Colonel A. R. Clarke on the Figure of the Earth. 83 



The following Table contains in the second column the 



reo- 



detic longitudes as given by Colonel Walker, computed on 

 Everest's elements; viz. equatorial semiaxis a' = 20922932, 

 polar semiaxis c' = 20853375 : — 



Names. 



Geodetic longitudes 

 on Everest's spheroid. 



Geodetic longitudes on 

 undetermined spheroid. 



Yizagapataru 



83 19 4700 

 78 33 38-50 

 72 51 16-23 

 74 53 10-18 

 77 37 27-72 

 80 17 21-87 

 76 58 6-97 



4305-2-320^-2-401 v 

 37-51 -0-580 u - 0-600 v 

 18-804-l-511«+l-563u 

 1 1-44 +0-742 u +0-768 v 

 27-32 - 0-234 u- 0-242 v \ 



Hydrabad 



Bombay 



Maugalore 



Bangalore 



Madras 



19-85- 1-184 w- 1-226 v ' 



Bellary 





The third column contains (omitting degrees and minutes) 

 the same longitudes on the supposition that the elements are 



20855500 ( 1+ ™)' 



a + c 



590 



+ vsinlO", 



which I take for the undetermined elements of the spheroid 

 most nearly representing the mean figure of the earth. The 

 terms in u and v added to the longitudes in the above Table 

 are thus obtained : — Let A be the central point Bellary, B 

 one of the other stations, Q the point in which the normal at 

 A meets the axis of revolution ; let be the angle subtended at 

 Q by the curve distance A B, this curve being the intersection 

 of the spheroid with the vertical plane at A passing through 

 B ; then, if A B = s, and fa be the latitude of A, and « the 

 azimuth of B at A, 



= 



1 



{1+n) 



(1 + 2n cos 20x + n 2 ) 2 (l + §n<9 2 cos 2 fa cos 2 «). 



Thus for any variations of n and c a determinate variation 

 arises for 6 which may be expressed in the above u and v. 



Again, the variation of 6 gives rise to a variation of w, the 

 longitude of B computed from A, viz. 8co = sin B sec yfr . 89, 

 where B is the azimuth of the curve A B at B, and ^ is the 

 inclination of the line Q B to the equator. 



Let us suppose the easterly component of the local attraction 

 at A is i/i ; then, longitudes being measured positively towards 



G2 



