4. 



THE SECULAR ACCELERATION OF THE MOON'S MEAN MOTION. 



[!N the paper "Reply to Various Objections," Monthly Notices, April, 

 1860; Works, Vol. i., p. 174, Adams mentions that he has determined the 

 secular acceleration of the Moon's mean motion without recourse to develop- 

 ments in series. The following is the method employed.] 



If we ignore the parallactic inequalities and the inclination of the orbit, 

 the equations of motion become 



d?l /dlV _ /dff\- 

 d? + (dt) ~ (dt 



d*6 dd dl 



Ct't' Cvt \JU\j 



where I = log r. 



These may be satisfied, if e' be constant, by assumptions of the form 

 log - = a g + a. 2 cos (' + a 5 cos 2f + a s cos (2 <') + a 9 cos 



T 



8 sn 2- 

 where 



and a,, 6,, a 8 , 6 8 , a,, 6 9 involve e' in the first power, 

 and a 0) n, a.,, 6 8 involve e' 2 . 



