Glass _^E_4^3L_ Poole J^^S SMITHSONIAN DEPOSIT TABLES OF BEARINGS, DISTANCES, LATITUDES, LONGITUDES, &c. ASCERTAINED BV THK ASTRONOMICAL AND TRIGONOMETRICAL SURVEY OF MASSACHUSETTS. \ /(>/ TABLES ASTRONOMICAL AND TRIGONOMETRICAL SURVEY. TABLES BEARINGS, DISTANCES, LATITUDES, LONGITUDES, fa. ASCERTAINED BY THE ASTRONOMICAL AND TRIGONOMETRICAL SURVEY OF MASSACHUSETTS PUBLISHED AGREEABLY TO A RESOLVE OF THE GENERAL COURT, BY JOHN G. PALFREY, SECRETARY OF THE COMMONWEALTH. BUTTON AND WENTWORTH, STATE PRINTERS, NO. 37, CONGRESS STREET. 1846. ^ 1.-1 \^^^'^ ADVERTISEMENT. The General Court of Massachusetts for the year 1829-1830 passed Resolves (chap. 50) requiring each town in the Common- wealth to forward to the Secretary's office an accurate map of its territory, from actual surveys, on the scale of one hundred rods to an inch. Another Resolve of the same year (chap. 58) empowered the Governor to appoint a Surveyor, with assistants, to make a Trig- onometrical Survey of the Commonwealth, accompanied by astro- nomical observations. A Resolve of the next General Court (chap. 18) authorized the further measure of a Geological Survey. Gov- ernor Lincoln, whose long administration was signalized by substan- tial and permanent monuments of the most liberal and enlightened policy, and to whose persevering exertions the accomplishment of this, among other objects of high public utility, is materially in- debted, took the first steps towards executing the will of the Leg- islature, by appointing Mr. Robert Treat Faine, of Boston, Chief Engineer, with Mr. James Stevens, of Newport, Rhode Island, for his Assistant, and Professor Hitchcock, of Amherst College, Geolog- ical Surveyor. Towards the end of the year, Mr. Stevens, having proceeded to Washington, and borrowed some instruments from the jjublic offices, selected a place for measuring a base line, and employed jMr. Simeon Borden, of Fall River, to construct an apparatus for the measure- ment. The winter was spent by Mr. Borden in making the appa- ratus and repairing the instruments. In the spring of 1831, the astronomical and chronometrical observations were commenced by the Chief Engineer, and the surveys and triangulations by the ADVERTISEMENT. Topographical Surveyor. In 1834, Mr. Stevens resigned the charge of the Survey, which, from that time, devolved on Mr. Borden. In 1838, the Chief Engineer also made his final report, and Mr. Borden was entrusted with the completion of the work. At this time, the field-work was supposed to be finished, and a sufficient number of the main triangles had been calculated to cover a section of fifty miles square of the western portion of the State. The town surveys having also been lodged in the Secretary's office, Mr. Borden proceeded to the compilation of the map. Here a serious dif- ficulty occurred, which miglit very naturally have been anticipated. Some of the town surveys, made, of course, by practitioners of very different degrees of skill, were found to be extremely inaccurate. The boundaries of adjacent towns, as delineated by them respect- ively, did not coincide ; the corresponding points of rivers and roads did not meet each other ; and Mr. Borden had to go again into the field, with four or five assistants, to make corrections. At length, in 1842, the map was projected, ready for the engraver, on a reduced scale of two and a half miles to the inch, or one eighth part of that of the original plans. Accompanied by a delineation of the Geolog- ical Survey, on a reduced scale of one half of that of the principal map. it was engraved on six plates by Mr. G. G. Smith, of Boston, in the best style of that eminent artist, and was printed and published in the autumn of 1844. Its dimensions are seven feet by four feet and a half. It shows the boundaries of towns, the roads, rivers, mountains, the sites of some principal edifices, the topography of the country generally, and the elevations of the principal stations of the triangulation. The whole cost, independently of that of the town surveys, which has not been reported, exceeded seventy thousand dollars. The General Court of 1845, considering that the detailed results of the Survey ought to be made generally accessible for use in laying out roads, measurements of towns, and other like operations, passed a Resolve (chap. 106) directing the Secretary " to cause to be print- ed such portions of the tables deposited in his office, exhibiting re- sults obtained from the recent Trigonometrical Survey of the Com- monwealth, as would be useful" for these purposes; a measure, which has led to the present publication. AUVEKTISEMENT. Ill The base line for the triangulation of the Commonwealth was measured, 7.3882 miles in length, on the west side of Connecticut River, between points in the town of Hatfield, and on the southern bank of Bloody Brook, in Deerfield. The apparatus for the measure- ment, invented and made by Mr. Borden, proved so perfect, that two separate and independent measurements of this long line differed from each other only 0.237 of an inch, a degree of precision which has reasonably excited the admiration of scientific men. A full des- cription of this apparatus, which has since been introduced in the Coast Survey of the United States, maybe found by the professional inquirer in a paper published in the ninth volume of the Transactions of the American Philosophical Society, pp. 33-91. In the opera- tions connected with the triangulation, a twelve-inch repeating the- odolite, with a vertical circle attached, made by Troughton, for Mr. Hassler, of the Coast Survey, was used to measure the vertical angles, and a telescope, forty-six inches in focal length, mounted by Mr. Bor- den, to measure the azimuth angles. The results of the triangulation were verified by the series of astronomical observations by Mr. Paine, who thus determined the Latitudes and Longitudes of twenty-seven places in and near Mas- sachusetts. Several of them have also been verified by the United States Coast Survey. The line six or seven miles long between Po- casset Hill, in Tiverton, and Quaker Hill, in Portsmouth, Rhode Island, one of the most distant lines from the measured base, differed but 0.22 of a foot, as determined by the two surveys respectively. In digesting the town surveys, in his compilation of the map, so as to reduce the sum of their errors to the lowest possible point, Mr. Borden availed himself of another important invention, first suggested to him by Mr. Alvan Clark, of Cambridge, which has also been introduced into the United States Coast Survey, and into the office of the Topographical Engineers, and by which, it has been said, on good authority, that a sum of not less than five thousand dollars will be annually saved to the country in those offices. It consists in a novel and most ingenious application of the Camera Lucida to the purposes of topographical drawing. The Resolve directing this publication was passed only the day before the prorogation of the General Court. As soon as I was able IV ADVERTISEMENT. to give attention to the subject, I perceived that I could but very partially make the Tables " useful," which it was my duty to do, witiiout accompanying them with a plan of the triangulation. I have accordingly caused to be prefixed a lithographed delineation of the triangles, copied with great exactness by Messrs. Bufford & Co. of Boston, from a lithograph accompanying the communication to the American Philosophical Society, above referred to. As the printing of the Tables proceeded, it further became obvious, that, for the same reason, it required to be accompanied by a collection of such mathematical formula as would make it available for the purposes of surveyors. I applied successively to Mr. Borden and to his accom- plished Assistant, Mr. Charles O. Boutelle, now of the United States Coast Survey, to furnish these formulae. Both evinced the same liberal disposition towards the object, which has so uniformly and honorably distinguished their course ; but the engagements of both have been so urgent as not to leave the requisite time at their com- mand. The printing of the Tables was completed last September. But the publication has been delayed to the present time, for want ot the desired mathematical explanations, which, at much inconvenience to themselves, these gentlemen have at length had the great kind- ness to furnish. J. G. P. Secretary's Office ; March 21, 1846. INTRODUCTION. The survey of the State of Massachusetts, on which the map lately published is founded, was begun under an Act of the Legislature, passed in 1831. It was divided into four sections, Geological, Astronomical, Trigonometrical, and Topographical ; the last three properly forming parts of one great work, whose ultimate object was to furnish data for a complete and thorough map of the State. The Tables here given form a part of the data obtained by the Trigonometrical Survey, conducted by Simeon Borden, Esq., combined with the separate astronomical observations made by R. T. Paine, Esq. They may be made useful to Engineers, Surveyors, and others, in all parts of the Commonwealth, in various ways, as follows : — 1. By furnishing accurate data for determining the magnetic variation, and the ratio of its change from year to year, and by affording a test of the existence of local attraction, and a measure of its amount. 2. By enabling Rail-road Surveyors, or others, having occasion to measure upon long, irregular routes from one town to another, to check their measurements and determine the amount of their error either in length or direction, every time they reach a Trigonometrical point. 3. By affording bases and azimuths for local surveys of towns and of large farms, more accurate than the small instruments in ordinary use are generally able to give. 4. By making public the exact relative position of some five hundred points, in all parts of the Commonwealth, to be used for future reference. These will always afford a basis upon which future Topographical Surveys in detail may be made, whenever the changes in the surface of the State shall call for a new map, or for corrections to the present one. 5. By furnishing the absolute geographical position, in latitude and longitude, of about four hundred points, many of them on the coast, where a knowledge of their true position may be useful to the mariner, and all interesting to the scientific astronomer, or astronomical amateur, who may always refer his observations to some point in his vicinity, upon which many thousand observations have been brought to bear, and which cannot, m the nature of things, be greatly in error. 6. Generally, by awakening in some, and keeping alive in others, a fondness for exactness in their field surveys and calculations, and thus B VI INTRODUCTION. leading to that reform in the present method of land surveying, which the rapidly increasing value of real estate in the greater part of the State, loudly calls for. In tjie following explanations, it is taken for granted, that the reader is conversant with the ordinary principles of Trigonometry, and with the use of Logarithmic Tables. Those who are not, and who wish to avail them- selves of the data in this book, are referred to the works of Flint, Davies, and Gurnmere on Surveying. The first named book contains Logarithm and Traverse Tables. For a higlier order of surveying, Hassler's Log. Tables will be found accurate, useful, and portable. They are carried to seven places of decimals. Examples are given of the methods of working all the formula. Where practicable, rules are given in addition to the ordinary algebraic formulae. EXPLANATION OF THE TABLES. A Trigonometrical Survey consists in measuring, with the utmost care, a Base Line, in some favorable location, and upon it building a series of triangles. The first has the measured base for one of its sides, and the others gradually enlarge from the base as the configuration of the country will allow. All the three angles, in each triangle, are thus carefully measured, and their sum, if correct, will be equal to two right angles, -phts a small quantity, which is due to the spherical figure of the earth, and is called the spherical excess. At some central station, the direction of the true meridian is obtained by astronomical observations, and the angles made with it, by the sides of triangles radiating from that point (called the azimuths) are measured. The latitude of this, and other points of the triangulation, is determined by celestial observations. Care is taken that these points shall have as great a difference of latitude as the figure of the country surveyed will allow. If the survey extends through a degree, or more, of latitude, the astronomical observations, combined with the results of the triangulation, will give the value of a degree in that latitude ; i. e., the number of feet or yards there are in a degree of latitude on that particular part of the earth's surface covered by the survey. This value, again combined with a similar one, determined by similar means, in a distant latitude, (as for example, a degree measured in Massa- chusetts combined with a degree measured in Peru,) will give a value for the cUipticity, or compression of the poles of the earth ; or, in other words, the quantity the polar radius is shorter than the equatorial radius. If the survey does not cover a sufficient difference of latitude to enable the observer to determine the ellipticity from his own observations, recourse is had to those of others; and, in such cases, the mean elements of the earth's figure and magnitude, given by M. Bessel, are probably the best extant. INTRODUCTION. VU They will be tound in the explanations of the mode of determining the latitudes and longitudes given further on. When a survey is sufficiently extensive, however, every observer will prefer to determine the ellipticity for himself, since, the more such surveys are multiplied, the more they seem to show that the earth's figure is not a regular splieroid, or that there are other, as yet, unknown causes which serve to render the most careful observations uncertain. The elements of the earth's figure and magnitude being thus determined by observation, or taken from the observations of others, the differences of latitude, longitude, and azimuth, of all the points of the triangles, are com- puted by means of the azimuths and distances between the stations, commencing at some point where the direction of the meridian has been obtained by observation. The same result may be arrived at, by starting from the observed meridian and computing the Northing or Southing, Easting or Westing, made on every course, on parallels to the meridian of the starting point and its perpendicular. These latitudes and departures, as they are usually called, are then combined so as to proceed from some one zero point, and the diflerence of latitude and longitude computed by means of tables prepared for the purpose, and based upon the elements of the earth's figure and magnitude adopted or observed, as above explained. The latter method has been adopted in the Massachusetts survey, and will be more fully explained and illustrated hereafter. The general principles, of which an outline has been given above, were applied to practice in Massachusetts, in the following manner : — A base line was selected and measured on the West side of the Con- necticut River, extending from the South part of Deerfield, Franklin County, to near the centre of Hatfield, Hampshire County. It is 7.3SS miles long, and was measured twice over, with a compensating apparatus, constructed by Mr. Borden for the purpose. The two measurements differed 0.237 inches, and its final length, reduced to the level of the sea, is 39009.73 feet, of the 82 inch copy of Troughton's scale, belonging to the U. S. Coast Survey, at 62° Fahrenheit; the Logarithm of the base is 4.5911729. Upon this base, all the measures contained in these tables are founded. The angles were all measured by Mr. Borden, and azimuths observed at French's Hill, in Peru, Berkshire County ; at Boston ; and at Fall River, Bristol County. At the same time, astronomical observations were made at twenty-five points, in different parts of the State, by Mr. Paine. The sides of the triangles were then calculated, and the latitudes and de- partures computed. For greater accuracy and convenience in constructing the map, ]\Ir. Borden divided the State into five sections, each having its own central meridian on parallels, to which, and its perpendicular, all the directions given in these tables are based. Section I comprises all that part of the State lying West of Connecticut River, except Gill, and part of Northfield, and is based upon the meridian of French's Hill, in Peru. Vlll INTRODUCTION. Section II is bounded West by Section I, and includes, upon the East, Pepperell, part of Groton, Harvard, Bolton, Berlin, Northborough, West- borough, Upton, and Uxbridge. It is based upon the meridian of Tuft's Hill, in New Braintree. Sections III and IV are, in fact, as one, lying North and South of each other, and both based upon the meridian of the State House, in Boston. Section III is bounded West by Section II, and East by the ocean. Sec- tion ly is bounded West by Rhode Island, and includes, on the East, Plymouth, Tisbury, Chilmark, and the Island of No Man's Land. Section V comprises all that part of the State lying East of Section IV, and is based upon the meridian of Hyannis station, in Barnstable. There are four Tables to each Section : and, as the principle of con- struction is alike in all. Sections III and IV will be taken as examples by which to explain the others. Tables 1 and 2 in each section are alike in their mode of construction and application. Table 1 refers to the primary stations or points where all the three angles in each triangle have generally been measured, and the position of every point carefully determined. Table 2 refers to secondary objects, principally churches, (marked upon the State map by a triangle with a cross upon it, thus^^) and less labor has been bestowed upon them. Their positions are generally accurate to within six feet. The same is the case with the Tables 3 and 4 ; Table 3 giving the relative and absolute positions of the primary, and Table 4 those of the secondary stations. Of Tables 1 and 2. Table 1 of these sections contains the bearings and distances from one station to another on parallels to the meridian of the State House, with the Northings and Southings, Eastings and Westings, made on each course. The bearings, at the State House, of the other stations in siglit from it, are determined by direct observation, and of all the others in the section, by combining them with the angles df the triangles observed at each station. Page 38. State House to Prospect Hill, 'Waltham, is N. W. 77" 47' 13".25. If we suppose the meridian at Prospect Hill parallel to that of the State House, we have, for the direction of the line. Prospect Hill to State House, the same course reversed, viz. : S. E. 77° 47' 13"25. The angle* at Prospect Hill, between State House and Blue Hill, is 47° 2ry 06".S9. Blue Hill being South or to the right of the S. H. as seen from Prospect Hill, the angle must be deducted from the above course, and we shall have 30° 21' 06". 