00 t THE EASTERN OBLIQUE ARC OF THE UNITED STATES OSCULATING SPHEROID > ^TREASURY DEPARTMENT^ U. S. COAST AND GEODETIC SURVEY m O. H. TITTMANX SUPERINTENDENT GEODESY THE EASTERN OBLIQUE ARC OF THE UNITED STATES OSCULATING SPHEROID By- CHAS. A.. SCHOTT, Assistant, Coast and Greodetio Survey WASHINGTON GOVERNMENT PRINTING OFFICE I 902 Treasi*ry Department, Document No. 2232. Coast and Geodetic Survey. His- It) 03. Treasury Department, Office of the Secretary, Washington, July 16, igoi. Sir: It affords me pleasure to approve the publication of the discussion of the Eastern Oblique Arc of the United States, herewith presented to the public. It appears that the value of this arc to geodesy is very great, but that the results are only incidental to the immediate purposes for which the triangulation was made. The results, however, could not have been obtained if the general plan of the Coast Survey had been less systematic or comprehensive'. Thus, in applied science, as well as in many other things, the far-sighted wisdom of our earlier statesmen, who gave direc- tion to our beloved country's policies, has borne fruit. Respectfully, L. J. Gage, Secretary. Mr. O. H. Tittmann, Superintendent Coast and Geodetic Survey, Washington, D. C. LETTER OF SUBMITTAL. Treasury Department, Office of the Coast and Geodetic Survey, Washington, D. C, July 16, 1901. Sir: I have the honor to submit to you for publication the manuscript of Special Publication No. 7, giving the results of the completed measurements of the Eastern Oblique Arc of the United States. This is the second of the publications intended to give the results of the principal arc measurements made by this Service, and like the first, which relates to the Transcontinental Arc of the Thirty-ninth Parallel, it was prepared by Assistant Charles A. Schott, whose knowledge, mature experience, and ability fitted him especially for the task. The Eastern Oblique Arc, though treated separately, intersects the Transcontinental Arc, and the two triangulations have several lines in common. The former extends from the Bay of Fundy to the Gulf of Mexico, and parallels the Appalachian mountain system, while the latter crosses the axes of the great mountain systems of this country, and extends from the Atlantic to the Pacific Ocean. Invaluable as the Transcontinental Arc is as a contribution to geodesy and the geography of our country, it does not in itself contain the data for determining the figure of the earth. The Oblique Arc, however, contains within itself all that is necessary for determining the dimensions of a spheroid which corresponds most nearly with the existing geoid within the area covered by triangulation. It is unique in that it is the first one which utilizes on a grand scale a measurement oblique to the meridian. The peculiar power of an oblique arc for determining the compression of the earth was pointed out by Tobias Mayer (1 723-1 762), but the first practical application of such an arc to geodesy was made by Bessel. This was before the introduction of telegraphic longitudes had made it possible to utilize such an arc to its fullest extent. The results of previous discussions of parts of this arc led to the abandonment by this Survey, in 1880, of Bessel's spheroid of reference and the adoption of Clarke's (of 1866), and the final discussion of the complete arc here presented sustains the grounds on which the change from one spheroid to the other was made. Taken in connection with the Transcontinental Arc of the Thirty-ninth Parallel, this discussion has enabled the Survey to decide upon the retention of the Clarke's spheroid and to adopt geographic coordinates for the whole extent of this country based on a uniform system. Further information as to these standard coordinates for geographic purposes, which differ slightly from those here published in connection with the Eastern Oblique Arc treated independently of other triangulations, will be published in due time. Very respectfully, The Secretary of the Treasury. O. H. Tittmann, Superintendent. 7 CONTENTS. Introduction PART I. THE BASE LINES AND BASE NETS. Page. 19 A. General remarks 25 B. The base lines of the eastern oblique arc, their measurement, resulting length, probable error, and adjustment of base nets 27 1. Epping base line and base net. Location, measurement, and length 27 Adjustment of the base net 28 Resulting angles and sides 35 Descriptions of stations 39 2. The Massachusetts base line. Location, measurement, and length 41 Connection with the main triangulation 42 Descriptions of stations 42 3. The Fire Island base line and base net. Location, measurement, and length 44 Adjustment of the base net 47 Resulting angles and sides 53 Descriptions of stations 54 4. The Kent Island base line, base net, and extension. Location, measurement, and length 56 Adjustment of the base net 5S Extension of the base net 63 Resulting angles and sides 68 Determination of probable error in the sides Osbornes Ruin Turkey Point, and Tobacco Row Spear 72 5. The Atlanta base line and base net. Location, measurement, and length 72 Adjustment of the base net 75 Resulting angles and sides 85 Descriptions of stations 87 6. The Dauphin Island base line and base net. Location, measurement, and length 90 Adjustment of the base net 93 Resulting angles and sides 97 Descriptions of stations 97 C. Synopsis of the measurements and results of the base lines of the eastern oblique arc 100 9 IO CONTENTS. PART II. THE MAIN TRIANGULATION. Page. A. General treatment of the reduction of the main triangulation between Calais, Maine, and New Orleans, Louisiana 103 B. The triangulation. 1. Northeastern terminus to Epping base net 105 Abstracts of horizontal directions 106 Figure adjustment 108 Resulting angles and sides no 2. Epping base net to Massachusetts base and to Fire Island base net 1 11 Abstracts of horizontal directions 114 Figure adjustment 122 Resulting angles and sides 130 3. Fire Island base net to Kent Island base net extended 135 Abstracts of horizontal directions 137 Figure adjustment 142 Resulting angles and sides 145 4. First, or Virginia section, south of the transcontinental triangulation 148 Abstracts of horizontal directions 149 Figure adjustment 151 Resulting angles and sides 154 5. Second, or North Carolina section, south of the transcontinental triangulation 156 Abstracts of horizontal directions 158 Figure adjustment 1 62 Resulting angles and sides 163 6. Third, or South Carolina section, south of the transcontinental triangulation 164 Abstracts of horizontal directions 1 65 Figure adjustment 1 69 Resulting angles and sides 173 Adjustment of the position of Mount Mitchell, in North Carolina 176 7. First section west of the Atlanta base net 178 Abstracts of horizontal directions 179 Figure adjustment 182 Resulting angles and sides 185 8. Second section west of the Atlanta base net 187 Abstracts of horizontal directions 188 Figure adjustment 191 Resulting angles and sides 192 9. Third section west of the Atlanta base net 194 Abstracts of horizontal directions 195 Figure adjustment , 1 96 Resulting angles and sides .' 198 10. Fourth section west of the Atlanta base net 199 Abstracts of horizontal directions 200 Figure adjustment 204 Resulting angles and sides 206 11. Fifth section west of the Atlanta base net 209 Abstracts of horizontal directions 210 Figure adjustment 213 Resulting angles and sides 216 Remarks on the accord of the Atlanta and Dauphin Island bases 218 CONTENTS. 11 B. The triangulation continued. 12. First section west of the Dauphin Island base net Abstracts of horizontal directions Figure adjustment Resulting angles and sides 13. Second section west of the Dauphin Island base net Figure adjustment Resulting angles and sides 14. Some statistics of the triangulation C. Resuming Geographic Positions of the Principal Stations of the Triangu- lation, Calais, Maine, to New Orleans, Louisiana D. Additional Geographic Positions which were Derived Differentially and for which Triangles are not Given in this Paper E. Additional Geodetic Azimuths Computed Directly from the Given Positions of the Stations Page. 219 219 222 224 226 228 232 234 237 247 248 PART III. THE ASTRONOMIC MEASURES. A. Results for latitude . 1. General statement 251 2. Details at stations: Agamenticus, Maine 276 Atlanta, Georgia 306 Atlanta Middle Base, Georgia 305 Aurora, Alabama 304 Bangor, Maine ' 257 Beacon Hill, New Jersey 289 Bull Run, Virginia 292 Calais, Maine 253 Cambridge, Massachusetts ( Cloverden Observatory) 282 Cape Henlopen, Delaware 292 Cape May, New Jersey 292 Cape Small, Maine 271 Causten, District of Columbia 292 Charlottesville, Virginia 292 Clark, Virginia 292 Coast and Geodetic Survey Office, District of Columbia 292 Coon, Alabama 310 Cooper, Maine 255 Currahee, Georgia 299 Dover, Delaware 292 Fast Pascagoula, Mississippi 312 Elliott Knob, Virginia 292 Farmington, Maine 258 Fort Morgan, Alabama 313 Gunstock, New Hampshire 274 Harvard College Observatory, Massachusetts (Cambridge) 281 Hill, Maryland 292 Howard, Maine 263 Humpback, Maine 256 Isles of Shoals, Maine 278 12 CONTENTS. A. Results for latitude continued. 2. Details at stations continued. Kahatchee, Alabama King, North Carolina Lavender, Georgia Long Mountain, Virginia Lower Peach Tree, Alabama Manomet, Massachusetts Marriott, Maryland Maryland Heights, Maryland Mobile, Alabama Montgomery, Alabama Moore, North Carolina Mount Desert, Maine Mount Harris, Maine Mount Independence, Maine Mount Pleasant, Maine Mount Rose, New Jersey Mount Tom, Massachusetts Naval Observatory (new), District of Columbia Naval Observatory (old), District of Columbia New Orleans, Louisiana New York, New York Paris, South Carolina Pooles Island, Maryland Principio, Maryland Ragged Mountain, Maine Rockville, Maryland Sabattus, Maine Sandford, New York Sawnee, Georgia Seaton, District of Columbia Soper, Maryland Strasburg, Virginia Sugar Loaf, Maryland : Taylor, Maryland Thompson, Massachusetts Unkonoonuc, New Hampshire Wachusett, Massachusetts Webb, Maryland West Hills, New York Yard, Pennsylvania Young, North Carolina 3. Summary of results for latitude B. Results for longitude. 1. General statement 2. Results for longitude at stations: Atlanta, Georgia . Calais, Maine Cambridge, Massachusetts Cape May, New Jersey Charleston, South Carolina Charlottesville, Virginia Dover, Delaware Page. 307 295 301 292 309 284 292 292 310 307 292 264 260 272 270 290 282 292 292 314 288 297 292 292 266 292 269 286 302 292 292 292 292 292 279 278 280 292 287 291 294 315 317 318 3 18 31S 318 318 318 318 t CONTENTS. B. Results for longitude continued. 2. Results for longitude at stations continued. New Orleans, Louisiana Washington, District of Columbia Strasburg, Virginia 3. Details at stations: Bangor, Maine Charleston, South Carolina .' Columbia, South Carolina Lower Peach Tree, Alabama . . . .- Macon, Georgia Mobile, Alabama Montgomery, Alabama New Orleans, Louisiana Petersburg, Virginia Raleigh, North Carolina Seaton, District of Columbia Statesville, North Carolina Wilmington, North Carolina 4. Summary of results for longitude C. Results for azimuth. 1 . General statement 2. Details at stations: Agamenticus, Maine Atlanta Middle Base, Georgia Aurora, Alabama Beacon Hill, New Jersey Beaconpole, Rhode Island Blue Hill, Massachusetts Bull Run, Virginia Cape Henlopen Light-House, Delaware Cape Small, Maine Cat Island 1855, Mississippi Causten, District of Columbia Clark, Virginia Cooper, Maine Copecut, Massachusetts Currahee, Georgia East Pascagoula, Mississippi Elliott Knob, Virginia Ethridge, Alabama Fort Morgan, Alabama Gunstock, New Hampshire Harvard Observatory, Massachusetts Hill, Maryland Howard, Maine Humpback, Maine Indian, Massachusetts Kahatchee, Alabama King, North Carolina Lavender, Georgia Long Mountain, Virginia Marriott, Maryland 13 Page. 318 318 318 318 321 321 322 322 323 322 323 320 320 319 319 321 326 327 334 359 361 345 341 339 351 347 332 366 350 351 328 341 357 365 352 363 364 335 338 348 328 329 340 362 355 360 351 348 14 CONTENTS. C. Results for azimuth continued. 