcenfion are numbered upon the ceieliial globe. 403. If from that inftant of time, when the i'tar y of pegafus is upon the meridian, we conceive the ftars to be immoveable, and that we, together with the globe of the earth, are turned from weft to eaft upon the M 2 equatorial 164 Description and Use of the equatorial axis, we fliall perceive our own meridian, to pafs fucceffively under every de- gree and ftar on the celeflial equator. 404. And that the reader may thoroughly underftand what is meant by this uniformity in the two fpheres, let him imagine the celeftial globe to be delineated upon glafs or any other tranfparent matter, which £hall inveft or funound the terreftrial globe, but in fach a manner, that either may be turned about upon the poles of the world, whilll the other remains fixed; and fuppofe the firft point of aries, on the inverting globe, to be placed upon the firft point of aries on the terreftrial globe, (which point is in the meridian of London,) they will then reprefent that fituation of the heavens and the earth, we have been juft: deicribing, on that inftant, when the firft point of aries is upon the meridian ; and then every flar on the celeftial will lie upon every particular place of the terreftrial globe, to which it is a correfpondent ; each ftar will then have the degree of its right afcenfion directly upon the correfponding degree of terreftrial longitude ; their declination will alfo Celeftial and ^errejlrial Globes, io;^ alfo be the fame with the latitude of thofe places upon which they lie. 405. Now if the reader conceives the celeftial inverting globe to be fixed, and the terreftrial globe to be gradually turned from weft to eaft, he will readily underftand, as the meridian of London partes from one degree to another under the inverting fphere, that every rtar thereon becomes a corref- pondent to another place upon the earth \ and fo on until the earth has completed one diurnal revolution, or till all the rtars, by their apparent daily motion, have pafl*ed over every meridian of the terrertrial globe. Hence arifes an immenfe and an amazins: variety in the harmony of both fpheres. 406. If the fun and a rtar tranlit the meridian on any particular day, the next day the rtar will precede the fun about 4 minutes j in two days the acceleration of the ftar with refped: to the fun will be about 8 minutes, in 4 days 16 minutes, in 8 days 32 minutes, and in fifteen days the apparent motion of the rtar will be accelerated one hour, whilrt the fun, with refpcift to the rtar, will feem to be retarded one hour; in one nx)nth the ftar will be two hours before the i66 Description and Use of the fun, in three months fix hours, in fix months twelve hours, and in one year twenty-four hours. 407. So that a year after the fun and fi:ar have crofied the meridian together, they will meet again nearly at the fame time i but the ftar inftead of feeming to make 365 revo- lutions will have made 366, one more than the earth to the fun in a year. 408. The right afcenfion of the firft point of aries, is the complement of the fun's right afcenfion to 360 degrees of the equator, or to the 24 hours of a natural day : this is the point from which the right afcenfion of the fun, fi:ars, and planets is always reckoned. 409. The reader will pleafe to obferve, that in fpring and fummer, the firft degree df right afcenfion, which is the firfi: point of aries, comes to the meridian with us be- fore noon 5 there are no fl:ars then vifible in the night, but thofe which follov/ the firfi: point of libra j that is to fay, thofe ftars which have more than 1 80 degrees of right afcenfion : in autumn and winter thofe ftars are vifible in the night, which follow the firft point of aries, having lefs than 1 80 de- grees of right afcenfion. 410, Ob^ Cekjlial and Terrejlrial GloB-ES. i 67 410. Obfeive alfo, that the Interval be- tween the piflage of the firft point of aries over the meridian of any place, and that of the firft point of libra over the fame meri- dian, is not 1 2 complete hours, but only 1 1 hours 58 minutes, to which attention mud be paid, leaft thefc two minutes fliould be niiftaken. 41 1. By the paifage of the flars over the meridian, we are taught the knowledge of thofe degrees of the equator, which are then riiing and fetting ; for that degree, which is fetting precedes that on the meri- dian 90 degrees, or iix hours i and 180 de- grees or twelve hours that which is rifing ; and that degree of the equator, which is oa the meridian under the elevated pole, is 180 degrees diftant from that point of it which \% pafling the meridian. M A. Problem i68 Description ajid Use of thc Problem XLVII. To find the time of the right afcen- fion of the firft point of aries upon any meridian. 412. We have already fhewn by an eafy calculus, how to find the times of equinox to any meridian, but we have not yet fhewn their application to the right afcenfion of the firft point of aries. 413. The diurnal difi^erence of right af- cenfion, at the time of a vernal equinox, is 3 min. 38 fee. which we have formed into a table, entitled, 'The horary difference in the Motion of the firfi point of aries at the time of a 'vernal equinox ; to which is annexed, a table of the difference of the paffage of the frfi point of aries o'ver the meridian for every day in the year. The ufe of the tables of right afcenfion. 414. Having found the time of any ver- nal equinox, and transferred it from the fixed Celcjlial mid Terrejirial Globes. 169 fixed to your own meridian by the addition of your meridian diftance. Take out of the table of horary dif- ferences, the motion anfwering to the hours and minutes of the time of the vernal equi- nox, and their fum will be the time of the palfage of the firft point of aries over that meridian ; the day on which, but before the equinodial interfedion happens. Thus, 415. A. D. 1769, the vernal equinox falls on March 19th, 19 h. ^y min. min. fee. hours 19 2 5^ min. 37 o 6 Rieht afcenfion of Y G , up- 7 o on the equinodial day J^ 59 paft noon. 416. A. D. 1770, the fun will enter aries March 20, i h. 26 min. min. fee. hours 109 min. 26 04 Right afcenfion of Y on? «. the equinoftial day, at j ^ ^ 3 pa^ noon. 417- A, 170 Description and Use of the 417. A. D. 1 77 1, the vernal equinox falla on March 20, 7 h. 15 min. min. fee. houx-s 714 min. 15 o 2 Right afcenfion of T O on the 7 ^ n equinoxial day, at J ^ ^^ noon. 418. A, D. 1772, the fun will enter aries, March 19, 13 h. 4 min. min. fee. hours 13 I 58 min. 40 I I 59 419. The right afcenfion of the firft point of aries, thus found for the day on which the equinox happens, holds good for the whole year, and is to be added to the dif- ference of the paffage of the firfl point of aries over the meridian found againfl the day of the month ; and their fum will be the time of day when the firft point of aries will pafs the meridian. 420. Obferve when the equinox falls on the 19th day of March in a common year, to feek the day of the month in the right hand column of the table > and when it falls Cckjlial and Terrejlrial Globes. 171/ falls upon the 20th day of March, feek the day of the month in the left hand column, over which in either cafe, *and under the name of the month> you ~ have the proper difference of right afcenfion to be added to that found above for the day of the equinox. 421. In billextile years, feek the day of the mom-h in the left hand column, to the end of February, and for the intercalary day or 29111 of February, take out the dif- ference of rijiht afcenfion anfwerins: to the firft of March, after which to the year's end feek the day of the month in the right hand column. 422. Having thus found the right af^ cenfion of the firft point of aries for any day in the year, add thereto 1 1 h. 58 min. and you. obtain, the time of the right afcenfion of die lirft point of libra. Example ]^^ Description and Use of the-^ Example I. ,;, 423. A. D. 1769, equinox March 19. h. min. (tc. Jan. 25, 3 23 24 Right afcenfion Y G, 3 26 23 Nov. 14, 8 36 31 + 259 Right afcenfion To, 8 39 30 Example II. A. D. 1770, equinox March 20. h. min. (tc. Feb. 25, I 24 52 -I- o 13 Right afcenfion TO, i 25 5 Oa, 18, 10 26 6 -f- o 13 Right afcenfion Y o, 10 26 19 Example Cekftid and 'terrejlrlal Globes, i y^ Example III. A. D, 1 771, equinox March 20. h. min. fee. Jan, 12, 4 22 46 4-16 Right afcenfion TO, 4 23 52 ■ ^— » Decern. 16, 6 22 58 + I 6 Right afcenfion TO, 6 24 4 Example IV. A. D. 1772, equinox March 19. Biffextile year. h. min. fee. Feb. 28, I 13 ^^ " ^ J 59 Right afcenfion TO, i 15 34 The intercalary day, Feb. 29, i 9 ^o "^ I 59 Right afcenfion T G, II 49 March 1,1 6 7 H- I 59 Right afcenfion Y 0, Auguft28, 13 28 17 Right afcenfion Y o, 13 30 16 Thefc «Vy4 Description- and Use of the Thefe four examples are- quite fufficient, if the reader compares them with the tables and precepts. "■''^^ ■ ■ In the 42d and 43d problems, we have Ihewn how to find the hour that any known ilar comes to the meridian; and alfo to 6nd the time of the year any ftar paffes the meridian at any hour propofed, art. 317, 318. but in that place we were not pre- pared to apply the right afcenfion of the firft point of aries, fo properly for an obfer- vation of the ftars, as by the following Problem XL VIII. To find the time of the right afcen- fion of any ftar^ upon any par- ticular meridian, on ' any day in the year. 424. Firft find the time of the right afcenfion of the firft point of arles, art. 412, by problem 47, agreeable to your own meridian. Then apply to the celeftial globe, and bring the given ftar under the graduated fide Celeflial and 'terrcfirial Globes. 