36 S. E., as the direction from Prospect Hill to Blue Hill, parallel to the meridimi of the State House ; and reversing this course, Blue to Prospect will be N. W. 30° 21' 06".36. The angle at Blue Hill, between Prospect * Whenever angles are named in these explanalions, the station on the left of the observer is always men- \\oneA first. The central station is generally referred to, in «hal follows, as the "prime meridian" of the section. INTRODUCTION. IX Hill and State House, = 44° 45' 27".55, whence we have Blue Hill to State House, = N. E. 14° 24' 21". 19, or State House to Blue Hill, = S. W. 14° 24' 21".19, as given on Page 38. In this manner, the bearings, parallel to the meridian of the starting point, are carried through Tables 1 and 2 of each section. The distance, in feet, on each line is given in Table 1, and is the hypothenuse of a right-angled triangle, of which the bearing is one of the angles, and the numbers in the other two columns, the legs. Let B^ihe bearing of any side, a= the distance, c^ latitude, and 6 = departure on each course ; then (1) 6^a Sin. i? ; (2) c=a Cos. i?; that is, the de- parture, or Easting and Westing, is the measure of the sine of the course, and the Northing or Southing is the measure of its cosine. Page 38. Example. State House to Blue Hill = S. W. 14° 24' 21".19. Distance = 54956.13. B=14° 24' 21".19 Log. Sin. = 9.3958318 Cos. = 9.9861255 = 54956.13 Log. =4.7400161 Log. = 4.7400161 Departure = i = 13672.50 Log. = 4.1358479 Lat. = c = 53228. 18 Log. = 4.7261416 corresponding with the numbers given in the table. In this manner, all the latitudes and departures have been computed, both in Table 1 and Table 2 of each section. Table 2 differs from Table 1 only in having the distances from the station to the object observed left out. It may be sup- plied from the two legs of the right-angled triangle, which are given by transposing either of the preceding formula;, viz. : (3) a := ^^^ ; or, (4) Page 43. Example. The bearing of Bunker Hill Monument* from the State House is given N. E. 6° 46' 14"; Northing, 6625.94 feet. Required, the distance. By formula (3) a = 'ij^^b c = 6025.94 =3.8212475 J5 = 6° 46' 14" Cos. = 9.9969607 a = distance = 6672.47 = 3.8242868 The same result would be obtained by dividing the Easting by the sine of the course, as in formula (4) a = -g — ^ The angles may be deduced from the bearings m either Table 1 or 2, or both combined, as the case may be ; thus, it is required to know the angle at Blue Hill, between Wachusett Mountain and Holt's Hill. Page 29, we find Blue to Wachusett = N. W. 63° 54' 3G".58 Blue to Holt's = N. E. 00° 47' 51".93 Angle required = 64° 42' 2S".51 * The name of the town in which the object is situated precedes the name of the object. The reader will therefore look for Charlestown. INTRODUCTION. What is the angle at Blue Hill, between the State House and Prospect Hill, Hingham ? Blue to State House* =: N. E. = 14° 24' 21".19 Blue to Prospect, Hingham, S. E. = 8 4° 19' 3r)^'.0Q 1 80° — 9 8° 43' 56". 19 Angle required = 81° IG' 03".81 In this case, both courses are on the same side of the meridian, one North and the other South ; their sum deducted from 180°, is, therefore, the angle. Required the angle at INahant station, between Blue Hill and Cohasset Church. Page 34, Table 1, we find Nahant to Blue Hill = S. W. 33° 35' 31" and page 43, Table 2, Nahant to Cohasset Church = S. E. 25° 24' 49" 59° 00' 20" = angle required. Fractions of seconds may be rejected, in all ordinary cases, where these tables will probably be used. Of the columns of Southings and Westitigs in Tables 3 and 4. Tables 3 and 4 contain, in the first two columns, the Southings and Westings of every station and secondary object in the section from the Northeastern-most point in it, viz. : Salisbury Marsh in the N. H. State Line. They arc constructed from the Northings, Southings, Eastings, and Westings of the first two tables, in the following manner : Salisbury Marsh is called Zero, and all the other stations are South, and nearly all, West of it. On Page 36, we find Prospect Hill, Rowley, to Salisbury Marsh, N. E. 17° 28' 26"; the Northing = 60737..53 ; Easting = 19120.12. Prospect Hill is, therefore, S. and W. of Salisbury Marsh by these quantities, and they are registered accordingly in Table 1. On Page 35, we find Powow Hill to be 2255.80 South, and 31574.40 West of Salisbury Marsh ; and also on Page 36, we find Powow Hill to be 58481.13 North, and 12454.76 Westf of Prospect Hill, Rowley. But the latter station is 60737.53 South, and 19120.12 West of Salisbury Marsh ; therefore, 60737.53 19120.12 — 58481.13 + 1 2454.76 Powow Hill S. = 2250.40 W. = 31574.88 of Salisbury Marsh. The mean between tliis result and that obtained directly from the Zero Point is registered as in Table 3, the true Southing and Westing of Powow Hill. * The reader will observe, that he cannot find the stations, in the Tables, named in the order they are here quoted ; — he will therefore in this case, and in all simil.ir cases, look for them reversed. For example : the course from Blue Hill to the State House caiuiol he found in the Tables, but the course from the Slate House to Blue Hill can j — the reader, therefore, has only to reverse that course, which will be the course required. t By a typographical or clerical error, this bearing has been printed N. E., it should be !V. W. INTRODUCTION. XI In the same manner, all these three points are then brought to bear upon the position of Railcut Hill, in Gloucester, which being East of Salisbury Marsh, has the inimis or negative sign prefixed in the column of Westings, in Table 3, (thus, —46325.96) signifying that it is 46325.96 feet East of the meridian of Salisbury Marsh (parallel to the prime meridian). Proceeding thus from station to station, we have, in the end, the mean relative positions of every point in the Section, referred to one Zero Point, and now so connected together as to allow us to change this Zero Point at will. In Section I, the Zero Point is the S. W. corner of the State, and all the others are North and East from it ; in Section V, the stations are all South and East of the Zero Point, but the principle of construction and iise is the same in all, only difl'ering in the mode of its application. This table requires much labor in the preparation, and great care in combining the means of the relative positions so as to produce the most accurate re- sult, and, once formed, it is the most important table of all ; since from it the whole of the others may be reproduced. It may be used to determine the direction and distance between any two points in the same section, whether visible from each other or not. Example 1. What is the direction and distance from the State House, in Boston, to the New Bedford Court House? Page 56. N. B. Court House S. of Sal. Marsh = 450996.10 W. of do. =28950.07 Page 58. State House S. of do. = 1&7269.65 W. of do. = 65251.09 Dif. = S. =263726.45 Diff. E. = 36301.02 These differences are the legs of a right-angled triangle, of which the di- rection is one of the angles, and the distance the hypothenuse. Using the notation before given, we have, by the rules of Trigonometry, (5) Tang. ^ = 4 and by (4) a = ^ N. B. Court House E. of State H.=*= 36301.02 Log. = 4.5599188 Log. = 4.5599188 do. S. of do. =c =263736.45 Log. = 5.4211530 Direction = J? =7° 50' 14" Tang. = 9.1387653 Sin. =9.1346896 Distance a =266213.00 Log. =5.4252292 Example 2. What is the direction and distance from Bunker Hill Monument to Boston Light ? Page 54. Boston Light S. of Sal. Marsh = 198240.05 W. of do. 18318.83 Page 60. Bunker Hill Monument S. of do. =180643.75 W. of do. 64164.78 Dim S. = 17596.30 E. = 46145.95 Boston Light E. of B. H. Monument = J = 46145.95 = 4.6041336 do. S. of do. = c = 17596.30 = 4.24542 1 4 =4.2454214 Direction S. E. = B = 69° 07' 38" Tang. = 0.4187122 Cos. =9.5518970 Distance = a = 49377.00 = 4.6935244 XU INTRODUCTION. The foregoing problem may be made useful in almost every case in which these tables may be used. In order to render more plain the above formula, it is given, also, in the form of a proportion, and a rule for work- ing it by Logarithms is added. For finding the direction and distance between any places named in Tables 3 and 4. (1) c : Radius : : b : Tang. B (2) Cos. B : c : : Radius : a (3) Sin. B : b :: Radius : a Rule. For the direction or course. From the Log. of the departure (Easting or Westing,) subtract the Log. of the latitude (Northing or South- ing;) the remainder will be the Log. Tangent of the course, (parallel to the meridian on which the section is based.) For the Distance. From the Log. of the latitude subtract the Log. Cosine of the course, the remainder will be the Log. of the distance ; or, from the Log. of the departure subtract the Log. Sine of the course, the remainder will be the Log. of the distance, as before. On the Convergence of Meridians. Hitherto, we have considered all the courses as parallel to the central meridian on which each section is based; but, as all meridians converge to the poles of the earth, a correction must be applied to every course, com- puted as above, to obtain the true direction of the meridian. This cor- rection varies with the latitude, and may be calculated to a very close degree of accuracy by the following formula : — (6) Tang. ^ C=Sin. L Tang. J P, in which Z, == latitude ; P = difference of longitude between central sta- tion and that for which the convergence is required ; C = angle of convergence between meridian of central station and that of the observer. Example. "What is the convergence of the meridian of Hyannis Station, in Barnstable, with the meridian of the State House ? Page 7L Lat. of Hyannis Station = 41° 37' 53".36 : Long.=70° 18' 42".92 Long, of State House = 71 04 09 .00 Diff. of Long. = P, 45 26 .08 L = 41° 37' 53".36 ; Sin. = 9.8223885 i P = 22 43 04 ; Tang. = 7.S200S97 C=30'H".04; i C= 15 05.52; Tang. = 7.6424782 INTRODUCTION. XUl The angle of convergence of any two meridians, in any part of the State, may be more readily ascertained from the following table : — Lat. Feet of Dep. in I" of conv. Logarithms. Diff. Lat. Feet of Dep. ill 1" of conv. Logarithms. Dif. Lat. Feet of Dep. in I" of conv. Losarilhma. Diff. / o / o / « 16 115.701 2.0633365 - 41 48 113.555 2.0552032 5078 42 20 111.452 2.0470870 5068 18 .565 28275 5090 60 .422 46955 5077 22 .322 65802 5068 20 .430 23186 5089 52 .289 41878 5077 24 .192 60735 5067 24 .295 18098 5088 54 .157 36802 5076 26 111.062 55668 5067 24 .160 13011 5087 56 113.025 31726 5076 28 110.933 60602 5066 26 115.025 07925 5086 41 58 112.893 26651 5075 30 .804 45536 5066 28 114.890 2.0602840 5085 42 00 .761 21577 5074 32 .675 40471 6065 30 .756 2.0597756 5084 02 .629 16503 5074 34 .546 35406 5065 32 .622 92673 5083 04 .497 11450 5073 36 .417 30342 5064 34 .488 87591 5082 06 .366 06358 5072 38 .288 25279 5063 36 .354 82509 5082 08 .235 2.0501287 5071 40 .160 20216 5063 38 .220 77428 5081 10 112.104 2.0496216 5071 42 110.032 15154 5062 40 114.087 72348 5080 12 1I1-.973 91146 5070 44 109.904 10092 5062 42 113.954 67268 5080 14 .874 86076 5070 46 .776 2.0405030 5062 44 .821 62189 5079 Ifi .712 81007 5069 48 .648 2.0399969 5061 41 4C 113.688 2.0557110 5079 42 18 111.582 2.0475933 5069 42 50 109.520 94908 5061 The second column of this table gives the number of feet of Easting or Westing in one second of convergence, i. e. in lat. 42° 00', for every 112.761 feet of departure made on any course, that course will change 1" ; for twice that distance it will change 2" ; and for 60 times that distance, or 6765.66 feet, the course will change one minute. When the point at which the true bearing is required is east of the prime meridian, the correction for convergence is additive to the N. E. and S. W. courses, and subtractive from those which are N. W. and S. E., and vice versa when the point is wesl of the prime meridian. Example 1. Page 38. The bearing from the State House to Prospect Hill, Waltham = N. W. 77° 47' 13".25. What is the true direction from Prospect Hill to State House 7 Page 38. Westing of Prospect Hill from S. H. =51349.61= 4.7105372 Page 57. Approx. Lat. of do. = 42° 23' 20". Tab. Log. = 2.0462424 Angle of convergence at Prospect Hill= 7' 41."63 = 461".63 =2.6042948 77° 47' 13".25 + 7'41".63 = 77° 54' 54".88, S.E. = true bearing, c XIV INTRODUCTION. Example 2. A surveyor in Hopkinton wishes to know the true bearing of a line from Hopkinton Church to Siierburne Church, that he may determine the varia- tion of his compass. Page 64. Sherburne Church S. of Sal. Marsh = 229853.64 Page 61. Hopkinton Church S. of do. =2338 23.16 Diff'. N. = 3969.52 W. of do. = 148290.67 W. of do. = 188585.63 Diff. E. = 40294.96 By For-> Sherburne Ch. E. of Hopkinton Ch. = i = 40294.96 =4.6052508 mula(5.)5 Do. N. of do. =c= 3969.52 =3.5987380 Direction N. E. (par. to prime meridian,) = B= 84° 22' 26" Tang. = 1.0065128 Hopkinton Church W. of Salisbury Marsh =188585.63 State House W. of do. = 65251.09 Hopkinton Church W. of State House =123334.54 =5.0910847 Page 61. Approx. Lat. of Hopkinton Church = 42° 13' 47. Tab. Log. =2.0480625 Angle of convergence at Hopkinton Church = 18' 22". 61 = 1102".61 =3.0424222 84° 22' 26" — 18' 23" = 84° 04' 03" = true bearing N. E. The difference between this course and that given by the compass would be the magnetic variation of that compass at Hopkinton. Ex.iMPLE 3. Page 46. Prospect Hill, Waltham, to Hopkinton Church, S. W. 51° 18' 07", (par. to prime meridian.) What is the true bearing at each end? S.W. 51° 18' 07"— 7' 42"* = 51° 10' 25" S. W. = true course Prosp. Hill to Hopkinton Ch. N. E. 51° 18' 07"— 18' 23" = 50° 59' 44" N. E. do. Hopkinton Ch. to Prosp. Hill. In this manner, the direction of the true meridian may be determined at any point given in these Tables. The difference between the magnetic bearing of any line and its tabular bearing, corrected for convergency, will be the magnetic variation of the compass at the time and place of observa- tion. As it is important that the method of applying the correction for convergency should be clearly understood, an example in each section is added. Example 4. Page 1. Section I. Dug Hill, in Blandford, to Mount Tom = N. E. 80° 43' 00".39, (parallel to prime meridian.) What is the true bearing at Dug Hill ? Page 9. Dug Hill E. of S. W. corner of State = 157727.33 French's Hill E. of do. =131437.45 Dug Hill E. of French's, = 26289.88 = 4.4197887 Page 9. Approx. Lat. of Dug Hill = 42° 12' 25". Tab. Log. = 2.0490090 Angle of convergence at Dug Hill = 3' 54".84 = 234".84 = 2.3707797 80° 43' 00".39 -f 3' 54".84 = 80° 46' 55".23 N. E. = true bearing required. * The angles of convergence are taken from Examples 1 and 2. introduction. xv Example 5. Page 22. Sect. II. Wachusett Mountain to Worcester Unitarian Ch. = S. E. 16° 30' 20", (parallel to prime meridian.) What is the true bearing at Worcester Church 1 Page 24. Tuft's Hill W. of Pepperell = 133776.60 Page 27. Worcester Church W. of Pepperell = 56933.00 Worcester Church E. of Tuft's Hill = 76843.60 = 4.8856077 Approx. Lat. of Worcester Church = 42° 16' 13". Tab. Log. = 2.0480458 Angle of convergence at Worcester Ch. = 11' 28" = 687".96 = 2.8375619 16° 30' 20"— 11' 28" = 16° 18' 52" N. W. = true bearing required. Example 6. Page 68. Sect. V. Sampson's Hill to Nantucket south-towered Ch. = 71° 43' 55", S. E. (parallel to prime meridian.) What is the true direction at Nantucket Church ? Page 71. Nantucket south-towered Ch. E. of Telegraph Hill = 162929.91 Hyannis Station E. of do. =105783.39 Nantucket Church E. of Hyannis Station = 57146.52 = 4.7569897 Page 71. Approx. Lat. of Nantucket Church = 41° 16' 57". Tab. Log. = 2.0630947 Angle of convergence at Nantucket Church = 8' 14". 19 = 494". 19 = 2.9638950 71° 43' 55" — 8' 14" = 71° 35' 41" N. W. = true bearing required. The primary and secondary trigonometrical lines given in these Tables are so numerous, and may be multiplied to such an extent by means of Tables 3 and 4 of each section, that surveyors, in almost all cases, may find some line in their immediate neighborhood, on which a compass may be placed to determine the variation. It may happen, however, that local attraction of the magnetic needle exists at the point selected for this pur- pose. To detect it, let the surveyor observe the bearing of some object, witliin half a mile of his instrument, making an angle of about 60° with the trigonometrical line on which his compass is placed ; then the bearing of another object, making an angle of about 120°, and so around the hori- zon, carefully noting the bearings of objects about 60° apart. Although the compass may not give the true magnetic bearings of the points observed • upon,U will give the angles sufficiently correct between them and the trig- onometical stations. The true astronomical bearings of these points may then b^educed from the angles, as has been before explained. This done, let the 3rveyor place a conspicuous mark at the place occupied by his instrumet and, going to the different objects observed upon, take the magnetic \aring at each of the central stations he has left. The magnetic variation oJuced from all these bearings, taken at different points, should be very nes^he truth.* * Magnetic variation may be best determined about 10 A. M. XVl INTRODUCTION. Example. In Example 2 of the paragraph on convergence on meridians, the true bearing of a Hne from Hopkinton Church to Sherburne Church, was foimd to be N. 84° 04' E. A surveyor finds its magnetic bearing to be S. 89° 20' E., giving a magnetic variation of 6° 36' West. Knowing the variation to be more, he suspects local attraction, and, to detect it, takes the following bearings to objects from a third to half-mile distant, his compass standing at a point which we will call A, in the line between the two churches and near the western one. Magnetic. True. 1. To a poplar tree, = S. 31° 44' E. + 6° 36' = S. 38° 20' E. 2. To a chimney of white house, = S. 35 25 W. — 6 36 = S. 28 49 W. 3. To a yellow birch at corner of fence, =N. 28 00 W.