62. 



THE LUNAR INEQUALITIES DUE TO THE ELLIPTICITY OF THE EARTH. 

 [From the Observatory, No. 108 (1886).] 



IT is well known that M. Delaunay was unfortunately prevented by a 

 premature death from completely carrying out his purpose of determining 

 all the sensible inequalities of the Moon's motion by means of his very 

 original and beautiful method of treating that subject. Happily the two 

 magnificent volumes in which he determines the inequalities which are 

 caused by the disturbing force of the Sun, on the supposition that the 

 motion of the Earth about the Sun is purely elliptic, are complete in 

 themselves. The small effects due to the action of the planets and the 

 spheroidal figure of the Earth, as well as those which arise from the 

 disturbances of the Earth's motion, remained to be determined. 



Mr G. W. Hill, who is already well known for his skilful treatment 

 of special portions of the lunar theory, has, in the paper now to be noticed, 

 produced a valuable supplement to Delaunay's work by applying the same 

 method to the determination of the lunar inequalities which are due to 

 the ellipticity of the Earth. This paper forms part 2 of vol. in. of the 

 valuable series of astronomical papers prepared for the use of the American 

 Ephemeris and Nautical Almanac. 



The author begins by developing the terms of the disturbing function 

 which are introduced by the ellipticity of the Earth, by substituting for 

 the Moon's coordinates their disturbed values as already given by Delaunay's 

 work. Some idea of the length and complexity of this substitution may 



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