175 fide of the ftrong brafs meridian, which will cut its right afcenfion, or rather its diftance in time or degrees, upon the equinodial ^ add this quantity expredcd in time to the right afcenfion of the fir ft point of arics, and you will obtain the time of the paiTage of that ftar over the meridian very near the truth. Thus, The ftar marked y in the head of draco, will have 268 degrees, or 17 h. 52 min. art. 372. of right afcenfion or diftance from the firft point of aries, which added to the right afcenfion of that point for the 13th day of July, A. D. 1772, gives the true time of its right afcenfion that evening, at 10 h, 12 min. this ftar will be over the heads of the inhabitants of London at that time, its declination being 51 deg. 32 min. equal to the latitude of this capital city. Note, In this method of working, when the hours exceed 24, dedutll: 24 hours therefrom, and you obtain the true time fought. Problem ^7^ Description a fid Use of the Problem XLIX. To reftify the cdeftial globe for any time in the evening of any day in the year, by the knowledge of the time when the iirft point of aries {hall pafs the meridian that day. 425. As the degrees and hours upon the equinodtial line on our new globes, are numbered from the firft point of aries. Firft find the right afcenlion of that point by problem 47, art. 4 1 2, for the given day, and redify the globe to your latitude, art.i 1 6, then bring the firft point of aries upon the globe, under the graduated fide of the ftrong brafs meridian, and fet the horary index to the hour and minute of the pafifage of aries o, firft found, turn the globe until the given hour is under the horary index, and place it due north and fouth by the mariners com- pafs, attending to the variation of the needle, and you will have a perfed: reprefentation of the ftarry firmament, not only for that inftant. Cekjlial and ^errejlrial Globes. Ajf inftant, but as long as you pleafe to apply yourfelf to the knowledge of the ftars that Evening, by only moving the globe to any other minute under the horary index as the time advances. 426. Thus on the 25Ch of February, A. D. 1770, about 26 minutes after V m the evening, the Aar called al-debaran, or the bull's eye, will be upon the meridian of London, or places adjacent; about VI o'clock that evening, Orion will begin to pafs the meridian, and prefent a glorious view to the eyes of the obferver, there being fo many eminent ftars in that conftcUation, then fuc- ceflively palling over the meridian until \ paft VII ; all the flars in auriga, or the charioteer, will be pafling the meridian at the fame time -, after which canis major wiU fucceed with fyrius, the dog-ftar, at the fide ©f his jaw ; then canis minor and geminr or the tv/ins will follow, and fo on for the remainder of the night. This appearance may be obferved feveral months, but at dif- ferent hours in the night, which may be found by this problem. 427. Alfoon the 8th of May in the fame? year, the firft point of aries will pafs ouf N meridian 178 Description and Use of the meridian at 20 h. 58 min. 29 Tec. but if we reckon the hours from midnight, at 58 minutes paft VIII in the morning, at which time no ftars can be feen ; therefore we muft have recourfe to the right afcenfion of the firft point of libra, which is thus obtained, h. min. fee. To the right afcenfion of the firft 1 o • - f ■ > 20 58 20 point of aries 3 add II 58 o 32 56 29 When the hours exceed 24, fub- ) ftraa therefrom J 24 o o The rleht afcenfion of the firft") ,. . , • ° i- i-L A T^ I 8 t;6 2Q in the point of hbra, A. D. 1770, > ^ > . May 8th, at 3 evening. 428. Now in the precept to this problem, read libra inftead of the word aries, and the rule will hold good in this as well as in the firft cafe. Therefore, Bring the firft point of libra to the gra- duated fide of the ftrong brafs meridian, and fet the horary index to 56 minutes paft VIII in the evening, turn the globe until the horary index points to 10 minutes paft X o'clock, and you will find the ftar called Spica virginis, being that in the ear of corn file Celejiial and 'Terr eft rial G l o e f s . 179 ilie holds in her hand, a ftar of the firft magnitude marked a, upon the meridian at that time. If you then look at the firma- ment, you will fee the conftellations cancer, leo minor, leo major, the great bear, with the head and wings of virgo, on the weftern fide of the meridian j and on the eaftern fide thereof, the ballance, fcorpio, bootes, Her- cules, &c. fuccefiively following the fir ft point of libra in their pafiage over the meridian* The correfpondency of the fixed ftars. 429. Before we attempt an obfervation of this kind, a fignal or warning ftar muft be firft obtained ; that is, fuch a ftar is to be fought, as ftiall have the fame or nearly the fame quantity, either in degrees or time of right afcenfion, reckoned from the firft |X)int of aries, as the place, over which any other ftar ftiall then happen to be a corrcfpondcnt, ihall have of longitude, reckoned eaftward of London. 430. It has been fliewn that declination in the celeftial and latitude on the terreftrial N 2 globe, i8o Description and Use of the globe, mean one and the fame thing, both being meafured by their diftance from the equator ; confequently, if the declination of any ftar is equal to the latitude of any place, that ftar, by a line conceived to be drawn from it to the center of the earth, will de- fcribe the parallel of that place j whence it becomes a correfpondent, not only to that particular place, but alfo to all thofe places which lie in the fame parallel of latitude, by paffing perpendicularly over the heads of them all once every 24 hours. But as a preparation to this proportion, we muft firft fhew, by the following problems, how to find thofe places to which any ftar is a cor- refpondent, and thofe ftars which are corref- pondents to any place. Problem L. To find all thofe places to which any ftar is a correfpondent. 431. Firft find the declination of the ftar on the celeftial globe by problem V, art. ^^. and remember whether it be north or fouth; count the fame number of degrees upon the Cikjlial and T^errefirial Globes. i8i fhe ftrong brafs meridian of the terreftrial globe the fame way from the equator, and note the place by holding the edge of a card thereto ; turn the globe from eaft to weft, and all thofe places which pafs under that point, will be correfpondents to that ftar, becaufe they will be in the line palTing from the center of the earth throucrh the very place upon its furface, to which the ftar is at that time vertical. Thus, The declination of the ftar marked y^ \w the head of draco, is 51 deg. 32 min. equal to the latitude of London ; therefore this brilliant ftar of the fecond magnitude may be called the ftar of this metropolis, without being deprived of its own name j it may like- wife take the name of any other place in the parallel of London. 432. The reverfe of this problem being to find all the ftars which are correfpondents to any place, is fo eafy as to require no far- ther explication, than that of applying firft to the terreftrial globe. The apparent diurnal motion of one ftar only, will fucceflively ftiew its perpendicu-. larity to various countries, as will appear by A general 182 Description fi?2d Use of the A general defcription of the paffage of the ftar marked ? in the head of the conftellation draco^ over the parallel of London. 433. This eminent ftar traces the parallel of London, and is a ftar of perpetual appa- rition to the inhabitants of the Britannic Ifles i it comes upon the meridian of London with the 268th degree of right afcenfion, and is at that time diredly perpendicular to or over the heads of the people in this city, two minutes of an hour after its warning ftar marked k in the milky way, has paffed the meridian. 434. Note, This ftar marked k is the fouthermoft of a group of live ftars, fituated between the fliouldcr of ferpentarius and Sobicftci's fliield, which in the firmament appear in the form of a Roman V, as may be feen upon the globe. 435. The declination of our correfpon- dent ftar y in the head of draco, is 5 1 deg. 32 min. equal to the latitude of London; with which apply to the t&rreftrial globe, and Celefttal and Terrejirial Globes, i %'^ and bring London to the graduated fide of the ftrong brals meridian, and fet the edge of a card thereto, holding it to the brafs meridian with your right hand, while you gradually turn the globe from well: to eaft with the other hand, and that point of the card which is upon the globe will then re- prefent the interfcdion of that line upon the furface of the earth, which we have fup- pofed to pafs from the center of the earth to the ftar ; and as this point, though at reft, palTes over the parallel of London upon the globe, fo does the central ray, proceeding from the ftar, really pafs over every point of land, and fea, upon that part of the earth which is circumfcribed by the parallel of London. 