2. Details at stations continued. Maryland Heights, Maryland Moore, North Carolina Mount Desert, Maine Mount Harris, Maine Mount Independence, Maine Mount Pleasant, Maine Mount Rose, New Jersey Mount Tom, Massachusetts Paris, South Carolina Principio, Maryland Ragged Mountain, Maine Sabattus, Maine Sandford, Connecticut Sawnee, Georgia Seaton, District of Columbia Shootflying, Massachusetts Soper, Maryland Spencer, Rhode Island Sugarloaf , Maryland Thompson, Massachusetts Unkonoonuc, New Hampshire Wachusetts, Massachusetts Webb, Maryland West Hills, New York Yard, Pennsylvania Young, North Carolina Page. 350 352 330 330 333 334 345 343 356 347 33 1 332 343 35S 349 339 349 342 350 336 336 337 34S 344 346 354 PART IV. DETERMINATION OF AN OSCULATING SPHEROID FOR THE REGION COVERED BY THE TRIANGULATION. A. Comparison of the astronomic and geodetic results 369 1. The astronomic latitude stations. Reduction to sea level 370 Reduction for variation of pole 370 Comparison of astronomic and geodetic latitudes 372 Review of latitudinal deflections 373 2. The astronomic longitude stations. Comparison of astronomic and geodetic longitudes 374 Review of longitudinal deflections 374 3. The astronomic azimuth stations. Comparison of astronomic and geodetic azimuths 375 Review of azimuthal deflections 376 B. Determination of an osculating spheroid for the region covered by the TRIANGULATION 377 The method and formulae employed 377 Collection of constants and tabular quantities required in the computation for estab- lishing the conditional equations 380 CONTENTS. 15 Page. B. Determination of an osculating spheroid for the region covered by the TriangulaTion continued. Selection of stations for which data were admitted into the equations of condition 381 Conditional equations derived from latitude comparisons 385 Conditional equations derived from longitude comparisons 386 Conditional equations derived from azimuth comparisons 386 Formation of normal equations 387 The relative weights of the observation equations 387 Resulting normal equations 388 The precision of the adjusted or resulting values of the length of the equatorial radius and of the compression as found from the measure of the arc 390 Resulting spheroid 391 Comparison with other spheroids 394 ILLUSTRATIONS. Page, i. United States Coast and Geodetic Survey Office Frontispiece. 2. Epping base. View of line as graded for measurement 27 3. Epping base. Placing base apparatus over mark 27 4. Epping base net, Maine 29 5. Massachusetts base, and connection with the primary triangulation of Massachusetts 42 6. Diagram 7. Fire Island base net, New York 45 , 47 8. Diagram _ 57 9. Kent Island base net, Maryland 58 to. Kent Island base and extension of the triangulation to the westward and southward 64 1 1 . Ferdinand Rudolph Hassler 44 1 2. Atlanta base net, Georgia 13. Alexander Dallas Bache 14. Dauphin Island base net, Alabama : 76 90 93 15. Diagram 1 94 16. Triangulation, Epping base net to northeastern terminus 105 1 7. Mount Desert, Maine 114 18. Mount Washington 116 _ 19- 75-cni. or 30-inch theodolite. Troughton and Simms ....'. 135 20. 30-cm. or 12-inch theodolite. Designed and constructed in the Instrument Division, Coast and Geodetic Survey Office 1 35 21 . Triangulation, Epping base net to Fire Island base net 112 22. T riangulation, Fire Island base net to Kent Island base net, extended 135 23. Triangulation, first section south of the transcontinental arc 148 24. Triangulation, second or North Carolina section 156 25. Triangulation, third section, North Carolina to Atlanta base net 164 26. Mount Mitchell, North Carolina 176 27. Triangulation, adjustment of Mount Mitchell 176 2S. Triangulation, first section west of Atlanta base net 178 29. Triangulation, second section west of Atlanta base net 187 30. Triangulation, third section west of the Atlanta base net 194 31. Triangulation, fourth section west of the Atlanta base net 199 32. Triangulation, fifth section and junction with the Dauphin Island base 209 33. Gulf coast triangulation west of Dauphin Island base net 219 34. Gulf coast triangulation to New Orleans, Louisiana 226 35. Extended Lambert equivalent projection, showing the location of principal arc measures and areas of osculating spheroids 369 36. Naval Observatory, Washington, D. C 377 37. Plan of Naval Observatory grounds 377 38. Subsidiary telegraphic longitude stations between Washington and New Orleans 320 MAPS. A. Area covered by the eastern oblique arc of the United States triangulation from Maine to Louisiana In pocket. B. Distribution of astronomic stations along the eastern oblique arc of the United States from Maine to Louisiana In pocket. 4192 Xo. 7 02 2 17 t THE EASTERN' OBLIQUE ARC OF THE UNITED STATES, FROM MAINE TO LOUISIANA, 1833-1898. INTRODUCTION. The general course of this inclined arc is indicated in the title, and is shown on a projection with elliptical outline * facing Part IV of this publication. The triangulation upon which it is based begins at Calais, Maine, on the St. Croix River, opposite the Canadian boundary, in latitude 45 11' oo" - 4, and in longitude 67 16' 57"'9 west of Greenwich, and, following the trend of the Appalachian chain of mountains, reaches the Gulf coast at Dauphin Island, near Mobile Bay, and terminates at New Orleans, Louisiana, in latitude 29 57' - 24" 4, and in longitude 90 04' 24"'4 west of Greenwich. The geodetic line covers 23 30' 57", and its total length is 2 6i2'3 kilometers, or 1 623^2 statute miles, with an azimuth of 57 3o'"7 at Calais and of 223 22 ,- 5 at New Orleans, as counted from south around by west. Its extremes differ 15 13' 45" 'o in latitude and 22 47' 26" "5 in longitude, and in its course it traverses sixteen States, f Near the middle of the arc the triangulation crosses the thirty-ninth parallel, and for some distance in Maryland and Virginia the same triangulation is used in discussing the oblique arc as was employed in the discussion of the arc of the thirty-ninth parallel, an important feature, as will appear in the following pages. Looking at the gradual development of this arc, extending over two-thirds of a century-, it can be seen that in its historical aspect it is readily divisible into several well-defined groups, and as a whole it will appear that its existence must be ascribed to necessity rather than to any preconceived idea of measuring such an oblique arc. Previous to the invention of the telegraphic method of determining differences of longitude, first employed in October, 1846, by the U. S. Coast Survey, in determining the difference of longitude between Washington and Philadelphia, and up to a somewhat later epoch, when the great accuracy of the method had been fully demonstrated, oblique arcs as well as arcs of the parallel were held in small esteem by geodesists, for the reason that the earlier methods did not determine differences of longitude with a degree of accuracy comparable with that obtained in observations for latitude. Consequently their attention was almost exclusively confined in practice to the measure of meridional arcs from which to deduce the earth's magnitude. Compared with an arc of the parallel, an arc inclined to the meridian is less favorably conditioned for discussing the figure of the earth on account of the greater effect of any uncertainty in the measure of A Lambert equivalent zenithal projection extended over a planisphere, fSee Map A (in pocket). 19 20 THE EASTERN OBLIQUE ARC. azimuths, and greater accuracy is demanded in the latter case than is required when the arcs follow a meridian or parallel. Oblique arcs should no longer be regarded with any special disfavor, and while they entail very much more labor, comparatively, when they are utilized in determining the figure of the earth, they are well adapted, when of sufficient extent, for the determination of an osculating spheroid for the region covered by them. _ The existence of the arc discussed in this publication is the result of the necessity for a main triangulation binding together the detached surveys of the harbors on the Atlantic coast and forming a base upon which all subordinate triangulation along the coast could be brought into accord. The immediate object of the main triangulation was thus to secure uniformity and systematic treatment for both the astronomic and geodetic measures in the preparation of the geographic position of the trigonometric stations. This was a leading idea from the beginning of the Survey under its first Superintendent, and when fully developed resulted in the work under discussion. There could be no doubt of the necessity of firmly binding together in this way the small tertiary triangulation and traverse measures along the coast which wind, unbroken, following the indentations of the coast, from the Canadian boundary to Cape Florida and thence into the Gulf of Mexico, following the coast to the Mexican boundary. The measurement of the oblique arc was thus identical with the progress of the ordinary operations of the Survey in this portion of the country. The first period, covering the years 1833 to 1844, witnessed the execution of the work from central Long Island, New York, to the head-waters of Chesapeake Bay, uniting on the way the surveys at New York, New York, and Philadelphia, Pennsyl- vania, and this work was nearly all completed under Superintendent Hassler. During the second period Superintendent Bache, pursuing the same general plan, had the work carried from Rhode Island to the Canadian boundary, at Calais, Maine, on the St. Croix River, and this work was completed in 1859. In 1865 the branch primary triangulation across the State of Connecticut, connecting the main scheme with some older work in this region, was completed. This period closed in 187 1, when the Potomac River was reached and crossed. In the third period, covering the years 1873-1877, the work was extended to the Atlanta base, in Georgia. The fourth period begins in 1885 and extends to 1898, and during this time the work was extended to Mobile, Alabama. The triangulation between Mobile and New Orleans, Louisiana, was done between 1846 and 1874. While the field work, as completed, apparently covers a very long period, the first measures dating back to the year 1833 and the last measures being made in 1898, as has been stated, this interval contained many years when no work was done upon this arc. The slow rate of progress was thus only apparent, as it depended upon and was subordinate to the ordinary requirements of the Survey on this part of the coast, and of the general operations of which it was only an incidental feature. Part I deals mainly with the base lines and Part II with the intervening triangu- lation. The astronomic determinations of latitude, longitude, and azimuths are numerous INTRODUCTION. 21 and well distributed over the whole arc. There are available, for the computation and comparison of geodetic and astronomic positions, results at 71 latitude stations, at 17 longitude, and at 55 azimuth stations. The latitudes depend almost exclusively on observations with zenith telescopes, and the longitudes on telegraphic transmission of time. The azimuths depend upon a variety of methods, using the pole star most frequently. Abstracts of the individual and final results of the astronomic measures are presented in Part III of this publication. The distribution ,of the astronomic stations over the region covered by the arc is shown on Map B (in pocket), and the A two maps and B have the same scale as the similar maps accompanying U. S. Coast and Geodetic Survey Special Publication No. 4, containing the discussion of the trans- continental arc of the parallel in latitude 39 N. Part IV contains the comparison of the geodetic and astronomic measures and the determination of an osculating spheroid for the region covered by the arc. Preliminary publication of the greater portion of this arc has already been made in the following reports of the Survey: Report for 1865, Appendix No. 21, pp. 187-203, ' ' Results of the primary triangulation of the coast of New England from the northeastern boundary to the vicinity of New York;" Report for 1866, Appendix No. 8, pp. 49-54, "Report on the geodetic connection of the primary base lines in New York and Maryland, their degree of accordance and accuracy of the primary triangulation intervening, with the resulting angles and distances as finally adjusted," and Report for 1878, Appendix No. 8, pp. 92-120, "On the adjustment of the primary triangulation between the Kent Island and the Atlanta base lines." These reports contain also more or less complete accounts of the six base lines located in the arc. Other references will be given in their proper place. The present publication is complete in itself, and while no important facts or statements are omitted, much simplification has been effected by referring to the publication above mentioned, covering the transcontinental arc of the parallel, the same general treatment and method of reduction of the triangulation having been employed in reducing that arc as is used in the following discussion of the oblique arc. > PART I. THE BASE LINES AND BASE NETS. 23 > THE BASE LINES AND BASE NETS. A. GENERAL REMARKS. The unit of length is the same as that used from the beginning