V.] THE VARIATION. 23 



and divide both equations by (n n')~; we get 



+ 2m, + -m, 2 ) 4 8 (1 +m,) &, 6 + 2(1 + m 1 ) 2 



27 

 -3(1+ m,) m, 2 a 2 - m, 4 = 0, 



8 (1 +m,) a 4 - 166 4 + [4 (1 + m,) - 2 ( 1 + TO,)] a./ + 3m, 2 fl + imJ a 2 + -^ m, 4 = 0. 



\ Z / ID 



Simplify and multiply the last equation by ^(l+wj, 



/ 9 \ /13 1 \ 

 ( 19 + 6m, + - m " a, 8 (1 + m,) o, h m, m, 2 a 2 



\ 2 / \2 4 / 



-3(l+m,)m 1 2 a 2 - 3 ^m I 4 -0, 

 (4 + 8m, + 4m, 2 ) a 4 - 8 (1 +m,) 6 4 + (1 + 2m, + m, 2 ) a 2 2 



+ ~(l+m,) (l+^m,jm, 2 a, + (1 +;/i,)m 1 4 = 0. 



Subtract the latter from the former and b t will be eliminated ; we get 



( 1 5 - 2m, + \ m, 2 ) a 4 - (^ + 3m, + f m, 2 ) a, 2 

 \ / \ 4 / 



3 / 1 \ 9 



--(1+m,) (S + ^rn, TO, 2 a.,- (4 + m,)m, 4 = 0, 



A \ X / i ^ 



which gives a t ; and this being known 6, is found from 



3 / 1 \ 9 



. a. 2 2 + f 1 + - m.J m, 2 a 2 + m, 4 . 



Taking m = '07480 as in Lecture IV, we find 



a t = -00004,580, 

 6 4 = "00004,237 = 8"740. 



