2] RELATION TO THE MOTION OF THE NODE OF THE MOON'S ORBIT. 91 

 therefore we have 



vq? 7r^ 4 ( 15^-3 59' + 8) 



+ sm air \ A -v + -- -- - 

 2 - 



(9 Feb. 74.) 



[The work was resumed in 1875 when we find the following.] 



We will now try the simpler mode of finding 2 (p, >}, &c., which 

 occurred to me on the evening of Wednesday November 3, when on my 

 way to attend the Ray meeting. 



We have 



a 2 



so that 



) 2 -K 2 ] 2 [(y+^ + i)'-<r 



Let y +p K = X; then 



Develope this in ascending powers of x, 

 coefficient of x~~= - 



4K 2 (2/c+l) 2> 



^y4 O O ~~j 



coefficient of x~ 1 = , rr, - 2 - = ^?,~ *-r\r' 



4/c 2 (2/c+l) 2 L 2 2/c+lJ 4/< 3 (2/c+l) 3 



Next let y +p + 1 + K = x ; then 

 In this 



coefficient of x 2 = 



2 ' 



2 2 1 a 4 (4/c 2 + 6/c+l) 



= 



ffi . 



= 4 



Also it is evident that the other two pairs of terms merely differ 

 from the above in having K in place of K. 



122 