-|- 6 36 = N. 34 36 W. 4. To a guide-board at corner of road, = N. 26 43 E. — 6 36=N.20 07 E. Then placing a signal at A, and going to each of these points, he takes the following magnetic bearings : 1. Point A, from poplar tree, = N. 28° 52' W. Mag. var. = 9° 28' 2. " A, from white house, = N. 38 15 E. " " =9 26 3. " A, from yellow birch. = S. 25 15 E. " =9 21 4. " A, from guide-board. = S. 29 36 W. " =9 29 Mean magnetic variation. = 9 26 West. Showing local attraction* at A, amounting to 2° 50'. The "Three-point Problem" may be used to such great advantage in connection with these Tables, that a concise explanation of the mode of working it, with an example, may not be out of place. If. At a point P, (see figure,) from whence I could see three points A, B, C, forming a triangle, the elements (i. e. the angles and sides) of which are known, I meas- ured the angles APC and CPB. It is hence required to determine the direction and distance of my station P from each object. Let ^C = a; BC = b- BCA = C; APC=P; ana' CPB = P'- alsomake R ^360°— P—P'—C; x^CAP, and y= PBC. Then will (7) Cot.a; = Cot.R.{,,^^^^£^^ + l); and (S) y = I-x. For an investigation of these formnlse, the reader is refrred to Gal- braith's Mathematical Tables, pages 47 to 50, or to the wor** of Gregory and Lacroix, on Trigonometry. A good method of consuction may be • This example is hypothetical ; the writer has no reason to suppose tlial local altrao'" ^^'^'s at Hopkinton. INTRODUCTION. XVll found in Malortie's Topography, or in Alexander's edition of Simms on Mathematical Instruments and Surveying, (Ed. of 1844, Baltimore, F. Lu- cas, publisher.) The use of these formulae need not be embarrassing if care is taken in properly applying the signs of Cos. and Cot. R. When R is less than 93°, both Cos. and Cot. a.xe plus ; between 90° and 180°, both are minus ; be- tween 180° and 270°, the Cos. is minus, and-^ie Cot plus; between 270° and 360°, the Cos. is plus, and the Cot. nanus. Example. At a point P, near *Jne new Observatory in Cambridge, the following angles were me^osured, viz : Bunker Hill Monument and State House = 20° 05' 53" = P State House and Roxbury Church = 35 06 08 = P' It is hence required to determine the direction and distance of the point of observation from each of these places. The data required from the Tables will be. X b ^ State House to Roxbury Church, ^ ment = C. The distances must be computed by formula (3) or (4), and the angle C obtained from the bearings given in the Tables. P. 43. State House to B.H. Monument = N.E. 6° 46' 14" = 5. Cos. = 9.9969607 ^Byfor- " Northing = 6625.94 = c. = 3.8212475 ( mula Distance State House to Monument = 6672.47 = a. =3.8242868) (3). P. 50. State House to Roxbury Ch. = S. W. 34° 22' 52" = B. Cos. = 9.9166117 ^ By for- " Southing = 10301.11 =c. = 4.0128840 \ mula Distance State House to Church = 12481.66 =i. =4.0962723) (3)-* C = 180° — 34° 22' 52" -f- 6° 46' 14" = 152° 23' 22" P-\-P' = 55 12 01 C+P + P' = 207 35 23 360 00 00 360°— C — P — P> = R = 152 24 37 The above comprises all the data required in the calculation of formula (7). R being in the second quadrant, (between 90° and 180°,) both Cos. and Cot. are minus. To save labor and space, the arithmelical comple- ments of the Logarithms of the terms {b. Sin. P. Cos. R') are added to the Logarithms of (a. Sin. J°'), instead of subtracting the Logarithms them- selves. The result is, of course, the same. * Substituting b Tor a. XVlll INTRODUCTION. a = State Kouse to B. H. Monument = 6672.47 6 = State House to Roxbury Church = 12481.66 P'= State House and Roxbury Church = 35° 06' 08" P = Monument and State House = 20 05 53 J? =200- — c — P — P' = 152 24 37 a.Sin.P Log. = 3.8242868 Ar. Co. Log. = 5.9037277 Sin. = 9.7596958 Ar. Co. Sin. = 0.4639117 Ar. Co. Cos. = — 0.0524258 i. Sin. P'. Co.?. R a. Si.i. P h. Sin. P'. Co9 Th+' Adding 1, R: — 1.009364 + 1: = — 0.009364 152° 24' 37" 618 58 24 By formula (8) = — 0.0040478 Log. = — 7.9714614 Cot. = — 0.2818647 Cot. =4-8.2533261 y = 63 26 J 3 X in this case = Angle at Monument between State House aind Station P. y " " = Angle at Roxbury Church between Station P and" .State House. In each of these triangles we have now given two angles and a side to find the rest. Triangle Bunker Hill Monume7it, State House and Station P. As Sin. of Angle at P = P = 20° 05' 53" Is to distance State House to Monument = 6672.47 So is Sin. of Angle at State House = 70° 55' 43" To distance Monument to Station P =: 18352.00 ^^^;^^ or sum of first two Log's, Angle at Monument —x =88° 58' 24" Distance State House to Station P = 19414.62 Ar. Co. = 0.4639117 Log. = 3.8242868 = 9.97548 34 = 4.2636819 = 4.2881985 Log. Sin. = 9.9999303 4.2881288 Triangle Roxbury Church, State House and Station P. As Sin. of Angle at P = P' = 35° 06' 08" Is to distance State House to Roxb. Ch. = 12481.66 So is Sin. of Angle at State House = 81° 27' 39" To distance Roxbury Ch. to Station P = 21465.21 BC Bin. BPC Angle at Roxbury Church = y Distance State House to Station P = 19414.63 or sum of first two Log's, = 63° 26' 13" Ar. Co. = 0.2403042 = 4.0962723 = 9.9951588 = 4.3317353 = 4.3365765 = 9.9515525 = 4.2881290 The bearings State House to Monument, and State House to Roxbury Church, combined with the angles deduced by calculation, give us the following directions, viz : 1. Bunker Hill Monument to Station P = N. W. 84° 15' 22" 2. State House to Station P = N. W. 64 09 29 3. Ro.xbury Church to Station P = N. W. 29 03 21 The second of these directions will sufiice on as short a line, and we shall have, by formula (I) and (2), INTRODUCTION. XIX B = 64° 09' 29" a = 19414.62 Departure = b= 17473.24 Log. Sin. = 9.9542445 Log. = 4.2881289 Log. = 4.2423734 Cos. = 9.6393683 = 4.2881289 Lat. = c = 8462.48 = 3.9274972 P.58. Tab. 4. State House S. of Salisbury Marsh = 187269.65 , W. of do. = 65251.09 Northing, Station P from State House =—8462.48; Westing =+ 17473.24 Station P South of Sahsbury Marsh =178807.17; West of do. = 82724.33 And thus we have finally the means of determining the direction and dis- tance from P to any other point in the section, as has been before explained. There are three positions which may be taken for the point P, in all of which formula (7) will give an accurate result ; 1st, that shown in the figure, where the point of observation P is outside of the known triangle ABC] 2d, where P is inside the triangle; 3d, where P is outside, but Station C is reversed, so that the line PC will no where intersect the line AB. In all these cases, ACBP should be considered as forming a quadri- lateral of which we know two sides a and b, and two angles (P -|- P') and C. Therefore their sum from 360 = i? = a- -j- y, either of which being known, all the rest may be found by the ordinary rules of trigonometry. In the third case, care should be taken in deducing R, to use the exterior angle at Cin the triangle ABC] i. e. its complement to 360°. The three-point problem is indeterminate when P falls upon the periphery of a circle passing through ABC. A case of this nature in practice is of rare occurrence ; but, to guard against it, an angle might be measured to a fourth trigonometrical point, if one can be seen ; or it may readily be de- tected by a geometrical construction of the figure. We now proceed to give an example of computing the bearings and dis- tance between points, of which we have no other data respecting their relative position than their Latitudes and Longitudes. For this purpose we select the Southwest corner of the State and Chatham South Light. Let P = the angle at the pole, or ditference of Longi- tude ; b = Co. Lat. of the Southwest corner of the State ; a = Co. Lat. of the Southwest corner of the State -[- the difference of Latitude of the points chosen in an arc corresponding in value with the perpendicular degree for the Latitude of the Southwest corner of the State. Then, by Spherical Trigonometry, determine the angles A and B and the side /;. The angle A being greater than 90°, its supplement will be the course from the Southwest corner of the State to Chatham South Light ; the angle B being less than 90°, will be the course from Chatham South Light to the Southwest cor- ner of the State. XX INTRODUCTION. The side p having been determined in an arc of the value of the perpen- dicular degree, may be readily reduced to feet, and, of course, to any other measure of length required. The above operations, when performed, will give results sufficiently accurate for all common purposes. But, if greater accuracy is required, we may assume a second spherical triangle, as fol- lows, viz. : P = the angle at the pole will be the same in both cases. Let the side a^the Co. Lat. of Chatham S. Light, and the side 6=a minus the difference of Lat. in an arc corresponding in value with the perpendic- ular degree for the Lat. of Chatham S. Light. Then by spherical trigo- nometry, with these new elements, re-determine the angles A and B, and the side p, and a mean of the angles and sides thus determined, will ^ive the result very nearly exact. The following example will show the details of the operation: — Calculations of the Bearings and Distance from the Sonthv)est corner of the State to Chatham South Light. Page 10. Lat. of the S. W. corner of the State, 42° 02' 59". 54 Long. 73° 31' 42".66 " 71. " " Chatham South Light, 41 40 16 .16 " 69 57 12 .89 Difference of Latitude =00 22 43 .38 Long.= 3 34 29 .77 = i' FORMUL.*;. Tang.K^+5): ■ Cat 1 P f"os4^D0 b) . Tang. l{Aai B)=Goi.\ P. , p Sm.J{aMA) ■Sm.i(«+A) First. To find the difference of Latitude in an arc of the value of the perpendicular degree for Latitude of the Southwest corner of the State, we have, Difference of Latitude = 1363". 38 Value of a minute for a mean of Latitudes of S. W. "j corner of State and Chatham Lights, . . I = 6072.1437 ft. Taken from Table B, for facilitating the calculation f Latitude and Longitude, . . . . J = 60" Ar. Co. Log. value of 1", from Table C, of perpendicular arcs for Lat. of S. W. corner of the State, Difference of Latitude in an arc corresponding in value with the perpendicular degree, for Lat. )= 0.22' 39" = 1359" S. W. corner of the State, . >=0.S Log. = 3.1346169 Log. = 3.7833421 Log. = 8.2218487 Ar. Co. Log. = 7.9934088 ^ Log. = 3.1332165 i = 47° ' 57' 00".46 i-|-22' 39" = u = 48 19 39 .46 a-(-A = 96 16 39 .92 a w i == 00 22 39 .00 4(a + J)=48 08 19 .96 Ar. Co. Cos. = 0.1756611 Ar. Co. Sin. = 0.1279810 4(aM J) = 00 11 19 .50 Cos. = 9.9999976 Sin. = 7.5177636 h P = 1 47 14 .88 Cot. = 11.5057438 Cot. =11.5057438 J(4-|-B)=88 48 25 .03 Tang. = 11.6814025 h{AviB) = 8° 04' 02". 25 = Tang. = 9.1514884 i(Ac/3i?)= 8 04 02 .25 A = 96 52 27 .28 B = 80 44 22 .78 INTRODUCTION. XXI Sin. i. Sin. P or Sin./): To find ». Formula Sin. » = ' ^^ jg^ ^ ^ Sin. is Ar. Co. Sin. = 0.0056972 Sin. = 9.8707332 Sin. = 8.7948638 Sin. = 8.6712942 Sin. a. Sin. P Sin. 4 B = 80" 44' 22".78 i =47 57 00 .46 P = 3 34 29 .77 ■p = 2 41 20 .07 p in sec. = 9680".07 Log. = 3.9858786 Value of 1" in feet, Log. = 2.0065912, taken from Table C, for Lat. of S. W. f in ft. = 982810.4 ft. = Log. = 5.9924698 [corner of State. We thus find that the Southwest corner of the State bears from Chatham South Light, N. W. 80° 44' 22".78 ; and that Chatham South Light bears from the Southwest corner of the State, S. E. 83° 07' 32".72. But when greater exactness is required, we make the second calculation described above. Thus in this instance, making use of the same symbols used in the preceding, we have a = Co. Lat. Cliatham South Light = 48° 19' 43".84 Difference of Lat. in seconds = 1363". 38 Log. = 3.1346169 Value of a minute for a mean of the Lat. = 6072.143 feet. Log. = 3.7833421 60" Ar. Co. Log. = 8.2218487 Log. value of 1" of a perpendicular degree for Latitude of Chatham South Light, Ar. Co. Log. = 7.9934172 Diff. of Lat. in sec. of perp'r arc, 22' 39".02 = 1359".02 = Log. = 3.1332249 a=48°19'43".24 a— 22'39".02 = i = 47 57 04 .22 a-\-h = 96 16 47 .46 a en 6 = 00 22 39 .02 4(fl+i)=48 08 23 .73 Ar. Co. Cos. = 0.1756700 4(acnA)= 11 19 .51 4 P = 1 47 14 .88 i{4+B)=88 48 25 .12 h[A mB)= 8 04 02 .20 A = 96 52 27 .32 B . = 80 44 22 .92 Cos. = 9.9999976 Cot. =11.5057438 Tang. = 1.6814114 Ar.Co.Sin.= 0.1279739 Sin. = 7.5177700 Cot. = 11.5057438 4(Am5) = 8° 04' 02".20 Tang. = 9.1514877 Sin. = 9.8707399 Sin. = 8.7948638 Sin. = 8.6753008 To find y, we have B = 80° 44' 22".92 Ar. Co. Sin. = 0.0056971 J = 47 57 04 .22 P = 3 34 29 .77 p = 2 41 20 .22 p in seconds, 9680".22 Log. = 3.9858852 Value of one second in feet, Log. = 2.0065828 p in feet = 982806.4 feet. Log. = 5.9924680 Therefore, XXll INTKODUCTION. We have by the first result, A = 96° 52' 27".28 second do. A = 96 52 27 .32 From a mean we find A = 96° 52 27 .30 We have by the first result, B = 80° 44' 22".78 second do. B = 80 44 22 .92 From a mean we find B = 80° 44' 22". 85 We have by the first result, p = 982810.4 second do. p = 982806.4 From a mean we find p = 982808.4 ft. = to 186.138 miles From the preceding results, we find the bearing from the Southwest cor- ner of the State to Chatham South Light, to be S. E. 83° U7' 32".70 The bearing from Chatham South Light to the Southwest corner of the State, to be N. W. 80° 44' 22".S5 In the following Tables of the result of the Trigonometrical Survey, there are many points whose Northings or Southings, Eastings or West- ings (according to the notation of the section in which they are situated), are given in feet ; their Latitudes and Longitudes having never been calcu- lated ; and inasmuch as it seems to be necessary to know the Latitudes and Longitudes of such stations, in order to obtain the bearing and distance be- tween them, it may not be amiss to give an example of the mode of calcu- lation. Suppose it was desirable to know the bearing and distance between Blue Hill station, situated in the third section of the survey, and the Holyoke House, situated in the second section. By examining Table 4, Section II, it will be seen, that the Latitude of Holyoke House has never been calcu- lated ; neither can there be found, in the Tables of Section II, the Southing and Westing of Blue Hill station, computed from the meridian and paral- lels to the meridian of Tuft's Hill. By an examination of Table 3, Section HI and IV, the Latitude and Longitude of the Blue Hill station will be found, but the Southing and Westing of Holyoke House cannot be found in these Tables. It therefore becomes necessary to know the Latitude and Longitude of Holyoke House, as one of the elements to be used in the cal- culation. To compute the Latitude of Holyoke House, we have, from Table 3, Section II (page 24), the Southing and Westing of a point from which to calculate the Latitude and Longitude of the section (which point we gen- erally designate as the Cardinal pouH, and shall so call it in the calculations which we arc about to introduce). We also have, from Table 4, Section II (page 25), the Southings and Westings of Holyoke House. To ascertain the bearing from the Cardinal point to Holyoke House, sub- tract the Log. of the difl'erence of Southing from the Log. of the difference of Westing, which gives the Tangent of the course. Thus, \c INTRODUCTION. XXUl Southingof Card'l Pt. (p. 24) = 126229.50 Westing of do. = 133777.43 " of HolyokeH.(p. 25)= 148860.03 " of do. = 27 0004 .85 HoIyokeH., S.of Card'l Pt. = 20630.53 West of Card. P.= 136227.42 Log. =5.1342645 20630.53 Log. =4.3145104 (1) Course from Cardinal Pt. to Holyoke H., S. W. 81° 23' 18".45 = Tang. = 0.al'J7541 JP Having thus obtained the bearing from the Cardinal / \ point to Holyoke House, we put P for the pole, C for the / \ Cardinal point, A for Holyoke House, R for a point in the / \ meridian of the Cardinal point, corresponding in Southing / \ with the point A. I \ We now proceed to find the Latitude of R. We have found i? =20630.53 feet south of C, and from Table B (for facilitating the calculations of Latitude and aS'^- Ik Longitude), we find the mean logarithmic value of a second standing against the distance which nearest corresponds to the distance named above =2.00.52210, to which we may add 1 as its proportion of the difierence between this Log. and the preceding Log. of the Tables (the distance against the mean Log. second being about a thousand feet greater than the distance given above). We therefore have, 20630.53 feet. Log. = 4.3145104 Log. value of a mean second, Log. = 2.0052211 Difference of Latitude in secon ds = 203".84 Log. 2.3092893 0° 3' 23".84 Latitude of C being = 42 21 30 (2) " " R " = 42 18 06 .16 If we now let -p represent the side opposite the polar angle in arc, we then have the Log. of AR minus Log. value of a second of a perpendicular degree in feet = Log. p in seconds. Thus, A west of J? = 136227.42 ft. Log. = 5.1342645 From Table C, we find tlie Log. value of perp. second for Lat. iJ, Log. = 2.0065967 ■p in seco nds, 1341". 74 Log. = 3.1276678 or = 0° 22' 21". 74 We now have, Co. Tang. P = Co. Tang. p. Sin. a ; a = Co. Lat. R = 47° 41' 54".78 p = 0° 22' 21".74 Cot. = 12.1867512 a = 47 41 54 .78 Sin. = 9.8690052 (3) P = 30 14 .08 Cot. = 12.0557564 We have thus found the angle P or the difference of Longitude by Spher- ical Trigonometry, which probably gives it as accurately as the problem will admit. This method should be followed in all cases where the polar angle exceeds 35' ; but when the polar angle is less than 30' or 35', we may, with sufficient accuracy for every practical purpose, determine the polar angle by the following method, viz. : having determined the Latitude of R, XXIV INTRODUCTION. then, from the Log. of the difference of Westing of C and A, subtract the Log. vakie of polar seconds (from Table D) or differences of Longitude, and the remainder will be the Log. of the number of seconds and decimal parts of a second contained in the polar angle or difference of Longitude. Thus, for example, Difference of Westing of C A, Log. = 5. 1342645 Tabular Log. (from Table D) for Lat. of R = 42° 18' 05". 