436. Thus you will fee the ftar marked 7, in the head of draco, pafs from London over the road to Briftol, and dart his perpendi- cular rays upon that city j then croffing the fea, it reaches Ireland between Kinfale and Cork, and leaving that kingdom, will fhine over the Atlantic Ocean, until he is perpen- dicular to the north cape of Newfoundland ^ whence it will be vertical to Efkimos, and pafs between lake Achoua and the north- N 4 cru 184 Description and Use of the ern coall of the gulph of St. Lawrence, then he will crofs St. James's Bay, Kriftino, &;c. and pafs weftward over a vaft fpace of land but little known to the Europeans ; thence will leave the weftern coall of North America, to fhine upon the northern part of the Pacific Ocean, until he is perpen- dicular to feveral iflands, one of which is called St. Abraham 5 it croiles the fouthern land of Kamfchatfkia, and the iiland San- galien ; thence it becomes perpendicular to the continent, neai' Tclmen on the eaft lidc of Mongales in Chinefe Tartary, and fo pro- ceeds to caft its perpendicular rays over a vafl: country in Afia, being fometimes a zenith point to the Chinefe, at other times to the Ruffian Tartars, and paffing over Bielgorod, becomes vertical to Mufcovy, Po- land, Germany, and Zeland, and fo crolTes the fea again to return to its perpendicu- larity over the city of London : all which is performed by the earth's diurnal motion in fo fliort a time as twenty-three hours and ^fty-fix minutes. 437. When a beginner has been thus exercifed with the general palfage of two or three principal flars over their correfpondent parallels Celeftial a?2d TerreJInal Globes. 185 •parallels on different parts of the earth, his ideas will be lb greatly improved, that maps ^nd charts may then be laid before him with propriety, in order to confirm him in the knowledge of the particular parts of thofe very parallels of which he has aheady .attained a general idea upon the globe. Problem LI. To find a fignal or warning ftar, that {hall be upon or near the meridian of an obferver, at the time any known ftar is perpen- dicular to any place on its cor^ refponding parallel. 438. Bring the given place to the gra- •duated fide of the flrong brafs meridian on the terreftrial globe, and it will cut the de- grees of its longitude, reckoned eaftward from London, upon the upper row of figures ,over the equator 3 then Apply to the celeftial globe, and fet the given ftar under the graduated fide of the ftrong i86 Description a72d Use of the ftrong brafs meridian, which will cut the de- gree of its right afcenfion on the equinodlial. If the fituation of the obferver is weft of the given place, fubftradt the ter- rcftrial longitude from the right afcenfion of the ftar j if eail, add the longitude, and move the celeftial globe, till the fum or reiidue thereof is under the graduated fide of the ftrong brafs meridian, and then that fame fide will be directly over thofe ftars which are upon, or have juft pafled, or are not quite come up to the obferver's meridian, at the moment the given ftar is vertical to the place propofedi either of which will corredly anfwer the prefent purpofe, and become the fignal or warning ftar , that upon its arrival on the meridian will declare the given ftar to be vertical to the place afligned. Thus let the obferver be in or near Lon-^ don, and the bright ftar in lyra or the harp of the firft magnitude be given, it is called vega and marked cc • this ftar is a corref- pondent to the fouth weft cape of the ifland of Sardinia in the Mediterranean. 439. The longitude of this cape from ^London is 9 degrees, and the right afcenfion of the ftar vega is 277 degrees, as London is Cekfiial and 'lerrefirid Globes. 187 is weft of Sardinia; 9 degrees fubftraded from 277 degrees, leaves 268 degrees of right afcenfion, to which the celeftial globe being fet, the graduated fide of the ftrong brafs meridian will be found diredly over the ftar y in draco, and alfo over a ftar of the fourth magnitude in one of the heads of Cerberus. Thefe are eminent fignals, and both upon the meridian, when at the fame time the ftar marked 0, in the knee of Hercules, will have pafted the meridian about two minutes of an hour, and the ftar marked P, of the fourth magnitude in the milky way, will want about two minutes of an hour of coming to it. 440. Hence when the ftar marked 7, in the head of draco, lends forth its perpendi- cular rays upon the city of London, the ftar vega in lyra will alfo be perpendicular to the S W cape of the ifland of Sardinia. At which time an obferver at London will be fenfiblc of the diftance between the zeniths of the two places, and may note the bearing of Sardinia from London upon his fenfible horizon, to which he may refer at any time in the day. An obferver at Sardinia may note the fame with refped to the diftance and bearing of London from him. 441. To iH8 Description and Use of the 441. To excite ftudents who have an afpiring emulation to improve themfelves in this extenfive fcience of geography and aftro- nomy, the principal requifites whereby they may acquire univerfal knowledge, we fhali proceed to illuftrate this fyftem of the natural agreement between the celeftial and ter- reflrial fpheres, by a few interefting ex- amples. Example I. 442. When the flar marked y in the head of draco, is perpendicular to the city of London, the twelve fol- lowing ftars may be feen from thence at the fame time, when they will alfo be perpendicular to as many places upon the earth. 443. The fignal or warning ftar is y in the head of draco, which comes upon the meridian with the 268th degree of right afcenfion j it will be vertical to the city of London two minutes of time, after the ftar marked k, in the milky way, near the equi- noXj Ceiefiial and Terrejirial Globes. 189 nox, has pafled the meridian, at which time the twelve following ftars will be vertical to the places they ftand againft. Weft of London. Rig. 26?i 267! 261 198 191 Knee of Hercules Wrift of Hercules agus.Scr- 7 irius \ Rasallia penta; Spica Virgin is Deneb Alafad, ) Lyon's tail \ Alioth, I ft in tail 7 Great Bear C Decl. and Lat. 37 30t } W. Lou Carthagena, Old Spain Frontiers of Mo- rocco and Tar- gua Kingdom Kom- bergrada, Africa Peru, South-America' Chapa in Mexico IfleBelchier,Hud- fons Bay 7 70 03 77 Eaft of London. Afc. ' 277 Viga, in Lyra 295 Atair, Eagle's neck'a 290 Swan's beak,Al- bireo 308 Deneb, Swan's / rump ^ 343 jSheat, in Pegafus 309 Swan's So. Wing Decl. and Lat. 38^ 27 S. W. Cape, Iflc of Sardinia Frontiers of Be- nin and Nigriti, Africa Mid. Levata in Tagua, Africa 44| Palmyra Middle of Mogul's \ Empire Frontiers of Tur^ key in Afia, am Dcfart Arabia 449" Eafl Loo. [ ^ 9 J 17 \ 22 40 s 75 \ 41 The 190 DEScRrpTioN and Use of the 444. The ule of a warning ftar is t<> point out the true time of the phenomenon, which is to be firft nearly found by obtain- ing the time of the right afcenfion of that ftar for the evening, on which the obferva- tion is intended to be made. This table of correfpondents was formed as follows, 445. The right afcenfion and declination of the ftars was found in round numbers upon the celeftial globe, and written in two columns, inclofing the names of the ftars ; the columns for the names of the corref- pondent places being left blank for their infertion afterwards. 446. Next, as the longitude on our new terreftrial globes Is numbered both ways from the meridian of London, whatever the right afcenfion of the fignal ftar may happen to be, that point of the celeftial fphere is likewife conlidered to be upon the meridian of London. Therefore, 447. To gain the longitude in the laft column of the table, if the given ftars were eaft of the fignal, the right afcenfion of the warning ftar was fubftraded from the right afcenfion of the given ftar. But Celejlial and I'errejirial Globes. 191 But the weft longitude was obtained by fubftrad;ing the right afceniion of the given ftars from that of the iignal. 448. The reveiTe of this example is to find, what ftars will be perpendicular to any place upon the earth, a warning ftar being known, that fhall be upon the meridian of an obferver, when the ftars to be fought ftiall be vertical to the places affigned, which the reader will eafily perform from what has been already faid. 449. When a ftar is known to be per- pendicular to any afligned place, its corref- pondence to that terreftriai point may be equally affirmed to all thofe who can fee it at that inftant from any part of the earth, or fea, they may then happen to be upon. 450. If an obferver in Palmyra, another m the middle of the Mogul's empire, a third at Levata in Africa, and a fourth at Chapa in Mexico, Ihould look at the ftar 7, in the head of draco, the moment k is in the zenith of London, they will fee its correfpondence to that metropolis at one and the fame inftant of time ^ their hour only will be different according to the difference of meridians, as thofe places arc fituatcd either eaft or weft from London. 