J. N. Stockwell—Inequalities in the Moon’s Motion. 7 
as the facilities for referring to any part of the work by means 
of the margina] numbers are much better than in the original. 
I shall also change the notation somewhat, putting e for A, and - 
a for g —1 in some cases, and shall also put f= 1. The num- 
bers inclosed in brackets refer to the corresponding marginal 
numbers of the Mécanique Céleste. 
The expression of the force R, [5362] becomes by using the 
value of 8, which is given by equation (1) of this paper, ; and 
putting f=1, 
FB CF asin. (16) 
In this equation s denotes aa tangent of the moon’s latitude. 
This value of # gives the following values of the partial differ- 
ential coefficients, 
(dR\ _ a’ p 
(= —6— ssin2, (17) 
aR\ a Be 
fe = 2—;8¢cosv, (18) 
a) 3 wt. (19) 
The equation which ious the value of dv, is Vege 
namely, : 
t 
dov=3 farto tor (); (20) 
and the value of dR is 
dk= =(+ ) ee (= det (SS) a. (21) 
The value of s is S giv en by the equation [5376], namely, 
s=ysin(gvu—Q), 
in which I have changed @ to @, in order to avoid oan 
of symbols. Now (22) gives by differentiation 
ds = gy dv cos (gv — 8). (23) 
If we neglect the eccentricity of the orbit we shall have dr=0, 
consequently the term (oar will vanish from the value of 
ak. Now substituting the value of s, (22) in (18), and multi- 
plying (19) by ds, which is given by (23), we shall get, 
(3) ao=a a’ 5 y dv {sin (gv + ¥— Q) + sin (gv — v —Q)§. (24) . 
(% a) a= =a'g® y dw jsin (gv + v— Q) —sin(gu-—v—2®)}. (25) 
If we substitute these values in equation (21), and retain only 
the term depending on the shits 
v—v—Q), it will become 
