XI.J THE EQUATION OF THE CENTRE AND THE EVECTION. 49 



Hence in place of the former equations, we get the following 



+ [2 ( - ri) (n - 2n' +p) + | gj 0,0* + [2 ( - ri) (3n - 2ri -p) + 1 



+ f - 2 (n - n') (n - 2ri + p) b s + f w' 2 l 6 n 

 L ^ J 



+ [ -2(w-n')(3n-2w / -p)& s + | 



-2(n -pY(l + b t ) + 2n (n -p} - &ri*b, ( 



-2(n- n') (n - 2n' +p) 4 21 + 2 (n - n') (3n - 2n' -p) 6 2 a.,, 



(n - ri) (n - 2n' +p) a, - ' a b n 

 I - 2 (n - n') (3n - 2n' - js) a, + 1 TO"! 6 M = 0. 



w 



Multiply the second by , and add to the first ; this will 



n p 



eliminate 1 + 6 . 



n + - + - '^-b., (l+b a ) + 2(n- n') (n - 2ri +p) [,.,, - 6 5 6 2l ] 



Ct 72- p 



9 3 



+ 03 [* + a ^ a J + o w/2 [ & =i + M + 2 (n - n') (3n - 2w' -p) [o,a., 2 - & 3 6J 



_ '' Zi 



W 



+ 4 - (n w') (n 2n' + p) [& 2 a 21 a 2 6. 21 ] 



- 4 (n - w') (3w - 2n' - />) [6 2 a^ - a,6J + 3w' 2 [60, - 6 J = 0. 

 np np 



Also the equations obtained by equating the coefficients of ecos(2i// nt 

 and e sin (2i/ n^ + ra-) to zero are 



n - 2w' +J9) 2 + a n - 2 (n - 2n' +p) b a = 0, 



4 (w - n') (n -p) ( 1 + &) a, - 2 (w - ft') (n -p) 6 2 - 3n" ( 1 + 6 ) - (n - 2n' 

 + 2n(n- 2ri +p) a a = 0. 



A. II. 



