170 Mr. Lubbock on the Divergence of the iiujuerical Coefficients 



arguments in the reciprocal of the radius vector ; so that with 

 respect to these only, and to terms of the same nature in other 

 arguments which 1 have examined, a tolerably approximate 

 value would be obtained from the expression 



= tA{"} 



ri4 and r^^ are thus deduced from the well-known equation 



d^.r^ u. a ^ r^ T^ ^'^R 



Ti-ATy — — + — + 2/d R + -J— = 

 2d^=^ r a '^ dr 



If — =1+7) a^n^ = lu 



r^ a® 3 



— -= -— -a'^ f -~a*p2-2a5 2'3 + &c. 



if p = XrnEnCos(int + q) t= ^ s? j)^ -2 o? j)^ ■\- &c. 



'^ dr a 



The differential equation gives for determining 



n at foot being the index of the argument. 



21 , 1113 , , . 3 , .o 



15 17 



ri5 = — -g TO — g^ Wi2 + ^j5 7n3 + &c. 



- 2 I [2+«z+m*+&c.] { |-«^2+ ^»^^+ ^w^^+&c.} 



+ 24 W4 + &c. i- . 



Lubbock on the Lunar Theory, p. 177. 



r 5 « 1 f 3 „ 221 , , 6133 ^ , „ i 



f r o ~] r 9 , 3 , , 12289 . , g "I 



- 2 j L2+'»;+wi'+&c.J j- g-w2— ^7»H ^56"^ +&c.| 



- ^ Wi4 + &c. j 



33 