451. Ths 192 Description and Use of the 451. The fignal or warning ftar to each of thefc places, is the perpendicularity of that ftar exprelTed in the preceding catalogue of twelve ftars. 452. From the obfervation under either of thefe ftars in the catalogue, may be feen the other twelve flars, when they are fhining over the heads of the inhabitants of all the other countries therein named. 453. This conftitiites the fyftem of aftro- nomical geography before fpoken of. It affords us a real affiftance from the heavens, whereby we not only fee the marvellous diftances of a multitude of celeftial bodies, eompofing that part of the univerfe which we are permitted to behold 3 but it alfo enables us to comprehend the diftances and bearings of the moft remote countries from that point of the earth upon which we iland. Example II. 454. When the bright ftar marked (3, in the head of caftor, is upon the meridian of London with the 1 1 oth degree of right afcenfion, the twelve following correfpon- dents will be vertical to the places annexed. Weftward» Celejiial ahdT^errejlrial Globes. 193 Weft ward. Kigt. Dec. Lon. Ale. and Lat. W. '4 Girdle of Andro- ^ meda, Mi/.ar 5 /? 34 Kichuans, Louifiana 96 18 27 42 Caffiopea's thigh Almaak, foot of ) Andromeda \ Shoulder of Perfcus y y 59 4' 52 P.Walesfort, Hud- ) fons Bay J Twightees, S, of 7 Lake Michigan J Eflcimos between \ L. Otter andL. / 92 68 Pitctibi, Nor?hr America 3 47 AlgcnibjPerfeus'sfide et 49 Cape RiHier, G. ? St. Lawrence 5 63 76 Rigel, Orion's foot !S 9 Sea and Coall: of I Olinda f 34 Eaftvvard. Rigt. Dec. E. Afc. . and Lat. Lon. 132 Great Bear's foot K 47 Middle of Hungary 22 139 Hydra's heart A S Kingdom Mafiey, i Africa 5 29 143 Corner of the ^ Lyon's mouth \ m 25 NahafTa, in Egypt 33 149 Regulus, Lyon's S heart \ Third in the Sq. ~i Great Bear 5 A 13 Abvflinia, Africa 39 .76 7 55 OiViakis,S.W.part 1 of Siberia \ 66 192 M. Wing of Virgo, 7 Vindematrix ', 12 e 1 Sea 2° E. of Pon-? dicherry ^ 82 Tbefe ftars are vifible in the months of Janiiarv., February, and March. O Example 194 Description and Use of the Example III. 455. When the bright ftar marked a in the ear of corn, which the virgin holds in her hand, called fpica virginis, is upon the meridian of London with 198 degrees of right afcenfion, the following twelve flats will be vertical to the feveral places in the following table. Weftward. Rigt. Afc. 90 113 139 149 175 191 Decl. and Lat. Firft flar In the foot 7 of Caftor 5 Head of Pollux Hydra's heart Regulus, Lyon's 7 heart > Lyon's tail, Alafad Firft in tail Great 1 Bear, Alioth J hUzI Iflesof Tres Ma-T rias. New Spain \ } jW. Lon 7t 16 57 Sea near C.Efcon- did. Florid Yamari, a Branch") of the Amaze- > rian River J Sea 1 2'' E. of the } Antilles Near Bonavifta, C. Verd Ides Weftern Ifles of Scotland I 108 85 61 49 7 Eaflward. Cekjiial and Terrejirial Globes, i 9 ^ Eaftward. Rig'. Afc. 212 243 N. Hand of Bootes Scorpion's heart 277 290 ^94 Decl. and Lat. 52 249 In the Back of I Hercule* \ Vega, in Lyra Albiero.the Swan's ha beak S Atair, in the Eagle ,^ S. of Berlin, in Prufia S. Coaflof Mada- gafcar S.EaftoftheCaf- pian Sea Coten, in Tartary ToudJang, in Thi- bet Major Eallern Sea, or Coaft of Mal- locca K. Lon, •4 45 S' 79 9Z 96 This phenomenon may be (ttn in the months of April, May, and June. Example IV. 456. When the 289th degree of right afcenfion is upon the meridian of London, fignified by one minute of an hour after the ftar marked ^ in the fouthern wing of the eagle has pafled the meridian, then the twelve following places will have the annex- ed ftars in their zenith." O 2 Weiiward^ 196 Description and Use of the Weftvvard. Rigt. Ale. 2c6 219 226 236 240 267 Dec. and Lat. The ftar in the leg \ « of Bootes J Southern Scale of \ Libra \ Northern Scale of ^ /2 Libra A ftar in Scorpio Hand of Serpentarius'jN iKnee of Hercules 15 Sea 2° S. Cape } Corrente, Cuba } Collao, in Peru Amazonia, America Paragua, America N. W. part of Brazil N. of St. Michael, in the Azores LOD. 83 70 63 53 49 22 Eaftward. Rigt. Afc. 321 Side of Cepheus 328 Shoulder of Aquarius 331 Firft in the head"? of Cepheus \ 343 'Markab in Pegafus 359 360 Andromeda's head A ftar in Pegafus Dec. and Lat. 70 Fro. Sea near Ifle 7 WarduSjLaponia \ Between Sio and "J . Ampaia, Zan- J* guebar J Ruffia, 4° E. of? Mofcow J Sea Coaft, in Per- ? fian Gulph \ TalajMogul's Empire Sea near Ifle Lak- } dinas \ E. LonJ Thefe ftars may be obferved in the months of July, Auguft, and September. Example Cele/iial and Terrejlrial Globes, i 97 Example V. 457. When the ftar marked 9 in the iide of the whale is upon the meridian of London, with 1 8 degrees of right afcenfion, the twelve following ftars will be in the zenith of the annexed places. Weft ward. Rigt. Ale. 290 294 308 324 331 341 The Swan's beak Firfl in the Swan's wing Deneb, in the Swan's rump Side of Cepheus Head of Cepheus Fomahaut, mouth of Piices Notius } Dec. and Lat. /S }i } iSjGulphMexicOjjo S. Mififipi 'Lake Michigan, ) ■^M Canada \ 'New England 70 Cumberland near 1 I Baffin's Bay f 56N.iJea, E. ofLa- ) t brador \ 30 Middle of the At I lantic Ocean W. Lon, 84 70 57 47 37 03 Eaftwar4# 198 Description and Use of the Eaftward. Afc. 42 43 53 96 112 Almaak, foot of Andromeda Shoulder of Perfeus iVienkar, Whale's mouth The Pleadies North foot of Pollux Procyon, little Dog Dec. I I E. I and Lon. Lat, ^41 jSea coaft of Sardinia 9 y ^2 Brifac Luthania 24 si, 2 'Bake Bake, Africa zc [Frontiers of Egypt 7 5 1 and Nubia \ 35 ^ Golconda, Afia 78 > 16 at, 6Scai°N.W.Achem7 ! 1 Summatra > j °^ The flars in this example may be feen in the months of Odober, November, and December. Problem LII. The phenomena of the harveft moon. 458. When the moon is at or near the full about the time of an autumnal equinox, fhe rifes nearly at the fame hour for feveral nights together, which phenomenon is call- ed the harveji moon. To Celejlial and Terrefirial Globes. 199 To account for this upon the celeftial globe, fet the artificial fun upon the firft point of libra, where the fun muft necef- fai'ily be at every autumnal equinox, and place the artificial moon upon the firft point of aries, where fhe muft be if a full moon fhould happen at that time. 459. Redtify the globe to the pofition of a right fphere, art. 234. which anfwers to the inhabitants of the equator; bring the center of the artificial fun to the weftern edge of the broad-paper circle, and the horary index in this cafe being the graduated edge of the ftrong brafs meridian, will cut the time of the fun's fetting, and the moon's rifing ; hence it is obvious the moon will rife when the fun fets, which will be at VI o'clock, becaufc they are both fuppofed to be in the celeftial equator, but in oppofite figns. Therefore on that day the fame phe- nomenon will happen in all latitudes be- tween the equator and either pole. 460. But as the moon's motion in her orbit, which we ftiall at prefent confider as coincident with the ecliptic, is about 1 3 deg. 10 min. every day, which retards her diur- nal motion about 51 min. 56 fee. of time O 4 with 200 Description and Use of the with refpedt to the firft point of aries, this daily difference as it relates to the fun is generally reckoned at 48 minutes of time, or two minutes for every hour. 4.6 1 . Let us now enquire upon the globe, what time the moon will rife the next night after the autumnal equinox, at which time the fun will have advanced one degree in libra, and the moon 1 3 deg. 1 o min. in aries, which is 1 2 degrees more than the fun has done in the fame time, therefore place the center of the artificial fun upon the firfl de- gree of libra, and the artificial moon on 1 3 deg. 10 min. of aries, the globe being rectified as before to the polition of a right fphere, bring the artificial fun under the graduated fide of the flrong brafs meridian, and fet the horary index to XII, turn the slobe until the artificial fun coincides with the weilern fide of the broad-paper circle, the horary index will fliew he fets that evening at VI o'clock, and the globe being turned till the artificial moon coincides with the caftern fide of the broad-paper circle, the horary index will fhew the moon's riling that evening to be about 48 minutes paft yi o'clock, with 5 degrees of amplitude northerly, Celejtial and Terrejirial Globes. 201 northerly, as llie is now entered into the northern half of the ecliptic. 462. Now elevate the north pole of the globe to the latitude of London, every other redification remaining the fame, and bring the artificial moon to the eaft fide of the horizon, and the horary index will point to 20 minutes paft VI, her time of rifing and her amplitude at that time will be about 8 degrees, three degrees more than at the equa- tor the fame evening. 463. If we thus invcftigate the time of the moon's rifing for two or three nights to- gether before and after the autumnal full moon, it will be found nearly the fame. 464. The reafon is that the full moons which happen at this time of the year, are afcending from the fouthern into the north- ern figns of the zodiac, whence the moon defcribes a parallel to the equator ever)- night more northerly, which increafes her rifing amplitudes confiderably, and more fo as the latitude is greater, as in the prefent ejcample ; hence it is plain the nearer any celeftial objed: is to either pole, the fooncr it ^fcends the horizon. 