8 J. N. Stockwell—Inequalities in the Moon’s Motion. 
dk=— a’ Ey (9-1) dosin (gv— v — 2.) (26) 
This gives by integration 
JAR =a ® y cos (gu —v — Q). (27) 
If we substitute the value of s in equation (17) and multiply 
by r it will become 
dR B 
r = )=- 8a" y cos (gu—v— 2). (28) 
Substituting (27) and (28) in (20), it becomes 
dév = — 3a* FY cos (gu —v — 2), (29) 
This is the same as LaPlace has given in [5368 
But LaPlace has given a second term depending on the same 
argument. This second term arises from the variation of the 
sun’s disturbing force which is due to the variation of the 
moon’s latitude produced by the earth’s oblateness. The 
expression of this force is given in equation [5372] and is as 
follows : 
OR=$m'u"r’ sds. (80) 
I shall now show that this value of dR is the same as the 
value of & given by equation [5362], except that it has a 
contrary sign. 
According to [5874] we have : 
gm’ u?r? =p aol, (31) 
and if we substitute this in (80) or [5372] it becomes 
éR=2 q—" 66s. (32) 
And if we substitute in this, Se value of ds a by [5876], 
which reduced to the notation of this article i 
6s=—a gn” (33) 
it becomes 
6k=— 2a". E sin v. (34) 
This is the same as (16) or (5362) except that it has a contrary 
sign. This force is therefore the reaction of the force expended 
by the sun in giving motion to the moon ’s node, which in turn 
produces the inequality in the moon’s latitude. 
But in this second part of his work LaPlace seems to have 
committed a grave oversight, for he has treated his equation 
[5372] in the construction of [5373], as though ds were con- 
stant; whereas it is a function of oth r and v, according to 
