888 = J. N. Stockwell—Inequality of the Moon's Motion. 
the earth’s center, but also on its distance from the equator. 
If the attracted point were situated in the plane of the earth’s 
equator the attraction of the earth upon it would be greater 
at a given distance than if the earth were spherical. The 
attraction would also be greater either north or south of the 
equator until we reached the paralled of about 35° 16’, at 
which points the attraction of the earth would be nearly inde- 
pendent of its spheroidal form. For all points situated beyond 
the parallels of 35° 16’ the attraction of the earth is less than it 
] 
uniform, on account of the redundancy or deficiency of matter 
beneath the different parts of its course. It is evident that the 
motion in an orbit perpendicular to the equator would suffer 
greater variations from the unequal distribution of matter, 
than it would for any other inclination. ! 
We shall now apply the preceding considerations to the 
motion of the moon around the earth, supposing for greater 
simplicity that her orbit is circular. : 
ince the inclination of the moon’s orbit to the equator 1s 
spherical. But since the inclination varies between the limits 
of about 18° 19’ and 28° 35’ during a period of about nineteen 
years, it follows that the earth’s attraction undergoes sensible 
variations ; and hence the moon’s place at an iven time 
requires to be corrected on account of the varying inclination 
of its orbit to the equator. The corrections to the moon’ 
longitude and latitude arising from this cause have been calcu- 
lated, and applied to the moon’s place during the whole of the 
becoming less, it follows that the plane of the moon’s orbit is 
gradually app 
mean motion must b Increasing. All thes 
are fully =r aggen by mathematical analysis, and were 