of the Survey until 1889, viz, an iron bar, 1 meter long, standardized at Paris in 1799 and brought to this country by Mr. F. R. Hassler in 1805. Its use was discontinued after the receipt of the new prototype platinum meters in November, 1889. This meter, known on the Survey as the Committee Meter, is an end measure and is represented by an iron bar with square end surfaces, now slightly defaced by corrosion and perhaps by use. It will suffice to refer the reader to the full account given of this meter in Part I of the ' ' Transcontinental Triangulation and the American Arc of the Parallel ' ' across the United States in the vicinity of latitude 39 , published by the Coast and Geodetic Survey in 1900. In that publication, after some historical notes, the results of the numerous comparisons, direct and indirect, by different observers, by different methods and at different times, are completely set forth, and the final conclusion is reached that this bar at o C. represents so nearly the length of the prototype meter that no reliable value of the difference can be stated. The weighted mean of all comparisons gave the result i"'+o'2yuzho'6/u, and in all computations depending upon this standard it has been taken as equal in length to the prototype meter with a probable error of about three-quarters of a micron. There are six base lines irregularly distributed along the arc, and they are described in the order of location, beginning in the extreme northeast and ending on the Gulf coast. For each line all needful information is given in connection therewith, such as position, physical features, elevation above sea level, apparatus used for the measure, name of observer, computation of length and final result, with its probable error. A sketch of each base net is presented, and it is followed by the abstracts of horizon- tal directions, observed and adjusted, for each station forming part of the net. These abstracts contain the following information: County and State, date of measure, instrument used and observer's name, and also, in the first column, the number of each direction. These numbers, when in parentheses, indicate the corresponding corrections as given by the net adjustment. In the great majority of cases direction theodolites were employed, and for these Bessel's method* of reduction at the station was used. When repeating theodolites were used the station adjustment followed the ordinary method t of combination with the introduction of relative weights. Below the abstracts of directions resulting from station adjustment there is given the probable error of a single observa- * See T. W. Wright's " Treatise on the Adjustment of Observations." New York, 1884, pp. 315-322. tlbid., p. 139 and foil.; also p. 217 and foil. 26 THE EASTERN OBLIQUE ARC. ^ tion of a direction (mean of the direct and reversed series) deduced from e'= 1 o'4<*;s n5 ^' , a-\-\ = = = where n number of observations, 5 number of series, d number of directions, and = A differences of observed and adjusted values. The figure adjustment of the triangulation generally proceeds on the supposition of equal weights to all directions used in the adjustment, except, as in the case of the Epping base net adjustment, where special weights are introduced.* To carry weight equations from the station adjustment into the figure adjustment is not practiced or favored in the Survey on account of the increased complexity and the doubtful advantage of the pro- ceeding. The errors brought to light by geometrical conditions, and which have been called triangle-combination errors, are of a different character from those developed by a comparison of the measures made at a station, where defects of centering at observing and observed stations, effects of large local deflections of the vertical at a sta- tion, persistent lateral refraction along a line, etc., do not show; that is to say, weights pertaining to one operation are not those proper for the next operation. Further par- ticulars of figure adjustment with statement of formulae may be found in "The Trans- continental Triangulation," Part I. Fo* the computation of the sides of the triangles Legendre's theorem was used, and since none of the lines of the oblique arc are very long the spherical excess was computed by the simple formula ab sin C 2pm pn sin l" = where C the plane angle included by the sides a and b and the subscripts to p refer to the radius of curvature in the meridian and in the prime vertical. Appendix No. 9, Coast and Geodetic Survey Report for 1894, page 291, contains a table to facilitate the computation of the spherical excess, the argument being the latitude of the center of the triangle. The computation of the geodetic positions along the oblique arc is made according to the formulae and tables in the same appendix, the differences in latitude, longitude, and azimuth for two points of known distance and azimuth being given by where Dh E A' . -Aa ^ % F = A\ sin (Kai'ble error given bj fvt = /_ , where [xx] represents the diagonal coefficient cf the direction in the normal equation. t BASE LINES AND BASE NETS. 2J B. THE BASE LINES OF THE EASTERN OBLIQUE ARC, THEIR MEAS- UREMENT, RESULTING LENGTH, PROBABLE ERROR, AND ADJUSTMENT OF BASE NETS. I. THE EPPING BASE LINE AND BASE NET, MAINE, 1857. Locatioti, measurement, and resultiyig length of the Eppiny baseline, Maine, 185J. The site of this base is on Epping Plains, near Cherryfield, Washington County, A Maine. reconnaissance of the locality was made in 1853, and the measurement of the base followed in July and August, 1857, under the immediate direction of Superin- tendent A. D. Bache. The Annual Report for 1865, Appendix No. 21, pages 189-191, contains a full account of the measure and of the result. It will therefore suffice to present herex only the salient points of the operation. The measure was made with the Bache-Wiirdemanu contact-level compensating apparatus, and is the sixth primary line where this apparatus was employed, the Dauphin Island base, Alabama, being the first, an account of which is given further on (q. v.). The apparatus is fully described with illustrations in Coast Survey Report for 1854, Appendix No. 35, and reprinted in Coast Survey Report for 1873, Appendix No. 12. The essential part of the apparatus consists of two 6-meter bars, one of brass and one of iron, placed parallel to each other, one being above the other and firmly connected at one end. At the opposite or free end is the lever of compensation, so proportioned in its arms with respect to the actual and differential expansion and contraction with changes of temperature that the end of the apparatus remains at a constant distance from the opposite end. The spirit-level contact piece terminates in an agate, ground to a knife edge, whereas the agate at the opposite presents a slightly convex surface. The apparatus was standardized by means of a standard 6-meter iron bar, the length of which was determined at different times in terms of the Committee Meter. The length of this base is about 8*72 kilometers (or 5^42 statute miles), its middle point is in latitude 44 40' "8 and in longitude 67 53'" 1, with a mean azimuth of 106 54'. Much labor had to be spent preparing the ground for the measure by leveling it, removing bowlders, and overcoming other obstacles, the handling of the apparatus demanding a wide and fairly smooth roadway. The average height of the tubes above the mean tide level of the Atlantic was 76'45 meters. The 6-meter base bars or tubes were compared with the standard 6-meter bar just before and immediatel}- after the base measure. Taking the length of the latter and its coefficient of expansion as determined in i860 and published by Assistant J. E. Hilgard in CoastSurvey Report for 1862, Appendix on No. 26, viz, 5 '999 941 meters, and o'ooo 54 for the centigrade scale, the following 2 4 results for the length of the tubes were obtained: Three sets of 23 comparisons, made with Saxton's reflecting comparator* on July 16th and 17th, gave tube No. 1 shorter than the standard (at i8'3C.) 1 300^4 divisions of the comparator and tube No. 2shorter 1 0887 2'0 2"2 * The instrument is known as Saxton's pyrometer, and it is described in detail, with illustrations, in the Report of the Superintendent of Weights and Measures for 1856. and the Report of the same bureau for 1862 contains, on page 249, a general description of it. One turn of the screw equals 357-11 scale divisions and one scale division equals 136 microns. The head is divided into 100 divisions. 28 THE EASTERN OBLIQUE ARC. divisions; again, after the base measure, on August 6th and 7th, from 4 sets of 27 comparisons, tube No. 1 shorter than the standard (at 2i'oC. ) 1 411 '8 divisions and from 3'3 4 sets of 23 comparisons tube No. 2 shorter 1 195 '3 divisions. Having regard to the - 2g weights, the above comparisons give the values for length of tubes, for No. i a , 5 '999 459 o meters,* 49 for No. 2, 5 '999 750 6 meters. 49 Although the comparisons of the tubes with the standard bar were made with rising and falling temperatures, there remained an uncertainty respecting the indication of the y thermometers in air giving the temperature of the metallic bar even within x . Further, some allowance had to be made for any defect in the mechanical compensation, for pos- sible error in making contacts and transfers to the ground, and for other small uncertain- ties in connection with the base measure, and this was arbitrarily fixed as =fc 9'7 M- The + probable error of the length of a tube during the measure was taken as V(4'9) 2 8 (9'7) = = = io'9 n, hence that for the whole length 1 453 X 109 /* o'oi58'", which equals T j TVjs part of the length. In this case, as in that of the other bases of this arc, except the Atlanta base, the single measure fails to provide proper means for a more We reliable value of the probable error of the length. have for the length of the Epping base: 1 452 tubes of mean length, 8 7ii n"4262 One odd tube, No. 1, +5'9994 Correction for inclination of tubes, 2 -So4o Defect of last tube at East Base, + 1 '4250 Reduction to half-tide level of ocean, 0^1044 Resulting length of base, And its logarithm, 394031434 8 m 7i5 9422 0-00000079 o"'oi58 The Eppiiuj base net and results of its adjustment. As shown on the following sketch, this net of triangles is included within the primary quadrilateral Humpback, Mount Desert, Howard, and Cooper, and involves 6 geodetic points. The figure is a very strong one and demands that 35 geometric conditions lie satisfied. The reduction of this base net is complicated on account of the employment of both direction and repeating theodolites, five of the stations having l>een occupied with the latter instruments. An account of the adjustment of this base net iscon.ained in Coast Survey Report for 1864, Appendix No. 14, and may be referred to for particulars; the results are here transcribed, except that the notation has been changed for one more convenient. I11 connection with the station abstracts there is added a column containing the approxi- Comparing these values with the corresponding values of 1847 (Dauphin Island base) and of 1872-73 (Atlanta base), it will be seen that the lengths are not invariable, but it should l>e noted that one of the agates of tube 1 was accidentally broken in 1S55, and after the new agate was substituted the tube was found to be 0430 millimeter shorter than before. BASE LINES AND BASE NETS. 29 mate value of the probable error of a resulting direction, depending on the formula = 0-455 ^d* . e' FT- ffTT^ in case of direction observations. In case of repetitions the prob- able error will depend upon the comparison of a resulting angle with each of its 20 measures (each of 3 repetitions direct and 3 repetitions reversed), from which an average and approximate value of the probable error of a single measure of an angle and of a direction has been derived, as well as the probable error 'of a resulting direc- We tion. have approximately N from the 20 measures of each angle the probable error of a Co op era single observation of an angle ^5 f = e~ n { n- -.V) * hence . the probable error of a single observation ( 3 D. and 3 R. ) of a = direction e s e L /J2, also ap- proximately for a resulting = direction e, eJ^2o. The last column of the abstracts con- Humpback tains the final adjusted directions, the first direction having again been made zero by sub- tracting the correction to the initial direction from each of the corrections to the other directions, as given in the preceding column, f In the adjustment of the base net special weights were assigned to the directions, as explained at length in Coast 10 20 Statute Miles Survey Report for 1864. If we deduce the probable error of a direction from the closing errors in the sum of the angles of the 46 triangles, we find from the sum of the squares of these errors the mean = closing error of a triangle -Jf54'49_ 46 i"'09, hence the probable error of a direc- = = tion o'674 X 1 "09/76 :0"- 30. On the other hand, the average value of the probable error of observation of the 116 directions in the net is about o"'24, whence the triangle combination error = = e c s V{o"3o) 2 (o'24) o"'i7 (nearly), and the square of this was added as a We constant to each of the previously deduced squares of the observing errors. then = + have f ," *,* and the weight to any direction p 1 The values of p thus have "The half bracket indicates sum of similar quantities, disregarding their signs. tThe mean of the 4 values of fi derived from a single measure (D. and A*. ) with the 75cm theodolite is i"'04 and 'he mean of the 5 values of et derived from a single measure (3D. and 3^.) with the 25cm repeating theodolite is l"*i6, or one measure with the first instrument is about equal in accuracy to three with the latter. 