16 = 1.8756052 Difference of Longitude in seconds = 181409 Log. = 3.2586593 (4) Difference of Longitude = 30° 14' 09", varying only 0".01 from the previous determination. I would here remark, that this method may be used for calculating the Longitude of any and every point which has not been heretofore calculated. Having thus obtained the polar angle and the Latitude of B, we might, by a solution of the right-angled spherical triangle PRA, find the length of the side PA, the complement of which will be the Latitude of A, sufficiently near for all practical purposes. Thus, Tan" . AP = . = Cos.P PR = 47° 41' 53". 84 Tang. = 10.0409659 P = 30 14 .08 Cos. = 9.9999832 Co. Lat. of A = AP = 47 41 57 .8 1 Tang. = 0.0409827 (5) Lat. of .A =42 18 02 .19 We have thus readily foimd a near approximate Latitude of .4 ; but if it is desirable to ascertain strictly the Latitude of A, the labor of calculation is somewhat increased. To determine the Latitude of A, strictly, we must, in the first place, find the distance AC. Let D = distance from C to A, and .8 = the bearing, W the Westing, N the Northing. Then D = , or i3 ^ Sm.Ji' Cos.B From Computation (1), we find W= 136227.42 Log. = 5.1342645 , £ = 81° 23' 18".45 Sin. = 9.9950761 (6) D = 137780.7 ft. Log. = 5.1391884 Having obtained the distance D, we assume a point .r in the meridian AP of the same Lat. as C. The distance xA and the angles AxC and xCA, in the small triangle AxC, being required, we find it convenient to determine the angles at x and C, in the spherical triangle xPC. To deter- mine the angles x and C, we have Cot.x=GotC^= Cos. PC. Tang. J P. PC = the complement of Lat. C= 47° 38' 30" Cos. = 9.8285080 From (3) 4 p = 00 15 07 .04 Tang. = 7.6432041 (7) a:=C=89 49 48 .87 Cot. = 7.4717127 Having thus found the angles AxC and ACx, and substituting for AxC, x", and for ACx, C", the angle at A being the same in both triangles, we INTRODUCTION. XXV shall always represent it by an unaccented A ; we now have 180° — x=x", and 180°— [C+^ (from 1)]=C". (8) Thus, 180°— 89° 49' 48". 87 =90° W 11". 13 = a/'. (9) And 180°— [89 49 48 .87-J-81 23 18 .45] = 8° 46' 52".68 = C". Having proceeded thus far, it becomes necessary to calculate approxi- mately the area of the small triangle AxC, for the purpose of ascertaining the excess of the three angles of said triangle over 180°, that we may be able to calculate, according to the method of Legendre, the length of the side xA:* To compute the spherical excess, we have to find the approximate area of the small triangle ACx. Let iS^ area, a= the side xC, and 7?=^ the side J. C, and 6'=: the angle arC^. We then have 9.63' 10584.04 1 60947.82 Hilliard's Knob, N. E. 72 38 49.66 12188-2.05 116335.48 36352.95 Jackson's Hill, S. W. .57 20 23.41 23300.13 19764.37 12682.00 Mount Lincoln, N. E. 67 34 02.27 151200.90139774.03 57704.04 Mount Tom, - N. E. 80 43 00.39 80159.39 79109.54 12930.90 Proven's Mountain, - S. E. .55 16 24.51 78042.40 64141.52 44157.05 Rattlesnake Mountain, S. E. 66 35 14.44 157839.54144644.17 1 02717.60 Winchel's Mountain, S. E. U 00 52.98 55270.15 10501.12 54257.86 French's Hill - - - to Bald Peak, - S.W. 42 11 22.29 159078.48107237.83 1 118110.14 Becket Station, S.W. 32 41 18.51 54313.11 29332.94 45709.03 TRIGONOMETRICAL SURVEY. SECTION I. TABLE 1 — Continued. NAMES OF STATIONS. Direc- tions. Bearings. Distances in feet. Eastings or Westings in (eet. Nortliings or Southings in leet. French's Hill - . - to Berlin Mountain, N. W. O / // 34 39 40.71 117416.30 66777.48 96578.30 Dug Hill, S. E. 18 08 07.39 84463.74 26290.47 80267.69 High Ridge Hill, - N. E. 84 44 43.75 86568.34 86204.66 7927.94 Hilliard's Knob, S. E. 72 53 08.9] 149234.69 142626.36 43916.22 Jilson's or Rowe & Wlii- ) tingham line Station, ) N. E. 20 35 41.88 121119.33 42604.86 113378.63 More'sHill, - N. E. 78 39 59. 9C 69856.25 68494.10 13727.96 Perry's Peak, . - - S.W. 88 40 51.40 94254.54 92430.04 2128.28 Saddle Mountain, - N. W. 24 18 48.44 83965.12 34570.81 76518.00 Spruce Hill, - - . N. W. 5 28 24.70 88894.12 8479.23 88488.76 Walnut Hill, - N. E. 40 50 37.05 108208 35 70767.90 81859.34 High Ridge Hill - - to Bear Mountain, N. E. 57 05 17.98 93677.84 78643.44 50899.46 Hilliard's Knob, S. E. 47 25 29.81 76623.95 56425.24 51840.35 Mount Grace, . - - N. E. 47 30 11.70 131823.91 97195.82 89053.42 Mount Lincoln, S. E. 69 05 26.18 85483.00 79853.57 30508.11 Mount Tom, - - - S. E. 14 18 36.00 77672.57 19198.18 75262.60 Packard's Mountain, N. E. 8G 58 59.89 96735.02 98598.20 5196.12 Jackson's Hill - - - to Bccket Station, N. W. 37 11 13.13 59294.5) 35838.68 47238.00 Seymore's Hill, S.W. 30 23 19.34 48381.33 24474.38 41734.39 Winchel's Mountain, S. E. 36 07 28.00 51473.42 30345.71 41577.08 Jilson'sorRoweiSiWhi- ) ^^ tingham Stat'n,Vt. line, ^ High Ridge Hill, - S. E. 22 27 40.36 114108.34 43596.00 105451.87 More'sHill, - S. E. 14 33 48.04 102958.57 25888.95 99650.55 Mount Grace, - - - S. E. 83 21 24.38 141745.33 140793.20 16398.04 Walnut Hill, - S. E. 41 46 50.57! 42268.00 28162.40 31519.18 Here's Hill - - - - to Bear Mountain, N. E. 64 55 04.50106383.10 96351.32 45097.52 Dug Hill S.W. 24 10 46.05103034.64 42202.58 93995.12 Hawes'Hill, - S. E. 89 32 23.54 • • • ;_^ High Ridge Hill, - S. E. 71 51 46.81 18636.58 17710.07 5801.37 Hilliard's Knob, S. E. 52 08 01.91 93905.86 74133.72 57640.41 Mount Grace, - - - N. E. 54 04 33.64 141894.46 114907.00 83251.04 --. ■• Mount Lincoln, S. E. 69 35 09.48 104099.91 97562.07 36310.22 TRIGONOMETRICAL SURVEY. SECTION I. TABLE 1 — Continued. NAMES OF STATIONS. Direc- tions. Bearings. Distances in feet. Eastings or Westings in feet. Northings or Southings iu feel. More's Hill - -- - to Mount Tom, - - . 1 o / // S. E. |24 28 43.71 89009.20 36906.42 81063.20 Packard's Mountain, S. E. 89 42 05.05 1 110307.37 116305.78 606.13 Proven's Mountain, - S. E. 9 00 15.34 140179.32 21939.02 138451.86 Mount Esther - - - to High Ridge Hill, - s.w. 83 42 46.09 14474.97 14387.91 1585.20 Hilliard's Knob, - S. E. 38 11 46.18 67978.70 42035.00 53424.40 Mount Lincoln, S. E. 63 53 04.34 72907.48 65464.29 32092.51 Mount Tom, - - - S. E. 3 34 51.20 76997.72 4809.09 76847.40 North end of base, - N. E. 55 34 51.46 17307.07 14277.01 9782.66 South end of do. - S. E. 25 27 50.58 32309.87 13917.27 29225.31 Mount Lincoln - - - to Hilliard's Knob, - S.W. 47 40 .54.22 31684.21 ■ • Mount Tom - - - to Hilliard's Knob, - N.E. 57 49 25.35 43981.62 • • Peaked Mountain, - S. E. 'so 04 10.45 109534.25 . • Rattlesnake Mountain, S. E. 40 59 26.27 100220.30 • • North end of base - to Hilliard's Knob, S. E. 23 42 52.00 60033.00 27763.58 63203.90 Mount Lincoln, S. E. 50 43 04.21 66136.20 51191.90 41873.50 South end of base, - S.W. 00 31 28.00 39009.73 357.00 39008.10 Perry's Peak - - - to Alander Mountain, - S.W. 15 49 44.15 126149.81 34409.48 121366.23 Bald Peak, - - - S.W. 7 15 50.28 117117.75 14808.45 116177.81 Becket Station, S. E. 55 21 55.39 76686.14 63096.84 43583.87 Pittsfield Church, - N.E. 73 43 55.97 35657.92 34230.28 9988.70 Proven's Mountain - to Hilliard's Knob, N.E. 32 51 27.67 96199.54 52193.47 80809.04 Mount Tom, - - - N.E. 14 37 00.49 59307.60 14906.45 57388.11 Peaked Mountain, - S. E. 83 33 56.31 99803.84 98964.90 12913.04 Rattlesnake Mountain, S. E. 77 15 01.44 82747.34 80707.12 18261.57 Saddle Mountain - - to Bald Peak, - - - S.W. 20 27 16.85 207938.57 72667.55 194827.90 Berlin Mountain, N. W. .■58 04 44.25 37936.10 32199.30 20058.72 Clarksburg Station, - N.E. 3 07 27.20 35421.77 1930.52 35369.12 High Ridge Hill, - S. E. 60 24 23.24 138893.80 120775.22 08591.88 Jilson's or Rowe & Whi- ? tingham Stale line Stat'n, I N.E. 64 28 11.55 85525.22 1 77174.24 36800.15 More's Hill, - S. E. 58 38 55.32 120682. 47| 103061.97 02789.14 TRIGONOMETRICAL SURVEY. TABLE L SECTION 1— Continued. NAMES OF STATIONS. Direc- tions. Bearings. Distances in feet. Eastings or Wcsiings in feet. Northings orSouUniiga in feel. 1 II ! Saddle Mountain - - to Mount Grace, - - - N. E. 84 38 13.91 218927.66 217969.40 20461.40 N. W. corner of State, - N. W.33 42 29.54 47658.65 26148.82 39646.39 Perry's Peak, - - - S.W. 36 20 29.20 97634.72 57858.03 78644.70 Pittsfield Church, - S.W. 18 59 26.71 72608.02 23627.80 68656.06 Spruce Hill, - - - N. E. 65 21 18.05 28704.77 26090.01 11969.73 Walnut Hill, - N. E. 87 05 53.45 105471.85 105336.58 53394.27 Scyraorc's Hill, - - to Becket Station, N. W. 7 16 44.91 89695.04 11364.68 88972.28 Winchel's Mountain, N. E. 89 50 13.00 54820.29 54820.10 156.00 Spruce Hill - - - - to Berlin Mountain, N. W. 82 05 57.31 58847.67 58288.84 6088.76 Clarksburg Station, - N. W.45 54 57.50 33634.32 24160.23 23399.82 Jilson's or Rowe & Whi- ? tingham State line, ^ N. E. 64 01 17.25 56825.55 51083.80 24891.55 Walnut Hill, - S. E. ^85 13 07.43 79522.40 79245.70 6628.36 Williamstown Church, N. W.67 IG 33.15 41030.65 37845.65 15849.92 South end of base - - to Hilliard's Knob, S. E. 49 17 20.00 37097.41 28120.13 24196.06 Mount Lincoln, S. E. 86 49 00.99 51628.54 51548 90 2866.73 S. W. corner of State to Conn't State line bound, - S. E. 89 01 48.17 7225.. 37 7224.03 122.30 Walnut Hill ... to Bear Mountain, S. E. 76 14 33.66 96857.74 94079.02 23033.77 High Ridge Hill, - S. E. 11 47 36.08 75529.82 15437.00 73935.30 Hilliard's Knob, S. E. 29 44 28.23144854.27 71659.70 125773.43 Leydon and Guilford, Vt. ? State line Station, ^ N. E. 50 47 49.80 46561.80 36081.35 29430.13 Mere's Hill, - S.W. 1 54 41.19 68168.48 2273.70 66125.02 Mount Grace, . - - N. E. 82 21 16.56113643.29 112633.03 15119.31 Warwick (N. H.) State line. N. E. 77 42 34.20124849.49 121938.03 26576.51 Winchel's Mountain - to Birch Stake Station, S. E. 11 09.13 6689.62 21.70 6G69.59 Hilliard's Knob, N. E. 49 24 53.85139271.74 105768.66 90606.84 Mount Tom, - - - N. E. 45 34 23.41 95983.89 68546.40 67188.50 Peaked Mountain, - S. E. 88 49 52.62 152574.35 152549.67 3112.20 Proven's Mountain, - N. E. 79 38 04. OC 54465.00 53576.10 9799.72 Rattlesnake Mountain, S. E. 86 23 38.81 134550.28 134283.90 8462.29 TRIGONOMETRICAL SURVEY. SECTION I. TABLE 2. This Table shows the Bearings, with the Northings, Sojithi7igs, Eastings or Westings made on each course, from jn'imitive stations to secondary objects, in the first section, on parallels to the meridian of Frenches Hill. WHAT OBJECTS FROM WHAT STATIONS. Direc- tions. Bearings. Norlhings or Southings in feet. Eastings or Westings in feet. Adams North Church, " South Church, Becket, Wadman's Station, (( It " . . « Church, (i « _ _ ■ Bemardston Church, - Blandford, North Church, - (( (t (t . . " South Church, - u « « . . Cheshire, Round's Rocks, - a (( « . , (( f( « . . " Church on hill, - " Church in valley, Chester, old Church, Chesterfield Church, - " « . . . Dalton Church, Deerfield Church, " Bloody Brook Church, from Spruce Hill, - " *' » - Seymore's Mountain, Becket Station, More'sHill, - Dug Hill, Mount Grace, - High Ridge Hill, - Mount Tom, - Winchel's Mountain, Proven's Mountain, Perry's Peak, - Pittsfield Church, - French's Hill, Spruce Hill, - Dug Hill, More's Hill, - French's Hill, More's Hill, - Pittsfield Church, - High Ridge, - N. W, S.W. N.E. S. E. S.W. N. W. S.W. N.E. S.W. N. W, N. W, N. W. N.E. N.E. N. W, S.W. S.W. N.E. S.W. S. E. S.W. N.E. N.E. N.E. O / 46 07 19 37 48 08 1 10 19 70 04 46 49 05 46 50 06 16 81 30 46 28 57 30 79 38 22 11 00 45 9 19 07 59 54 51 38 29 21 15 54 39 36 13 20 19 10 20 33 28 20 8 20 53 30 37 37 76 25 50 29 56 47 70 44 37 40 27 00 66 31 36 10818.50 18400.30 84231.00 4743.60 65789.37 28204.63 7794.00 81259.32 14410.49 52779.00 45130.65 35330.30 61527.00 51538.42 59400.50 34726.00 39128.22 30195.20 03800.00 12837.30 20565.44 9319.44 35719.44 13239.00 11250.70 14274.00 1723.12 13090.00 75939.00 33737.66 52230.41 44900.45 78822.12 10271.15 7405.48 60982.72 48921.82 14691.65 43510.00 12075.13 25871.12 4430.87 37771.70 53187.07 15304.44 20077.22 30455.16 30486.42 6 TRIGONOMETRICAL SURVEY. SECTION I. TABLE 2 — Continued. WHAT OBJECTS FROM WHAT STATIONS. Deerfield, Bloody Brook Church, Easthampton Church, Egremont, Hollenbeck's Church, " Little York Church, Goshen, North Church, - (( an , ^ " South Church, - tt t( i( _ _ Great Barringlon, Gibson's Hill, " " Church, Granville, Skunk Hill, - t: tt tt ^ _ " West Church, - " East Church, - Greenfield Church, Hatfield Church, - (( tt . _ . Hawley Church, ... tt tt _ . . Heath Church, ... tt tt ... Toby three point station, - tt tt tt _ _ It tt tt _ . Lee Church, - - . . Lenox Cliurcli, on hill, ft tt (( _ ^ Middlefield Church, tt tt ^ ^ _ from Walnut Hill, - Winchel'a Mountain, Proven's Mountain, - Bald Peak, tt tt . . More's Hill, High Ridge Hill, - More's Hill, - High Ridge Hill, - Bald Peak, tt tt _ _ Winchel's Mountain, Dug Hill, Skunk Hill, - Winchel's Mountain, High Ridge, HiUiard's Knob, Mount Esther, - Saddle Mountain, Spruce Hill, Saddle Mountain, More's Hill, - Pitlsfield Churcli, Perry's Peak, - Becket Station, Toby Station, - Bald Peak, Alander Mountain, - Dug Hill, Wadman's Hill, Direc- tions. S. E. N. E. N. E. N. E. N. W S.W. s. w. S.W. S.W. N. E. N. E. N. W, S. E. N. W, N. E. N. E. N. W, S. E. S. E. S. E. N. E. N. W. S. E. S. E. S.W. N. W. N. E. N. E. N. W. N. E. Bearinsrs. I Northings i or Southings in feet. 37 OG 39, 38 34 15 7 10 33 13 14 05 3 35 40 39 58 02 88 34 50 28 16 37 83 21 25 25 46 47 29 53 55 58 22 20 3 37 19 56 52 20 G3 24 20 31 42 12 45 25 10 31 27 38 74 13 26 55 37 55 81 47 59 7 42 24 1 16 33 29 19 26 53 18 34 1 33 33 23 20 55 31 09 42 21 25 32 45 47 27 60699.41 77941.50 68142.00 21373.20 34837.30 6370.98 571.20 8388.90 2588.30 31836.06 33843.52 4565.10 49690.65 2633.36 3245.55 50G88.72 23200.00 30224.80 20984.30 32954.64 13366.63 76154.40 73855.23 63865.90 20283.04 21374.60 95131.70 100321.62 51531.00 21709.53 Eastings or Westings in feet. TRIGONOMETRICAL SURVEY. SECTION I. TABLE 2 — Continued. WHAT OBJECTS FROM WHAT STATIONS. Direc- tions. Bearings. Northings or Soulhings in feet. Eastings or Westings ill feet. / // Mount Washington Church, - from Bald Peak, S.W. 84 43 41 823.29 8922.32 C( (( (C _ u Alander Mountain, - N. E. 67 45 25 4366.55 10677.00 New Marlborough South Church, " Bald Peak, S. E. 88 25 25 1491.87 54210.60 Northampton Church, - - " Hilliard's Knob, N. W. 81 44 22 4746.96 32696.80 « « - - " Winchel's Mountain, N. E. 37 27 53 95353.00 73073.60 tC (C ^ _ (t High Ridge, - S. E. 26 44 26 47092.60 23726.90 * Otis, East Church, - - - « Seymore's Mountain, N.E. 24 30 57 41577.02 18961.62 ((It n ■ - . " Jackson's Hill, - S.W. 88 22 26 156.49 5512.25 " Filley's Hill, three point, - Seymore's Mountain, N.E. 3 25 59 58029.14 3481.16 tt U (( (( li _ it Becket Station, S. E. 23 37 51 30943.00 14845.90 " Centre Church, - - " Filley's Hill, - S.W. 2 22 40 8133.80 337.75 Peru Church, ... « Saddle Mountain, S. E. 23 55 03 72533.00 32108.64 " " . . . . " Spruce Hill, S. E. 4 06 50 84505.00 0077.98 « " . . . . " French's Hill, - N. W. 31 06 29 3981.31 2402.44 Pittsfield Church, - - - Saddle Mountain, S.W. 18 59 27 68656.06 23627.80 (( (C _ _ _ « Perry's Peak, - N.E. 73 43 56 9988.70 34230.28 Richmond Church, - - - ' ** " - - S. E. 16 55 28 11110.11 3380.70 Sandisfield, Morley's Hill, - " Jackson's Hill, - S.W. 86 50 57 2143.90 40896.76 tt f( tt ^ it Seymore's Mountain, N. W. 22 31 42 39592.40 16422.70 tt tt tt _ tt Bald Peak, N.E. 72 19 19 23217.60 72846.60 tt (( (( _ (( Becket Station, S.W. 5 51 05 49380.16 50G0.60 " Fargo Station - " Morley's Hill, - N. W. 88 26 42 127.68 4703.47 " North Church, no spire, " " " . . S.W. 8 50 18 5751.50 894.32 Village Church, - Jackson's Hill, - S.W. 57 15 32 22104.33 34376.76 C( (( (( ^ tt Seymore's Mountain, N. W. 26 46 37 19628.40 9905.10 Sheffield Church, - - - " Bald Peak, N.E. 81 56 30 3026.05 21373.52 Tolland Church, no spire, - " Seymore's Mountain, N.E. 70 34 40 8720.52 24732.63 ti it U . _ (C Winchel's Mountain, N. W. 74 06 20 8566.15 30082.78 Tyringham Church, - - " Fargo Station, - N. W. 43 40 05 12159.32 11606.71 Washington Church, - - " Dug Hill, N. W. 43 33 06 57933.73 55076.42 TRIGONOMETRICAL SURVEY. SECTION I. TABLE 2 — Continued. WHAT OBJECTS FROM WHAT STATIONS. Direc- tions. Bearings. Norlhings or Southings in feet. Eastings or Westings in feel. Westfield Church, - - - from Proven's Mountain, - N. W. o / // 42 55 27 12908.00 12005.00 " **_-_" Peaked Mountain, - N. W. 76 54 03 25821.91 110970.30 West Springfield Church, - " Proven's Mountain, - N. E. 62 51 52 10993.22 21449.80 (( li u . . c( Mount Tom, S. E. 7 57 19 46395.00 0483.46 " " Ireland Parish, " " *' . - S. E. 16 31 2G 17044.56 5056.56 (( i( a and longitudes of 1st section, ) Peru, - 112013.20 131437.45 • 73 02 39.27 Clarksburg Station, - . - Clarksburg, - 249067.70 98795.67 42 44 03.90 73 09 55.90 College Chapel, ... Amherst, 117047.81 271765.07 42 22 15.01 72 31 28.49 Connecticut line at - - - Granville, —4785.32 167975.81 42 02 15.65 72 54 34.72 " lino bound at - Mount Washington, —122.30 7224.30 • • • Dug Hill, . - - , - Blandford, 56916.01 157727.33 42 12 25.46 72 56 49.70 French's Hill, - - - - Peru, - - - 137180.66 131437.45 42 25 38.67 73 02 39.27 Greenfield Church, - - . Greenfield, - 195792.40 248951.70 42 35 14.78 72 36 27.21 High Ridge Hill, Williamsburg, 145106.67 217042.20 42 26 55.38 72 43 28.01 Hilliard's Knob, Amherst or Granby, 93267.74 274004.38 42 18 20.38 72 30 59.83 Holcomb'a House, . - - Southwick, - —13428.30 194385.31 42 00 49.70 72 48 44. 8S Jackson's Hill, - - . - Blandford, - 44234.55 137942.98 42 10 20.29 73 01 12.81 Jilson's or Roive and Whiting- > ham Station, - - - ) Vermont line. 250559.18 174042.32 42 44 18.48 72 53 07.95 Lcyden and Guilford Station, C( u 248470.00 238380.77 42 43 .55.78 72 38 40.57 More'sHill, . . - - Goshen, 150908.49 199931.55 42 27 53.29 72 47 22.67 Mount Esther, - - - . Whately, 146691.85 232028.75 42 27 10.45 72 40 16.48 10 TRIGONOMETRICAL SURVEY. SECTION I. TABLE 3 — Continued, NAMES OF STATIONS. Towns in which situated. Northings in teet. Eastings in leet. Latitude, Longitude. Mount Grace, . - - - Warwick, 234159.27 314837.80 O / // 42 41 29.56 / // 72 21 41,92 Mount Lincoln, - - - - Pelham, 114598.42 297494,75 42 21 49,01 72 25 45.80 Mount Tom, . - - - Northampton, C9845.50 236836.70 42 14 30.95 72 39 17.08 Northampton Church, " _ - 98014.87 241368.56 42 19 09.09 72 38 14.93 North end of base, Deerfield, 150473.22 246304.46 42 28 46.44 72 37 05.28 Northwest corner of State, Williamstown, 253344.52 70417.85 42 44 45.58 73 16 17.63 Peaked Mountain, Monson, 456.44 320832.96 42 02 51.06 72 20 47.03 Perry's Peal{, . - - - Richmond, - 135052.31 39007.79 42 25 15.81 73 33 12.48 Pittsfield Church, Pittsfield, - 145041.07 73237.70 42 26 55.00 73 15 36.12 Proven's Mountain, - - - West Springfield, - 12457.80 221869.72 42 05 04.58 72 42 39.12 Rattlesnake Mountain, Connecticut line, - —5803.96 302573.63 42 01 59.06 72 24 49.86 Saddle Mountain, . . - Adams, 213698.49 96866.64 42 38 14.42 73 10 22.11 Seymore's Hill, - - - - Sandisfield, - 2499.15 113468.60 42 03 27.85 73 00 37.64 South end of base, - - - Hatfield, 117465.84 245946.00 42 22 21.07 72 37 12.67 Southwest corner of State, - . • 42 02 59.54 73 31 42.66 Springfield Court House, - Springfield, - 18577.06 253048.60 42 06 03.59 72 35 44.93 Spruce Hill, - . . - Adams, 225668.20 122956.71 42 40 12.93 73 04 32.87 Stale House, - . . - Boston, 118213.65 664843.00 42 21 30.00 71 04 09.00 Tufls'Hill, . - . - New Braintroe, 98467.07 389265.20 42 19 01.90 72 05 24.96 Wachusett Mountain, Princeton, 161806.52 441791.92 42 29 21.21 71 53 33.885 Walnut Hill, - - - - Charlemont, - 219039.91 202205.42 42 39 06.37 72 46 51.00 Williamstown Church, Williamstown, 241518.22 85110.22 42 42 49.08 73 13 00.26 Winchel's Mountain, - Granville, 2655. IC 168288.66 42 03 29.17 72 54 30.41 TRIGONOMETRICAL SURVEY. 