2 J. N. Stockwell—Inequalities in the Moon’s Motion. 
In the paper referred to above, it was shown that the motion 
of a body moving in a circular orbit in the plane of the 
equator would be uniform ; and that the motion in a circular 
orbit which was inclined to the equator would be subject to 
inequalities, the magnitude of which would depend on the 
inclination of the orbit to the equator. Now the ecliptic i is 
inclined to the equator at an angle of 23° a and the moon’s 
orbit is inclined to the ecliptic at an angle of 5° 8’. If, then, 
the ascending node of the moon’ s orbit is at the vernal equinox, 
the inclination of the moon’s orbit to the equator will be 28° 
35’; and she will attain to that degree of declination twice 
during each sidereal revolution. In this position of the node, 
the inequalities of the earth’s attraction on the moon attain 
their maximum values. Suppose, now, that the ascending 
node is at the autumnal equinox. It is evident that the incli- 
nation of the orbit to the equator will be only 18° 19’, and that 
she will only reach that declination twice ducing each revolu- 
tion. ‘he in equalities of the eart 's attraction on the moon, 
node is caused by the sun’s attraction, we must, in the calcula- 
tion of the separate effect of the spheroidal form of the earth 
on the moon’s pola neglect the sun’s attraction and regard 
the elements of the moon’s orbit as constant, except so far as 
they are affected by the form of the earth itself. From these 
general considerations it follows that the moon’s declination, 
on which the inequalities of the earth’s attractive force depends, 
is affected by two conditions: namely, the longitude of the 
moon and the longitude of the node. TI shall therefore in the 
present paper consider only the inequalities which depend on 
these two elements, either separately or in combination. 
In the calculations which I have made, the oblateness of the 
earth has been taken as g4,; and i n the few equations which 
are given, the symbols have the Sollowing significations: @ and 
nt denote the moon’s mean distance and mean longitude; v 
and @ denote the moon’s true longitude and latitude. y and Q 
denote the inclination and longitude of node of moon’s orbit ; 
e denotes the obliquity of the ecliptic, and D denotes the mean 
radius of the earth; p and g denote the oblateness of the 
earth, and the ratio of the ecnbiitapal force to the gravity at 
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