30 THE EASTERN OBLIQUE ARC. smaller range than they would have had without the addition of the constant; still the maximum weight is to the minimum weight as 5 "4 to 1 . The effect of the intro- duction of weights is small in cases like the present, a base net of great complexity and fair measures. There was no special necessity for a reduction of the horizontal measures to sea level on account of the elevation of the signals sighted. The following table gives the approximate heights of the ground at the stations: BASE LINES AND BASE NETS. 31 Abstracts of resulting horizontal directions observed and adjusted at stations forming the base net, /8$6-rS^g continued. Burke, Washington County, Maine, September 30 to October 10, 1859. 25"' repeating theodolite No. 43. C. O. Boutelle, observer. No. of directions. 32 THK EASTERN OBLIQUE ARC. Abstracts of resulting horizontal directions observed and adjusted at stations forming the base net, 1856-1850 con ti 11 ue< 1 . Humpback, Hancock County, Maine. July 19 to September 6, 1858. cm 75 direction theodolite No. 1. A. D. Bache and G. \V. Dean, observers. No. of directions. BASE LINES AND BASE NETS. 63 Abstracts of resulting horizontal directions observed and adjusted at stations forming the base net, 1856-1850 continued. Howard, Washington County, Maine. July 15 to August 8, 1859. 75' direction theodolite No. 1. A. D. Bache and G. W. Dean, observers. No. of directions. 34 VI THE EASTERN OBLIQUE ARC. h BASE LINES AND BASE NETS. 35 The reciprocals of the weights introduced for the several directions are as follows: Dir's 36 THE EASTERN OBLIQUE ARC. Resulting angles and sides ofthe lipping base net, Maine continued, No. Stations. Tunk Epping West Base Burke Tunk Epping East Base Burke observed angles. 50 45 II '850 49 ' 45 33 80 13 02 '640 34 4o 37 '840 25 46 43 060 119 3 2 3 8 '49 Correction. Spher- ical angles. Spher ical o 039 1 o 300 203 II "8l I 45 630 02 -843 OO94 OO94 OO95 -o '945 +1-591 +0 283 36 "895 44-651 38 -773 o 106 o -106 0-107 I,og. distances. Distances in meters. 4 -032 670 78 4-021 66233 4-137 328 24 4"'38 343 64 4021 66233 4 -322 778 80 IO 781 291 i<>5" '443 13 7>9>83 '3 751 296 105" '443 21 027 -072 Pigeon Epping West Base Epping East Base 19 56560 64 55 08 -300 96 03 55 -500 -i-i8o 55-380 0178 +0-951 09-251 0-178 +0 -402 55 -902 0-177 3 "940 314 34 4 '384 324 57 4 -424 896 92 8 715 -942 24 228 391 26 600 -936 Pigeon Burke Epping East Base Pigeon Tunk Epping East Base Pigeon Burke Epping West Base Pigeon Tunk Epping West Base Pigeon Tunk Burke 33 44 59 '30 101 48 19 "820 44 26 42 '6oo 0-174 58-856 0-197 1-005 18-815 0-197 +0 -322 42 922 0-198 49 08 - 34 3i 60 37 58 '620 70 13 25 660 +0 -629 +0 -084 -f-i'9'3 34 939 58 -704 27-573 0-405 0-405 o -406 14 44 02 470 141 07 55 -670 24 08 03. 450 + 1 -006 03 476 o 099 -0 -925 54 745 O "IOO -1-373 02-077 099 30 07 37750 76 42 32 '630 73 09 48 780 + 1-809 +0 -990 -i'o73 39 '559 33 '620 47 707 0-295 o -296 0295 15 23 35 '280 25 57 20 780 138 39 01 690 +0 -803 + 1 -029 +0 -723 36 083 21 809 02 -413 O'lOI O "I02 O "I02 4 138 343 64 4 '384 324 56 4 -238 847 61 4 322 778 80 4 '384 324 57 4 -417 660 18 4 -032 670 78 4 -424 896 91 4 238 847 61 4-13732824 4 -424 896 91 4 -417 660 18 4 021 662 33 4 -238 847 61 4 -417 660 18 13 751 -296 24 228 -390 17 33' '957 21 027 -072 24 228 391 26 161 352 10 781 291 26 600 936 '733' '957 13 719 '183 26 600 -936 26 161 352 10 511 -443 '733' "957 26 161 352 Humpback Epping East Base Epping West Base Humpback Epping East Base Burke 9 55 37 '650 27 41 01 -oio 142 23 21 940 M 25 3' '879 79 18 13-910 75 10 31 '480 -0-051 +0-320 0551 37599 01-330 21/389 0-I05 o -106 o -106 0-220 14 659 0352 1^0-400 14-310 o-352 +0 -609 32 089 "353 3 "94o 3'4 34 4 -370 860 02 4 "489 329 42 4 138 343 64 4 496 419 39 4 '489 329 43 8715-942 23 488 -756 30 855 275 13 751 296 31 363 129 30 855 276 Humpback 13 Epping East Base Tunk Humpback 14 Epping East Base Pigeon 42 39 01 097 53 3 1 3 '850 83 49 30 54o 24 26 46 698 123 44 56510 31 48 17 670 o -042 01 -055 0-441 1 192 29-658 0-441 +0 -070 30 6lO 0-441 -o 358 +0 72I +0 -335 46 -340 57-231 18 -005 0525 o'525 0526 4 322 778 80 4-397 '74 17 4 '489 329 43 4 '384 324 57 4 -687 346 90 4 489 329 42 21 027 072 24 955 '954 30 855 -276 24 228 -391 48 679 590 30 855 -275 BASE LINES AND BASE NETS. 37 Resulting No. 15 16 17 18 19 23 24 25 26 38 THE EASTERN OBLIQUE ARC. Resulting angles and sides of the Epping base net, Maine continued. Xo. Stations. 27 28 29 3 31 32 33 34 35 36 37 38 BASE LINES AND BASE NETS. 39 Resulting i les and . Stations Howard 39 Pigeon Mount Deser Howard 4" Mount Desert Humpback Cooper 4i Burke Humpback Cooper 42 Mount Desert Burke Cooper 43 Howard Burke Cooper 44 Mount Desert Humpback Cooper 45 Howard Humpback Cooper 46 Howard Mount Desert 40 THE EASTERN OBLIQUE ARC. A perpendicular to the base at the center of the monument passes through the intersec- tions of cross lines in copper bolts in tops of two granite reference monuments, 3 '5 feet long and 1 foot square, set at distance of 36 and 72 meters north of station. When the station was visited in 1884, these reference monuments were found undisturbed, also a third, not described, with a hole drilled in top, 108 meters north of the station. The marble monument was then found overturned and broken, but the granite surface mark remained undisturbed, except that the head of the copper bolt had been hammered so that the cross lines were no longer visible. Epping West Base. This station is about 2 miles west of Schoodiac Hill, and has no subsurface mark. The surface mark is the intersection of cross lines on a copper bolt in a monument 3 feet square, made from the solid ledge by cutting away the rock to a depth of 6 or 8 inches around it. Similar marks 1 foot square were made north and south of the center in a line per- pendicular to the base, with copper bolts and cross lines placed in position. Over the surface mark was placed the monument of marble of same dimensions as that described for Epping East Base. When visited in 1884 the marble monument was found overthrown and broken, while the copper bolt had been hammered so that no cross lines were visible. The mark south of the center was in perfect condition. The one to the north had been destroyed by vandals, but the remains of the hole in which the copper bolt had been placed could be distinguished. The distance from the station to these marks is about 10 meters. Burke. This station is on the southernmost one of a range of rocky hills about 3 miles west of Cherryfield village and about 20 rods north of the line between Mount Steuben and Cherryfield. It is tnarked hy hole in a granite ledge at the north end of a small hollow on the summit of the hill, and it is about 3 feet below highest part of ledge, which is too narrow for a signal. Tunk. This station is on a mountain of the same name, the most commanding mountain (except Mount Desert) east of the Penobscot River. It is about 1 mile north of the stage road from Ellicott to Cherryfield and about 3 miles west of the nearest house in Cherryfield. It is marked hy & hole drilled in a granite ledge about 150 feet south- west of the highest part of the summit and about 4 feet below it. Pigeon. This station is on the highest part of a hill close to the ocean on the western side of the outlet of Narraguagus River. It commands the coast from French- mans Bay to Head Harbor Island, and is 9 miles from - Cherr3 field. It is marked by a hole drilled in a flat rock. In range to Mount Desert, 53'25 feet distant; to Saunders, 56'25 feet distant; to Humpback, 3533 feet distant, and to Mitten Mountain, 36'83 feet distant, there are holes and piles of stone. Humpback. This station is on the mountain of the same name, near the western line of Brewster Township. The highest point of the mountain is about 400 feet northeast of the station and is 4 or 5 feet above it. It is marked by a hole drilled in the rock. Range marks, consisting of holes drilled in the rock and heaps of stones, were made toward Harris, Saunders, and Mount Desert, distant 14, 1742, and i3'5o feet, respectively. Mount Desert.. This station is marked by a copper bolt in a ledge which is in the % center of a small depression in the large bare rock and 22 inches easterly from the southeast corner of a crevice. BASE LINES AND BASE NETS. 41 Single range marks, consisting of a hole in the rock, were made toward Peaked, Blue, and Ragged mountains, distant from center 53'i7, 1752, and 2i'83 feet, respectively. Toward Saunders and Harris there were two such marks, distant, in the first instance, 3592 and i42"5o feet, while in the latter, i9'Q2 and i36'6o feet from the center of the station. Howard. This station is on a steep, precipitous hill, about 6 miles below Machias- port and near Bucks Harbor. It is marked by a drill hole in a rock. Range marks were established toward Mount Desert, Humpback, and Cooper, distant 33'67, 66'25, When and 2 1 "30 feet, respectively. visited in 1884, the station was recovered. Cooper. This station is on the northern end of the summit of Western Ridge, about one-fourth mile west of the road running through the village of Cooper and about three-eighths of a mile northwest of Cooper Church. It is marked by a drill hole in a broad, fiat granite ledge. Range marks, consisting of drill holes in the rock, were made toward Mount Desert and Humpback, distant 22'8o and I9'65 feet, respectively. 2. THK MASSACHUSETTS BASE LINE, MASSACHUSETTS, 1844. Location, measurement, and resulting length of the Massachusetts base line, Massachusetts, 1844. This base was the third and last one measured with the Hassler base apparatus and followed within a few months the measure of the Kent Island base. Its site is on the Boston and Providence Railroad, in Bristol County, Massachusetts, and about 12 kilo- meters (7^ statute miles) to the northward and eastward of Providence, Rhode Island. An account of this base is given in the Coast Survey Report for 1865, Appendix No. 21, page 189, and little need be said here respecting the apparatus, a description of which can be found in the account of the measurement of the Fire Island and Kent Island bases. Its middle point is in latitude 41 58'"9 and in longitude 71 is''3, the mean azimuth is 27 49''2, and its length 1754 kilometers (or nearly ioj^ statute miles). There are but two bases in the United States (both in California) which exceed this length. The line was measured by Assistant Edmund Blunt during September, October, and November, 1844. As in the case of the two bases previously measured by the Survey, but one measure was made. The length adopted for the compound 8-meter bar rests w upon the comparisons of 1844-45, ' tri tne resulting length of 7*999 87 16 meters at o" C. 55 (see account of the Kent Island base). The mean temperature of the bar during the measurement was I4"92 C. (or 58'85 F. ); the average elevation of the apparatus above the half-tide level at Boston Harbor was 44'"'83. The record at this base is defi- cient in details. The resulting length of the base is as follows: 2 165 boxes Correction for excess of temperature Correction for inclination Fractional part of a box at Northeast Base Correction for 10 difference of temperature for above Additional length measured by scale Reduction to half-tide level m I7 3i9 '722i -\- 3 "2383 C5629 -f- 3 9999 00003 4- 01012 01 220 Resulting length of base 17 326""3763 42 THE EASTERN OBLIQUE ARC. To form an estimate of the accuracy of this measure, we find, from the probable error assigned to the base bars, that of the base to be o'"'oi 19. With reference to tempera- ture, 702 boxes were laid with rising and 579 with falling temperature, and for the rest of the boxes the temperature was stationary. The assumed probable error from this con- dition and probable lag, and from graduation error is o'"'o332, and the probable error from instability of the microscopes is taken as o'"'oo59. Combining these three independent values, we get for the probable error of the base o""o358, which equals We fBS^BTr of its length. have, therefore, the final result for the length of the Massachusetts base 17 3263763 meters, and its logarithm 4^238 70774. L O358 90. The connection of the Massachusetts base with the main triangulation. The Massachusetts base is connected with the main triangulation in an unusual way that is, with a base net so simple as to render a special adjustment of it unnecessary. The conditional equations, therefore, which subsist between the three northern base- lines were extended to reach directly to the Massachusetts base without any interven- Jilwc Hi, No. 5. tion of a special base net adjustment. The diagram shows the direct con- nection of the base with the triangula- tion of the New England States, the quadrilateral Beacon Pole, Copecut, Manomet, and Blue Hill being an integral part thereof. One advantage which the base possesses over the other two is its great length. The following table gives the ap- proximate elevation above the Atlantic of the stations adjacent to the base: Massachusetts South Base Massachusetts North Base Beacon Pole Great Meadow Copecut Manomet Blue Hill Meters. 