J. N. Stockweli—Inequalities in the Moon’s Motion. 5 
6Q3=— F ingee -Ol eek ala Q 
o ; (8) 
oy = + F eos Q <= — 8”'2233 cos Q 
a being the ratio of the motion of the node to the moon's 
mean motion. These inequalities of the elements give rise to 
the following inequality in the latitude: 
60 = - sinnt == ~ 8-080 cin nb. (9) 
This is exactly the same as LaPlace and subsequent investi- 
gators would have obtained had they used the same yalue o 
the earth’s ellipticity. This inequality in the moon’s latitude 
is equivalent to the supposition that the moon’s orbit, instead 
of moving on the plane of the ecliptic with a constant inclina- 
tion, moves, with the same condition, upon a plane passing 
always through the equinoxes, between the ecliptic and equator 
and inclined to the ecliptic by an angle which is equal to £, as 
a 
LaPlace has remarked. 
I have:not, however, been equally fortunate in reproducing 
the value of the inequality in the moon’s longitude, which 
LaPlace and later investigators have obtained. I find as 
directly resulting from the motion of the moon’s node, the fol- 
lowing inequality in the longitude: 
i ~ £ ysing=—184"8 sing. (10) 
But the preceding inequality in latitude gives rise to the 
two following inequalities in the longitude : 
dv=4F ysing—45 y sin (2nt— a) 
: : 
= +184"°3sinQ + 0°°37 sin (2nt— Q) 
_ The first of these two inequalities derived from the perturba- 
tions in latitude exactly cancels the preceding inequality in 
the longitude which is sfeong ee directly from the retrograde 
abies of the node; and we have as the resultant of the two 
orces, 
(11) 
do=—4F ysin (Qnt — Q) = + 037 sin (2nt — Q). (12) 
I find, however, that the radius vector of the moon’s orbit is _ 
affected by the inequality 
dv = 8a By cos 2, ( 
and this produces the following inequality in the longitude, 
fp 
a 
13 
dv=-6—ysinQ =+4"4438inQ, | (14) 
