II.] ACCELERATIONS OF THE MOON RELATIVE TO THE EARTH. 9 



Then 



' = 0-0', 



and the accelerations of M relative to E are 



24 



uw 2 ra'(l+s 2 )r E-M 1 (a . "I . 



-.+ ^JT- ! + -p TM--J- 3 cos (0- 6') + ...... 



1+s- r"u \_ E + Mi J u 



. 



m ME, 



parallel to GS. 



Call these quantities U and V respectively ; then if we resolve 

 parallel to M'G, perpendicular to M'G in the plane of the ecliptic, and 

 perpendicular to the plane of the ecliptic, we have the following quantities 

 which we call P, T, S; viz. : 



P= 



S= Z7 

 and also 



S-Ps= Vs cos (0-0'). 



From these we find 



3 E-M I /9 3 



r. 



- o o 17 TUT 1 ( I O o o 



S-Ps= -|| + |cos2(0-0') + ^f i|(T-4 



7"M |_iJ il Mi -\- 1VL T U \^\ o A 



+ cos 3 (0-i 



A. II. 