33 70 1 67 S05 1075 1 20 194 Feet. 108 231 548 264 353 394 635 BASE LINES AND BASE NETS. 43 on the west side of the road in the line toward Beaconpole Hill, 6 inches being above ground, and distant 33 feet from the termination of the base. ' ' * Massachusetts North Base, 1844.. The station is marked by a brick tower, stated by G. Bradford to be 44 feet in height, when reoccupied October 18, 1884. The center of + the station is indicated by a brass bolt in the center of a stone, thus . It is central with the tower. The capstone (of 1844) had a mean diameter of 0^32 meter. Beaconpole, 1844. This station is located about 2 miles northeasterly from the village of Cumberland Hill. The station was visited and reoccupied in September, 1884, by Assistant G. Bradford, who remarks: ''Found here, guided by E. H. Pickering, an old resident, a copper (brass?) bolt set in lead and filling a hole drilled in a ledge of A rock some 30 feet in diameter, which occupies the summit of the elevation." tripod signal was built over the station in '1884. There is also a description of 1896 by H. B.. Wood, of the "Survey of the Commonwealth of Massachusetts." Copecut, 1844. Station on Copecut Hill between Fall River and New Bedford. Assist- ant G. Bradford found here in November, 1884, a copper bolt in a rock, presumably A the center of the station. large pile of stones was found about the bolt, covering it. The place is surrounded with bushes and small trees, and is difficult to find without a A guide. The road to it through the woods is extremely rough. tripod signal was built here in 1884. Great Meadow, 1843. This is one of the Borden Survey stations; about 3 miles north of west of Rehoboth village, 7 miles from Taunton, and 12 from Providence, Rhode Island. Assistant G. Bradford, in September, 1884, found here a hole in the rock, where, an old resident says, the signal once stood. The trees have grown up, and are now to the northward and westward some 40 to 50 feet high. The following description is by Assistant C. H. Van Orden, in 1889: "The hill is well known and is called Great Meadow Hill by the people about North Rehoboth. It is best approached from the south side. It is a large flat hill, with a growth of timber on the east and west sides. Directly north of the station is an open lot or meadow, noticeable from a distance." Manomet, 184.5. Near Plymouth, Massachusetts. Assistant C. O. Boutelle states, in his record of the latitude observations of July, 1867: " The triangulation station at Manomet has been more permanently marked by drilling three holes, forming an equi- lateral triangle around the copper bolt, and each hole is distant 6 inches from it. The two holes south of the bolt are east and west from each other and the third hole is north from the bolt. Each hole is five-eighths of an inch in diameter and 2 inches deep." In September, 1877, Assistant G. A. Fairfield writes: "Visited this station and found it undisturbed; had no difficulty in finding the rock with copper bolt and three drill '' holes. Blue Hill, 1845. Near Dedham, Massachusetts. The Coast Survey station is distant from the Borden survey station of Blue Hill 8 337 meters, and the azimuth of the Borden station is 11 16', as deduced from computation of December, 1884. The Borden station was located in the middle of a square inclosure of stones. In November, 1886, Assistant C. H. Van Orden visited the station and found the Coast Survey copper bolt (outside the old Borden inclosure) in good order. Borden's "Blue Hill" is under the stone tower of the "Blue Hill Observatory." The private meteorological observatory at this place was established by Mr. A. L,. Rotch in 1885. It is a two-story circular tower, 12 feet in diameter inside and 25 feet high, built of the broken stone found on the hill. Extending southward from this * I-'rom original record of the base measurement. 44 THE EASTERN OBLIQUE ARC. tower is a one-story, hip-roof house, built of stone, with a wooden shed attached, heliotype in Annals of the Astronomical Observatory of Harvard College, Volume XX, Cambridge, 1896). There is also a description of 1896 by H. B. Wood of the "'Survey A of the Commonwealth of Massachusetts. ' ' sketch shows the Coast Survey station with reference to the tower. 3. THK KIKK ISLAND BASE LINE AND BASE NET, NEW YORK, 1834. Location, measurement, and resulting length of the Fire Island Base Line, Neic York, 1834. The site of this base is on the southern shore of Long Island, New York, on the narrow Fire Island beach between the Great South Bay and the Atlantic Ocean, and distant nearly 80 kilometers, or 50 statute miles, to the east from New York City. It was the first and only primary base measured by Superintendent F. R. Hassler, and the measurement was made with an apparatus of his own design. He has left a full descrip- tion, with illustrations, in detail, of this apparatus in the Transactions of the American Philosophical Society, Philadelphia, Pennsylvania, new series, 1825, Volume II, pages 273-286. The essential parts of the apparatus are enumerated in No. 12 of his cata- logue of instruments, which probably dates back to the year 1816. These parts appear to have been made by Troughton, of London, in 1813. Two other primary base lines were measured with the same apparatus, viz, the Kent Island and the Massachusetts bases. The beach over which the measure extended is sandy, interspersed with low hum- mocks and ridges, and subject to changes from storms, which caused the west end of the base to be finally lost, notwithstanding a strong timber protection surrounded the hillock. The eastern terminal point was further removed from the beach, which caused a bend in the line close to the monument, and necessitated the measure of an angle at the bend. The insecurity of this exposed base and the danger of its loss caused the transfer of its length, a few years later, to be made to a primary line located on the central hills of Long Island. The base net, therefore, in this case consists simply of a quadrilateral. 8^ The length of the base is about 14 kilometers (or statute miles). The central point is in latitude 40 38' '9, and in longitude 73 o8'"i. The mean of the forward and backward azimuths is 72 56''8. For convenience of reference, a brief description of the Hassler base apparatus is repeated here from his description, and further remarks on this subject will be found in connection with the Kent Island base. It makes use of one measuring bar and of optical contact. The bar is 8 meters in length and is composed of four 2-meter iron bars placed in contact lengthwise. These pieces are of square section * and are firmly held together by means of collars clamped over the bar ends and bringing them together by means of screw bolts. The whole or compound bar is supported on 15 rollers, resting on a wooden beam, itself adjustable upon another similar support. The whole is placed in the bottom of a wooden trough. There are eight thermometers, two placed on the upper surface of each of the single bars to A ascertain their temperature. sector for measuring the inclination is attached to one end of the supporting beam, and all required mechanical appliances for the adjustment and alignment of the bar, as well as for the manipulation of the micrometer micro- scopes, are provided. The trough itself rests upon five trestles. The two microscopes are likewise mounted upon trestles. For alignment of the base the trough or box carries at one end a small telescope and at the opposite end a short vertical pin to * The same as that of the Committee Meter. FERDINAND RUDOLPH HASSLER (1770-1843). 3* BASE LINES AND BASE NETS. 45 define the axis of the apparatus and the direction of the line of measure. The micro- scopes admit of adjustment for verticality of axis. Their objectives are composed of two half lenses of different foci, one for pointing on spider threads stretched across small central half-circular notches cut vertically into the end faces of the protruding measuring bar, the other focus serving for a verification of the steadiness of the optical axis, the pointing being made upon cross lines ruled on an ivory plate resting on the support below the microscope. For the standardization of the measuring bar repeated comparisons were made at different times by different observers and by different means. The Hassler double end- meters, known as bars A, B, C, and D, were first compared in February and March, 8 1 1 7, with the Committee Meter and a standardized iron a bout meter by Lenoir. In the same year Hassler determined their coefficient of expansion and found it o'ooo 006 963 for Fahrenheit's scale or o'ooo 012 534 for the Centigrade scale, a value somewhat large yet probably applying to these particular bars, but this could not be verified, the bars having long since been lost. In May, 1834, and March, 1835, in connection with the Fire Island base, comparisons were made involving the Troughton brass scale and the Committee Meter. The last comparisons date from 1 844-45 , and were made with a Bessel level-contact comparator, using the Lenoir iron meter. The results were, for the combined length at oC: 2 From comparisons of 1817 = 7"'999 9506 From comparisons of 1834-35 8'ooo 0414* From comparisons of 1844-45 242 7'999 8716 55 When the comparisons in 1835 in connection with the Fire Island base had been A made an examination of bars and B showed them to be rusty. After cleaning them they were again com- pared, and the new 1835 2= value fn 'g9g 9764 re- sulted. The last obser- vations indicate a decided apparent shortening, which has not been ac- counted for satisfactorily except it be due to the manner in which the 8-meter bar was built up. Upon the whole, it has been thought best to adopt the Hassler value of 1834-35 for the reduction of the Fire Island base as representing the conditions then existing. But one measure of the base was made, owing probably to the labor and time required to measure such a long line. The measure was made during the months of August, September, and October, 1834. The above diagram shows the condition at The value found in connection with the Fire Island base. 46 THE EASTERN OBLIQUE ARC. the eastern end. The distances 2 to 3, 3 to 4, and 4 to 5 were measured with the base apparatus, and the angular horizontal directions of the fine and heavy lines at the points 1, 2, 3, 4, and 5 were obtained by means of a theodolite. Calling West Base No. 6, the points 6, 5, 4, and 3 were placed in line. For reduction of the measured length of the base to sea level, the average height of the bar above the half-tide level of the Atlantic was taken as 275 meters. The mean temperature of the bar during measurement was 26'6o C. (or 79'90 F. '). The resulting length from West Base to East End was as follows: 1 725 boxes , oC Correction for excess of temperature over Correction for inclination Reduction to half-tide level of ocean 13 .Socyoyu + 4"6o3i 02055 o -oo6o Resulting length Similarly we have the short measures Line measured Number of boxes Corresponding length Correction for expansion Correction for inclination Defect of last box at eastern end BASE LINES AND BASE NETS. 47 The. Fire Island base net and results of its adjustment. In this net we include the quadrilateral which transfers the measured base to the so-called mountain base, and the two other quadrilaterals, one within the other, which start from this derived base. The line Wooster to Sandford will be the connecting link with the northeastern triangulation, and the line West Hills to Bald Hill will form the link for the south- No. 7. western branch. The elevations of the stations above the sea level are very moderate and the horizontal directions needed but very small corrections, the maximum being less than o"'o2, but no account of this was taken when less than o"oo3. The approximate heights of the trigonometric stations are as follows: Meters. 