the Semi-axis Major of the Moon's Orbit. 31-1 



and it is sufficient to take 

 da 



1 / d*R /> , , dtf. \ 



= IT- ( 3 w TT- / 8 d t -- -7 8 ) 



a*n\ Ac* J dc ) 



d*R\ 8a / d 2 R \ S c d 2 /? 8e 

 dadc/0 \ d c 2 / w de dc an 



S d*R \ 8 co / d a fl \ 8y / d* R \ 8_*-} 

 \d co d c) a n \d y d c) a n \d at d c) a nj 



This equation is similar in appearance only to the equation (A) 

 of Poisson, p. 259, for the quantities 8 , 8 c, 8 e, &c., are here dif- 

 ferently defined. 



I omit here all consideration of the terms 



d/2. \ 



ad^ -y- 8a), 

 dc / 



because the proof which Poisson has given in his Memoire sur le 

 Mouvement de la Lune, is completely satisfactory with reference to 

 them. 



8 c e 



In the terms , . &c.. it is necessary to consider the va- 

 a n a n 



riation of the quantities [ff, co], [e, eo], &c., and also that of the 



, J_ da _ dn _ d a d R 



' a n~ na z n a~ ~~ 2 n a 2 ~ a d c 



i ' 



d e contains the term 



which may be taken as a type of others ; 



1 / n /d R\ ,, / [e, co] /d R 



/ [^ ] ( -i ) d * = / J * J ( -J 

 a nJ L ^ J \dco/ ^/ aw\d 



, 1 f r -, /d.R\ , , 

 + d . / [e, co] I -T ) d t 

 anj L J \dco/ 



/ [e, co] /d 72\ , . d R / _ /d ,R\ , 

 = / tJ J ( T ) d ^ -- T /[?>] ( -j I d A 

 / aw\dco/ jM.dc7^/ l - 7J \dco/ 



