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POPULAR SCIENCE REVIEW. 
it not for the fact that Jupiter and the perigee of the lunar 
orbit have nearly the same period of revolution. Owing to this,, 
the influence of Jupiter on the motion of the moon is very much 
augmented. It has also been discovered that Jupiter produced 
a still larger inequality in the motion of the moon, one twice as 
great as that discovered by Professor Newcomb, and having a 
period of more than seventeen years. This new inequality also- 
derives its magnitude from the commensurability in the periods 
of revolution of Jupiter and the perigee of the lunar orbit, as 
from this reason the attraction of Jupiter continues to accumu- 
late for nearly nine years at a time, amounting, at the end of 
this period, to an effect of appreciable magnitude. 
A most able paper has been recently published by Mr. C. W. 
Hill, a mathematician connected with the American Nautical 
Almanac, in which he calculates the portion of the motion 
of the lunar perigee which is independent of the eccentricity 
and inclinations of the orbits of the sun and moon. The 
theoretical determination of the motion of the lunar perigee has 
always been a task of considerable difficulty, so that even the 
best strictly theoretical value of the period of revolution of the 
perigee around the lunar orbit differs from the observed value 
by about five minutes. This is a very considerable amount in 
the present advanced condition of the lunar theory, seeing that 
theory gives within a few seconds the same value as the observed 
period of the revolution of the line of nodes of the lunar orbit. 
Mr. Hill devised an entirely new method of determining the 
motion of the lunar perigee by skilfully utilizing some of the 
later developments in mathematical analysis. In this manner 
a very accurate value for the motion of the lunar perigee was 
obtained. In England, Professor Adams had independently 
arrived at the same method of solving this problem, and he had 
moreover determined the rate of motion of the line of nodes in 
the same manner. In these papers a most important contri- 
bution has been made to the lunar theory, for they open a means 
of determining the values of the inequalities in the motion of 
the moon which promises to be of great value. Its intricacy, 
and the great labour it involves, will probably however, restrict, 
its use to special cases. 