11 SECTION I. TABLE 4. This Table shows the Northings and Eastings, from the Southwest corner of the State, of secondanj objects in the first section, together with their Latitudes and Longitudes. NAMES OF OBJECTS. Norlhings in feel. Eastings in feet. Latitude. Longitude. O f II o / // 230486.70 111706.01 42 41 59.74 73 07 03.71 207267.90 108682.71 42 37 11.04 73 07 43.83 86723.63 115192.81 42 17 20.06 73 06 15.55 85120.18 123991.11 42 17 04.27 73 04 18.40 226365.48 262608.12 42 40 16.10 72 33 22.18 55434.58 158016.04 42 12 10.81 72 50 45.88 47786.95 160885.09 42 10 55.22 72 50 07.80 190.580.48 87928.80 42 35 25.14 73 12 21.34 190942.20 110881.68 42 34 29.75 73 07 14.21 186539.98 97085.59 42 33 46.11 73 10 18.01 87110.15 162159.05 42 17 23.74 72 55 50.23 124343.20 184625.76 42 23 31.22 72 50 49.90 154360.51 99914.92 42 28 28.19 73 09 40.19 180826.11 248097.36 42 32 46.95 72 30 39.70 158343.08 248129.34 42 29 04.82 72 30 40.78 80598.23 230446.09 42 16 17.50 72 40 41.42 40249.10 29224.04 42 09 38.09 73 25 17.40 53713.20 22008.94 • • 144536.49 194591.04 42 26 50.49 72 48 30.32 142519.00 195418.68 • • 50711.96 39573.62 • • 52719.42 43657.14 42 11 42.50 73 22 06.26 7223.11 160874.48 • • 9856.47 156839.18 42 04 40.48 72 57 02.19 5900.71 174771.46 . • Adams North Church, ... " South Church, Becket, Wadman's Station, " Church, Bemardston Cliurch, - - - . Blandford North Church, - - - " South Church, - Cheshire Rounds' Rocks, ... " Church on the Hill, " " in Valley, Chester Old Church, - - - - Chesterfield Church, - - . - Dalton Cliurch, . - . - . Deerfield Church, .... " Bloody Brook Church, - Easthampton Cliurch, .... Egremont Church by Hollenbeck's Tavern, " " Little York, - Goshen North Church, ... " Soutli Church, Great Barrington, Gibson's Hill, - " " Church, - Granville Skunk Hill, « West Church, - " East Church, 12 TRIGONOMETRICAL SURVEY. SECTION I. TABLE 4 — Continued. NAMES OF OBJECTS. Norlhlngs in feet. Eastings in leet. Latitude. Lonsritude. Greenfield Church, - - - - - Hatfield Church, . - - - . Hawley Church, ..... Heath Church, ------ Lee, Toby 3 point Station, Tyringhatn, Lee Church, -.-... Lenox Church on Hill, - - - . Middlefield Church, ..... Mount Washington Church, ... New Marlborough South Church, Northampton Congregational Church, . Norwich old Church, no spire, ... Otis East Church, ..... « Filley's Hill 3 point Station, " Center Church, Peru Church, -..-.. Pittsfield Church, Richmond Church, ..... Sandisfield, Morloy's Hill, . - - - " Fargo Station, .... " North Chtirch, no spire, - " Village Church, Sheffield Church, Southampton Church, - - . . - Tolland old Church, no spire, - - - Tyringham Church, . - . . - Washington Church, . - - . . Westfield Church, West Springfield Church, (north of Academy,) " " Ireland Parish Church, - 195795.39 116467.40 192713.87 227064.00 71186.71 92561.31 114007.64 108435.38 18052.61 17384.03 98014.87 83042.62 44077.10 60528.10 52394.30 141163.55 145041.07 123942.20 42091.59 42219.27 36340.09 22128.88 21901.95 65121.93 11220.49 54378.59 114850.31 25365.63 23450.76 52803.12 248952.30 250522.14 171143.50 189623.74 74882.91 74301.11 05263.26 137510.02 15275.03 78407.94 241368.56 185252.53 132430.47 110949.78 116612.03 129035.00 73237.70 42388.49 97044.84 92341.37 96150.52 103504.80 45570.86 214549.24 138203.55 80734.66 102650.91 209863.69 243319.84 241894.43 42 35 14.78 42 22 10.97 42 34 47.00 42 40 26. 42 18 17.10 42 21 48.76 72 36 27.21 72 36 11.73 72 53 48.18 72 49 39.81 73 15 20.18 73 17 21.36 42 20 54.65j 73 01 18.34 42 05 58.73| 73 28 21.26 42 05 54.40 73 14 23.19 42 19 09.091 72 38 14.93 42 16 43.13 72 50 42.89 42 11 40.88 73 05 50.36 42 26 18.01 42 26 55.60 73 03 11.33 73 15 36.12 42 23 26.16 73 22 26.80 42 06 41.71 42 06 38.06 42 13 45.20 42 04 54.08 42 11 59.99 42 21 57.85 42 07 12.55 42 06 52.27 73 08 49.33 73 21 39.29 72 44 13.77 73 01 09.48 73 13 53.35 73 09 03.01 72 45 17.88 72 37 53.75 TRIGONOMETRICAL SURVEY. SECTION I. TABLE 2 — Continued. 13 NAMES OF OBJECTS. Northings in feet. In feef Latitude. Longitude. West Springfield, Feeding Hills Church, Westhampton Church, - . . Whately Church, .... Williarastown Church, - . . Williamsburg old Church on Hill, Windsor Brick Church, ... Worlhington Church, ... 7837.85 92864.70 142148.23 241518.22 127392.27 168592.05 126984.65 226780.02 201947.60 240080.71 85110.22 212310.52 126379.06 158423.21 42 18 19.73 42 26 25.20 42 42 49.08 42 24 00.57 42 30 49.01 42 23 57.76 72 47 00.24 72 38 29.30 73 13 00.26 72 44 40.63 73 03 46.86 72 56 39.35 The following are the results of work done with the small si.\-inch Theodolite that reads to a minute only, in the minor triangulation. From the manner in wliicli these results were obtained, they are probably not so accurate as they would have been had they come more direct from the primitive stations; still it is presumed that none will be found in error to exceed ten feet, and the most of them are much nearer. Marshall's Hill, - Manatuck Mountain, Oak-Tree Boundary in Connecticut State Line at Gran- ville, marked in 1717, - - . . - Boundary Stone in Connecticut Line at Granville, in west part of town, ----- -^ Boundary Stone in Connecticut Line, on road from ) Sandisfield to Colebrook, . - - . ^ Chimney of Amasa Holcomb's House in Southwick, Boundary Stone at N. W. corner of Southwick Jog, - " " at S. W. corner of Southwick Jog, " " at S. E. comer of Southwick Jog, " " at N. E. comer of Southwick Jog, " " in Connecticut Line, on east side ot ) Connecticut River, - - ) " " in Connecticut Line, on west side of Connecticut River, " " in Connecticut Line, on road from Sheffield to Salisbury, - -22933.64 183419.76 -18968.75 203529.23 —4752.981 176064.08 —4666.14 —3239.20 —13428.30 —5064.90 —19286.50 —17215.30 —5159.38 —9262.72 — 6908.&3 —336.00 150798.00 109068.30 194385.80 192198.84 191332.50 205000.52 207916.10 249318.63 247259.23 39760.20 42 02 15.84 72 52 47.44 42 02 17.03 72 58 22.52 42 02 31.11 73 07 35.94 42 00 49.70 42 02 12.39 41 59 51.89 42 00 11.98 42.02 11.00 42 01 28.74 42 01 52.10 42 02 58.11 72 48 44.80 72 49 13.51 72 49 25.47 72 46 24.23 72 45 45.07 72 36 36.31 72 37 03.46 73 22 55.27 14 TRIGONOMETRICAL SURVEY. gECTIOl^ lie TABLE 1. 2'Ae following Table shows the Bearings from one Station to another on Parallels to the meridian of Tufts'' Hill, with the Northings, Southings, Eastings or Westings made on each course. NAMES OF STATIONS. Direc- tions. Bearings. Distances m feet. Northings or Southings in feet. Eastings or Weslings in feet. o / // Alum Pond Hill - to Bald Hill, - N. E. 57 22 03.83 1C94S.28 9138.47 14273.54 Fay's Mountain, N. E. 24 12 27.83 87775.92 80059.00 35992.92 Hatchet Hill, - N. W. 88 25 52.17 86191.44 2361.56 86159.67 Mount Daniel, N. W.' 76 10 35.17 11275.43 2693.50 10948.51 N. E. corner of Conn. N. W. 84 31 45.17 10532.70 1003.67 10484.51 Bald Hill - - - to Chestnut Hill, N. E. 78 59 42.83 37684.15 7190.43 30991.02 Fay's Mountain, N. E. 17 01 38.13 74169.85 70920.52 21719.38 Miscoe Hill, - - - N. E. 49 19 17.83 45761.73 29828.83 34704.57 Bear Mountain - - to High Ridge Hill, - S. W. 57 43 40.23 93677.84 50018.97 79206.37 More'sHiU, - s. w. C5 33 27.83 106383.10 44019.53 96849.52 BumsketHill - - to Alum Pond Hill, - S.E. 19 50 55.37 108629.85 102178.03 36884.66 Bald Hill, S.E. 28 48 16.51 106175.41 93039.56 511.58.20 Chandler's Hill, - S.E. G9 50 29.11 32012.68 11035.13 30051.32 Colonel's Mountain, S. W. 75 15 08.80 93870.66 23896.73 90785.03 Fay's Mountain, S.E. 73 07 02.01 76159.24 22119.04 72877.58 Hatchet Hill, - s. w. 26 16 29.21 111312.38 99816.47 49275.01 Hawes'Hill, - N. W. 46 30 30.87 82455.04 56746.59 59818.18 Mugget Hill, - s. w. 14 45 18.53 63147.16 61067.45 16084.88 Packard's Mountain, N. W. G4 39 15.98 130170.47 58292.61 123074.12 Colonel's Mountain to Hilliard's Knob, N. W. 71 09 24.37 79343.12 25627.47 75095.07 Hitchcock's Hill, - S. W. 7 41 58.83 55344.12 54847.31 7412.29 Mount Lincoln, N. W. 47 45 34.77 09466.22 40696.10 51430.82 Mount Tom, - - - N. W. 88 39 48.37 112611.10 2022.60 112581.36 Peaked Mountain, - S,W. 23 11 08.53 74634.82 68610.33 29381.66 TRIGONOMETRICAL SURVEY. SECTION II. TABLE 1 — Continued. 15 NAMES OF STATIONS. Direc- tions. Bearings. Distances in feet. Northings or Southings in feet. Eastings or Westings iu feet. o / // Colonel's Mountain to Rattlesnake Mountain, - S.W. 32 53 16.33 87816.56 73748.28 47688.52 Fay's Mountain - to Chestnut Hill, S. E. 13 28 37.17 65528.55 63730.09 15271.64 Miscoe Hill, - . - S. E. 17 32 15.17 43092.38 41091.69 12985.13 Hatchet Hill - - to Mount Daniel, N. E. 89 44 29.83 75233.52 334.47 75211.16 N.W. corner of R. Island, S. E. 84 45 24.44 76441.67 6993.96 76115.86 Hilliard's Knob - to High Ridge Hill, - N. W. 46 47 07.57 76623.95 52466.13 55842.96 Mora's Hill, - N. W. 51 29 39.67 93905.86 58465.57 73486.11 Mount Esther, N. W. 37 33 24.17 67978.70 • • Mount Lincoln, N. E. 48 19 15.43 31684.21 21068. G3 23664.75 Mount Tom, - S.W. 58 27 47.58 43981.62 23004.87 37486.29 Peaked Mountain, - S. E. 25 52 41.17 104738.17 94237.80 45713.91 Rattlesnake Mountain, - S. E. 15 25 03.17 103084.50 99375.75 27406.55 Hitchcock's Hill - to High Rocky Ridge, S.W. 50 33 53.53 30415.93 19320.69 23493.57 Monson State Line, S.W. 9 30 55.53 19865.88 19593.31 3285.00 Mount Daniel - - to Bald Hill, - N. E. 75 39 46.83 26032.18 6444.97 25222.05 N. E. corner of Connec't, S. E. 15 21 26.17 1752.75 1690.20 464.08 N. W. corner of R. Island, S. E. 6 54 52.17 7381.03 7327.40 6S8.12 Mount Grace - - to Bear Mountain, S.W. 26 34 19.33 42425.95 37944.73 18978. 8D 1 High Ridge Hill, - S.W. 48 08 33.03 131823.91 879C.3.70 98185.26 1 Hilliard's Knob, - S.W. 16 46 44.53 146673.71 140420.83 42342.30 Ley den &Guilford,Vt. line, N. W. 78 46 09.86 77874.65 15164.55 76.383.01 More'sHill, - S.W. 54 42 55.83 141894.46 81964.26115828.41 Warwick State line, N. E. 39 51 21.83 14790.48 11.352.57 0479.37 Mount Lincoln - to High Ridge Hill, - N. W. 68 27 03.97 85483.00 31397.50 79507.71 More'sHill, - N. W. 08 56 47.17 104099.91 37396.94 97150.86 1 Mugget Hill - - to Chandler's Hill, - N. E. 42 40 49.90 68056.40 50032.32 46136.20 1 Colonel's Mountain, IV. W. 63 32 46.27 83424,52 37170.72 74700.14 Fay's Mountain, N. E. 66 21 13.86 97117.07 38948.41 68062.46 Hatchet Hill, - S.W. 40 33 57.67 51029.60 38749.02 33100.13 Hitchcock's Hill, - S.W. 77 50 35.03 83977.80 17676.59 82112.43 16 TRIGONOMETRICAL SURVEY. SECTION II. TABLE 1 — Continued. NAMES OF STATIONS. Direc- tions. Bearings. Distances in feel. Northings or Southings in feet. Eastings or We.siings in feel. MuggetHill - - to Mount Daniel, S. E. oil/ 1 47 34 33.43 56959.97 38417.08 42021.03 N. W. corner of R. Island, S. E. 43 10 56.40 62742.10 45742.98 42925.73 Packard's Mountain to Bear Mountain, N. W. 22 56 49.67 49869.76 45923.23 19442.56 Colonel's Mountain, S. E. 21 26 41.17 88302.46 82189.34 32289.10 High Ridge Hill, - s.w. 87 37 22.13j 98735.02 4095.74 98648.93 More's Hill, - - - N. W. 89 03 42.77j 116307.37 1903.70 116292.08 Mount Grace, N. W. 19 04.57 83870.24 83868.00 403.67 Warwick State line Stat'n, N. E. 5 24 33.83 95645.04 95320.53 9015.73 Peaked Mountain - to Hitchcock's Hill, - N.E. 57 56 22.43 25925.50 13763.02 21969.37 Monson State line, - S. E. 72 40 14.17 19576.14 5830.29 18684.36 Mount Tom, - - - N. W. 49 25 48.17, 109534.25 71232.93 83199.70 Rattlesnake Mount'n to *»",-- N. W. 40 21 04.17 100320.30 76370.88 64892.84 Tufts' Hill - - - to Bumsket Hill, S. E. 83 38 04.93 50941.80 5643.85 50628.58 Hawes'Hill, - N. W. 10 11 33.39 51922.78 51102.74 9189.60 Mount Grace, - N. W. 28 06 17.97 154760.04 136516.72 72909.21 MuggetHill, - S. E. 27 22 29.67 75125.42 66711.30 34543.70 Packard's Mountain, N. W. 53 59 24.94 89555.26 52648.76 72445.54 Wachusett Mountain, N.E. 40 18 21.11 82285.74 62751.17 53229.68 Watatick Mountain, N.E. 20 24 06.71 147702.20 138438.27 51487.78 Wachusett Mountain to Bear Mountain, N. W. 76 08 02.97 149472.75 35820.82 145117.78 Bumsket Hill, S.W. 2 10 39.28 68447.05 68395.02 2601.10 Chandler's Hill, - S. E. 19 03 52.57 84038.92 79430.15 27450.22 Colonel's Mountain, S.W. 45 20 05.95 131288.91 92291.75 9*386.12 Fay's Mountain, S. E. 37 49 31.74 114595.26 90514 06 70276.48 Hawes'Hill, - S.W. 79 25 45.29 63497.23 11648.43 62419.28 Mount Grace, - - - N. W. 59 40 51.69 146124 64 73765.55 126138.89 MuggetHill, - S.W. 8 12 49.10 130803.24 129462.47 18686.00 Packard's Mountain, S.W. 85 24 09.07 126078.12 10102.41 125675.22 Pepperell State Line, N.E. 45 44 56.22 112450.23 78468.25 80546.92 Watatick Mountain to Bear Mountain, S.W. 74 27 42.06 148815.55 39866.28 143375.88 TRIGONOMETRICAL SURVEY. SECTION II. TABLE 1 — Contintjed. 17 NAIVIES OF STATIONS. Direc- tions. Bearings. Distances in leet. Northings or Southings in feet. Eastings or Westings in feet. Watatick Mountain - to Hawcs'Hill, - S.W. o / // 34 47 23.47 106344.44 87335.53 60677.38 Mount Grace, S.W. 89 06 55.87 124412.73 1921.55 124397.00 Packard's Mountain, S.W. 55 18 31.68 150732.66 85789.51 123933.32 Pepperell State Line Stat'n, N. E. 68 03 52.01 8-2336.32 2781.15 82288.82 State Line, - - - N. W. 16 29 09.86 5531.15 5303.84 1509.29 Wachusett Mountain, S. E. 1 19 07.63 75707.24 75687.10 1741.90 Warwick, N. H. ) State line Station, ) Leyden &. Guilford, Vt. ) line, - - - J N. W. 87 27 31.59 85946.88 3812.00 858G3.31 18 TRIGONOMETRICAL SURVEY. SECTION II. TABLE 2. This Table shows the Bearings^ with the Northings^ Southings^ Eastings or Wcsdiigs 9nade on each course^ from primitive stations to secondary objects^ in the second sec- iion^ on parallels to the vieridian of Ti/fts^ Hill. WHAT OBJECTS FROM WHAT STATIONS. Direc- tions. Bearing's. Norlliings or Soulhiiigs ill (ect. Eastings or Weslmgs in feet. Amherst South Church, - « College Chapel, - " North Church, - ti t( (( Ashburnham Old Church on hill, i( (t (( it u (( (( U It u Ashby Church, ... u u _ _ . Atliol Soutli Church, (t u " _ - . " North Church, " " " . - - Barre Church, ... *' '•--__ Belchertown Church, tt " - _ . Boylston Cliurch, - - . u t* - . _ _ Brookfield Bemis Hill, " " " . . " Church, Charlton North Church, - from Hilliard's Knob, More's Hill, - Hilliard's Knob, High Ridge, Hilliard's Knob, Mount Grace, - Wachusett Mountain, Watatick Mountain, - Wachusett Mountain, Bear Mountain, Mount Grace, - Bear Mountain, Mount Grace, - Hawes' Hill, - Wachusett Mountain, Mount Tom, - Peaked Mountain, Bumsket Hill, - Wachusett Mountain, Colonel's Mountain, - Hitchcock's Hill, Colonel's Mountain, ■ Bumsket Hill, - N. E. S. E. N. W. S. E. N. W. S. E. N. W. S.W. S. E. N. E. N. E. S. E. N. E. S. E. S. E. S.W. N. E. N. W. N. E. S. E. S. E. N. E. S. E. S.W. 8 31 45 64 07 21 4 52 30 74 09 01 7 59 51 81 35 57 8 29 36 19 04 43 70 55 32 14 27 45 89 59 02 45 18 07 88 09 39 45 38 54 15 11 54 67 47 13 79 00 50 10 55 41 66 25 11 39 55 22 58 34 02 48 35 22 77 45 16 17 41 40 12G67.60 34659.40 23804.60 14332.70 38140.65 17385.12 56381.61 19305.70 6750.45 68936.73 16.11 37921.54 1796.71 36148.20 12460.61' 24107.23 12993.84 84232.20 19130.50 49267.87 19773.00 35071.20 7618.12 60984.06 1899.80 71449.55 2030.31 50483.36 5358.62 117720.00 8419.60 6677.12 19522.25 17780.12 57301.50 38333.35 559.53.80 36975.64 3385.08 59034.50 66934.12 16263.34 43829.26 41227.63 32351.67 39766.80 35100.04 19457.80 SE TRIGONOMETRICAL SURVEY. CTION II. TABLE 2 — Continued. 19 WHAT OBJECTS FROM WHAT STATIONS. Charlton North Church, Dudley Church, fiom U It Grafton Unitarian Church, (< a i( Granby West Church, S. E. 45 54 04.43 14981.00 10425.02 10758.67 Holt's Hill - - - to Ayers' Hill, . . . N. E. 12 22 50.00 61G87.00 00252.44 13225.93 Baker's Island tall Light, - S. E. 66 15 16.00 94340.02 37988.43 80353.46 Brandy Brow Hill, N. E. 11 22 28.41 71449.00 70045.02 14091.31 Coddon'sHill, - S. E. 56 15 32.98 81681.84 45369.12 67923.22 Gumpus Hill, - - - N. W. 65 44 23.25 75439.69 30996.76 687V7.52 Lowell Churcli, - - - N. W. 87 51 50.13 56971.53 2123.49 50931.95 Poplar Hill, N. W. 49 26 52.54 52739.92 34288.28 40072.61 Powow Hill, - - . N. E. 28 52 22.00 93552.44 81923.34 45173.34 Prospect Hill, Hingham, - S. E. 22 27 43.41 176643.65 103242.19 67490.51 " " Rowley, N. E. 67 51 57.64 02214.00 23440.60 57629.13 Rail-cut Hill, - S. E. 87 59 55.78123149.54 4.300.37 123074.45 Wachusett Mountain, S.W. 75 31 41.96217375.85 54322.54 210478.82 Watatick Mountain, - N. W. 84 13 22.48 212384.20 21378.26 211305.49 Hyannis Station - - to Chatham Station, N. E. 74 21 09.50 92597.10 24974.92 891C5.42 Falmouth Station, S.W. 81 27 01.00 85844.56 12762.31 84890.60 German Hill, - - - N. E. 50 15 19.00 34350.69 21962.73 26412.27 TRIGONOMETRICAL SURVEY. SECTIONS III. AND IV. TABLE 1 — Continued. 