Our Knowledge of the Earth's Shape and Size 4.1 



tical, in the plane of the prime vertical, 

 at the same place ; third, correction to the 

 equatorial radius of the reference sphe- 

 roid ; and, last, the correction to its com- 

 pression. 



In the combination of conditional equa- 

 tions arising from observations of a dif- 

 ferent nature, the question or their rela- 

 tive weights must be considered. In the 

 present case, four assumptions were made 

 and the consequent normal equations 

 solved, viz. : for equal weights, for 

 weights one-half, one-third, and one- 

 fourth to the azimuth equations, the lat- 

 ter being necessarily inferior to the 

 equations derived from latitudes and 

 longitudes. A comparison of these four 

 results showed that it was of small conse- 

 quence which of these hypotheses was fi- 

 nally adopted, since the corrections to the 

 equatorial radius of the reference spheroid 

 were practicall}' the same for any of these 

 hypotheses, and nearly the same could be 

 said of the resulting compressions. The 

 weight one-third to each of the azimuth 

 equations was finally decided upon, and 

 the resulting dimensions of an osculating 

 spheroid were found to be: Equatorial 

 radius, 6,378,157 ± 90 metres; compres- 



sion, 1/304.5 ± 1.9. The equatorial 

 radius, therefore, differs but forty-nine 

 metres from Clarke's value of 1,866 

 adopted on the Survey, while the Bes- 

 selian value is apparently too small by 

 eight hundred and nine metres. On the 

 other hand, the compression or the ratio 

 of the difference of the equatorial and 

 polar semi-axes to the former is in favor 

 of Bessel's spheroid, of which the com- 

 pression is 1/299.2 ; that is, one more 

 closely approaching a sphere. 



In the present state of our knowledge 

 there is no reason to suppose that the cur- 

 vature of the northern part of America 

 differs any more from that of a general 

 spheroid derived from arcs of all kinds 

 so far measured than local ones in either 

 hemisphere differ among themselves. A 

 comparison of a number of such locally 

 adopted spheroids will bring to evidence 

 the local deformities in the shape of the 

 earth's equilibrium surface and furnishes 

 the geodesists endless material for the 

 study of the earth's actual figure. 



The manuscript concludes with a com- 

 parative table of the dimensions of several 

 spheroids which of late have come more 

 into prominence. It is as follows : 



N. B.— The ± indicates probable errors. 