465. Every 202 Description and Use of the 465. Every thing remaining as before if we elevate the north pole of the globe to tt\ degrees, which is the latitude of the northern polar circle, and bring the artificial moon to the eaft fide of the horizon, fhe will be found to rife about the fame time that the fun fets the evening after the autum- nal full moon, which is about VI o'clock, at which time and place her amplitude will be about 13 degrees. 466. In this polition of the globe if the artificial moon be removed 13 deg. 10 min. upon the ecliptic, which is her mean motion therein for one day, and fo on for fourteen nights together, fhe will be feen to rife within the fpace of one hour during that time, which will be clear on obferving that half the ecliptic rifes at once. 467. It is remarkable that when the moon varies left in the time of her rifing, the diurnal differences are greateft at the times of her fetting. What has been faid with refpedl to north latitudes is equally applicable to fouth latitudes. 468. In like manner the new moons in fpring rife nearly at the fame hour for feveral Celeftial and Terrejirial Globes. 203 feveral nights fuccefTively, while the full moons rife later by a greater difference than at any other time of the year, becaufe at this time of the year the new moons are in the afcending, and the full moons in the defend- ing ligns. 469. This phenomenon varies in different years, the moon's orbit being inclined to the ecliptic about 5 degrees, and the line of nodes continually moving retrograde, the inclination of her orbit to the equator will be greater fometimes than at others, which prevents her haffening to the northward or dcfcending fouthward in each revolution with equal pace. Problem LIII. To find the time of the year ia which a ftar rifes or fets cofmi- cally or achronically. 470. The cofmical riling and fetting of a ftar, is when a ftar rifes with the fun, or fets at the time the fun is rifing. Elevate 204 Description and Use of the Elevate the pole of the celeftial globe to the latitude of the place, and bring the ftar to the eaftern edge of the broad-paper circle, and obferve what degree of the ecliptic rifes with it, which feek in the kalendar on the broad-paper circle, againft which is the day of the month when that ftar rifes cofmically. Turn the globe till the ftar coincides with the weftern edge of the horizon, and that degree of the ecliptic which is cut by the eaftern fide, gives the day of the month when the ftar fets cofmically ^ fo likewife againft the degree which fets with the ftar you have the day of the month of its acro- nical fetting, and if you bring it to the eaftern fide of the horizon, that degree of the ecliptic then cut by the weftern fide of the broad-paper circle fought in the kal- lendar, will ftiew the day of the month when the ftar rifes achronically. Problem Celeflwl end T^errefirial Globes, 205 Problem LIV. To find the time of the heliacal rifing and fetting of a ftar. 471. Elevate the pole of the celeflial globe to the latitude of the place, bring the ftar to the eaftern fide of the bioad-papcr circle, fix the quadrant of altitude to the zenith, and apply its graduated edge to the weftern fide in fuch a manner that its I2tli degree above the horizon may cut the ecliptic, the point oppofite to this will be I 2 degrees below the broad-paper circle on the ealtern fide, and is the fun's place iu the ecliptic at the time a fi:ar of the firil magnitude rifcs hcliacally, feek this point in the kalendar, or upon the ecliptic line on the globe, againll which you will find the day of the year when that ftar rifes hcliacally. . To find the heliacal fetting bring the ftar to the weftcrn fide of the horizon, and turn tiic quadrant of altitude on the eaftern fide till the 1 2th degree cuts the ecliptic, its op- pofite point is the fun's place, which fought cither upon the kalendar or ecliptic line. gives 2o6 Description and Use of the gives the day of the year when the ftar fets heliacally. Stars of the firft magnitude, according to Ptolemy, rife or fet heliacally when they are 12 degrees diftant from the fun, that is when the ftar is riling the fun muft be de- prefled in the perpendicular below the hori- zon 12 degrees, that the ftar may be far enough from the fun's rays to be feen be- fore he rifes. Stars of the fecond magnitude require the fun's depreflion thirteen degrees, and thofe of the third magnitude fourteen de- grees, &c. The manazil al kamer of the Ara- bian aftronomerSj from Ulugh Beigh, pubHfhed at Oxford 1665. 472. The manazil al kamer of the Ara- bian aftronomers, are XXVIII, they are fo called, i. e. the maniions of the moon, becaufe they obferved the moon to be in or near one of thefe every night during her monthly courfe round the earth, they are thefe that follow, to v/hich upon the globe the Celejiial and Herrejlrial Globes. 207 the Arabian characters are affixed, but omitted here for the want of an Arabian type. I. At Sheratdn^ thefe are the jfirft and fe- cond ftars of aries, or the ftars in the rams horns, marked /S and y^ with I, (T , fig- nifying the firfl man (ion of the moon, which the reader will pleafe to remember once for all. II. Botein the ftars in the rams belly accord- ing to Ulugh Beigh, by Bayer and on our globe £ and /3 III. Al Thuraigay the pleiades. IV. Al Debardny the bull's eye. V. Al HelSa, the three flars in the head of orion. VI. Al Hejiahy the flar marked J in the left foot of poUux. VII. Al Dira, the two bright ftars, one in the head of caftor, the other in pollux, marked a and ,'S. VIII. A! SdS Description andUs^o/the VIII. Al Nethrah^ the nebulae or group of ftars in cancer, marked e called by the Greeks c, XVI. Al Zubana, that is libra, the northern fcale is called Zubdnah Al Shemali, and is the ftar marked /3, the fouthern fcale marked a, is called Zubdnah al Genubi, fhemali fignifies northern, and genubi fouthern, they are exadtly mifcalled on the Celejlial ajid T^errejirial Globes. 209 the common globes of modern coi^flruc- tion. XVII. AUlcliU thefe are the four flars in fcorpio marked v (i S' --. XVIII. Al Kalby the fcorpion s heart marked a more fully. Kalh Al Akrab^ the word AntareSy if it is not a corruption, has no fignification, and is therefore omitted. XIX. Al Shaulahy the fcorpion's tail, or the Earmarked A. The w ovd Lefath we have omitted, being another pronunciation of Lafah, the true name is Shaulah. XX. Al Naainiy thefe are eight ftars in fa- gittary, marked y ^ i A fx a- (?4; Ulugh Beigh makes them only three, i.e. y (T 4. XXI. Al Beldah, this is that part of the horfe in fagittary where there are no ftars drawn, and if there be any in that part of the heavens, it is thought they are only telefcopic ftars. XXI r. Sad Al Ddbib, three ftars in Capri- corn, marked ci (i v. P XXIII. S^d 21 o Description and Use af the XXIII. Sad Al Bida, the ftar marked y in the hand of aquarius. XXIV. Sad Al Sufidy the flars marked /2 and ^ in aquarius. XXV. Sad Al Achbigah, three ftars in a- quarius marked 7 ^ ^. XXVI. Al Pherg al Miihaddem, the ftars marked « and /3 in pegafus. XXVII. Al Pherg al Muaechir, thefe arc two ftars, one in the head of Andromeda, marked cT, the other in the wing of pe- gafus, marked y. XXVIII. Al Rijljd, the flar marked /S in the girdle of Andromeda. Thefe are a divifion of the heavens, dif- ferent from any thing the Greeks were acquainted with, and therefore was not bor- rowed from them. Problem Cdeftial and 'Herrejirial Globes. 211 Problem LV. To find a meridian line. 473 . Bring the fun's place In the ecliptic on the celeftlal globe, to the graduated fide of the ftrong brafs meridian,- and fet the ho- rary index to that XII. which is mod ele- vated ; turn the globe, till the ftar marked y in CafTiopea's hip, is under the graduated fide of the ftrong brafs meridian, with about 1 1 degrees of right afcenfion, at which time the polar ftar, in the extremity of the tail of the little bear, will be above the pole, and upon the meridian alfo. If you find in this application of the globe, that the horary index points to any hour of the day, when the globe is redlified to the latitude of your fituation, turn the globe again, till the ftar marked ?, called Alioth, being the firft in the tail of the great bear, is under the graduated lide of the ftrong brafs meridian, and then the polar ftar wfll likewife be upon the meridian, with about 191 degrees of right afcenfion, but under the north pole, and the horary Index will P 2 point 212 Description ami Use of the point out the time of the night when this phenomenon is to happen, before which you are to have the following apparatus properly prepared, that you may be ready to attend tlie obfervation, that is, to find your meridian line. Sufpend two plumb lines, and let their weights be imm.erfed in water, to prevent their vibrating, but in fuch a manner that the firing of one of them may be diredtly between the polar ftar and the firing of the other. After this adjuflment of the two firings, if they remain untouched till the next day at noon, a meridian line may be obtained at any window in the houfe which has a fouthern afpedl, by fufpcnding lines as above fi'om the ceiling, that next the window may be fixed, but the other fliould be moveable in a diredlion nearly eaft and wefl, the weights of thefe ought alfo to be immerfed in water ; then, if two perfons attend a little before noon on the next day, one of them at the two firfl plumb lines which were adjufled to the polar fiar, and the other at the two plumb lines in the houfe v/hich are then to be adjufted, each of them holding a flieet of white paper in ■ their Cekjlial and 'Terrejlrial Globes. 