33 NAMES OF STATIONS. Direc- tions. Bearings. Distances in feet. Norlhings or Southings in feet. Eastings or We^iliiigs iji feet. / // Ilyannia Station - to Holmes' Hole Windmill, - S.W. 51 14 32.00 104137.60 65193.20 81206.46 Indian Hill, ... S. W. .53 41 06.00 125303.55 74207.82 100966.30 Monomoy Light, S. E. 73 3G 36.00 89453.60 25241.48 85818.50 Nantucket south-towered Ch. S. E. 24 42 46.00 139362.60 126599.03 58263.27 Pine Hill, .... N. W. 68 44 17.00 76104.90 27598.10 70924.62 Sampson's Hill, ... S.W. 27 13 32.00 104199.70 92055.64 47670.80 Succonnesset Station, S.W. 59 53 56.00 52889.29 26525.43 45750.72 Indian Hill - - - to Bird Island Light, N. W. 7 21 37.00 88007.64 87282.50 11274.49 Clark's Point Light, - N. W. 45 57 51.00 85257.74 59203.35 61292.14 Cuttyhunk Light, S.W. 85 36 49.00 74823.00 5722.62 74603.85 " Station, - S.W. 87 11 57.00 70304.87 3435.40 70220.88 Gay Head Light, S.W. .55 29 24.00 52471.07 29727.50 43237.60 Knobskey Light, N. E. 10 46 04.00 32018.17 31454.42 5981.92 Naushawn Station, N. W. 38 57 55.00 28308.13 22010.40 17801.59 Prospect Hill, Chilmark, - S.W. 39 07 07.00 30091.56 23346.29 18985.61 Round Hill Light, N. W. 59 32 49.00 77G93.60 39377.62 66975.36 Tarpaulin Cove Light, N. W. 57 09 05.00 26178.04 14199.52 21992.35 West Chop Light, - N. E. 46 28 57.00 28208.91 19423.98 20456.09 Joe's Rock Hill - to Burnt Swamp Signal, S. E. .53 52 48.26 7704.60 4541.68 6223.65 College Hill, - S. E. 00 47 44.30 70269.92 70203.15 975.77 Fall River Station, - S. E. 30 58 20.17136393.09 116940.19 70191.35 Great Meadow Hill, - S. E. 42 26 08.59 75334.27 55599.33 50832.76 Great Rock Hill, S. E. 26 42 41.88 70439.18 62921.93 31602.44 Red Brush Hill, S. E. 87 27 33.00 8591.87 380.89 8583.42 Sprague's Hill, . - - S. E. 85 17 48.24119426.38 9792.41 119024.25 Manomet Hill - - to Bourne's Hill, ... S. E. 22 19 24.00 76168.27 70458.23 28931.22 German Hill, ... S. E. 50 47 24.00134949.31 1 85310.20 104560.94 Gurnet Light, ... N. W. 5 57 19.00 27810.36 27660.27 2885.38 Highland Light, N.E. 73 39 02.00149821.00 42173.86 143762.70 Pine Hill, .... S. E. 5 10 58.00 79998.95 79671.86 7226.56 34 TRIGONOMETRICAL SURVEY. SECTIONS III. AND IV. TABLE 1 — Continued. NAMES OF STATIONS. Dlrec- lioiis. Bearings. Distances in feel. Norlhiiis;s or Souiliiiigs in Icel. Eastings or \\'estmgs in lee I. Manomet Hill - - lo Plymouth Court House, N. W. o / // 62 32 22.00 • 10794.44 20770.82 Telegraph Hill, - N. W. 23 09 58.00 741G0.09 68180.40 29174.43 Marsh & Jones' } Station, (, Lowell Church, - - - S.W. 10 01 22.85 24222.30 23852.61 4215.74 01(1 Pine Tree Boundary in ? Slate Line, - - S S.W. 44 27 20.97 7571.40 5404.39 5302.70 Mendal's Hill - - to Falmouth Station, S. E. C2 53 09.00 815G6.20 37175.03 72602.10 Great Hill, N. E. 85 50 32.00 440G7.85 3195.0G 43951.87 Indian Hill, S. E. 29 49 08.30 1I3G75.97 98G25.40 56520.65 Manomet Hill, - - - N. E. 43 45 21.50 114715.74 82858.22 79336.07 New Bedford Court House, S.W. 28 20 52.00 27548.33 24244.78 13080.56 Pine Hill, - - - - N. E. 87 53 30.42 86G21.32 318G.89 80562.70 Monk's Hill - - to Great Hill, S. E. 00 22 12.00 91G82.0C 91G80.14 592.05 Gurnet Light, - - - N. E. C4 41 51.00 3GG00.40 15G42.9] 33089.10 High Land Light, N. E. 80 28 30.00 182248.08 30158.03 179735.40 Manomet Hill, - - - S. E. 71 31 37.50 37928. 8(i 12018.00 35974.52 Mendal's Hill, - S.W. 24 33 40.00104313.80 1 94875.30 43359.44 Pine Hill, - - - - S. E. 25 13 43.00101358.00 1 91689.90 43201.92 Plymouth Court House, S. E. 85 24 00.00 . 1223.20 15202.76 Telegraph Hill, - N. E. 6 54 13.00 5G572.G3 5G1G2.45 6800.00 Monomoy Light - to Nantucket south-towered Ch. S.W. 15 12 43.00 10503G.7? 101350.44 27560.63 Mount Hope - - to Toweset Neck, - - . N. E. 15 19 38.00 1441G.G3 13903.89 3810.77 Nahant Station - to Baker's Island tall Light, - N. E. 42 20 19.33 53795.54 39701.10 36301.30 Blue Hill, - - - - S.W. 33 35 31.09 94390.32 78G27.04 52223.80 Boston Light, - - - S. E. 12 58 32.00 37321.10 36368.14 8379.91 Coddon's Hill, - N. E. 28 5G 48. CO 3G937.03 32.322. 4C 17877.44 Dorchester Height, - S.W. 44 IG 41.31 48337.53 31607.72 33746.47 Eastern Point Light, - N. E. 51 01 52.50 88702.00 55784.34 68964.82 Long Island Light, S.W. 14 54 39.88 3G891.90 35649.62 9493.00 Prospect Hill, Hingham, - S. E. 11 31 20.52 87309.00 85549.46 17440.01 Scituate Hill, - S. E. 19 32 45.12 73578.88 69338.83 24G16.65 TRIGONOMETRICAL SURVEY. SECTIONS III. AND IV. TABLE 1 — Continued. 35 NAMES OF STATIONS. Nahant Station - to New P.edford Court House to Nootas' Hill Pocasset Hill Poplar Hill Powow Hill - to - to to to Scituate Light, - Clark's Point Light, - Cuttyhunk Light, " Station, - Dartmouth Station, - Falmoulli Station, Gay Head Light, Indian Hill, Knobskey Light, Naushawn Island Station, Pine Hill, - Prospect Hill, Chilmark, Round Hill Light, West Chop Light, Dartmouth Station, Joe Sandford Signal, - Quicksand Pond Station, Bullock's Neck Station, Mount Hope, Munroe's Signal, Nootas' Hill, - Gumpus Hill, Powow Hill, State Line Boundary, Annisquam Light, Brandy Brow Hill, Newburyport Light, - Rail-cut Hill, - Salisbury Marsh Station, Direc- tions. S. E. S. E. S. W. S.W. s.w. S. E. S. E. S. E. S. E. S. E. N. E. S. E. S. E. S. E. N. E. N. W S. E. Bearinsrs. 34 28 28 47 3 34 00 27 48 51 81 25 14 12 43 06 GO 24 44 41 74 36 27 23 4 17 58 36 C5 00 6 10 4 26 31.18 48.00 N. W.'53 28 N. W..-8 56 N. W.37 13 S. E. S.W. N. E. N. E. S. E. S.W. S. E. S. E. N. E. 23 53 83 27 CO 48 14 05 43 00 (JO 05 58 00 42 05 85 54 13.50 16.00 04.00 03.62 43.00 01.00 28.00 19.00 36.00 00.00 46.00 29.00 47.00 21.00 26.00 30.00 51.50 35.50 56.50 43.62 15.14 24.13 Distances ill feet. 98392.42 17243.85 80254.82 77815.82 35739.9,1 86647.92 107391.10 101867.19 86921.58 73658.09 103349.43 110053.63 35091.20 105499.48 28336.96 20815.34 13338.25 56792.90 15380.24 56653.54 46107.75 28893.30 97653.30 556.27 16.18101.3Q7.65 I 12.68 33275.43 26. 3g! 39619.55 I 50.58116200.91 48.61 31654.87 Northings or Soulliings ill feet. Eastings or Westings in feet. 81111.74 15111.38 80099.06 77813.35 23517.50 12930.51 104104.31 74379.23 42923.94 .52366.42 27427.70 97722.04 34992.58 54953.00; 11990.99 20694.02 13298.21 33801.64 ! 79a3.45 45110.38 42154.51 3289.79 47634.85 539.60 74100.93 11877.71 20990.87 86221.82 2255.80 55695.16 8306.48 4997.88 617.20 26912.23 85677.60 26365.54 69603.53 75583.70 51800.30 99643.52 50618.24 2628.72 90056.90 25730.00 2238.11 1032.71 45638.62 13176.19 34273.57 18679.41 28705.52 85247.24 135.44 69111.12 31083.33 33601.98 77900.24 31574.40 36 TRIGONOMETRICAL SURVEY. SECTIONS III. AND IV. TABLE 1 — Continited, NAMES OF STATIONS. Dlrec- lions. Bearings. Distances in feet. Norlliings or Southings in feet. Eastings or Westings in feet. / w Prospect Hill, in ? Chilmark,- - -$ Clark's Point Light, - N. W. 27 07 02.00 92813.00 82610.60 42305.32 Cuttyhunk Light, N. W. 72 24 50.00 58343.14 17627.73 55016.41 " Station, - N. W. G8 45 45.00 54969.10 19911.71 51236.00 Gay Head Light, s.w. 75 15 38.00 25077.66 6380.35 24252.42 Knobskey Light, N. E. 24 29 42.00 60217.. 30 54797.60 24966.92 Nausbawa Station, N. E. 1 29 43.00 45372.88 45357.44 1183.98 No-man's land Station, S.W. 23 43 12.00 44847.30 41058.70 18040.00 Round Hill Light, N. W. 37 24 59.00 78979.44 62728.70 47988.13 Tarpaulin Cove Light, N. W. 4 34 49. CO 37065.50 37545.22 3007.81 Prospect Hill, in ? ^^ Hinghara, - - - $ Baker's Island tall Light, - N. E. 8 33 50.00120664,58 125252.34 18861.90 Long Island Light, - » N. W. 28 21 16.67 56707.55 49904.07 20932.07 Manomet Hill, - - - S. E. 37 00 34.20120817.20 96476.84 72725.60 Monk's Hill, - S. E. 23 30 52.55 92108.54 84459.74 36749.72 Scituate Hill, - N. E. 23 52 56.80 17729.14 16211.11 7177.85 Prospect Hill, in ? , Rowley, - - - T" Ayers'Hill, N. W. 50 20 24.72 57670.47 36810.72 44402.08 Newburyport Light, - N. E. 29 25 33.00 43043.80 37490.83 21147.27 Powow Hill, - . - N. E. 12 01 21.70 59792.65 58481.13 12454.70 Rail-cut Hill, - S. E. 67 01 51.78 71082.15 27738.54 65446.49 Salisbury Marsh Station, - N. E. 17 28 26.25 03675.94 60737.53 19120.12 Squam Light, . . - S. E. 74 35 12.61 58770.05 15019.77 56656.35 Prospect Hill, in } . Waltham, - - -y Blue Hill, - - - - S. E. 30 21 06.36 74562.42 64342.83 37676.93 BumsketHill, - S.W. 79 59 38.07 176745.08 30709.97 174056.68 Fay's Mountain, s.w. 62 06 12.94 114793.11 53708.74 101453,56 Holt's Hill, N. E. 23 25 32.42 100239.71 91977.64 39851.22 Nahant Station, - - - N. E. 80 58 19.40 91028.42 14283. &3 89900.74 Scituate Hill, - S. E. 64 19 29.15 127066.71 55054.14 114520.70 Wachusett Mountain, N. W. 77 33 21.52 174735.40 37052.97 170030.36 Watatick Mountain, - N. W. 56 31 50.46 205541.00 113354.37 171459.20 Quicksand Pond ? to Station - - - ) Rock Boundary in Rhode > Island State Line, - J s.w. 43 49 16.00 317.26 304.40 TRIGONOMETRICAL SURVEY. 37 SECTIONS III. AND IV. TABLE 1— Continued. NAMES OF STATIONS. Rail-cut Hill to Red Brush Hill - to Rhode Island Station to Salisbury Marsh ) Station - - - S Sampson's Hill Scituate Hill - - to South end of Veri- fication base - Sprague's Hill :S» to Eastern Point Light, - Newburyport Light, - Prospect Hill, Hingham, - Salisbury Marsh Station, - Thatcher's Island N. Light, " " S. Light, Burnt Swamp Signal, College Hill, - Sprague's Hill, - Bullock's Neck, Joe Sandford Signal, - Mount Hope, Munroc's State Line Station, Nootas'Hill, - Pocasset Hill, - - - Quicksand Pond Station, - Newburyport Light, - Falmouth Station, Indian Hill, - - . Nantucket south-towered Ch Prospect Hill, Chilmark, - Succonnesset Station, Boston Light, . - - Long Island Light, Scituate Light, - - - Telegraph Hill, - North end of Verificat'n base, Alden's Hill, - Great Meadow Hill, - Direc- tions. Bearinors. Distances iu feet. a t II S.W. 13 00 15.43 18073.95 I N. W.34 10 52. G9 78849.24 I I S.W. 19 16 30.75 1G8381. 31 N. W.27 38 11.44 99870.25 N. E. !78 40 55.93 20341,94 I N. E. 81 02 48.27i 20155.78 S.W. 29 33 32.92 4783.31 S.W.I 6 12 34.78 70294.68 I I S. E. 85 07 46.57110843.13 N. W.25 37 19.50 65741.58 Northings or Southings in feet. Eastings or Westings in feet. 17610.42 4067.07 65229.13 44398.56 156942.25 55583.68 88475.86 3992.12 3136.82 4160.75 69882.26 4C325.88 19946.36 19910.20 23.59.71 76C3.56 I N. E. 83 11 38.00 33890. G8 N. E. 6 53 08.00 33652.81 N. W.13 35 21.00 72619.03 S. E. 65 04 33.00 39575.34 N. E. 34 02 26.00 30745.25 9410.82 110442.93 i 59276.94' 28428.85 4016.38; 3.3651.85 33410.07 4034.52 70586.42' 17062.53 16677.77 25476.20 S. E. N. W. N. W. S. E. S. E. 50 55 38.00 47558.52 29976.47 4 59 05. 8G 24 58 26.00 70 54 20.00 72 14 06.00 S.W. 86 07 27.00 1 39 28.00 26 13 05.57 45 21 22.155 S. E. 69 15 22.38 S. E. N E. N. W. N. W. N. E. S. E. S.W. 39 15 16.31 1 32 58.00 3 57 37.94 56 06 36.69 23336.06 23247.80 88140.40 79899.30 56398.371 18449.40 111241.26 33941.22 72445.45 4896.91 66157.36 66129.66 36747.58: 32906.83 47942.64 33689.05 33234.74 11771.40 57489.95 44516.93 39009.73 63808.54 82144.86 25598.00 63716.01 45803.75 35889.53 17210.56 36921.87 2027.73 37213.33 53295.36 105936.80 72279.77 1913.91 16234.75 34110.71 31080.26 36377.72 092.41 4411.36 68189.38 38 TRIGONOMETRICAL SURVEY. SECTIONS III. AND IV. TABLE 1— Continued. NAJIES OF STATIONS. Direc- tions. Bearings. Distances in leel. Northings or Souihings in feet. Eastings or Westings in feet. Sprague's Ilill - - to Manomet Hill, . - - S. E. / // 74 43 28.55 105909.32 27918.57 102223.50 Monk's Hill, - S. E. 7C 30 08.25 68132.92 15902.67 66251.05 Prospect Hill, Hingham, - N. E. 23 16 57.29 74633.52 08555.80 29300.11 Slate House - - - to Blue Hill, - - - - S.W. 14 24 21.19 54956.13 53228.18 13672.50 " " Bleridian Mark, S.W. 14 45 36.00 55043.32 53227.00 14023.43 Bond's House Cupola, } Cauibrirlge, - ^ N. W. G9 11 46.00 14922.40 5300.00 13949.47 " Sonth Merid. Mark, ? Dorchester, - ^ S.W. 3 11 13.C0 15187.28 15163.78 814.37 " Transit, Dorchester, S.W. 3 34 39.35 13329.00 13502.04 844.21 Castle Hill, N. E. 6 11 40.26 47852.35 47572,65 5163.44 Dorchester Height, - S. E. 27 33 49.90 10380.54 9207.62 4800.24 Hollis Street Church, Boston, S.W. 2 56 36.00 3058.53 3055.85 137.12 Nahant Station, - N. E. .'56 37 17.50 46167.33 25399.75 38552.24 Prospect Hill, Waltham, - N. W. 77 47 13.25 52538.67 11114.36 51349.61 Scituate Hill, - S. E. 55 10 41.90 76947.59 43938.95 63168.81 Succonnesset Station to Holmes' Hole, Wind Mill, - S.W. 42 30 50.00 52458.40 38607.76 33449.80 Telegraph Hill - - to High Land Light, S. E. 81 26 54.50 174880.00 26004.44 172933.70 Plymouth Court House, S. E. 8 19 50.00 • 57383.93 8402.96 For the purpose of locating secondary objects, it became necessary to introduce several new stations into the survey. This was done by measuring two angles only of the triangle in some cases, and by the three- point problem (so called) in others. It is not to be supposed that they are so accurately located as they would have been, had they been connected with the work earlier. The following Table shows from what stations the new stations were located. Being in the third and fourth sections, they are a continuation of bearings, &c. on parallels to the meridian of the State House. Ayers' Hill - - - to Bald Pate Hill, - - 1 S. E. 17 30 48.00 1 37606.46 33920.50 11334.88 Harris St. Ch., Nen buryport, N. E. 88 50 50.00 49503.70 908.13 49497.43 Spigot Hill, - S.W. 78 27 17.00 35903.60 7197.84 33235.94 Bald Hill - - - - to Chestnut Hill, - - N. E. 79 41 25.00 87684.15 6744.30 37075.73 Miscoe Hill, - N. E. !50 01 02.00 45761.73 29404.54 35064.12 TRIGONOMETRICAL SURVEY. 39 SECTIONS III. AND IV. TABLE 1— Continued. NAMES OF STATIONS. Direc- tious. Bearings. Beacon Pole Hill - to Blue Hill - to Blue Hill Signal - Chestnut Hill - - Cupola of Mr. Bond's I house, Cambridge, | Distances in lecl. Northings Eastings or Southings or Westings in feet. in leet. Fay's Mountain - to Gumpus Hill Holt's Hill Lowell Church Moose Hill - to - - to - - to - - to Mount Pleasant - to Brusli Hill, Chestnut Hill, - Miscoe Hill, Pegan Hill, Brush Hill, Chestnut Hill, - Moose Hill, Pegan Hill, Mr. Bond's House, Cambr'ge, Miscoe Hill, . - . Blue Hill, Meridian Mark, - Transit of Harvard Observ. Brush Hill, - - - Chestnut Hill, - Miscoe Hill, - . - Moose Hill, - . - Pegan Hill, Forest Hill, Mount Pleasant, St. Ann's Church, Lowell, - Bald Pate Hill, - Mount Pleasant, Spigot Hill, - . . Mount Pleasant, Brush Hill, Chestnut Hill, - Miscoe Hill, ... Pegan Hill, Forest Hill, N. E. 10 25 47.00 02872.38 N. W.55 55 42.00 41899.54 N. W.38 31 01.00 N. E. 22 52 04.00 98701.50 N. W.78 41 57.00| 74559.95 S. W. 66 51 • 37 . 00 135536 . 65 S.W. 40 12 27.00 42022.30 N. W.74 35 44.00 53491.77 N. W.OO IC 22.50 58529.17 N. W. 5 04 25.00 22748.15 S.W. 00 04 19. Oo' 58526.15 S.W. 79 13 08.00 33.22 N. E. 86 33 54.00 66136. 3Q S. E. 12 46 56.00 05528.55 I S. E. 10 50 35.00 43092.38 I S. E. 69 07 03.00119875.61 I N. E. 87 40 01.00 87631.94 I S.W. 48 20 58.00 34796.16 S. E. 36 23 05.00 32001.00 S. E. 25 02 55.00 32074.00 ! N. E. 45 16 07.00 34575.66 N. W.83 59 46.00 N. W.22 31 50.00 57439.00 S. E. 00 28 34.00 7786.88 N. W.44 33 44.00 65538.63 S.W. 77 44 41.00 99773.92 N. W.89 08 39.00 99526.05 N. W.27 49 57.00 52351.85 N. W.86 38 42.00 45061.21 91337.92 23473.35 90944.00 14610.80 53262.49 .32098.08 14209.07 58528.50 22059.02 58525.43 0.123 3962.63 63904.67 41243.81 42729.97 3567.34 23125.04 25762.51 29057.40 24333.80 53055.00 3107.99 46093.54 21178..30 1486.54 46295.60 2637.10 16812.63 34706.96 38356.00 73114.37 124632.66 27127.81 51570.08 278.79 2011.74 73.488 32.03 66017.50 14497.92 12486.07 112001.40 87559.-32 26000.11 18983.16 13579.72 24563.04 22009.24 7139.74 45987.37 97500.24 99514.90 24442.47 44984.00 40 TRIGONOMETRICAL SURVEY. SECTIONS III. AND IV. TABLE 1— Continued. NAMES OF STATIONS. Direc- tions. Bearings. Di.slances in t'eel. Noriliings or Soulliings in leet. Easlings or VVesiings ill (cet. Mount Pleasant - - to St. Ann's Cliurch, Lowell, - s.w. / // 58 37 34.00 6328.80 3294.90 5403.44 PeganHill - - - to Brush Hill, N. W. 88 56 37.00 21546.90 397.25 21543.20 Chestnut Hill, - S.W. 47 16 34.00 99450.42 67473.73 73059.45 Perkins' Hill - - - to Ipswich outer Light, - N.E. 22 21 41.00 21293.95 19692.71 8101.23 Tilton's Hill, - N.E. 3 16 28.00 18254.55 18224.75 1042.70 Prospect Hill, Rowley ,to Bald Pate Hill, - N. VV. 88 27 IG.OO 33076.80 892.14 33064.80 Harris St. Cli., Newburyport, N.E. 7 41 18.00 38061.14 37719.00 5093.00 Perkins' Hill, - - - S. E. 43 49 46.00 37213.66 26846.10 25771.00 Tilton's Hill, - S. E. 72 10 28.00 28165.95 8622.16 26813.67 Prospect Hill, Wal- : tham, to Blue Hill, Meridian Mark, - S. E. 30 07 09.00 74384.53 61341.41 37326.17 Brush Hill, S.W. .35 28 18.00 61068. G3 49734.45 35438.15 Cupola of Bond's House, > Cambridge, - - ) S. E. 81 09 45.00 37848.75 5814.80 37399.42 Moose Hill, S. E. 6 14 38.00 1 97008.92 96433.70 10550.78 Pcgan Hill, S.W. 15 29 28.00 52024.00 50134.06 13895.03 State House, - - - to Blue Hill, Meridian Mark, - S.W. 14 45 36.00 55043.32 53227.00 14023.43 Cupola of Bond's House, ) Cambridge, - - y N. W. 69 11 46.00 14922.40 5300.00 13949.47 Moose Hill, - - - S.W. 25 33 23.00 94567.50 85315.10 40796.33 Pegan Hill, S.W. 59 07 03.00 76022.13 39020.57 65243.84 Squam Light - - - to Perkins' Hill, - S.W. 70 01 28.00 32862.45 11226.45 30885.40 Tilton's Hill - - - to Ipswich outer Light, - N.E. 78 15 06.00 7209.60 1467.96 7058.55 TRIGONOMETRICAL SURVEY. 41 SECTIONS III AND IV. TABLE 2. Tills Table shows the Bearings, with the Northings, Southings, Eastings or Westings made on each course, from -primitive stations to secondary objects, in the third and fourth sections, on parallels to the meridian of the State House. WHAT OBJECTS FROM WHAT STATIONS. Direc- lioiis. Norlliings Easiirig^s Bearings. or Souilmigs or Wesiiiigs in I'eet. 1 in feet. / // i Abington two-steeple Church, from Monk's Hill, N. W. 5.3 34 54.00 42937.22 58199.80 1 " Mothuen, - - . . |) Spigot Hill, - N. E. 30 04 59.00 2821.07 1634.20 Boxborough Church, - - - " Fay's Mountain, - N. E. 16 52 18.00 91527.34 27758.70 " **._-« Pegan Hill, - N. W.W 12 30.00 87962.00 59797.63 Boxford new Church, - - " Bald Pate Hill, - S. E. 15 45 44.00 1 15948.46 4.501.60 (( **«_._ " Holt's Hill, - N. E. 73 54 29.00 1 8384.70 29064.83 Bradford West Church, - - . " Ayer's Hill, S.W. 19 23 05.00 14361.00 50.53.00 it it H _ _ (( Haverhill tall-spired Ch. S. E. 6 22 45.00 3823.95 428.03 Braintree Church, . - - « Blue Hill, - S. E. 80 57 45.00 4583.96 28819.22 « " ... 1' Scituate Hill, S.W. 73 53 09.00 13873.00 48019.62 Bridgewater Church, . - " Blue Hill, - S. E. 24 16 10.00 81278.00 36646.17 " « . - - « Joes Rock Hill, - S. E. 82 18 33.00 15598. 42' 11 5507. 60 Brighton large Church, . - " Dorchester Height Stat'n, N. W. 78 18 10.00 6001.64 28989.26 a « (£ _ _ ft State House, S.W. 82 26 56.00 3205.70 24183.01 Brookline, Dr. Pierce's Church, - " Blue Hill, - N. W. 6 01 04.00 41955.. 52 4459.88 (( it a _ u State House, S.W. 58 08 01.00 11271.46 18132.06 " Baptist Church, - " Blue Hill, - N. W. 1 39 10.00 44183.90 1274.90 it (( <( _ _ (t State House, S.W. 58 49 50.00 9043.83 14951.12 Cambridge stone-colored Church, " Blue Hill, - N. W. 1 16 27.00 59214.61 1317.05 u It a _ II State House, N. W. 68 13 40.74 5986.83 14989.36 Canton Gothic Church, - - " Blue Hill, - S.AV. 21 55 07.00 13353.31 5373.03 it U (1 _ _ (t Moose Hill, - . - N.E. 49 15 30.00 18739.61 21754.80 Carlisle Church, ..." Bumsket Hill, N.E. 61 09 59.00 81675.80 148361.50 II "-.-.« Wachusett Mountain, - N.E. 84 45 04.00 13314.63 144933.00 TRIGONOMETRICAL SURVEY. 