J. N. Stockwell—Hill’s Supplement to Delaunay. 161 
from which it follows that were the earth and moon to revolve 
But I find on careful examination that there has indeed been 
a remarkable oversight committed in the developments of this 
work, and that not more than two of the inequalities, if indeed 
any of them are deserving of any confidence in point of accu- 
Ta r can these two be correct to terms of a higher order 
than the third or fourth. 
n older to give a general explanation of the oversight which 
ms to have been committed in this work, I would observe 
that Mr. Hill has first determined the disturbing force which 
is due to the earth’s figure on the supposition that the moon’s 
Motions are not affected by the sun’s attraction. The real 
disturbing force of the earth is, however, a function not only 
of the earth’s figure, but also of the moon’s codrdinates, and 
Since the moon’s codrdinates are affected by the sun’s attrac- 
Hon, it follows that there must be a modification of the earth’s 
force arising from that cause. This effect of the sun Mr. 
Hill 
Sider these terms if we propose to carry the approximations to 
terms of the order of the products of the disturbing masses. 
*troneous, no matter to what extent the develo ment in terms 
of the eccentricity and inclination may be carrie 
R=R,+R, (1) 
But since R is a function of the moon’s codrdinates 7, v and 
