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Geodesy. the Eastern Oblique Arc of the United States and Osculating

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Geodesy. the Eastern Oblique Arc of the United States and Osculating 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 Trans- continental 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, O. H. Tittmann, Superintendent. The Secretary of the Treasury. 7 CONTENTS. Page. Introduction 19 PART I. THE BASE LINES AND BASE NETS. 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 1 1 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. 1 1 B. The triangulation continued. Page. 12. First section west of the Dauphin Island base net 219 Abstracts of horizontal directions 219 Figure adjustment 222 Resulting angles and sides 224 226 13. Second section west of the Dauphin Island base net Figure adjustment 228 Resulting angles and sides 232 14. Some statistics of the triangulation 234 C. Resuming Geographic Positions of the Principal Stations of the Triangu- lation, Calais, Maine, to New Orleans, Louisiana 237 D. Additional Geographic Positions which were Derived Differentially and for which Triangles are not Given in this Paper 247 E. Additional Geodetic Azimuths Computed Directly from the Given Positions of the Stations 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 253 282 Cambridge, Massachusetts ( Cloverden Observatory) 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. Page. Kahatchee, Alabama 307 King, North Carolina 295 Lavender, Georgia 301 Long Mountain, Virginia 292 Lower Peach Tree, Alabama 309 Manomet, Massachusetts 284 Marriott, Maryland 292 Maryland Heights, Maryland 292 Mobile, Alabama 310 Montgomery, Alabama 307 Moore, North Carolina 292 Mount Desert, Maine 264 Mount Harris, Maine 260 Mount Independence, Maine 272 Mount Pleasant, Maine 270 Mount Rose, New Jersey 290 Mount Tom, Massachusetts 282 Naval Observatory (new), District of Columbia 292 Naval Observatory (old), District of Columbia 292 New Orleans, Louisiana 314 New York, New York 288 Paris, South Carolina 297 Pooles Island, Maryland 292 Principio, Maryland 292 Ragged Mountain, Maine 266 Rockville, Maryland 292 Sabattus, Maine 269 Sandford, New York 286 Sawnee, Georgia 302 Seaton, District of Columbia 292 Soper, Maryland 292 Strasburg, Virginia 292 Sugar Loaf, Maryland : 292 Taylor, Maryland 292 Thompson, Massachusetts 279 Unkonoonuc, New Hampshire 278 Wachusett, Massachusetts 280 Webb, Maryland 292 West Hills, New York 287 Yard, Pennsylvania 291 Young, North Carolina 294 3.
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