27] OF THE MOON'S MEAN MOTION, ETC. 21 & 



< - " 



- e' cos (20 - 2n't) 



~ 

 4 



tV cos (20 - 3n') - ? ?uV cos (20 - n't)\ . 



/ 4 /j 



Hence the constant part of H" is 



n being the actual mean motion. 

 Hence 



- - ~ - " 



S / 5 \ 21 ^ 1 



- - m 2 1 - - e' 2 cos (20 - 2wV) .- mV cos (2^ - 3n') + 7 mV cos (20 - n't) 



a \ a I 4 4 



21 3 1 



- m-e' cos (20 - 3rit) + - mV cos (20 - n't) , 



and therefore the constant part of -^ is 



li L 135 4 1881 4 /2 



1 J 1 __ _ /m* __ *W*i* 



n 2 a 4 1 32 l 64 



3. Also 



and 



~ = - J - m 3 e' sin /i' - 2m 2 ( 1 - - e" j sin (20 - 2n't) 



- 7mV sin (20 - 3n't) + mV sin (20 - n't) \ , 



-^ = - 1 - 4m 2 ( 1 - jj e' 2 ) cos (20 - 2n't) - 1 4?nV cos (20 - 3n't) 

 atr a [ \ 2 / 



2mV cos (20 -'<)] ; 



