18 LECTURES ON THE LUNAR THEORY. [LECT. IV. 



Also we have found 



P- s 1 /a 



~ - 



= ?i'-x T00280, 



which is the relation between the actual mean motion and the actual 

 mean distance (or rather mean reciprocal distance) of the Moon. 



Without the Sun's disturbing action, the relation between the mean 

 distance and the mean motion, or rather between the radius of the orbit 

 supposed circular and the uniform rate of angular motion along it would be 



M 



~. = n: 



' 



Hence in the actual orbit, the mean motion for a given mean distance 

 is smaller than it would be without disturbance ; 



Or, for a given mean motion, the mean distance is smaller than it 

 would be without disturbance. 



In fact, the relation between the mean distance and the mean motion 

 is the same as it would be if the sum of the masses of the Earth and 

 Moon were diminished in the ratio of 1 '00280 to 1. 



