27] OF THE MOON'S MEAN MOTION, ETC. 221 



for that quantity in the second differential equation, and equate the non- 

 periodic parts which result from this substitution, 



2dn 4da 2421 4 ,de' 165 4 ,de' _ 1617 4 ,de' 33 4 ,de' 



_95 4 ,de'_931 4 ,de_' 19 4/ de_' 

 "~2~ r '~dt~ ~8 e d^"~8~ 7 S d7' 



2d , da 963 . ,de' 285 ,de' 

 -.7 + 4 + _mV^=- mV^-, 



c? c?a 2103 , ,de' 



. J_ v WiP 



ndt adt 32 dt ' 



8. The substitution of the values of Sv and 8rj in the first differential 



de' 



equation introduces no non-periodic terms depending on -, ; consequently 



ctt 



the value of ^ remains of the same form as before. 

 V 



Hence 



V1 - 1 +3e "> 



da 3 2 /de' 1173 4 ,de' 2 /dm\ 

 adi = ~2 me di" " 32 m& ~dt~ m \rndt) 



71^^1173^^. 



< 



ndt ad< 



/3 1173 A ,d g ' ,/dn\ 

 = - - m- + -r=- m 4 e' -TT + m 2 - 7 - , 

 \2 32 / di \ndtj 



n' , dm dn 



since m = , and .'. , = r-, 



ri mat ndt 



n' being constant. 



Hence 



, ,, dn da I 1173 A , de' 



(4 - 2m 2 ) - j + 6 j- = - 3m 2 + - -m^e'-j-, 

 ' ndt adt \ 16 /at 



from above 



dn , da 6309 . .de' 



_1_ ft mi f> * 



j, i U -77 oo ^7-* ' 



i, 2 \ ^ /o 3963 \ 



.-. (l-2m 2 ) j-= - 3m a -- 5 --m 4 



7 d< \ 32 / 