2ij their hands, to receive the fliadow of the two firings call thereon by the fun -, the iirft obferver is to give a fignal to the fecond of the inftant the two fliadows on his paper are united in one and the fame hnc, at which time the fun will be precifcly upon the meridian. The other oblcrver in the hoLifc is likewife to attend with dihsence» and as the fun is coming nearer and nearer to the meridian, he is conflantly to remove his moveable plumb line, and keep the Sha- dows of his two firings always united in one difi:in6l fliadow, that his obfervation may be compleat, when his afhftant gives the definitive fignal. 474. If this be repeated four or five times, a very accurate meridian hne mav be obtained, and may be drawn on the window, the floor, or a pavement, by their fhadow when united by the fun's rays, and the plumb hnes may be occafionally fulpen- ded from two fixed hooks, when you chufe to obferve the pafTage of the flars a-crofs the meridian. P 3 Problem 214 Description and Use of the Problem LVL Of the equation of time. 475. As time flows with great regula- rity, it is impoflible to meafure it accu- rately, and compare its feveral intervals wich each other, but by the motion of fome of the heavenly bodies, whofe pro- grefs is as uniform and regular as itfelf. Ancient aftronomers looked upon the fun to be fufficiently regular for this purpofej but by the accurate obfervations of later aftronomers, it is found that neither the days, nor even the hours, as meafured by the fun's apparent motion, are of an equal length on two accounts. - I ft, A natural or folar day of 24 hours, is that fpace of time the fun takes up in pafling from any particular meridian to the fame again, and one revolution of the earth, with refpedl to a fixed ftar, is performed in 23 hours, 56 minutes, 4fecondsi there- fore from the unequal progreftion of the earth through her ecliptical orbit, as fhe takes almoft eight days more to run through the Cdeftial and Herrejlrtal Globes. 215 the northern half of the ecliptic, than ^\z doe5 to pafs through the fouthcrn, is the reafon that the length of the day is not exactly equal to the time in which the earth performs its rotation about its axis. 2dly, From the obliquity of the ecliptic to the equator, on which lafl: we meafurc time, and as equal portions of one do not correfpond to equal portions of the other, the apparent motion of the fun would not be uniform j or, in other words, thofe points of the equator which come to the meridian^ with the place of tlic fun on different days, would not be at equal diftanccs from each other, which as to the time of the fun's appearing upon thj meridian, or fliewing the time of t]\e day upon a dial, is the fame as if it had an irregular motion thro' the equator, and therefore caufes it to ren- der the days unequal among themfelves. This lad: is eafily feen upon the globe, by bringing every tenth degree of the eclip- tic to the c;raduated fide of the ilron^ brafs meridian, and vou will find that each tenth degree on the equator will not come thi- ther with it, but in the following order from T to Q, every tenth degree of the P 4 ecliptic 2i6 Description and Use of the ecliptic comes fooner to the ftrong brafa meridian than their correfponding i oths on the equator ; thofe in the fecond quadrant of the ecliptic, from S to ~ , come later, from A to vs fooner, and from vs to aries later, whilft thofe at the beginning of each qua- drant come to the meridian at the fame time ; therefore the fun and clock would be equal at thefe four times, if the fun was not longer in paffing through one half of the ecliptic than the other, and thefe two inequalities joined together, compofe that difference which is called the equation of time. 476. Thefe caufes are independent of each other, fometim^es they agree, and at other times are contrary to one ano- ther. 477. The time marked out by a uniform motion, is called true time, and that fliewn by the fun, is called apparent or folar time, and their difference is the equation of time. 478. We now proceed to (hew How the terreftrlal globe will repre- fent Gekjiuil and I'irrejirial Globes. 217 fent the real phenomena relating to the earth, when a£lually compared with the refulgent rays emitted from the great fphcre of day. 479. The meridians on our new tcrrc- ftrial globes, being fecondaries to the equa- tor, are alfo hour circles, and are marked as inch with roman figures under the equa- tor, and at the polar circles. But obfervc, there is a difference in the figures placed to the fame hour circle ; if it cuts the Hid hour upon the polar circles, it will cut the IXth hour upon the equator, which is Hx hours later, and fo of all the reft. 480. Through the great Pacific fea, and the interfed:ion of libra, is drawn a broad meridian from pole to pole, it paiTes thro' the Xllth hour upon the equator, nnd the Vlth hour upon each of the polar cir- cles ; this hour circle is graduated into de- grees and parts, and numbered from the equator towards either pole. 481. There is another broad meridian pafling through the Pacific fea, at the IXth hour upon the equator, and the Hid hour ur-on 2i8 Description ^W Use of the upon each polar circle ; this contains only one quadrant, or 90 degrees, the numbers annexed to it begin at the northern polar circle, and end at the tropic of Capri- corn. 482. Here we mufl Ukewifc obferve, there are 23 concentric circles drawn upon the terreftrial globe v/ithin the northern and fouthern polar circles, which for the future we fliall Q.2i}\ polar parallels-, they are placed at the diftance of one degree from each other, and reprefent the parallels of the fun's declination, but differently to what the 47 parallels between the tropics do. 483. The following problems require the globe to be placed upon a plane that is level, or truly horizontal, which is eafily attained, if the floor, pavement, gravel- walk in the garden, &C. fliould not happen to be horizontal. 484. A flat feafoned board, or any box which is about two feet broad, or two feet fquare, if the top be perfectly flat, will anfwer the purpofe, the upper furface of either may be fet truly horizontal, by the help of a pocket fpirit level, or plumb rule, if you raife or deprefs this or that fide by CeJefiial and Jerrejirial Globes. 219 a wedge or two, as the fpirit level {hall dire6t ; if you have a meridian line drawn on the place over which you fubflitute this horizontal plane, it may be readily trani- ferred from thence to the furface juft le- velled ; this being done, we are prepared for the folution of the following pro- bJems. Problem LVII. To obferve the funs altitude by the terreflrial globe, when he ITiInes bright, or when he can but juft be difcerned through a cloud. 485. Confider the fliade of extuberancy, which is that caufed by the fphericity of the globe, heretofore called the edge of the earth's enlightened difc, and th^rc rcprefented by the broad paper-circle, but here reallized by the natural light of the fuji himfelf. Elevate the north pole of the globe ta 66 \ degrees, bring that meridian or hour circle, which paffcs through the IXth hour upon 220 Description mid Use of the upon the equator, under the graduated fide of the ftrong brafs meridian, the globe being now fet upon the horizontal plane -, turn it about thereon, frame and all, that the fhadow of the ftrong brafs meridian may fall diredly under itfelf, or in other words, that the fliade of its graduated face may fall exadiy upon the aforefaid hour circle 3 at that inflant the fhade of extu- berancy v/ill touch the true degree of the fun's altitude upon that meridian, which pafles through the IXth hour upon the equator, reckoned from the polar circle, the moil elevated part of which will then be in the zenith of the place where this operation is performed, and is the fame whether it fliould happen to be either in north or fouth latitude. 486. Thus v/e may, in an eafy and na- tural manner, obtain the altitude of the fun, at any time of the day, by the terreftrial globe ; for it is very plain, when the fun rifes, he bruflies the zenith and nadir of the globe by his raySy and as he always illu- minates half of it, (or but a few minutes more, as his globe is confiderably larger than that of the earth) therefore when the fun- is Celeftial and T'errcfirial Globes. 221 js rifen a degree higher, he muft necef- farily illuminate a degree beyond the ze- nith, and (o on proportionably from time to time. J, But as the illuminated part is fomewhat more than half, dedud 1 3 minutes from the fliade of extuberancy, and you have the fun's altitude with tolerable exad:- nefs. If you have any doubt how far the fhade of extuberancy exactly reaches, hold a pin, or your finger, on the globe, between the fun and point in dilpute, and where the fliade of cither is loft, will be the point fought. 