48 THE EASTERN OBLIQUE ARC. = error t* c equals 2 (o'23) 2 (o'iq) or e c o"'i3, that is, the combination error is but slightly less than the observing error eo. If -15+18 Wooster Ruland West Hills 29 18 52 -587 61 26 2S '038 89 14 44 744 -26-27 -30+33 -n + 12 Wooster Tashua Ruland 28 53 58 -295 138 32 49-081 12 33 15 '263 -26-28 -3I-I-33 -15+16 Wooster Tashua West Hills 58 12 50-882 100 12 06536 21 35 06 485 -21+22 + - 9 '3 + -17 18 Sand ford Ruland West Hills 23 24 4i '555 101 19 14968 55 16 oS 1 96 22 23 -16- 17 -29+31 Sandford West Hills Tashua '9 12 16-869 12 23 30 -063 148 24 16 201 21 -23 -12+13 -29+30 Sandford Ruland Tashua 42 36 58 -424 27 19 31 667 no 03 33 '656 -22 24 -15+17 -25 28 Sandford West Hills Wooster 45 38 5' '567 33 58 36M8 100 22 39 -308 4 BASE LINES AND BASE NETS. 55 station for greater security. Four stone postswere placed to the north, south, east, and west of the center stone post. On the upper surface of the center stone post the inter- section of two lines marks the position of the center point of the Hassler crock of 1833. Around each post concrete was placed to secure it firmly in position. Upon the center stone was placed a stout stub of locust wood into the top of which, level with A the ground, a copper tack was driven, marking the center point. fuller description is given in the record of 1865, when the station was reoccupied. , West Hills, Suffolk County, New York. This station was established by Superin- tendent Hassler in 1836. It is marked by a red sandstone post, 4 feet high and 1 foot square, sunk in the ground, with stones well packed around it; the intersection of A diagonal cross lines upon the top marks the station point. crock, which had before served as station mark, was placed upon the post and a nail in a wooden peg driven cen- trally through it marks the station. Upon the side of the post facing Harrow were cut the initials U. S. C. S. The station was reoccupied in 1865, and again described. The place is 4 miles- from Huntington and 7 miles from Farmingdale railroad sta- tion. The point is on the summit of a hill. An examination had been made in i860, when the stone post appeared not to have been disturbed, but the crock was broken and the stub decayed. To mark the point more securely, posts arranged about the center post, north, south, A east, and west of the station, were sunk to a level with the surface of the ground. stout wooden stub, with a nail driven into it, was placed over the center of the old post to mark the station. Some further remarks are given in the 1865 description. Tashua, Fairfield County, Connecticut. This station is located in Trumbull town- ship, Fairfield County, Connecticut. It was established and occupied by Superintendent Hassler in 1833. The station was reoccupied in 1863 by the party of Superintendent Bache, by whom the following description is given: " The station point is marked by a copper bolt inserted in the top of a granite post sunk 2 feet below the surface of the ground. Four similar posts, 8 inches square and 2j4 feet in length, were adjusted 6 feet distant to the north, east, south, and west of the center point. The tops of the posts are marked by two lines intersecting at right angles and the letters U. S. C. S. Four directions to signals visible from the station are marked by copper tacks driven into hickory stubs at distances 171 feet 3 inches toward Ruland, 121 feet 7 inches toward West Hills, 73 feet q inches toward Wooster, and 70 feet 3 inches toward tower in Warren." Sandford, New Haven County, Connecticut, 1862. This geodetic point is located on the highest and most western summit of Sandford Mountain, 5 feet from a pile of stones which marks the boundry line between New Haven and Bethany townships. The point is marked by the center of a half-inch drill hole in the top of a granite post which is 234 feet in length and 1 foot square at the upper surface. Two cross lines and the letters U. S. C. S. are cut on its top, which is 1% feet below the general surface of the ground. For greater security four granite posts, each 2 l /i feet long and 6 inches square at the top, were sunk into the ground at points about 6 feet to the north, east, south, and west of the station. The tops of these posts were flush with the ground. To this description Assistant G. W. Dean adds the following: " The top of the stone post marking the station was sunk 20 inches below the plane of the four surrounding stones. 56 THE EASTERN OBLIQUE ARC. A copper tolt was driven into the central stone and the center accurately marked by A intersecting lines. cedar stub was placed immediately over the center of the granite post, the top of which was flush with the ground and firmly secured with earth. The station point was further marked by a composition nail driven into the top of the cedar '' stub. Bald Hill, Fairfield County, Connecticut. This station was established in 1833 by Superintendent Hassler and occupied by him in that year. The hill is situated in Wilton Township, about 4 miles south of Ridgefield. The station was visited by Assistant Farley in 1868, who found fragments of an earthenware crock (of the pattern of the Hassler crocks, or cones, as he called them), and marks cut on three rocks, but he was not able to identify the marks owing to the (apparent ) loss of the original description of the station by Superintendent Hassler and by Assistant Blunt in 1866. What made the search at the place more difficult was the fact that rock blasting had been going on there for some time. A second visit in 1869 elicited no certain information from want of application of proper means. The place was next examined . by Assistant G. Bradford in 1882 and 1884, when, by means of the determination of a temporary signal, the location of the crock (cone) placed by Assistant Blunt in 1866 was readily discovered. It is assumed that this crock occupies the position of the Hassler crock, because Assistant Blunt is said to have put it in the place of the fragments of the older one. The station appears to have been recovered. Woostcr, Fairfield County, Connecticut. This station was established in 1864 by the party of Superintendent Bache. It is located in Ridgefield Township, about 4 miles southwest of Danbury, on Wooster Mountain, known to the residents in the vicinity as Pine Hill. The station point is marked by a copper bolt, and is located on the highest point of gneiss which crops out near the summit of the mountain. The top of the ledge is quite limited, its length east and west being about 25 feet. 4. THK KENT ISLAND BASE LINE, BASE NET AND EXTENSION, MARYLAND, 1844. Location, measurement, iind resulting length of the Kent Island base line, Maryland, 1844.. Kent Island, in Queen Anne County, Maryland, on the western shore of which the base was measured, is situated on the east side of Chesapeake Bay, and is nearly opposite Annapolis Harbor. Originally it was intended as a check on the main triangulation which extended from the Fire Island base southward and westward, but its position near the latitude of 39 rendered it desirable to incorporate it in the eastern part of the transcontinental triangulation. An account of the measure and length of this base is contained in the Coast Survey Report for the year 1866, supplement to Appendix No. 8, page 140, and again in Special Publication No. 4, "The Transcontinental Triangulation." The middle point of the base is in latitude 3S 56'" 1 , and in longitude 76 2i'"2, the mean azimuth is 14 35' '4, and the length 87 kilometers (or 5*4 statute miles). The surface of this part of the island is slightly undulating, and the line crosses cultivated fields, with some portions covered by swamps and woods. The elevation is very little alxjve the surface of the bay. The shore is subject to erosion, in consequence of which the terminal monuments, each consisting of an upright stone surface mark with a copper BASE LINES AND BASE NETS. 57 bolt in a piece of slate below the surface, the whole being protected by rubble masonry, have disappeared. The base was measured by Assistant J. Ferguson, in May and June, 1844, by means of the same apparatus as was used for the measure of the Fire Island base ten years before. It is known as the Hassler base apparatus,* and consists of four rectangu- H B lar iron bars each 2 meters long, put together endwise and aligned in a wooden trough. The protruding ends of this 8-meter bar have semicircular notches ' across which was stretched a spider thread; over this was mounted, f. ') on 111 independent stand, an adjustable micrometer microscope, by means of which the measure was held while the bar was brought forward into a new position. All needed adjustments for the apparatus were provided for and the temperature of the bar was read from thermometers attached to the top of the 2-meter bars placed in the bottom of the trough, which is supposed to have been covered with canvas. At the end of a day's work or at other times when necessary, the end of the last bar laid was transferred to the ground, generally by a plummet. Only one measure was made, and the total time consumed was a little over one month. The four 2-meter bars made by Troughton, of London, about 1813 were standardized in 18 1 7 by Hassler, by using the Committee Meter, in 1834-35 by using the Troughton brass scale, and finally, in 1844-45, by Superintendent Bache, J. Saxton, and \V. Wiirdemann, by using a Bessel comparator, with the following results: In 1817 1834-35 1835 1844-45 2=7"'-999 9506 at o C. 8-ooo 0414 t7"999 9764 7-999 8716 55 This last value, after verification in July, 1854, was finally adopted for the two bases measured with this apparatus in 1844. The coefficient of expansion of the bar which was determined in 1817 by Hassler at Newark, viz, o'ooo 012 534 for the centigrade scale, was adopted and, though somewhat large, may nevertheless be true for these particular bars, now lost. The mean temperature of the bar during measurement of the base was 25' 18 C. (or 77 '33 F. ). The deduced length of the base is as follows: 1086 boxes 8687"' 8606 Excess of last box over end mark at South Base, as measured by Bar D and scale 2 '0508 Correction for excess (25'44 C. ) of temperature of bars over o C. and graduation error of thermometers ( -o0, 255C.) 127424 Correction for inclination of boxes 5o Reduction to half-tide level of bay for surface elevation and height of boxes I 0007 o '0069 Resulting length of base' S6S7""5446 The probable error of this value can only be estimated, since the base was meas- ured but once. Supposing the combined length of the four 2-meter bars subject to rfc 20^, the effect on the base will be o""o22; an assumed error of j' part in the * For a description, with illustrations, of the apparatus, see the Transactions of the American Philosophical Sock t\ , Philadelphia. Pennsylvania, for the year 1825, pp. 273-286. See also the preceding account of the Fire Island base measurement. t Result of comparisons made after cleaning two of the 2-meter bars which were found rusty when examined. 