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The National Geographic Magazine 



end closely to that of the Clarke sphe- 

 roid; whereas, for the remaining three- 

 sevenths, or for the region across the 

 Rocky Mountains to the Pacific, the cur- 

 vature comes more nearly to that of the 

 Besselian spheroid. In the published 

 paper two tables are given containing the 

 results needed for combination with any 

 other arc and, in conclusion, some pre- 

 liminary rough combinations of Ameri- 

 can arcs are presented ; all of which point 

 to a reference spheroid of larger dimen- 

 sions than those of the Besselian and are 

 in favor of continuing the use of Clarke 

 for reference. 



The second arc imder consideration 

 extends from Calais, Me., in the north- 

 east and opposite the Canadian boundary, 

 to the Gulf of Mexico, and terminates at 

 New Orleans, La. It is known as the 

 Eastern Oblique Arc of the United States. 

 Its length is 2,612 km., or 1,623 statute 

 miles; its difference of latitude is 15° i', 

 and of longitude 22° 47'. The general 

 direction is, therefore, favorable and the 

 length ample to secure fair results for an 

 osculating spheroid. In the main the tri- 

 angulation follows the Appalachian chain 

 of mountains ; in Western North Carolina 

 and Eastern Tennessee it bifurcates, leav- 

 ing an oval space between the two 

 branches. The length of sides depends 

 upon six base lines, and in general the de- 

 velopment is closely accommodated to the 

 hypsometric and other natural conditions 

 along the course. It includes among its 

 stations the two highest points in the east- 

 ern part of the United States, viz.. Mount 

 Washington, N. H., rising to about 1,920 

 metres, or 6,300 feet, and Mount Mitchell, 

 N. C, rising to about 2,038 metres, or 

 6,687 feet. 



The adjustment of the whole triangu- 

 lation is effected precisely as explained 

 in the use of the arc of the parallel ; 

 the small reduction to the sea-level of 

 the observed horizontal directions, on ac- 

 count of the altitudes sighted, was only 

 applied when exceeding 0.05". The prin- 

 cipal labor of adjustment was demanded 



by the necessity of bringing into accord 

 the measured lengths of the Fire Island, 

 the Massachusetts and the Epping base 

 lines, and fulfilling the geometrical condi- 

 tions of the intervening net of triangles. 

 This demanded the satisfying of fifty- 

 seven conditions and involved the simul- 

 taneous solution of an equal number of 

 normal equations and the working out of 

 one hundred and thirty-one corrections 

 of observed directions. Of astronomic 

 measures we have seventy-one latitude 

 stations, seventeen longitude stations, and 

 fifty-six azimuth stations, tolerably well 

 distributed over the whole extent of the 

 arc. The latitudes, as were those of the 

 arc of parallel, were corrected for height 

 of station or curvature of the vertical and 

 for variation of pole according to Dr. 

 Chandler's and Dr. Albrecht's researches. 

 The same scrutiny as before had been ex- 

 tended to the deflections of the vertical, 

 both regional and local. Partly on ac- 

 count of avoiding unnecessary labor, but 

 principally on account of the crowding to- 

 gether of astronomic stations in certain 

 very limited localities, and all of them, 

 therefore, partaking of the deflections 

 characteristic of this area, the total num- 

 ber of astronomic stations admitted into 

 the final equations for the determination 

 of the best spheroid were thirty-six for 

 latitude, fourteen for longitude, and thir- 

 ty-four for azimuth, or eighty-four condi- 

 tions in all. 



These eighty-four differences between 

 the astronomic and geodetic results con- 

 stitute the data needed for a new deter- 

 mination of a spheroid; next the func- 

 tional relations between the positions of 

 these stations upon the reference spheroid 

 to the earth's equatorial radius and to the 

 compression of the polar axis had to be 

 established. 



The final normal equations contain, 

 therefore, four unknown quantities, viz. : 

 the correction to the meridional deflection 

 of the vertical at the initial or reference 

 station of the oblique arc; second, the 

 corrections to the deflection of the ver- 