43 SECTIONS III AND IV. TABLE 2 — Continued. WHAT OBJECT3 FROM WHAT STATIONS. Direc- „ tions. Bearings. Northings or Southings- in feel. Eastings or Westings in feet. / // Carver Church, - - - - ^rom Monk's Hill, ' ' S. W. 54 15 46.00 1 15167.37 21078.71 Charlestown, Bunker Hill Monument (( Nahant Station, . S.W. 63 34 00.50 16773.90 37765.04 » U f( (( (( Stale House, N.E. 6 46 14.00 0625.94 786.64 Chelmsford North Church, - (( Forest Hill, S. E. 67 34 54.00 8928.90 21643.45 iC " ■ 1< . . (( Mount Pleasant, - S.W. 74 54 49.00 6291.80 23340.51 Chelmsford Church, - - - a Gumpus Hill, S.E. 2 59 53.00 46820.90 2452.20 ({ « _ - * « Poplar Hill, - S.W. 27 39 03.00 50109. .53 26253.25 " Middlesex Church, - u Forest Hill, - S. E. 72 05 19.00 9461.77 29274.32 a u <( Prospect Hill, Waltham, S. E. 1 35 42.00 36580.90 1018.60 New Bedford large-spired Church, (( Falmouth Station, N. W. 80 42 Go. 00 13816.62 84465.52 tt It it it ti Indian Hill, - - - N. W. 42 15 33.00 75264.37 68387.23 " " head of river Church (t Mendal's Hill, - S.W. 58 57 13.00 6546.40 10875.06 (( It &t It t( u N. Bedford Court House, N.E. 7 06 12.00 17698.40 2205.50 " " Mariners' Church, (( U " (1 N.E. 82 17 51.00 268.40 1984.50 tt it (t (( ti " large Church, S. E. 51 16 26.00 613.37 764.90 Newburyport Unitarian Church, - (t Ayer's Hill, - N.E. 88 10 07.00 1593.26 49828.70 TRIGONOMETRICAL SURVEY. 49 SECTIONS III AND IV. TABLE 2 — Continued. WHAT OBJECTS FROM WHAT STATIONS. Direc- tions. Bearings. Norlliings or fcsouihings in feel. Eastings or Westings in leel. Newbury Church, - . . from Powow Hill, S. E. o / // 40 10 35.00 24108.74 20356.40 u " - ■ . ti Salisbury Marsh Station, s.w. ■33 03 09.00 26363.30 11219.10 " {north of Port) Church, 11 Ayers' Hill, N. E. 84 20 37.00 4450.04 44929.65 tt ti ti u 11 Prospect Hill, Rowley, - N. E. 00 44 17.00 41261 . 10 531.53 Newburyport Unitarian Church, - 11 Powow Hill, S. E. 41 41 29.00 20077.46 17882.80 " Harris Street Church, ft Ayers' Hill, N.E. 88 56 56.00 908.15 49497.43 « ft (1 11 11 Prospect Hill, Rowley, - N.E. 7 41 18.00 37719.00 5092.00 Newton tall-spired Church, It Brush Hill, - N.E. 59 52 17.00 29898.80 51518.50 11 i( 11 . . 11 Moose Hill, ... N.E. 4 08 00.00 76599.40 5535.50 " Upper Falls Church, 11 Pegan Hill, - N.E. 42 40 03.00 23550.20 21706.76 « 11 If 11 If Prospect Hill, Waltham, S. E. 16 22 32.00 26583.88 7811.74 North Bridgewater Church, ff Monk's HiU, N. W. 60 51 51.00 45142.10 80985.10 11 11 ff . . ff Sprague's Hill, N. W. 26 44 40.00 29238.22 14734.04 Norton Church, ... 11 Beacon Pole Hill, S. E. 79 50 38.00 12516.81 69873.50 11 " . . . . 11 Great Meadow Hill, N.E. 13 59 17.00 32023.77 7977.33 Pawtucket Church, ... fi College Hill, N.E. 20 13 16.50 13867.50 5108.08 ff ff 11 Great Rock Hill, - N. W. 75 41 05.51 6527.20 25578.40 Penequese Island, ... fi Cuttyhunk Station, N.E. 14 25 57.00 10459.83 2691.95 11 11 ... It Indian Hill, - . - N. W. 84 03 41.00 7024.43 67528.90 Plymouth Beach Breakwater, 11 Monk's Hill, N.E. 69 53 42.00 6902.91 18858.00 CC If ff . . 11 Telegraph Hill, - S. E. 13 45 13.00 49258.63 12057.08 " Court House, It Manomet Hill, N. W. 02 33 22.00 10794.44 20770.82 1 « ff fi , . It Monk's Hill, S. E. 85 24 00.00 1223.20 15202.76 1 " Eel River Church, It ti ti _ . S. E. 71 01 40.00 6784.30 25551.71 fi If ft ft _ ti Telegraph, Hill, S. E. 16 06 18.00 64945.70 18751.75 " Harbor Monument, 11 Monk's Hill, N.E. 63 10 15.00 10018.13 19807.51 ft ft 11 _ _ 11 Telegraph Hill, - S. E. 15 44 33.00 46144.30 13007.52 Plympton Church, ... 11 Blue Hill, - S. E. 41 04 28.00 93271.70 81292.80 " " ... ft Monk's Hill, S.W. 85 41 31.00 1892.00 25123.50 Providence, R. I., College Chapel, tf Copecut Station, - N. W. 07 45 49.00 38347.40 93797.10 50 TRIGONOMETRICAL SURVEY. SECTIONS III AND IV. TABLE 2 — Continued. WHAT OBJECTS FROM WHAT STATIONS. Direc- tions. Northings Eiistin;^s Bearings. orSouilnngs or Weslings in feet. in feet. Providence, R. I., College Chapel, from Rhode Island Station, - N. W. / // 1 24 29 03.00 88880.20 40475.37 Quincy Stone Church, a Prospect Hill, Hingham, N. W.'ei 53 23. Oo] 21151.75 39596.61 *' ** « - - _ ti State House, S. E. 22 48 23.00 38988.77 16394.50 Randolph Church, (with clock) - a Blue Hill, - S. E. 47 20 49.00| 18040.00 19581.42 EC U U U a Sprague's Hill, - N. W.[l9 42 58.00 57435.73 20582.71 Randolph East Church, a Blue Hill, - S. E. 54 01 20.00 20G90.05 28500.65 " (i (( 11 Sloose Hill, - - - N. E. 78 24 57.00^ 11403.86 55628.46 Reading Church, - - - (t Bald Pate Hill, - S.W. 19 18 26.00 48303.60 16922.52 " *'---- a Holt's Hill, - S. E. 17 40 48.00 23969.80 7640.52 Reading Church, (wood end,) a Castle Hill, - N. W. 49 07 29.00 13549.83 15656.40 U <( (( (( (t Holt's Hill, - S. E. 1 22 25.00 41969.26 1006.37 Rehoboth new Church, a Great Meadow Hill, S.W. 34 22 12.00 14024.60 9592.05 (( a u _ _ t( Great Rock Hill, - S. E. 55 00 41.00 6702.90 9576.79 " no spire yellow Church, u Great Meadow Hill, - S.W. 41 01 53.00 13660.16 11887.74 U (C t( U £( (( Great Rock Hill, - S. E. 48 57 33.00 6338.48 7281.10 Rochester, Mattapoiset Church, - u Indian Hill, - - - N. W. 24 51 43 00 • a t( (( It New Bedford C't House, N. E. 71 26 07.00 10209.30 30398.20 Rockport, Squam Church, - 11 Powow Hill, S. E. 44 05 05.00 74182.80 71849.80 tC (( it _ _ tc Prospect Hill, Rowley, - S. E. 75 11 41.00 15697.63 59391.00 Rowley, Byfield Church, - 589778.70 —3029.15 41 15 11.0870 49 06.62 Nootas'Hill, - Westport, ... 486503.11 81595.96 41 32 13.2371 07 44.07 Nortli end of Verificat'n Base, Attleborough, . - - 351472.49 144619.03 41 54 26.17 71 21 39.38 TRIGONOMETRICAL SURVEY. 57 SECTIONS III AND IV. TABLE 3 — Contintted. NAMES OF STATIONS. Pegan, Hill, ..... Pepperell Line Station, - Perkins Hill, - . . . Pine Hill, - ^ . . Pine Tree Boundary, Pleasant, Mount, .... Plymouth Court House, - Poplar Hill, - - . . « " State Line Boundary, Pocasset Hill, - . - Powow Hill, ... Prospect Hill, - Towns in which situated. Quicksand Pond Station, - " " Stale Line Boundary Stone in Rail-cut Hill, - - . . Red Brush Hill, Rhode Island Station, Round Hill Light, - Saint Ann's Church, Salisbury Marsh Station, - Sampson's Hill, . . . Scituate Hill, - - - . " Light, - - South end of Verification Base, South Meridian Mark, Spigot Hill, - - - - 8 Natick, . - . N; H. Line al Pepperell Essex, - . - Sandwich, - . - State Line at Dracut, - Dracut, .^ . - Plymouth, .. . - Methuen, . - - N. IL Line at Methuen Tiverton, R. I. - Salisbury, - . - Chi I mark, - - - Hingham, - - - Rowley, . - - Waltham, - - . Westport, • . - R. 1. Line at Westport, Gloucester, Wrentham, Portsmouth, R. L Dartmouth, Lowell, . - - Salisbury, - . . Edgartown, Cohasset, . . - Scituate, . . - Seekonk, . - - Dorchester, Salem, N. H. . Southings in feet. 226291.52 G1011.90 87583.66 423565.58 63606.10 78945. OG 333099. 4C 49890.66 49351.13 444349.00 2256.10 548721.76 247419.68 60737.61 176155.24 499801.23 500118.57 88476.64 3065.59.00 469824.77 485993.11 82239.50 543825.00 231208.48 242980.73 377073.00 2024.33.42 31123.74 Westing's in feet. 130494.24 205738.48 —6650.90 —70693.35 134766.93 126541.41 —42695.35 116821.49 116686.05 100275.35 31573.85 —21669.01 9257.80 19120.12 116600.27 80563.50 80868.32 —46325.96 149203.48 117485.65 26319.66 131945.30 —93948.10 2082.28 — 2S996.83 145311.87 66095.46 98757.74 Latitude. Longitude. 42 15 03.5371 18 37.13 42 42 13.2971 35 32.02 41 42 31.1670 34 15.44 I 42 41 50.7871 19 40.59 41 57 26 42 44 06 42 44 12 41 39 09 42 51 57 41 21 56 42 11 35 42 42 19 42 23 19 41 30 OL ,5670 40 19.27 ,7671 15 40.52 09 71 15 38.72 I 5371 11 50.69 I ,7270 56 36.46 I 8270 45 08.27 I 0170 51 44.63 I 7170 53 50.71 I 2571 15 33.76 I 7871 07 30.38 41 29 58.6471 07 34.38 42 37 43 42 01 49 41 34 57 41 32 17 42 38 46 42 52 19 41 22 41 42 14 15 42 12 17 41 50 13 .4070 39 15.40 I 8371 22 42.21 I 4771 15 36.80 I 9670 55 36.71 I 7871 19 02.04 I 3270 49 32.11 I 4270 29 19.35 I 0070 50 08.66 I 64 70 43 15.84 21 71 21 47.40 58 TRIGONOMETRICAL SURVEY. SECTIONS III AND IV. TABLE 3 — Continued. NAMES OF STATIONS. Towns in which situated. Southings in leet. Westings in leet. Latitude. Longitude. Sprague's Hill, - - - Bridgewater, 315972.66 38759.43 O / // 42 00 18.17 o / // 70 58 17.87 Squam Light, - - - - Gloucester, Cape Ann, 76357.15 —37536.34 42 39 43, 5570 41 12.33 State House, - - - - Boston, . . - 187269.65 65251.09 42 21 30.0071 04 09.00 Succonnesset Station, Marshpee, - - - 477693.65 —95862.72 41 33 34.7670 28 48.26 Tarpaulin Cove Light, Naushawn Isl., Chilm'k, 511175.82 —18662.18 41 28 07.9470 45 46.01 Telegraph Hill, Marshfield, 275713.63 —34292.10 42 06 53.99 70 42 07.31 Thatcher's Island North Light, Gloucester, Cape Ann, 84486.30 —66273.61 42 38 21.7S3 70 34 48.06 « " South Light, u a a 85341.64 —66237.43 42 38 13.24 70 34 48.61 Tilton's Hill, - - - . Ipswich, - - - 69359.30 —7693.67 42 40 53.83 70 47 41.72 Toweset Neck Station in R. I. Line at Swanzey, 422510.88 109641.63 41 42 45.27 71 13 54.70 Trinitarian Church, - - - Taunton, - - - 353118.32 7.3263.43 • • Tuft's Hill, - - - - New Braintree, - 200600.50 341213.7142 19 01.90 72 05 24.96 University Hall, - . - Providence, R. I. 380945.00 157961.0041 49 34.48 71 24 34.41 Unitarian Church, - - - Sandwich, - - - 405250.66 —88932.9241 45 31.09 70 30 13.19 Wachuset Mountain, Princeton, - - - 138500.13 287228.5342 29 21.21 71 53 33.885 Watatick Mountain, Ashburnhani, 62799.43 288056.13 42 41 49.12 71 53 54.97 "West Chop Light, - Tisbury, Martha's Vin. 505950.93 —61109.40 41 28 57.69 70 36 27.71 TRIGONOMETRICAL SURVEY. 69 SECTIONS III AND IV. TABLE 4. Table of Southings and Westings of Secondary Objects, from Salisbury Marsh Station, in the third and fourth sections, together with their Latitudes and Longitudes. [Such objects as are east of the meridian of Salisbury Marsh Station (parallel to the meridian of the State House) have the negative si^i { — ) before them, and are registered in the column of Westings.] NAMES OF OBJECTS. Abington two-steepled Church, - " Northeast Church, Acton Church, - . - . Amesbury West Church, Andover Theological Seminary, - " Nortlieast Church, - Attleborough East Church, - Bedford Church, - - . - Bellingham tall-spired Church, Berkley Church, - - - - Beverly Church, - - - - " white-spired Church, Billerica tall-spired Church, - Bo.\borough Church, - - - Bo-xford new black-top Church, - Bradford West Church, Braintree Church, ... Bridgewater Church, . - - Brighton large Church, Boston, Fort Independence Flag Pole, « HoUis Street Church, Brookline Baptist Church, - " Dr. Pierce's Church, - Snulhings in leet. Westings in feet. Latitudes. Limgitudes. o / // o / // 286940.36 30708.84 42 04 45.16 70 56 30.63 270288.90 25044.15 140458.07 164981.21 42 29 30.13 71 26 21.10 ] 3462. 28 49065.29 42 50 07.18 71 CO 31.61 81651.15 &3722.83 42 38 53.47 71 08 16.34 68453.19 78318.65 42 41 03.89 71 07 04.08 337731.35 124747.26 41 56 42.55 71 17 16.86 138638.34 123527.76 42 29 29.76 71 17 07.41 286171.30 176619.24 42 05 10.14 71 28 47.03 375287.91 70594.21 41 50 32.20 71 05 19.64 117710.91 15248.30 • 107377.30 20108.16 42 34 38.92 70 54 05.20 113910.67 120702.67 42 33 34.16 71 16 30.46 138331.75 190293.37 42 29 30.17 71 31 59.20 75793.77 47683.83 • • 38287.10 68574.57 42 46 01.98 71 04 53.59 245081.55 50104.00 42 11 58.73 71 00 47.62 321775.89 42277.64 41 59 20.86 70 59 04.58 190475.58 89434.70 42 20 58.20 71 09 31.29 194418.12 51248.85 • • • 190325.50 65408.21 42 20 59.81 71 04 11.12 196313.62 80202.20 • • • • 198541.62 83384.16 42 19 38.56 71 08 10.57 60 TRIGONOMETRICAL SURVEY. SECTIONS III AND IV. TABLE 4 — Continued. NAIVfES OF OBJECTS. Southings iu ieet. Westings in feel. Latitudes. Longitudes. Cambridge stone-colored Church, - Canton Gothic Church, - - » - Carlisle Church, - - - . - Carver Church, - - - . - Charlestown, Bunker Hill Monument, - Chelmsford Church, - - - - " Middlesex Church, " North Church, - - - Chelsea Ferry Church, - . - , " Village Church, Cohasset Church, - . . - Concord Church, - - . . Danvers Church, - - - - - « Village Church, South Parish, Dartmouth, Padanaram Church, - Dedham Church, by Court House, « South Church, ... " West Church, Dighton, Richmond Hill three point Station, Dorchester, Dr. Harris's Church, - " Church, - - - . Dover Church, - - - - - Dracut Church, (near Patucket Bridge,) " " (old, without spire,) Dunstable Church, square-towered, Duxbury Church, yellow, (since rebuilt,) " Village Church, - East Bridgewater Church, - - . Easton Church, - . - - - Essex old Church, . . . - 181282.93 253850.74 125185.73 347044.45 180C43.75 100001.09 85769.20 85236.40 175342.27 168701.02 229062.74 150123.23 112008.56 120701.47 407549.30 220989.22 240451.53 239030.98 387904.01 205488.30 211839.09 228139.07 80558.70 73725.90 71817.40 304702.47 304595.12 307027.68 304.537.17 86893.22 80241.40 84297.03 142295.45 —6412.73 64464.78 14.3074.05 142251.11 149881.97 58294.79 49894.82 —5224.41 142087.14 37454.28 28232.02 31594.43 90085.71 102280.01 105012.80 82S37.07 64859.30 67278.26 124609.80 1.37491.26 129653.04 177942.97 —35604.93 —40918.71 35120.63 74365.59 —10837.45 42 22 29.11 42 10 32.06 42 31 42.13 41 55 10.20 42 22 35.47 42 38 11.58 42 24 33.41 42 14 35.99 42 27 35.75 42 31 28.14 41 35 20.14 42 14 57.30 71 07 28.85 71 08 22.13 71 21 18.69 70 48 10.39 71 03 58.52 71 21 19.87 71 00 44.15 70 48 31.36 71 21 14.78 70 55 54.27 70 56 45.77 71 10 59.28 42 18 29.99 42 14 46.42 42 39 03.20 71 04 03.77 71 17 18.77 71 20 10.37 42 40 27.90 71 29 18.63 42 02 08.34 42 01 46.51 42 02 11.29 42 38 00.50 70 40 31.08 70 57 29.48 71 00 09.87 70 47 10.38 TRIGONOMETRICAL SURVEY. 61 SECTIONS III AND IV. TABLE 4 — Contintjed. NAMES OF OBJECTS. Fall River Baptist Church, - - - Falmouth Church, - . - . " North Church, Foxborough tall-Bpired Church, - Framingham North Church, " Saxonville Church, - Franklin new Church, - - - - Freetown, Asaonet North Church, Georgetown tall-spired Church, Gloucester, Annisquam Church, - " Harbor Church, - Groton tall-spired Church, - - - Halifax Church, • - - - - Hamilton Church, - - - . Hanover Church, - - - Hanson Church, - - - - - Haverhill East Church, near Ayers' Hill, " new tall-spired Church, - " West Brick Church, Hingham, Dutch-built Church, " Great Plain Church, " Old Colony House, Holliston Church, . - - - Hopkinton Church, . - . . Hull, Nantaaket Fort Flag-staff, - Ipswich Church, - - - - - Kingston Village Church, , Lexington Church, - - . - Lincoln Church, - - - - - Little Compton, R. I. Church, Southings in leei. Westings in feel. 427099.54 479940.07 447721.89 294050.32 20G915.55 197964.37 284835.10 392098.68 55506.71 76437.07 94089.27 96650.59 320965.50 90838.03 276340.23 296149.34 28995.91 34457.78 30884.58 229824.49 240988.93 227477.09 244102.24 233833.16 206872.40 69374.02 320044.78 154002.34 161843.01 496558.02 90750.26 —56281.92 —56493.72 116111.08 165536.44 156265.95 156988.33 66543.30 44207.66 —40273.42 —41737.23 200786.24 10196.18 8935.59 —2252.82 13970.92 57623.07 69002.32 83908.17 17409.94 16594.21 13480.05 164505.84 188585.63 23210. 42 4084.41 —25229.58 110257.00 129863.39 94722.27 Latitudes. o / // 41 42 00.10 41 33 14.97 Longitudes. 71 09 45.37 70 37 29.46 42 03 54.38 71 15 23.77 42 18 13.73 71 26 24.53 42 05 23.24 41 47 46.10 42 43 11.75 42 36 48.17 42 36 21.40 41 59 28.34 42 37 22.09 42 06 48.94 42 03 33.63 42 47 15.04 42 14 52.45 42 12 06.35 42 13 46.76 42 40 54.03 41 59 36.33 42 26 58.26 42 25 40.33 71 24 25.79 71 04 26.21 70 59 26.89 70 40 17.17 71 34 22.66 70 51 59.43 70 51 35.21 70 49 12.73 70 52 48.72 71 08 19.38 70 52 40.17 71 26 08.67 71 31 29.55 70 50 20.49 70 44 09.93 71 14 09.74 71 18 31.15 41 30 33.69 71 10 36.61 62 TRIGONOMETRICAL SURVEY. SECTIONS III AND IV. TABLE 4 — Continited. NAMES OF OBJECTS. Southings ill ieet. Lowell Church, ---..- " Saint Ann's Church, - - . - Lynn Church, ..-.-. " East Church, Lynnfield Church, . - - - - Maiden black-top Church, - - - . " square-towered Church, - - - Manchester Church, - - . . - Mansfield Church, - . . . - Marblehead North, spired Church, " square-towered Church, (Unitarian, Marshfield Church, . - . . . Medfield Church, - . . . . Medford new Church, - - - . - Medway East Church, .... " Factory Village Church, " West Church, - . - " - Mendon Church, ...... Methuen square-towered Church, ... Middleborough domed-top North Church, " Four Corners Church, - " Ionic Church, ... Middletoa Old Church, .... " three point Station, ... Milford Church, Milton Old Church, " Stone Church, near Rail-road, - Nashawena House Chimney, ... Natick New Church, tall-spired, . - • " South Church, 82054.52 82239.50 148606.90 147001.32 121 188. C6 162941.41 103501.75 108111.08 308915.07 132935.54 133397.05 260002.19 249408.72 164550.77 257489.72 260348.53 204919.33 278901.09 52025.07 343.399.85 350929.89 351019.97 100032.90 99992.00 260690.73 225442.37 223779.26 522870.58 214147.91 218150.54 Weslings in feet. 133681.86 131945.30 S4982.92 31181.63 61093.79 66425.81 66129.93 —13315.91 100864.52 7062.95 7915.70 —22264.42 131074.62 79140.77 147142.86 150112.42 165254.75 198349.18 98115.79 42575.82 23693.67 16553.55 50138.09 44527.87 189515.18 69709.47 58687.88 11217.35 141901.14 133554.50 Latitudes. o / // 42 38 40.78 42 27 51.21 42 32 22.90 42 25 24.25 42 34 30.41 42 01 27.68 42 30 21.57 42 08 30.43 42 11 15.10 42 25 14.42 42 08 20.88 42 06 20.23 42 43 40.01 41 53 33.25 42 35 45.46 42 08 21.96 42 15 12.83 42 17 03.17 Longiludes. Q t If 71 19 02.04 70 57 24.88 71 03 13.43 71 04 20.73 70 44 24.43 71 13 21.74 70 51 23.00 70 45 46.51 71 18 43.97 71 07 14.32 71 24 15.91 71 33 35.97 71 11 29.65 70 54 59.15 71 00 46.80 71 31 39.56 71 05 08.33 71 21 09.45 TRIGONOMETRICAL SURVEY. 63 SECTIONS III AND IV. TABLE 4 — Continued. NAMES OF OBJECTS. Needham short-spired Church, . - - " tall-apired Church, ... New Bedford head of river Church, « " large-spired Church, " " Mariners Church, ... Newbury Church, . . . . - " north of Port Church, ... Newburyport Harris Street Church, " Unitarian Church, ... Newton tall-spired Church, .... " Upper Falls Church, North Bridgewater Church, .... Norton Church, ------ Pawtucket tall-spired Church, ... Penequese Island Flag Pole, ... Plymouth Beach breakwater extremity, - " Court House, .... " Eel River Church, " Harbor Monument or Duxbury Pier, Plympton Church, - - . . - Providence R. I. College, or University Hall, Quincy Stone Church, - - . . . Randolph East Church, .... " (with clock) Church, ... Reading North Church, .... " Wood End Church, Rehoboth New Church, - - . . « Old Yellow Church, - Rochester Mattapoisett Church, - - . Rowley, Byfield Church, .... Southings in feet. 212737.23 209811.91 433297.94 450110.77 450720.00 26364.10 19476.47 23018.40 22333.38 195998.04 202740.22 286734.76 329753.38 362572.65 518351.05 324973.21 333099.46 340600.35 321858.94 333769.52 380945.00 226263.17 261187.48 258537.29 108148.59 126147.39 375802.30 375437.93 440786.80 48624.98 Westings in feet. Latitudes. 