2] EELATION TO THE MOTION OF THE NODE OF THE MOON'S ORBIT. 87 



0= -2 a ! c -i + [> 2 -(l+o)] c o ~2 a i c i 



0= -2 a i c o + [(fl r + *) 1 -( 



0= -iaA+ 



. 

 Or if 



the equations become 



- ac_. 2 + [(y - 1 )'-' K 2 ] c_, - C6C 



= - e _ ! + [y' 2 - K-] c - ac 1 



0= -aco + ^y+ 



0= 



Now the determinant which equated to zero gives the values of y, is, 

 omitting terms of the order a 4 , 



a 2 a' 2 or 



&c. ad inf., 

 whence we find on separating each term into partial fractions 



= 1+ --7 



_l [_ _| + - (- 



. . . 5 - -- 



y o K y Z K ylK y K y+1 K 



1111 



y 3 + K y2 + K yl+K y + K y + 

 But we have 



l+K '"}' 



