LECT. II.] ACCELERATIONS OF THE MOON RELATIVE TO THE EARTH. 7 



the action of the Moon, if we choose as origin the Earth's centre, we 

 must allow for the disturbance of the Sun's position by the Moon. This 

 correction may be evaded by choosing as origin, not the Earth's centre, 

 but the centre of gravity of the Earth and Moon, with respect to which 

 the Sun describes a curve so closely elliptical E 



that no allowance is required. For, if S, E, M 

 denote respectively the Sun, Earth, and Moon, 

 and G the centre of gravity of E and M, the 

 accelerating forces of S are 



on E S/SE* in ES, 

 on M S/SM* in MS; 



and these imply accelerations of G of amount 



ft 1 S' 

 v jTf ~OE>2 parallel to 



S 



parallel to MS ' 



now the accelerations of S are 



E/SE* in SE, 

 M/SM* in SM; 



hence the acceleration of G relative to S is 



S+E + M E 



ES ' 



or 



Let 



SE 3 



S+E + M M^ 

 E + M SM- 



S+E + M/.., GE 

 E + M 



S+E + M 

 E+M 



EM=r, SG = r', 



GM . 



F S. 



-*--' CV TH'i 



SG . 



= a>; then 



T\JT 