58 THE EASTERN OBLIQUE ARC. coefficient of expansion would produce - o'" 055; again, the effect for imperfect tempera- ture correction, for inequality in number of boxes laid with" rising and with falling temperatures, may be taken as o"'"034; other minor uncertainties may be omitted. Combining the several values for probable error gives om 'o68, equal to ST J 00 of the length nearly. This may be taken to represent the measuring error, and to include the probable error due to our practical unit of length, the Committee Meter, taken as Yxr1 - Resulting length of Kent Island base, 8 687*5446 meters and its logarithm, 0680 3-938 897 05 3 40 Kent Island base net and results of adjustment. The following abstracts of observed and adjusted directions at the nine stations form- ing the base net proper, as well as the conditional equations and results of its adjustment with resulting length of triangle sides, were copied from Part I, Special Publication No. 4, "The Transcontinental Triaugulation, " and from Part III of the same publication the. results of two * triangles to the northward of the net and of 35 triangles to the westward and southward of the base.t The triangles of this last extension are shown on the follow- ing sketch: OsbornesRui Finlay , Turkey 'Poini,^ Kent Island. North. Base Marriott Kent Island South Base Kilometers Statute Miles * Shown on the above sketch by dotted lines. t For adjustment of this work see Special Publication No. 4. " The Transcontinental TrianRUlation.' > BASE LINES AND BASE NETS. 59 The heights of the stations above the half-tide level of the ocean are small and approximately as follows: 6o THE EASTERN OBLIQUE ARC. Abstracts of resulting horizontal directions, observed and adjusted, at the stations forming lhe"J>ase net, 1844-/897. Kent Island South Base, Queen Anne County, Maryland. May 30 to June 4, 1847. 30" repeating theodolite No. E. Blunt, observer. (Observations in 1844 by J. Ferguson superseded by above. ) Number of directions. Object observed. Resulting directions from sta- tion adjustment. Corrections from base net adjustment. Final seconds. Marriott o OO'OO +0-03 Taylor 46-24 -)-o '06 Kent Island North Base 11 1 1825 -o'oo, = Probable error of a single observation of a direction ( 6 I), and 6 A'. ), e, 00-03 46-30 1S16 0" 69. Kent Island North Base, Queen Anne County, Maryland. May 21 to 28, 1847. cm 3o repeating theodolite No. 11. E. Blunt, observer. (Observations in i844-'45 by J. Ferguson superseded by above. ) 4 BASE LINES AND BASE NETS. 61 Abstracts of resulting horizontal directions, observed and adjusted, at the stations forming the base net, 1844-iSgy continued. Webb, Anne Arundel County, Maryland. July 10 to August 14, 1848. 6ocm direction theodolite No. 2. A. D. Bache, observer. October 21 to December 2, 1850. cm 75 direction theodolite No. 1. A. D. CO. Bache, observer. September 18 to 25, 1868. cm 75 direction theodolite No. 1. Boutelle, observer. Number of directions. 62 THE EASTERN OBLIQUE ARC. Abstracts of resulting horizontal directions, observed and adjusted, at the stations forming the base net, /844-1897 continued. Finlay, Baltimore County, Maryland. August 29 to September II, 1844. 60" direction theodolite No. 2. J. Ferguson, observer. October 15 to December 27, 1896. 30CI repeating theodolite No. 16. G. A. Fairfield, observer. Telescope above ground 1-5 meters. Number of directions. Pinal seconds. r# BASE LINES AND BASE NETS. 63 The correlate and normal equations, when established and solved, gave the follow- ing values of corrections to the angular directions: (I)= Results of local adjustment. Coast and Geodetic Survey, J90J. The Eastern Oblique. Arc. Maryland Heights Wehb No. 10 Ml. Marshall] Fork THE KENT ISLAND BASE Triaiiulation to tin; Westward and Southward ^ BASE LINES AND BASE NETS. 65 Abstracts of resulting horizontal directions observed and adjusted at stations forming the extension of the Kent Island base net to the westward and southward continued. Peach Grove, Fairfax County, Virginia. October 1 1 to November 8, 1869, ami July 28 to August 15, 1870. cm 75 direction theodolite No. 1. C. O. Boutelle, observer. Telescope 1372 meters above ground. ObjJects observed. Results of local adjustment. Correction from . . 66 THE EASTERN OBLIQUE ARC. Abstracts of resulting horizontal directions observed and adjusted at stations forming the extension of the Kent Island base net to the westward and southward continued. Bull Run, Fauquier County, Virginia. September 22 to November 28, 1.S71. 75'"- direction theodolite CO. No. I. Boutelle, observer. Azimuth Mark o / // o 00 00 "oo Clark 1 07 09 -35 Fork 33 03 17 -51 Mount Marshall 53 39 05-53 Maryland Heights 157 20 07 -15 Sugar Loaf 190 54 06 -98 Stabler 225 12 0395 Peach Grove 242 29 57 -85 D = Probable error of a single observation of a direction ( . and R. ) , f, of circle, VII. // // .... +o'ii +0 -49 o '68 05-64 07 -64 06 -30 -j-o-oS 04-03 " r 09. o -co 57 S5 Number of positions Maryland //eights, Washington County, Maryland. September 16 to October 28, 1870. cm 75 direc- CO. tion theodolite No. 1. Boutelle, observer. Sugar Loaf 00 Azimuth Mark Stabler Peach Grove Bull Run Mount Marshall R Probable error of a single observation of a direction ( D. and of circle, VII. Clark, Orange County, Virginia. July 24 to September 5, "1871. C. O. Boutelle, observer. o / c,u 75 direction theodolite No. I. // // // Spear Peters Humpback Azimuth Mark Fork Mount Marshall Bull Run = Probable error of a single observation of a direction D. ( and R. ), *, of circle, VII. 1 -03. Number of positions BASE LINES AND BASE NETS. 67 Abstracts of resulting horizontal directions observed and adjusted at stations forming the extension of the Kent Island base net to the westward and southward continued. Fork, Madison County, Virginia. October 12 to December 24, 1874. 35^"' direction theodolite No. 10. A. T. Mosman, observer. July iS to August 6, 1879. 5ocm direction theodolite No. 114. Same observer. <* asas* r" jssl Peaked O / // o 00 00 -oo // // .... Slate Springs Mount MarsnaU Bull Run 20 16 00 -96 136 25 13 '62 161 06 3764 Clark 224 16 58 -6S Peters 270 56 24 '51 Spear . 303 52 39-51 Humpback 322 58 40-96 Elliott Knob 353 33 11-50 = Probable error of a single observation of a direction /). ( and R. ), e, tions of circle, XI in 1S74 and in 1879. -)-o "98 +039 1 -oi o \% 01 -94 14-01 36 '63 57 -82 .... o"io o -20 39-41 4076 -fo'So 12-30 i"-24. Number of posi- Humpback, Nelson County, Virginia. June 8 to 29, 1S75. 35" direction theodolite No. 10. A. T. Mosman, observer. May II to June 6, 1878. 50 direction theodolite No. 114. Same observer. August 18 to 28, 1879. 50cm direction theodolite No. 114. A. T. Mosman and W. B. Fairfield, observers. o / // // // Jarman o 00 00 'oo .... Clark 24 30 20-46 +' '37 21-83 Peters , ^ 31 40 01 -24 Spear Long Mountain Tobacco Row Bald Knob 126 14 25-02 154 41 57 'io 173 06 07-68 230 26 24-65 +0-44 .... 0-87 +0-17 25-46 06 -8 1 24-82 Elliott Knob 265 35 01 13 1-03 00 -io Slate Springs 300 08 53 -99 o 57 53 -42 Fork 357 28 32-18 +0-33 32-51 = Probable error of a single observation of a direction (D. and R. ),ez //i 43. Number of positions of circle, XI. Spear, Buckingham County, Virginia. July 30 to August 29, 1875. cm 35 direction theodolite No. 10. A. T. Mosman, observer. o / // // // Willis o 00 00 -oo .... Long Mountain 1 13 14 26 -50 .... Flat Top Tobacco Row 150 15 15-49 160 17 43-42 .... +022 43 -64 Humpback 233 59 02-50 0-44 02-06 Fork 266 07 14-11 +0-05 14-16 Peters 283 15 22 -59 Clark 288 05 31-91 Probable error of a single observation of a direction (D. and R.), e, positions of circle, XI. .... +017 //i 37. 32-08 Number of 68 THE EASTERN OBLIQUE ARC. Abstracts of resulting horizontal directions observed and adjusted at the stations forming the extension of the Kent /stand base net to the westward and sonthivard continued. Tobacco Row, Amherst County, Virginia. September 14 to 23, 1875. 35"" direction theodolite No. 10. A. T. Mosman, observer. September 6 to 9, 1879. 50"" direction theodolite No. 114. Same observer. Objects observed. Results of local adjustment. Flat Top Bald Knob Humpback Spear Long Mountain Smith Cahas Probable error of a single observation of a direction (D.a.m\R.),e,= of circle in 1875, XI. i"'43. Number of positions BASE LINES AND BASE NETS. 69 Resulting a 13 19 70 THE EASTERN OBLIQUE ARC. Wetern and southern extension of Kent No. 23 24 25 26 27 28 29 30 31 32 BASE LINES AND BASE NETS. 71 Western . No. 33 34 35 36 37 38 39 40 4i 42 43 44 45 72 THE EASTERN OBLIQUE ARC. Western and southern 46 47 48 49 BASE LINES AND BASE NETS. 73 is given in Coast Survey Report for 1854, Appendix No. 35, and in Coast Survey Report for 1873, Appendix No. 12. Further remarks will be found in the account of the Dauphin Island and the Epping bases in this publication. It will also appear from the seven values collected on page 131 of the Report for T873 that the average accuracy reached with this apparatus is about s^'iotf part of the length measured. In view of the complete publication already made, it will suffice to give the present account in an abbreviated form. The middle point of the base is in latitude 33 54' '4 and longitude 84 16' '5, with a mean azimuth 52 - o8' 2. The measurements were made by Assistant C. O. Boutelle. The first and second measures were made in opposite directions in November and December, 1872, and in January, 1873, and the third was made in Jul}' and August, 1873. The three measures were accomplished in 17, 13, and 14 working days, respec- tively. In connection with these several measures the tubes* were frequently compared for length with the standard bar, which was immersed in glycerin during the July and September comparisons. The summit of the ridge is narrow and crooked, but the slope of the measurement was confined within the maximum inclination the tubes would bear, namely, 5 . A gulch near the southwest end was crossed on trestlework consisting of two separate structures. The approximate elevation above sea level is 320 meters. The terminals are marked by granite monuments and the subdivisions of the line by small granite posts. The length of the 6-meter standard bar is 5"'"999 941 at C.,and its coefficient of 2 expansion o'ooooii 54. The numerous comparisons made for standardization of the 4 tubes and for testing their compensation showed that the latter was still close; that is, about 2 1 parts of 22 remained compensated between the range of temperature o to 22 C. , but between the temperatures from 22 to 38 C. the tubes compensated only about 10 parts inn. The comparisons were made with the Saxton reflecting comparator No. r , for which we have for the period November, 1872, to January, 1873, one division at 4 "4 C. equal i'384 microns and at 19 C. i'378 microns, values answering for the case 3 3 of the first and second base measures In connection with the third measure, observa- We tions in July and September, 1873, gave 1 div.= 1*376 ft. have also 1 turn of the screw at the temperatures 4 , 19 and , 28 C. equal to 35o'9, 352"3, and 353'o6 scale 18 divisions, respectively. As the result from the above comparisons we have the following values forthe length of the tubes, in which the uncertainty from the length of the standard is included: For first and second measures: = + Tube I] 5""999 999 7 o'odo 003 37 (/ u'2 C.) 144 ~ Tube 2 =5 999 647 8 +o'ooooo4 84 (/ 1 1'2 C. ) '9 3 and fcr third measure = Tube i 3 6""ooo 084 6 4" o'ooo 009 54 {t 112 2=5 Tube 999 730 3 r 0000 008 01 (/ 11 6 27'6 C. ) 27 S- C. ) Before making the comparisons tube No. i was supplied with a new agate. The Borda scale or differential thermometer as applied to the tubes is shown on plate No. 18 in the Coast Survey Report for 1873. 74 THE EASTERN OBLIQUE ARC. The minimum temperature at which the tubes were used was 7"7 C, and many were laid with temperatures below the freezing point; the maximum temperature at which the tubes were used was 4i"7 C, and many were laid with temperatures above 38 C. The three thermometers attached to each tube were read and the mean values were corrected for graduation errors. The maximum inclination of a tube laid was 4'7, and there were a great many with inclinations of 4 . The ruggedness of the ground caused the sum of the inclination corrections for the whole base to mount up to n io' '22i2 in the first and to io'""o375 in the last measure. Fractional parts of a tube at the base monuments and intermediate marks were measured with the brass Lenoir meter of the Survey, which is of standard length at i3'6 C. The following table shows the temperature of the tubes during the measures of the several parts of the base, their lengths as measured, corrected for inclination, but not reduced to sea level, and exhibits the difference of the individual measures from the mean of the three measures: Subdivisions of base. BASE LINES AND BASE NETS. 75 afford a check on the measure. Starting with the first or shorter distance and using the adjusted angular measures, the length of the base thus trigonometrically deduced comes out 9 n 338 '"502, or 22""" in excess of the direct linear measure. For the probable error of the measure of the base we have the following data: = Probable error from uncertainty in length of tubes in 1 556 tubes, 1 556 X 14'oyu 2 2 om '02i 78. For mere measuring error we have, after forming the values 3' tt 8*, 22 443 013 012 o 08 012 O "12 o '14 0-13 on Q-I2 OIO 015 0-14 ...... o '600 +0-598 054I +0542 Mean correction o "ooo Observations made in sets of 3 D. and 3 R. measures. =1' Probable error of a single observation of a direction (6 repetitions), e, 23- leaden 39'4o9 36 723 ' 1 -339 39 '28 % XI BASE LINES AND BASE NETS. 8l Observation equations continued. 