2] RELATION TO THE MOTION OF THE NODE OF THE MOON'S ORBIT. 95 



Adding these terms, with a negative sign, to the value of the deter- 

 minant found on p. 90, and completing the solution as it is there completed, 

 we find 



8 



f irq? 15q*-35q"-+8 4 _ rfq? 



1 ^ IW^) + 642* (2 s - W- 4) ^ 3 ^/ 3 (<f ~ !)' 



g 4 + 1652^-288 

 2562 s (2* -1)' (2 s - W- 9) 



This value of cosgTr may be put under the form 



f 7n/, 2 15 4 -35q" + 8 TT-qS 



cos Q-TT = cos OTT + sin cm { r + - r~ rri . X3 / ., TX w/i .. / ; TW cot 



* 2 - 3 - --- 



1057 10 - 1155(7 8 + 38157 6 -4705(? j + 1652^-288 

 l) s (</ a -"4") s T^ ~ 9 ) 



We will now substitute in it the value of cotq-rr in terms of q. We 

 have, namely, 



cot qir= -GOt(l-q) TT = 7 ~ ( ( 7 ~ l) ^ ~ (? ~ T ) 3 ^ 



4725 v - 93555 v 



Then we have, picking out terms of highest negative power of q, 



in coefficient of vq*, 64 3 / ._ iW^-4) t 15 ^ ~ 35r / + 8 - 29 (2 + 1) ('/ - 4 )] 





8 



_ 

 (q" - I) 3 (g 3 - 4) ~ 64q s (q - l) (q + l)" (^ ~ 4) ' 



in coefficient of ^ 256gt(g> _ 1)5( _ ^^,^[105^- 1155^ + 3815^ 



numerator = 902 10 - 1 5g 9 - 925(/ 8 + 230? 7 + 28 1 2g* - 1003(/ 5 

 4 + 1364 g 3 + 1364</ - 288? - 288 



-2668g 2 - 1440^-288), 



