we get 



4:94 Mr. J. Prescott on the 



Hence, on substituting a for r in (47) and multiplying up 

 by a, we arrive at the equation 



2A m [J-m(m-2)(m + 3)(m4-5)+(m+l)(m 2 + 5w-12)l =0. (48) 



That is, 



-42 A + 6A 2 + 204A 4 + 774A 6 + 1972A 8 + 4118A 10 



+ 7596 A 12 + 42854 A M + 20404 A 16 = 0. (49 ) 



Using the values of A 4 , A 6 , &c. from equations (46) 



-26-78A -5-004A 2 + 2-322 5 = 0. . . (50) 

 Similarly the equation (30 a) gives 



2A m (m 2 + 3m + 6) =: 0. 

 That is 



6 A + 46 A 2 + 34 A 4 + 60 A 6 + 94 A 8 



+ 436A 10 + 186A 12 + ... = 0. (54) 

 By means of (46) equation (54) gives 



2-78A + 46-64A 2 + 0'424s = 0. . . . (52) 



The values of A and A 2 determined from these equations 

 are 



A = 0-0945 51 



A 2 = -0-0441 * J (53) 



After expressing all the A's in terms of s we find 



= 10-.{945-411^ -nj +295-2$ + .}. (54) 



The ellipticity of the surface, obtained by putting a for r 

 in (54), is 



* 1= = 0-0544* 



= 0*0544 x (55) 



n 



But since?i = 8 X 10 8 grams per square centimetre, a = 637 x 10 6 

 centimetres, and w=l, 



wa = 637x10" = Q-796 f5Q) 



n 8 x 40 8 x g g v ' 