33i-(38)+(4o)-(3 f)+(a9)-(i7)+(i&) + + + 971- (9) (ii)-(28) (29 )--(i7) (i5) + . 35 i-(ii) + (i3)-(5o)4-(52)-(34) (28) + + !-296-(l0) (lI)-(28)-f(30)-(23) (2l) i 54 -(48) + (47)-(26) + (23)-(3o) + (33) 83i-(33) + (32)-(44) + (45)-(49) + (48) + + 3 i3-(26) (25 )-(43) + (45)-(49) (47) + 3oi-(22) + (26)-(47) (46)-(i9) -|-(i6) 152-0 -095(4) +0 -095(7 )-o-o26(8)+o -026(12)- 1 -505(35)+o-8i4(36)+o -691(37) , -124-0 -n6(4)+o -021(6) -(-0-095(7)4-0 -531 (ao)+o 795(21)- 1 -326(24) +0-344(36) '499(37) -0-843(39) ( -9420 -226(8)+o -199(9) -i-o -027( 12) -7 -676( 14)4-0 7g8( i5)-f-6 -878( 18) I -941(36)4-0 -344(37)4-4 -596(38) 4364-0 -140(8) o -199(9)4-0 -o6o( io)4-o -6g9( 14) -o 798( 15)4-0 -o99< 16) +0 1 -565(20)4-0 -531(21) -034(22) 1-004 4- 1 -883(21) ! '3 26(24) -0-557(27) 4-0 -9i7(37)--o-843(39)-o -074 (41) >726(5o)-o -496(51 )-o -230(53) 1 -915-0 "9i6( I5)4-o -207( 17)4-0 709( 18)- 1 -128(28)4-0 -237(29)4-0 -892(31 ) '692(37)4-0-311(38)^0-380(40) i '359+ '628(28)-o -892(31 )4-o -264(34)-(-o -306(37) o -380(40)4-0 -074(41 ) '305(50)4-0-075(52)4-0-230(53) 7924-0 -403( 9 )-o -500(10)4-0 -097(1 1 )4-o-i76( 15)4-2 '439(i6)-2 -616(17) 220(28) -5 -705(29) 4 5 "485(30) 463 ( o -223(23) -0-238(25)4-0 -016(26) 0-222(43)4-0 -2ro( 44)4-0 -012(45) 1 -194(47 )-o -404(48)4-0 -210(49) 619-2 7557( r6)4-2 '6l57( 17)4-0 -i4oo( 19)4-5 7048(29) 5 -9022(30)4-0 -1974(33) 1-5032(46)---0-6971(47)4-0 -1939(48) [491 --2 -6157(16) 4-2 -6157(17) -0-4212(22)4-0 -4212(25)4-5 7048(29) 5-6861(30) 0187(32)4-1 -8885(42)-2 -1104(43)4-0 -2219(44) liquations of correlatives. = (i) i-o(4-C) (2) = i-o(-C,-C2 ) (3)=i -0(4-0 C) = (4) i -o(C,4-Cs 0-095 C o-ii6 = -C (5) i-o(4-C6 8 ) C) = -C (6) i -o(-C4 5 4-C8 4-o-o2i O) = (7) 1 -C -o(4-C34-C4 6 +o-o95 04-0-095 O-o = (S) i -o(4-Ca 4-C, C 5 0-026 '226 04o-i4oO) = (9) l o(-( C7 -C, 2 + o-i99Ca ,-o-i99C 4-0-403 C26 ) O = - (lo) l o( 4-Cs C, + O '6o 0-500 Cat) -O+O+o (ii)=i -o( t-C,2 -097 O) 4192 No. 7 02 6 82 THE EASTERN OBLIQUE ARC. Equations of correlatives -continued. i ' : P (i2)==i o(-C-C3 -C7 +CIO+o-026 C+o-o27 C) (i3) = i-o(+C,-C,fC> c) = (i4) i -2( C6 +C8-7 '676 C-po -699 C C-o C-o = 3 (i 5 ) i ( C,+C+o 798 798 CO -916 4 +o -176 C+2 = (i6) i -i (-C8+C,8-o -099 -4394 C0-2 7557 Cs-a 6157 C,) = C (i 7 ) i -i( Ca+o-ao7 C-a-6i57 0,6+2-6157 C8+26157 C,) C+o (i8) = i-2(+C+C7 +C,+6 -878 709 c,,) = (i9) i 7( Cn+o -1400 Cs) = (2o) i o(+C4 +C5 -C8 +o-53i 0,0-0-565 C) = (2i) i 2(-C5 +C,+C+o795 0,0+0-531 C+i -883 C3) = (22) i -o(+C8-Cl8 +o-034 Q-o-42i2 C,9 ) = +o C ( 23 ) 1 1 ( -C, 4 +C, 5 -2230 7 ) = (24) i o(-C,-i'326C-i -3260,3) = ( 25 ) I -0(+C, 7 -0-23S5 C^+O'4212 Co) = C -C (26) i -i(-C I5 I7 +C8+o-oi55 7 ) (27 ) = i-2(-C-o'557C3 ) +C-C = (28) I i(-C,3 4 -i-i28C4+o-628C5+o-22oC6) C = (29) i 2(^-C+C,1,+o-237 4 -5 7048 Cs+5 7048 Cs+5 7048 C) = ( 30) i -i(+C^-C+5 '4851 C.-5 '922 Cs-5 -686i C) C = (31) 1 i(-C+o-892 4 -o-892Cs ) = C ( 3 2) i i(+C l6 -o-oi87 9 ) -C = ( 33 ) i o(-C,5 6 +o-i974 Cs) = (34) i 2(-C I3 +o-264C5 ) = (35) I- (- c I '55Co) C = ( 36) i i(-C3 -C4 +C+o-8i4Co+o-344CM -4-94iC.) = ( 37 ) i -o( +C,+C3 +C7 -C,o +0-691 C,o+o-499 C+o'344 ,,+0-917 0,3-0-692 4 +o'3o6 C,5 ) C (38) = i-2(-C-C7 -C+4-596C.+o-3iiC4) = < 39 ) i -2(+C4 - o -843 -o -843 C) C = (40) i o(+C,+o -380 4 0-3800,5) = C (40 1 -i(+C IO -o-o74 3 +o-074 C,5 ) = ( 4 2) i-i (+1-8885 Co) = C C) (43) i -o( C, 7 -o-22i9 -2 7 -1104 = C C) +o +o C (44) 1 -o( l6 -2097 7 -2219 = (45) ' o(+C,+C,,+o-oi22 C?) = (46) i -o( +0,8+0-5032 C,8 ) = , (47) i o(+C,s +C, 7 -C,8+o -1939 C -0-6971 C,8) (48) = 1 -(-Cs+Cs-o-^osg Cj+o-1939 Cs) = (49 ) i -o(-C,6-C 7 +o -2100 c,) o(-C+C-C = ( 50) i 3 +o726 0,3-0-305 C,5 ) (5i) = i-o(+C+o-496C,3) (52) = i-i(+C+o-o75C5) = (53) ' -o(-C,o-o -230 C3+0 -230 C,5 ) BASE LINES AND BASE NETS. 83 Normal equations. i 84 THE EASTERN OBLIQUE ARC. C, = 0-115 09 Ca =+0-193 18 C 3 =-0-071 44 C, = +o - iio 00 C s =-0-378 51 C = -o -337 23 C, =4-0-050 86 = Ce O -362 70 C, = +0-411 93 C, = +0-255 74 Resulfaig Correlates. C =+o-o83 78 =- C,a 0-350 90 C= 305 71 =- C,5 0-851 29 C, 6 =- 0-234 29 C,,= +0-978 52 C,g= -0-131 58 C,9 =+o-o8o 01 0,0= 1 726 74 and resulting corrections to observed directions: C=-o-i37 98 C=-i-i32 88 C= +0-952 70 C = +0-383 71 C =5 i 046 58 C*+o7S5 58 C=+ 0-689 15 = + Cs8 1 "339 4o C= -0-677 99 (1) = -01151 (2) 0-0781 (3) +0-1932 (4) 0-1144 (5) +0 -0255 (6) 0-1304 (7) +0-2194 (8) +0 -3708 (9) +0 -9042 (10) +0-0695 (II). : O '60I0 (12) +0 -oS25 (13) -o ;8262 (14) +0-2901 (15) +0-2258 (16) +0 -0491 (17) (18) (19) (20) +0-II02 -I 0555 +0 ^427 -0-I826 () (22) (23) (24) (25) (26) (27) (28) (29) (30) -0-8348 +0 -OI59 + -6689 +0-9164 +0 -5286 0-2729 I I3II -o -2745 -o -8561 -o -3963 + (31)= : I -3II2 (32) -o -2437 (33) -o -3526 (34) +0 -8473 (35) -o -3136 (36) -o 2452 (37) (38) o 6491 -o '3747 (39) +0-9150 (40) *o -6273 (4i) =+o-u86 (48) = +0-5984 (42) -1 -4084 (49) -o -5995 (43) +0 -2994 + (50) 1-8370 (44) +0 -2284 (50 00606 (45) +0 -7526 (52) -1-1669 (46) +0 -5424 (53) -0-7156 (47) -o -5413 We y _ have the probable error of a direction of unit weight C674 [^w] o"674 24 / 4 or V 29 o"'62 nearly, and since the average reciprocal of the weights is 1 '07, the probable error of an observed direction is nearly o"'65. BASE LINES AND BASE NETS. 85 Resulting angles and sides of the Allan la base net. No. Stations. 8 86 THE EASTERN OBLIQUE ARC. Resulting angles and sides of ike Atlanta base net -continued. No. Stations. 3 16 17 18 19 23 24 BASE LINES AND BASE NETS. 87 Resulting angles and sides 0/ the Atlanta base net continued. Station. 25 26 27 28 29 30 31 32 33 88 THE EASTERN OBLIQUE ARC. cross lines, in a copper 1x>lt driven into the center of the top of the upper block, marks the station. Over the upper monument is placed a granite shaft bearing the usual inscriptions on its faces. The station is further defined as the center of a square whose side is m- 24 75, each angular point of the square being a drill hole at the intersection of cross lines in a copper bolt driven into the top of a stone post 3 feet long and 6 inches square at top. The center of each reference mark is 18 meters from the station, and diagonal grooves are cut in top of each, with an arrowhead pointing to the station. Atlanta Northeast Base. This station is at a road crossing on the Southern Rail- way, near Norcross, Gwinnett County, Georgia. It is on the west side of the road and the west side of the railroad, on the place of J. H. Maloney. The station is marked exactly as described at Atlanta Southwest Base. Atlanta Middle Base. The station is in De Kalb County, Georgia, upon a small knoll in edge of woods 65 feet northwest of the Southern Railway and about a quarter of a mile northeast of the railroad station at Doraville. The underground mark is the center of the mouth of a short-necked bottle. The surface mark is a drill hole at the ' intersection of cross lines in the head of a copper bolt driven into a granite post. 1 foot square and 3 feet long, with diagonal grooves cut in the top, one in line with the base and the other perpendicular to it. The copper bolt with the cross lines and drill hole is placed at the intersection of the grooves. Around this central monument are buried four reference marks, two in line with the base and two in a line perpendicular to it. Each of the granite posts is 7 inches square and 3 feet long, and has in its top a diagonal groove with an arrowhead pointing to the station, from which the center of each reference mark is 5 feet distant. Stone Mountain. This station is in De Kalb County, Georgia, on the well-known mountain of that name, about 15 miles N. 76 E. from Atlanta, and about 1 mile from the post-office, Stone Mountain, on the Georgia Railroad, De Kalb County, Georgia. The station is marked by a copper bolt in the solid granite of the mountain. Around the bolt the rock is cut down to a level in a circle of 3>4 feet radius, the bolt 3^ being the center. In the periphery of this circle are six equidistant holes feet apart and 2 inches deep. Academy. This station is on the highest point of Academy Hill, in Lavvrenceville, the county seat of Gwinnett County, Georgia. The underground mark is the mouth of a bottle 3 feet below the surface. Over this is a granite post 30 inches long and 7 inches square, with the letters U. S. C. S. cut in top. Around the central monument are placed four reference marks aboift 30 W. of S., 30 N. of W., 30 E. of N., and 30 S. of E. The center of the SW. reference mark is 4 feet 6 inches from the center of the station, and the center of the other marks is 5 feet distant from station. In the top of each reference mark is a diagonal groove with an arrowhead pointing toward the station. Kenesaw. This station is on the highest part of Kenesaw Mountain, about 3 miles northwest of Marietta, Cobb County, Georgia. The station is reached by following the Marietta and Cartersville road for about 2j4 miles from the Kenesaw House, in Marietta, and then following the road which turns to the left, near a covered well, and finally along the spur of the mountain to the summit. The underground mark is a % cross in the head of a copper bolt driven into a hole drilled in the solid rock 2 feet 1 inches below the surface. Above this is planted a granite post 5 inches square, with BASE LINES AND BASE NETS. 89 the top projecting 2 inches above the ground. The intersection of two cross lines in the top of the post marks the station. The letters U. S. C. S. were also cut in top of post. The station has three reference marks A, B, and C these being the intersec- tions of cross lines cut in the heads of copper bolts driven into holes drilled in the rock. n The distances of these points from the station are 6'65 feet, 11 '35 feet, and 19 feet, A respectively. The angles subtended at the station by lines from to B, B to C, and A C to are 170 59', 47 06', and 141 55', respectively. Sweat Mountain. This station is in Cobb County, Georgia, the nearest post-office being Woodstock, almost 4 miles distant in a direct line on the Atlanta, Knoxville and Northern Railroad. The station is on top of the mountain, about ij^ miles from Mr. Dial's house, and is reached by following the Marietta and Gumming road to a point <)Y\ miles from Marietta, near Mr. Garrison's, and then taking the road along the southeast ridge of the mountain. The station is marked by a copper bolt driven in a hole drilled in the rock very near the edge, and has three reference marks, A, B, and C, which are copper bolts driven in drill holes in the most solid rocks available. These points are 6*2 feet, 7 '67 feet, and i2'3 feet, respectively, from the station. Taking the line to Kenesaw, S. 4833' W., as the initial or zero direction, and measuring angles counter-clock- wise, the directions of A, B, and C are 3 19' 30", 83 44' 30", and 231 12' 30", respectively. Sawnee. This station is on the most prominent or central peak of Sawnee Moun- tain, in Cumming Township, Forsyth County, Georgia, about 2 miles NTJ. of dimming and 12 miles from Buford, on the Southern Railway. The station was marked temporarily by a copper tack driven in a stub, with similar stubs for reference marks. The permanent marks are supposed to be the usual central marks with four reference marks. Pine Log. This station is on Pine Log Mountain, Cherokee County, Georgia, about 7 miles north of Wolf Pen. The station is reached by going east from Cartersville, to Wolf Pen; thence 9 miles to Moore's Iron Furnace; thence 3 miles to Mr. Lewis' house: thence to the station on top of the mountain. The underground mark is the neck of a jug 2 feet 6 inches beneath the surface. The surface mark is the intersection of cross lines on the top of a granite post 5 inches square, planted above the jug, the top of post projecting above the ground. The letters U. S. C. S. were cut in the angles of the cross lines. Around the station are four granite reference marks similar to the central monument, to the north, east, south, and west, each distant 6 feet from the station. In the top of each is cut an arrowhead pointing to the station. Grassy. This station is on top of Grassy Mountain, 3,290 feet high, in Pickens County, Georgia, about 6 miles in a direct line east of Jasper, the county seat, on the Atlanta, Knoxville and Northern Railroad. The station marks are supposed to be the usual central monument, and four reference marks to the north, east, south, and west, each 5 feet distant from the station.