487. When the fun does not fhlne bright enough to cafl a iliadow. Turn the meridian of the G:lobc toward the fun, as before, or dired: it fo that it may lie in the fame plane with him, which may be done if you have but the leaft glimpfe of the fun through a cloud j hold a ftring in both hands, it having firft been put between the ftrong brafs nieridian and the 222 Description and Use of the the globe, ftretch it at right angles to the meridian, and apply your face near to the globe, moving your eye lower and lower, till you can but juft fee the fun^ then bring the firing held as before to this point upon the globe, that it may juft obfcure the fun from your fight, and the degree on the aforefaid hour circle, which the ftring then lies upon, will be the fun's altitude required, for his rays would fliew the iame point if he (hone out bright. Note. The moon's altitude may be ob- ferved by either of thefe methods, and the altitude of any ftar by the laft of them. Problem LVIII. To place the terreftrial globe in the fun's rays, that it may reprefent the natural pofition of the earth, either by a meridian Hne, or with- out it. 488. If you have a meridian line, (tt the B or th and fouth points of the broad-paper circle diredtly Celejiid and Terrejirial Globes. 223 .diredly over it, the north pole of the globe being elevated to the latitude of the place, and Handing upon a level plane, bring the place you are in under the graduated fide of the llrong brafs meridian, then the poles and parallel circles upon the globe will, without fenfible error, corrcfpond with thofe in the heavens, and each point, king- dom, and flate, will be turned towards the real one which it reprefents. 489. If you have no meridian line, then by knowing the day of the month, find the fun's declination as before directed, which will dired: you to the parallel of the day, amongft the polar parallels, reckoned from either pole towards the polar circle 3 which remember. Set the globe upon your horizontal plane in the fun-lhine, and put it nearly north and fouth by the mariner's compafs, it being firft elevated to the latitude of the place, and the place itfelf brought under the gra- duated fide of the ftrong brafs meridian, then move the frame and globe together, till the ihade of extuberancy, or term of illumination, juft touches the polar paral- lel for the day, and the globe will be fettled as £24 Description and Vs^ of the as before ; and if accurately performed, the variation of the magnetical needle will l)e fhewn by the degree it points to in the compafs box. 490. And here obferve, if the parallel for the day fliould not happen to fall on any one of thofe drawn upon the globe, you are to eftimate a proportionable part between them, and reckon that, the parallel of the day. If we had drawn more, the globe would have been confufed. 491. The reafon of this operation is, that as the fun illuminates half the globe, the fbade of extuberancy will conftantly be 90 degrees from the point where the fun is vertical. 492. If the fun be in the equator, the {hade and illumination muft terminate in the poles of the world, and when he is in any other diurnal parallel, the terms of il- lumination muft fall (hoYt of, or go be- yond either pole, as many degrees as the parallel which the fun defcribes that day, is diftant from the equator j therefore when the fhade of extuberancy touches the polar parallel for the day, the artificial globe will be in the fame pofition, with refpedt to Cekjlial and Terr eflrial Globes. 22 j to the fun, as the earth really is, and will be illuminated in the fame manner. Problem LIX. To find naturally the fun's decli- nation, diurnal parallel^ and his place thereon. 493. The globe being fet upon an ho- rizontal plane, and adjuftcd by a meridian line or otherwiie, obferve upon which or between which polar parallel the term of illumination falls, its diftance from the pole is the degree of the fun's declination j reckon this diftance from the equator among the larger parallels, and you have the parallel the fun defcribes that day > upon which if you move a card, cut in the form of a double fquare, until its fliadow falls under itfelf, you will obtain the very place upon that parallel over which the fun is vertical at any hour of that day, if you fet the place you are in under the graduated fidv5 of the flrong brafs meridian. Q_ Note. 226 Description a?id Use of the Note. The moon's declination, diurnal parallel and place, may be found in the lame manner. Likewife when the fun does not fhine bright, his declination, 6cc. may be found by an application in the manner of problem ^j. Problem LX. To find the fun's azimuth natu- rally. 494. If a great circle at right angles to the horizon paffes through the zenith and na- dir, and alfo through the fun's center, its diftance from the meridian in the mornina: or evening of any day, reckoned upon the degrees on the inner edge of the broad- paper circle, will give the azimuth re- quired. Method I. 495. Elevate either pole to the pofitlon of a parallel fphere, by bringing the north pole in north latitude, and the fouth pole fti fouth latitude, into the zenith of the broad- Cekjiidl and T^errejirial Globes. 22^' broad-paper circle, having firfl: placed the globe upon your meridian line, or by the other method before prefcribedi hold up a plomb line fo that it may pafs freely near the outward edge of the broad-paper circle, and move it fo that the fliadovv of the firing may fall upon the elevated pole, then caft your eye immediately to its flia- dovv on the broad-paper circle, and the degree it there falls upon is the fun's azi- muth at that time, which may be rcclioned from either the fouth or north points of the horizon. Method II. 496. If you have only a glimpfe, or faint light of the fun, the globe being adjufted as before, i1:and on the (liady fide, and hold the plomb line on that fide alfo, and move it till it cuts the fun's center, and the elevated pole at the fame time, theii caO: your eye towards the broad-paper circle, and the degree it there cuts is the fun's azimuth, which mult be reckoned from the oppoGte cardinal point. 0^2 Pkobjlem 228 Description and Use of tie Problem LXI. To fhevv that in fome places of the earth's furface, the fun will be twice on the fame azimuth in the morning, and twice on the fame azimuth m the after- noon \ or in other words, When the declination of the fun ex- ceeds the latitude of any place, on either lide of the equator, the fun will be on the fame azimuth twice in the morning, and twice in the afternoon, 497. Thus, fuppofe the globe redlified to the latitude of Antego, which is in about 17 deg. of north latitude, and the fun to be in the beginning of cancer, or to have the greateft north declination, fet the qua- drant of altitude to the 21 ft degree north of the eaft in the horizon, and turn the globe upon its axis, the fun's center will be on that azimuth at 6 h. 30 min. and alfo at I oh. 30 min. in the morning. At S h. 30 min. the fun will be as it were ftationary Celefiial and Tet rejirial Globes. 229 flationary with refped to its azimuth for fbme time ; as will appear by placing the quadrant of altitude to the 17th degree north of the eaft in the horizon. If the quadrant be fet to the fame degrees north of the weft, the fun's center will crofs it twice as it approaches the horizon in the afternoon. This appearance will happen more or lefs to all places fituated in the torrid zone, whenever the fun's declination ex- ceeds their latitude -, and from hence we may infer, that the fliadow of a dial muft neceffarily go back fevcral degrees on the fame days. Problem LXIL To obferve the hour of the day in the moft natural manner, when the terreftrial globe is properlj^ placed in the fun-fliine. 498. There are many ways to perform this operation with relpedt to the hour, three of which are here inferted, being Ci^3 general 230 Description and Use of the general to all the inhabitants of the earth y a fourth is added peculiar to thofe of Lon- don, which will anfwer without fenfible error at any place not exceeding tlie di- ftance of 60 miles from this capital. I ft. By a natural ftile. Having rectified the globe as before dl- redled, and placed it upon an horizontal plane over your meridian line, or by the other method, hold a long pin upon the illuminated pole in the diredlion of the polar axis, and its fhadow will {hew the hour of the day amongft the polar pa- rallels. The axis of the globe being the com- mon fedtion of the hour circles, is in the plane of each, and as we fuppofe the globe to be properly adjufted, they will corre- fpond with thofe in the heavens ; there- fore the {hade of the pin, which is the axis continued, jiiuil fall upon the true JiGur circle. 2dly, Celejiial and Terrejlrial Globes. 231 sdly, By an artificial ftile. 499. Tie a fmall ftrlne with a noofe t> round the elevated pole, flretch its other end beyond the globe, and move it fo that the fhadow of the firing may fall upon the deprefled axis, at that inftant its HiadoviT upon the equator will give the fclar hour to a minute. 