502 LUNAR INEQUALITIES DUE TO ELLIPTICITY OF THE EARTH. [62 



If m have its usual meaning as before stated, and if c be a small 



positive constant depending on the ellipticity of the Earth, then the value 

 of the coefficient in question is approximately proportional to 



Now, if, as in the case of our Moon, c is very much smaller than 

 m 2 , so that we may neglect the square of c compared with that of m 2 , 



ft 



the quantity just mentioned becomes approximately = ^ ; whereas if m 2 



Tfb 



is small compared with c, the same quantity becomes nearly 1, and the 

 coefficient becomes nearly independent of the ellipticity of the Earth, as it 

 should do, since in this case the coefficient of this term is approximately 

 equal to the sine of the obliquity of the ecliptic. 



Mr Stockwell's second objection, that Mr Hill has omitted to take 

 into account the modification of the Sun's disturbing force which is caused 

 by the alterations of the Moon's coordinates due to the ellipticity of the 

 Earth, seems to arise from a misapprehension on his part of the spirit of 

 Delaunay's method. These alterations of the Moon's coordinates are implicitly 

 involved in the variables a, e, y, I, g, h, throughout the series of operations 

 by which Delaunay gradually removes from R the periodic terms arising from 

 the action of the Sun. 



CAMBRIDGE : PRINTED BY J. AND C. P. CLAY, AT THE UNIVERSITY PRESS. 



