A J. N. Stockwell—Inequalities in the Moon's Motion. 
evident that the earth’s attraction on the moon is at a maximum 
whenever the moon is in the equator, or twice during each 
revolution of the moon. We will now suppose that the longi- 
tude of the moon’s node is 90°, and examine into the conse- 
quences that must take place while it retrogrades through a 
semi-cireumference, or from +90° t to —90°. 
When Q= +90°, the moon’s orbit intersects the equator at 
a distance of 12° 45’ to the eastward of the equinox: and since 
the node retrogrades on the ecliptic about 1° 27’ during a 
sidereal revolution of the moon, it follows that the moon will 
arrive at the equator at a point a little to the westward of its 
previous crossing. In other words, the moon will make a 
complete revolution with respect to the center of force in a 
period somewhat shorter than the sidereal revolution. At the 
end of 9°8 years the longitude of the node will be —90°, and 
the orbit = ee the equator at a seo of 12° 45’ to 
the westw the equinox. ow the moon performs 
124°3256 sidered reine while the ode is retrograding 
through an are of 180°. But 124-3256 sidereal revolutions 
of the moon with reaper to the equator will exceed the time 
of the sidereal revolution by the same amount that it fell 
short of that quantity while rub gading through the other 
half of the orbit. It is also plain that the inclination of the 
equatorial node; and it is this pendulum-like motion of the 
equatorial node that gives rise to a number of inequalities in 
the moon’s motion which I now proceed to consider; give 
that the inequalities which are produced while the node 
advancing are ae Binet by means of the satee grails 
motion whic 
I now give the vahiie of the perturbations of the elements — 
and coordinates which I have obtained, as resulting from the 
otion of the moon’s node, which is ‘produced by the sun’s 
attraction. I find 