500 But remember, that either the au- tumnal or vernal equinoctial colure mud firft be placed under the graduated fide of the firong brafs meridian before you obferve the hour, each of thcfe being marked upon the equator with the hour XII. 501. The firing In this lafi cafe being moved into the plane of the fun, corrc- fponds with the true hour circle, and ccn^ fequcntly gives tjie true hour. 3dlyj Without any flile at all. 502. Every thing being redified as be- fprcj look where the fiiade of cxtuberancy ' ' Oof C'-tS 2^2 Description and Use of the cuts upon the equator, the colure being under the graduated fide of the flrong brals meridian, and you obtain the hour in two places upon the equator, one of them going before, and the other following the fun. 503. Note. If this' fliade be dubious, apply a pin or your finger as before di- reded. 504. The reafon is, that the fliade of extuberancy being a great circle, cuts the equator in half, and the fun, in what- foevep parallel of declination he may hap- pen to be, is always in the pole of the fliade, confequently the confines of light and fliade will fliew the true hour of the day. 4thly, Peculiar to the inhabitants of London, and its environs, within the diftance of fixty miles. The globe being every way adjufted as before, and London brought under the «-j-auuatcd fide of the flrong brais meridian, "" hold dJeJHal and T^erreflrial Globes. 233 hold up a plomb line, fo that its fliadovv may fall upon the zenith point, (which in this cafe is London itfclf ) and the lliadow of the ftring will cut the parallel of the day upon that point to which the fun is ^hen vertical, and that hour circle this in- terfedion falls upon, is the hour of the day ; and as the meridians are drawn within the tropics at 20 minutes diftance from each other, the point cut by the interfe(5lion of the ftring upon the parallel of the day, being fo near the equator, may, by a glance of the obfcrver's eye, be referred thereto, and the true time obtained to a minute. The plomb line thus moved is the azi- muth, which by cutting the parallel of the day, gives the fun's place, and confe- quently the hour circle which interfeds it. From this lail operation refults a corol- lary, that gives a fecond way of redifying the 2:Iobe to the fun's ravs. If the azimuth and fliade of the illumi- nated axis a2;ree in the hour when the elobe is reditied, then making them thus to agree jnufi: redify the globe. Corollary. 234 Description ami Use of the Corollary. Another method to redify the globe to the fun's rays. 505. Move the globe till the fliadow of the plomb line, which paiTes through the zenith, cuts the fame hour on the parallel of the day, as the fliade of the pin held in the diredion of the axis falls upon, amongft the polar parallels, and the globe is recti- fied. 506. The reafon is, that the fhadow of the axis reprefents an hour circle, and by its agreement in the fame hour, which the fhadow of the azimuth firing points out, by its interfedion on the parallel of the day, therefore the fun is in the plane of the faid parallel -, which can never happen in the morning on the eaftern fide of the globe, nor in the evening on the weftern fide of it, but when the globe is re(5lified. 507. This rediiication of the globe, is only placing it in fuch a manner that the principal great circles, and points, may con- cur and fall in with thofe of the heavens. The Celejlial and Terrejlrial Glob«es. 235 The many advantages arifing from thefe capital problems relating to the placing of the globe in the fun's rays, an intelligent reader will eafily difcern, and readily ex- tend to his own as well as to the beneht of his pupil. A Table 236 Description md Use of the A Table of Retroceflion and Autumnal Equi- noxes. Retroceflion, Autumnal Equinoxes. Years. D. H. M. Days. H. M. 6000 45 20 2191454 4 5000 3S 4 40 1826211 19 20 4000 30 13 20 1460969 10 40 3000 22 22 1095727 2 2000 15 6 40 730484 17 20 1000 7 15 20 365242 8 40 900 6 21 328718 3 800 6 2 40 292193 21 20 700 5 8 20 255669 15 40 600 4 14 219145 10 500 3 19 40 182621 4 20 400 3 I 20 146096 22 40 300 2 7 109572 17 200 I 12 40 73048 II 20 100 18 20 36524 5 40 90 16 30 32871 19 30 80 14 40 29219 9 20 70 12 50 25566 23 10 60 II 21914 13 50 9 10 18262 2 50 40 7 20 14609 16 40 30 5 30 10957 6 30 20 3 40 7304 20 20 10 I 50 I 39 3652 10 10 9 '3287 4 21 8 I 28 2921 22 32 7 I 17 2556 16 43 6 I 6 2191 10 54 5 SS 1826 5 5 4 44 1460 23 16 3 33 1095 17 27 2 22 730 II 38 I II 3*'^5 5 49 j Celejlial and Terreftrial Globes. 257 A Table of Months. S2 January Days a Kal. Jan. A 31 31 D 28 February 59 D 31 March 90 G 30 April 120 B 31 May 151 E 30 June 181 G 31 July 212 C 3^ Auguft 243 F 30 September 273 A 31 Oclober 304 D 30 November 334 F 31 December 365 A Table of Week- Days, 4 Monday 5 Tuefday 6 Wednefday Thurfday I Friday 2 Saturday 3 Sunday 238 Description and Use of ths A Table of the Horary Difference in the Mo- tion of the firft Point of Aries, at the Time of a Vernal Equinox. M. s. /'^ M. S. '" H. I M. S. H. 31 M. S. 9 4 42 2 i8 32 4 51 3 27 33 5 4 36 34 5 9 5 45 35 36 5 18 6 54 5 27 7 I 4 37 5 36 8 I 13 38 5 45 9 I 22 39 5 54 10 II I 3J 40 41 6 3 I 40 6 12 12 I 49 42 6 21 13 I 5« 43 6 31 14 2 6 44 6 40 15 2 16 45 46 6 49 16 2 25 6 58 17 2 34 47 7 7 ' 18 2 43 48 7 16 19 2 53 49 7 25 20 3 2 50 51 7 34 7 43 21 3 II 22 3 20 52 7 52 23 3 29 53 8 24 3 38 54 8 8 25 26 3 47 55 56 8 17 3 56 8 25 27 4 4 57 8 35 28 4 12 5H 8 45 29 4 22 59 8 55 ,30 4 32 60 9 5 Celejltal and "terrefirlal Globes. 239 A Table of the Difference of the Pafiage of the firft Point of Aries over the Meridianj for every Day in the Year. I. in January. ( February. March. G H. M. S. H. M. S. H. M. S. C3 » I 5 10 53 2 5S 46 I 9 5- 2 6 28 54 42 6 7 I S 2 4 50 39 2 24 2 4 4 57 40 46 37 58 41 3 5 6 53 16 4B 53 42 36 54 58 4 5 38 36 51 16 7 44 31 34 36 47 34 6 8 40 9 30 37 43 52 7 9 35 47 26 39 40 II 8 10 1 1 31 26 22 42 36 30 9 [ 27 6 18 45 32 50 10 12 22 46 14 50 29 10 II n 18 27 10 55 25 31 12 14 14 9 7 I 21 52 13 15 9 51 3 7 18 13 14 16 5 33 I 59 14 14 34 15 17 I 17 55 22 10 55 1(3 18 3 57 2 51 32 7" 16 17 IQ 52 47 47 42 3 38 18 20 48 33 43 52 000 19 21 44 19 40 3 23 56 22 20 22 40 b 36 14 52 44 21 2^ 35 54 32 26 49 6 22- 24 34 43 28 39 45 28 23 25 26 27 33 24 52 41 50 24 25 23 24 21 6 38 12 27 19 15 17 20 34 34 26 28 15 7 13 35 30 56 27 29 II 27 18 28 30 6 54 23 40 29 Jl 2 49 1 ?. 30 24^ Description andXJszofthe II. April. May. 1 June. ^1 Q H. M. S. H. M. S. H. M. S. I 23 16 24 21 25 12 19 22 28 2 12 46 21 23 18 22 r 3 9 8 17 33 14 16 2 4 5 29 13 43 10 9 3 5 } 50 9 52 6 2 4 5 6 22 58 11 6 I 55 7 54 33 2 8 18 57 48 6 50 54 20 58 16 53 40 7 9 47 14 54 23 49 32 8 10 43 35 .50 30 45 24 9 10 II 39 55 46 35 41 15 12 36 H 42 40 37 6 II 13 32 33 38 44 32 57 12 14 28 52 34 49 2& 48 13 15 25 II 30 51 24 39 15 16 21 30 26 54 20 29 17 17 47 22 56 16 20 16 18 14 4 18 58 12 II 17 19 10 21 H 59 8 I 18 20 6 38 II 3 51 19 20 21 2 54 7 17 59 42 22 21 59 II 2 59 55 33 21 23 SS 26 19 58 59 51 23 22 24 51 41 5458 47 14 23 25 47 SS 50 56 43 4 24 25 • 26 44 9 46 53 38 55 27 40 23 42 50 34> 46 26 28 36 36 3846 3» 37 27 29 3248 34 42 26 29 28 / 30 29 30 38 22 20 29 : 31 26 33 30.; CeJeJlial and T'errejirial Globes. 241 III. < July. ~Auguft~ September. H. M. S. H. M. S. H. M. S. I 17 18 II 15 13 26 13 17 22 2 H 3 9 33 13 45 I 3 9 56 5 41 10 8 2 4 5 48 I 49 6 31 3 5 6 I 41 14 n 58 2 54 4 5 16 57 3+ 54 8 12 59 17 7 53 28 50 18 55 40 6 *^ 49 22 46 29 52 4 7 ■^ 45 17 42 40 48 28 8 i.o II 41 12 3B 52 44 52 9 37 7 35 5 41 16 10 12 33 2 31 18 37 40 II 13 28 58 27 32 34 4 J2 14 24 SS 23 46 30 29 13 15 16 20 52 20 I 26 54 .J 15 16 49 16 16 23 18 17 12 47 12 32 i9 43 16 18 8 46 8 48 16 7 17 19 4 45 5 5 12 31 18 20 21 45 I 22 8 5b ^9 20 15 56 45 13 57 40 5 20 22 52 a6 53 58 I 44 21 23 48 48 50 i6 II 58 8 22 24 44 49 46 35 54 32 23 25 26 40 5? 42 55 50 56 24 25 36 54 39 14 4/- 20 ^^ 32 57 35 35 43 44 26 28 29 2 31 55 40 7 27 29 25 6 28 17 36 30 28 30 21 12 24 38 32 53 29 3i 17 18 21 -32. R 242 Description and Use, ^c. IV. 00 October. ( November. December. 1 rS Q H. M. S. H. M. S. H. M. S. I II 29 15 9 32 5<^ 7 28 50 2 25 37 28 55 24 29 I 3 21 59 24 58 20 8 2 4 18 20 21 15 47 3 5 14 42 17 2 11 25 4 5 6 II 3 13 3 7 3 7 7 23 9 3 2 40 6 8 3 43 5 2 6 58 17 7 9 2 I 53 54 8 10 II 10 56 21 8 56 57 49 30 9 10 52 40 52 53 45 6 12 48 58 48 49 40 41 II 13 45 i^ 44 44 36 15 12 H 41 33 40 38 31 50 13 16 37 50 36 31 27 24 H 34 6 32 23 22 58 15 17 30 21 28 14 18 32 16 18 26 36 24 5 14 5 17 19 22 50 19 54 9 39 i3 20 ig 4 15 44 5 13 19 21 15 17 II 32 46 20 22 II 29 7 19 5 56 19 21 23 7 40 3 5 51 52 22 24 3 51 7 5« 51 47. 25 23 25 2 54 36 42 59 24 -26 9 56 II 50 20 38 33 25 27 52 20 46 4 34 6 26 . 2B 48 27 41 47 29 40 27 29 44 34 37 29 25 14 28 3c 40 41 33 10 20 48 29 ■ 31 36 47 16 23 .mS FINIS. CATALOGUE o F Mathematical, Philofophical, AND Optical INSTRUMENTS. MADE and SOLD by GEORGE ADAMS, Mathematical Inftrument-Maker to the KING, At his Shop the Sign of Tycho Brahe*s Head, in Fleet-ftreet, London. Where Gentlemen and Ladies may be fupplied with fuch Inftruments as are either Invented or Impro- ved by himfelf ; and ConftrucSled according to the moft perfc