115581.14 127456.09 26744.67 27733.62 26966.84 11218.27 18590.42 14026.27 13692.12 100516.76 108788.00 53493.56 98974.95 151701.23 26873.59 —46349.31 —42695.-35 —53043.50 —47299.28 —2367.72 157961.00 48855.50 50423.36 59343.01 69108.04 75742.08 116544.88 118840.57 —1448.13 20640.24 42 17 46.44 41 38 06.46 42 48 32.15 42 20 03.49 42 05 07.18 41 58 01.90 41 52 36.27 41 57 26.56 41 57 21.48 41 49 34.48 42 15 04.66 42 09 45.83 42 34 31.78 41 50 20.56 41 39 44.05 Longitudes. o / // 71 17 57.30 70 55 44.39 • • 70 52 41.30 71 11 58.88 71 01 32.96 71 11 35.73 71 23 12.56 70 40 19.27 70 49 13.43 71 24 34.41 71 00 30.84 71 02 50.50 71 05 00.59 71 15 27.12 70 49 29.67 64 TRIGONOMETRICAL SURVEY. SECTIONS III AND IV. TABLE 4 — Contin tted. NAMES OF OBJECTS. Southings in lieet. Westings in feet. Latitudes. Lonsfitudes. Rowley Church, -.-.-. Roxbury, Mr. Putnam's Church, - - - . " Southwest Church, (Mr. Parker's,) - Salem East India Marine Hall, - - - . " tall-spired Church, - . . . . Salisbury New Church, . » . . . Scituate Church, ------. " Universalist Church, (Snapet,) Seekonk Clock Church, -..--. Sharon Old Yellow Church, - - - - Sherburne Church, . - . . - Somerset, Bowers' Shore Church, - . - ■ " Old Methodist Church, no spire, - Southborough Church, - - - - - South Reading Church, . . - - . Stone Boundary in N. H. State Line, at corners of i Haverhill and Methuen, - - - . i Stoneham Church, (since burnt down,) - Stoughton Clock Church, .... Swansey Church, (near Luther's Tavern,) Taunton Church, (opposite Bristol County House,) Tewksbury Church, . - - . - Tiverton, R. I. Stone Bridge, ... Topsfield Church, ... - Tyngsborough Church, . - . . " Secondary Station, Walpole Church, - . . . . Wareham bell-top Church, . . - - " Narrows (Church, - - - - Watertown turreted Church, ... " United States Arsenal pole. 55928.23 197570.54 212768. C3 127656.28 128268.04 10628.48 244703.47 260211.32 375449.96 2725G4.60 229853.64 400999.70 413775.97 205890.14 132980.05 28302.67 1423.30.24 272327.67 408523.72 353117.73 94601.27 454376.09 83695.31 71369.36 &3287.42 265239.25 402906.69 405940.91 183844.56 185924.52 —15961.87 72299.34 87450.74 19157.56 20948.04 10721.20 —18196.33 7940.42 143360.37 96623.79 148290.67 82516.98 93755.78 192816.08 67753.53 97123.54 73560.08 75426.57 109205.97 73263.45 110854.60 106253.51 35077.17 161904.57 154441.02 116597.04 —26811.08 —29302.46 97855.19 91901.87 O t It 42 43 07.16 42 19 48.21 42 31 18.52 42 50 34.00 42 12 01-02 41 50 29.32 42 07 27.04 42 14 27.77 41 46 18.08 42 18 22.52 42 30 26.41 42 31 12.40 42 07 29.55 41 45 03.38 41 54 11.28i 42 36 45.14 41 37 30.35 42 38 33.15 42 40 33.11 43 08 39.04 41 45 57.52 42 21 431.3 70 53 08.25 71 05 42.90 70 53 53.03 • « 70 51 56.53 70 46 39.53 71 21 21.66 71 11 05.61 71 22 33.76 71 07 57.02 71 32 27.89 71 04 42.43 71 11 14.90 71 06 24.12 71 13 49.29 71 05 55.03 71 14 19.30 71 13 09.26 70 57 24.99 71 25 43.81 71 15 31.06 70 43 53.33 71 10 04.24 TRIGONOMETRICAL SURVEY. 65 SECTIONS III AND IV. TABLE 4 — Continued. NAMES OF OBJECTS. Southings \a feet. Westings in feet. Latitude. Longitude. Wayland Church, - . - Wenham old Church, - - . West Bridgewater Church, - " Cambridge Church, - Westford Church, - . - West Newbury Church, Weston Church, - - - - Weymouth North Church, - " Yellow Church, - Wilmin^on Church, ... Wrentham North Church, - " Village Church, - " West Church, no-spired, 185601.60 99138.84 309790.48 166401 .90 105669.01 29472.52 183527.01 234127.45 253984.20 113856.38 274197.86 293291.10 307368.30 145154.82 9774.83 50933.39 89600.87 166355.80 45478.63 128469.24 33047.73 34865.63 92070.09 136343.72 136858.20 160413.08 42 21 45.11 71 21 54.09 I 42 36 00. lo' 70 51 49.39 42 01 19.36 42 24 56.06 42 34 54.04 42 47 28.98 42 22 06.12 42 10 30.62 42 33 35.19 42 04 01.33 71 00 59.18 71 09 33.85 71 26 41.40 70 59 43.63 71 18 11.75 70 57 25.18 71 10 07.61 71 19 59.05 66 TRIGONOMETRICAL SURVEY. TABLE 1. The following Table shows the Bearings from one Station to another, in the fifth sec- tion, on parallels to the meridian of Hyannis Station, with the Northings, Southings, Eastings or Westings made on each course. [The meridian of Hyannis Station is calculated from that of the Stale House by the application of Convergency.] NAMES OF STATIONS. Direc- tions. Bearings. Distances 1 Northings ^ Eastings in feet i"' Southings or Westings in feet. ' in feet. Bourne's Hill - - to German Hill, S. E. o / // 78 23 21.00 77076.34 15512.63 75499.13 1 1 High Land Light, N. E. 4G 03 18.00 1 160848.00111623.28115811.80 Mill Hill, - - - - N. E. 83 15 49.00 133135.70 15617.02132216.61 Pine Hill, - - - - S.W. 67 30 11.00 23599.35 9022.26 21784.95 1 Race Point Light, N. E. 28 56 34.00 136842.83119751.63' 66223.13 Scargo Hill, ... S. E. 89 59 23.00 86066.34 15.44 86066.34 1 Small's Hill, N. E. 50 35 50.00 158668.51 100717.70 122603.60 1 1 Wellfleet Light, N. E. 67 43 28.00 122346.11 46376.70113215.60 1 Chatham Station - to Chatham South Light, - S. E. 41 31 50.00 1 12740.68 9537.70 8447.32 Great Point Light, S.W. 8 58 28.00 113415.55 112027.13 17692.14 1 Monomoy Light, - - - S.W. 4 19 14.00 50327.91 50184.90 3791.53 Nantucket South Tower'd Ch. S.W. 12 01 39.00 154693.32 151297.42 32235.17 Scargo Hill, N. W. 75 58 55.00 53812.11 13034.78 52209.55 Cliff Station - - - to Brant Point Light, S. E. 72 28 17.00 5118.71 1541.63 4881.03 Great Point Light, N. E. 26 56 29.00 39156.35 34906.73 17740.92 Nantucket South Tower, - S. E. 36 15 51.00 5393.90 4349.08 3190.54 Falmouth Station - to Indian Hill, S.W. 15 09 55.00 63515.90 61304.00 16616.03 PineHUl, - - - - N. E. 19 35 13.00 42706.20 40231.96 14316.70 Point Gammon Light, - N. E. 87 34 06.00 96207.30 4081.87 96120.67 Succonnesset Station, - S. E. 70 06 47.00 41485.50 14111.93 39011.55 German Hill - - - to Barnstable Court House, N. W. 81 33 48.00 • 3843.54 25913.64 Chatham Station, N. E. 87 45 18.00 62826.73 2461.10 62778.50 Monomoy Light, - - - S. E. 51 01 32.00 7.5875.49 47723.70 58987.63 Scargo HUl, N. E. 34 17 48.00 18757.40 15496.06 10569.38 TRIGONOMETRICAL SURVEY. SECTION V. TABLE 1— Continued. 67 NAMES OF STATIONS. Direc- tions. Bearings. Distances in feet. Northings or Southings in feet. Eastings or Westings in feet. O 1 II Hyannis Station - to Bourne's Hill, ... N. W. 52 42 17.00 61463.00 37241.87 48695.30 Cape Poge Light, s.w. 27 16 20.00 85865.08 76320.27 39345.00 Chatham Station, N. E. 74 51 21.00 92597.10 24190.87 89381.34 Falmouth Station, s.w. 81 57 12.00 85844.56 12016.50 84999.38 German Hill, - . . N. E. 50 45 30.00 34350.69 21730.00 26604.08 Great Point Light, S. E. 39 13 04.00 113378.44 87839.74 71685.73 Indian Hill, ... S.W. 54 11 17.00 12.5303.55 73318.47 101613.92 Monomoy Point Light, S. E. 73 06 25.00 89453.60 25994.00 85593.56 Nantucket South Tower, - S. E. 24 12 35.00 139362.60 127105.67 57149.10 Pine Hill, . - . . N. W. 68 14 06.00 76104.90 28219.81 70679.40 Point Gammon Light, - S. E. 54 31 58.00 13659.26 7925.61 11124.75 Sampson's Hill, ... S.W. 27 43 43.00 104199.70 92233.34 48482.46 Succonnesset Station, - S.W. 60 24 06.00 52889.29 26122.90 4.5987.71 Manomet Hill - - to Barnstable Court House, S. E. 43 23 50.00 • 82381.38 77896.62 Bourne's Hill, - S. E. 21 49 13.00 76168.27 70711.15 28311.48 German Hill, ... S. E. 50 17 13.00 134949.31 86224.92 103810.31 Gurnet Light, N. W. 5 27 08.00 27810.36 27684.54 2643.03 High Land Light, N. E. 74 09 13.00 149831.00 40910.01 144127.40 Mill Hill, . . . . S. E. 71 03 32.00 169721.23 550090.86 160531.30 Pine Hill, . . . - S. E. 4 40 47.00 79998.95 79732.20 6526.77 Race Point Light, N. E. 62 34 55.00 106498.00 49040.13 94535.10 Scargo Hill, ... S. E. .58 16 15.00 134478.96 70723.10 114.380.18 Small's Hill, N. E. 78 45 13.00 153871.78 30009.38 150917.07 Telegraph Hill, - N. W. 22 39 47.00 74160.09 08433.90 28574.70 Mill Hill - - - - to Chatham South Light, S. E. 20 47 55.00 40866.60 38203.49 14511.09 Chatham Station, S. E. 11 56 38.00 29300.1] 28665.80 6063.76 Lombard's Hill, (new station,) N. E. 8 05 02.00 51328.00 50818.30 7217.93 Provincetown Church, N. W. 27 37 02.00 111442.87 98745.55 51660.72 Scargo Hill, S.W. 71 17 09.00 48721.48 15632.15 46145.62 Small's Hill, N. W. 6 26 47.00 85642.50 85101.00 9615.38 68 TRIGONOMETRICAL SURVEY. SECTION V. TABLE 1— Continued. NAMES OF STATIONS. Direc- tions. Beariuffs. Mill Hill - - - - to Monomoy Light - to Nantucket S. Tower to Sampson's Hjll - - to Small's Hill - - - to Succonnesset Station to Telegraph Hill - - to Wellfleet Light - - to Wellfleet Light, Great Point Light, Nantucket South Tower'd Ch, Brant Point Light, Cape Poge Light, Cliff Station, Nantucket, - Edgartown Harbor Light, - Falmouth Station, Great Point Light, Indian Hill, . - - Nantucket South Tower'd Cli Point Gammon Light, - Prospect Hill, Chilmark, Succonnesset Station, - High Land Light, Provincetown Church, - Scargo Hill, - . . Edgartown Harbor Light, - High Land Light, Provincetown Church, - Race Point Light, Lombard's Hill, - - - N. W, S.W. s. w. S. E. N. E. S. E. N. W. N. W. N. E. N. W, S. E. N. E. S.W. N. E. N. W N. W S.W. S.W. S. E. S. E. S. E. N. E. O / // 31 42 16. 1 12 40 19, 'is 42 54, 31 03 15 1 29 52 08, ,73 24 5C, '48 56 01 24 28 15 87 54 11 I 70 24 09, 71 43 55. ■35 15 39 86 37 38 j 2 09 40 31 54 02 I 72 01 11 19 56 01 7 15 25 80 56 43 79 46 55 81 02 50 52 35 00, Distances in feet. Norlliings j Eastings or Soulliings or Westings in feet. in feet. 36155. 63387. 105036. 3277. 18345. 106879. 7072, 88140, 120255. 56398. 111241, 103248. 00 72445. 00 66157. 00 12842. 00 44203. I 00107150. 00 61960. 00174880. 00139659. I 00 124627. I 00, 33011. 30760. 61843. 101110. 2807. 15908. 30506. 4645. 80222. 4400. 18916. 34870. 81305. 4262. 66110. 10902. 13645. 100731. 61464. 27522. 24774. 19394. 20058. 19001.20 13905.17 28449.47 1690.49 9136.45 102433.47 5332.06 36510.40 120174.55 53131.31 105634.75 59605.40 72319.97 2494.76 6786.45 42044.39 36531.08 7826.82 172700.72 137444.70 123109.37 26219.00 TRIGONOMETRICAL SURVEY. 69 SECTION V. TABLE 2. This Table shows the Bearings, with the Northings, So7ithi7igs, Eastings or Westings made on each course, from primitive statio}is to secotidary objects, in the fifth section, 071 parallels to the meridia/i of Hyannis Station. WHAT OBJECTS FROM WHAT STATIONS. Direc- tions. Bearings. Norlhings Eastings or Southings or Westings in feet. | in feet. Barnstable, Beacon on Bishop's and ? Clerk's Ledge, ^ from Hyannis Station, S. E. / // 36 44 46.00 20838.50 15.558.00 « « « - . u Succonnesset Station, N.E. 85 05 30.00 5285.35 61546.00 (( Beacon on Collier's Ledge IL Hyannis Station, S.W. 43 52 26.00 12646.50 12159.00 <( ({ (t (t ti Succonnesset Station, N.E. 68 16 45.00 13476.50 33829.00 (( Centerville Church, (t Hyannis Station, N. W. 64 14 07.00 5225.15 10825.76 (t " " _ - <( Succonnesset Station, N.E. 48 16 55.00 31348.04 35162.00 « Church, (( Manomet Hill, - S. E. 43 48 45.00 82707.54 79348.32 a *'---- (( Small's Hill, - S.W. 32 24 41.00 112719.10 71565.13 a Court House, (( German Hill, - N. W. 81 33 48.00 3843.54 25913.64 t( " ** _ (C Manomet Hill, - S. E. 43 23 50.00 82381.38 77896.62 <( Harbor Light, (( Bourne's Hill, - S. E. 85 50 55.00 4063.44 55983.84 a U it _ _ (( German Hill, - N. W. 59 36 38.00 11445.22 19516.15 (( Hyannis Church, - u German Hill, - S.W. 55 47 24.00 14401.00 21182.50 i< « « - - u Hyannis Station, N.E. 36 29 29.00 7333.25 5424.60 (C Oslerville Church, tc Bourne's Hill, - S. E. 15 46 33.00 37526.50 10602.00 u *< « - - (( Hyannis Station, S.W. 86 59 27.00 1128.20 21461.40 Brewster Church, - - - - f< Lombard's Hill, S.W. 27 31 12.00 56035.20 29195.00 (( " - . - - (C Mill Hill, - - S.W. 76 38 49.00 5217.41 21980.20 K Packet Signal, u Lombard's Hill, S.W. 34 20 12.00 62626.10 42779.20 U *» » - - - (( Mill Hill, - S.W. 71 37 55.00 11811.50 35.')70.00 Chatham Church, - - - - u Chatham Station, S. E. 33 16 49.00 3468.87 2276 91 a " - _ - - (( Mill Hill, - S. E. 14 33 01.00 32134.74 8340.70 Dennis, South Village North Church, tl German Hill, - S. E. 69 35 17.00 5406.50 14528.35 (i c( a (( tt a Harwich Church, S.W. 79 52 41.00 3909.14 21897.20 70 TRIGONOMETRICAL SURVEY. SECTION V. TABLE 2 — Continued. WHAT OBJECTS FROM WHAT STATIONS. Eastliam Church, - - - It ti _ _ _ " Nausett North Light, U (t tl II " " South Light, U (( (( it Edgartown Church, « "... Harwich Church, - - - ** " - - - " old no-spired Church, Orleans Church, - - - *' *' ... Provincetown Church, - Sandwich Church, (( " _ . . Truro Church, . . - " " ... Yarmouth North Church, (( a a " South Church, U it u from Bourne's HiU, - Mill Hill, - Lombard's Hill, Mill Hill, - Lombard's Hill, Mill Hill, - Falmouth Station, Indian Hill, Chatham Station, Scargo Hill, Chatham Station, Eastham Church, Mill Hill, - Small's Hill, - Manomet Hill, - Small's Hill, - Mill Hill, - Small's Hill, - Bourne's Hill, - German Hill, - Hyannis Station, Direc- tions. N. E. N. E. S. E. N. E. S. E. N.E. S. E. S. E. S.W. S. E. N. W, S. E. N.E. N. W, N. W, S. E. S.W. N. W S.W. S. E. N. W, S.W. N.E. Bearings. Norlhings or Southings in feel. 74 02 59. 12 50 46. 17 52 50. 23 41 54. 17 42 06. 23 56 20. 20 02 36. 71 12 17. 81 27 14. .56 41 02, 82 53 51 . 5 19 04. 66 48 34, 27 37 02. 72 01 U, 22 02 14, 53 59 06 10 19 32 50 45 43 81 46 05, 44 52 52, 19 33 58 72 35 19, Eastings or Weslmgs in feet. 39334 23717 19812 31006 20106 30716 76446 15145 3960 16995 1181 20574 3136 98745 13C45 61579 91588 80905 4187 10150 5374 15062 6663 14 12 15 00 34 40 10 43 20 00 60 10 97 55 05 00 24 60 71 07 85 00 .50 137625.03 5408.47 6391.72 13609.60 6417.40 13636.58 27889.60 44501.44 26353.06 25856.50 9483.04 1915.02 7322.10 51660.72 42044.39 24926.03 125991.06 14740.32 5127.70 70159.50 5352.60 5353.30 21248.41 TRIGONOMETRICAL SURVEY. n SECTION V. TABLE 3. This Table shoics the Smithiiigs and Eastings of Stations in the fifth section, from Tele- graph Hill Station ( Telegraph Hill being the northwesterly point of the section'), with their Latitudes and Longitudes. [The imaginary Station named in this Table as a point from which to calculate the Latitudes and Longitudes of the section, is situated north of the Telegraph Hill Station, and is designated by the negative sign ( — ), and the figures indicate the number of feet.] NAMES OF STATIONS. Towns in which situated. Southings in feet. Eastings in feet. Latitude. Longitude. Barnstable Court House, Bourne's Hill, ... Brant Point Light, ... Cape Poge Light, . - - Chatham South Light, - " Station, - Cliff Station, - - . - Edgartown Harbor Light, Falmouth Station, ... German Hill, .... Great Point Light, - - . High Land Light, - - . Hyannis Station, - . - Indian Hill, .... Lombard's Hill, ... Manomet Hill, ... Mill Hill, .... Monomoy Light, ... Nantucket South Tower'd Church, Pine Hill, .... Point Gammon Light, Barnstable, - Sandwich, Nantucket, - Edgartown, - Chatham, (( Nantucket, - Edgartown, - Falmoutli, Yarmouth, Nantucket, - Truro, - Barnstable, - Tisbury, Wellfleet, - Plymouth, Orleans, Chatham, Nantucket, - Sandwich, Yarmouth, - 150814.62 139145.72 300677.87 252715.08 161732.46 152195.00 299129.53 263976.70 188402.77 154657.51 264224.18 27523.05 176386.99 249706.10 72710.60 68433.90 123528.74 202380.37 303492.01 148167.09 184316.77 106472.00 56887.41 164615.84 66435.99 203614.93 195166.58 159730.25 51966.48 20784.97 132386.31 177470.90 172701.41 105783.39 4168.08 196322.57 28574.70 189104.87 191375.31 162929.91 35102.64 116905.44 41 42 06.07 41 44 00.90 41 17 24.45 41 25 18.78 41 40 16.16 41 41 50.73 41 17 39.84 41 23 27.02 41 35 53.19 41 41 27.94 41 23 24.333 42 02 23.36 41 37 53.36 41 25 46.75 41 55 38.91 41 46 34.31 41 33 35.00 41 16 56.62 41 42 31.16 41 36 35.00 70 18 33.81 70 29 28.25 70 05 51.67 70 27 19.74 69 57 12.89 69 59 03.86 70 06 55.73 70 30 29.46 70 37 22.41 70 12 52.03 70 03 01.72 70 03 55.33 70 18 42.92 70 40 57.77 70 35 44.96 70 00 22.47 69 59 56.24 70 06 13.88 70 34 15.44 70 16 16.37 72 TRIGONOMETRICAL SURVEY. SECTION V. TABLE 3 — Continued. NAMES OF STATIONS. Towns in which situated. Southings in feet. Eastings in feet. Latitude. Longitude. Point situated in the meridian of Hyannis Station, from "i ■nhich to calculate the latitudes and longitudes of this > section, - . . ^ . . . . ^ —88426.50 105783.39 f II / // 70 18 42.92 Provincetown Church, - Provincetown, 24779.60 137444.89 42 02 51.22 70 11 42.98 Race Point Light, - - t( _ , 19394.16 123109.5842 03 44.60 70 14 53.04 Sampson's Hill, Edgartown, - 268622.67 57297.1541 22 41.42 70 29 19.35 Scargo Hill, - Dennis, 139159.29 142956.7541 44 00.93 70 10 32.29 Small's Hill, - Truro, - 38425.75 179490.21 42 00 35.44 70 02 25.91 Succonnesset Station, . Marshpee, 202512.32 59794.70 41 33 34.76 70 28 48.26 Telegraph Hill, - . Marshfield, - • • 42 06 53.99 70 42 07.31 Wellfleet Light, - - - - Billingsgate Isl- ) and, Eastham, y 92768.76 170103.34 41 51 38.79 70 04 32.284 TRIGONOMETRICAL SURVEY. 73 SECTION V. TABLE 4. Tkl.t Table shoios the Southings and Eastings, from Telegraph Hill Station, of second- ary ohjecls in the fifth sectio?i, ieith their Latitudes and Longitudes; Telegraph Hill being the northwesterly point of the section. NAMES OF OBJECTS. Southings, in feet. Eastings in feet. Latitude. Longitude. Barnstable, Beacon on Bishop's and Clerk's Ledge, " Beacon on Collier's Ledge, - " Ccnterville Church, " Church, " Court House, ... - " Harbor Light, . . - . " Hyannis Village Church, " Ostetville Church, Brewster Church, ----- " Packet Signal, ... - Chatham Church, Dennis South Village North Church, - Eastham Church, . . - . . " Nausett North Light, " " South Light, - Edgartown Church, . . . . - Harwich Church, - . . . . " old Church, without spire, Orleans Congregational Church, - . . Provincetown Church, - - - - - Sandwich Unitarian Church, - . - Truro Church, Yarmouth North Village Church, - - . " South Village Church, - 10 197226.23 189034.65 171163.06 151143.14 150814.63 143211.22 169056.13 177515.19 128745.97 135338.47 155663.67 160063.70 99818.09 92522.75 92813.02 264850.20 1.56154.24 151013.40 120391.98 24779.60 130013.44 42618.30 149290.35 169721.50 121341.05 93624.05 94956.66 107924.05 106472.00 112871.70 111205.80 84322.00 167126.12 153539.12 197444.53 146915.42 194511.72 202714.38 202741.17 48672.04 168813.38 185683.54 190426.85 137444.89 53499.94 174363.53 127047.02 127032.40 41 42 06.07 70 18 33.81 41 43 21.20 70 17 09.36 41 45 43.33 41 40 34.31 41 50 28.30 41 51 40.0 41 51 37.20 41 23 18.50 41 41 12.46 41 47 04.93 42 02 51.22 41 45 31.09 41 59 .54.18 41 42 21.02 70 05 12.94 70 09 40.54 69 59 19.87 69 57 21.00 69 57 20.66 70 31 12.68 70 04 51.63 69 58 45.61 70 11 42.98 70 30 13.19 70 03 34.02 70 14 02.39