[ 66 J 
arc CP, the fluent of A* - ^A cy i ~ z3JC w iH m ve 
i+r x i — 3J 2 0 
the motions of the apfis. 
6. The quantity c being - x of the earth’s 
mean attractive force at the moon ; by computing, as 
above, it will be found, that while the moon moves 
from C to p, through an arc of 35° 15' 52'', the to- 
tal regrefs of the apfis is to the arc Cp as .0054.04 
( = n ) to unity: and that the fum of its direcft mo- 
tions, while the moon moves from p to A , is to the 
arc pA as .0105707 (=iV) to unity. 
It will be found likewife, by the inverfe operation 
hinted in § 2, that putting k = .00362552, and K = 
.006961 1 ; -\-k and — K are forces, which adting con- 
ftantly, the one from C to />, the other from p to A, 
would produce the fame motions of the apfis. 
7. The quantities k and K might have been found, 
pretty near the truth, only by fumming the ordinates 
iLR , or 1 — 35*, upon the arc A: in which cafe we 
fhould have had k — c x .648869 = .00370925, and 
K—C'a 1.24018 = .006939 : and the motions thence 
computed would not have been much different from 
their juft quantity. This however is mentioned, not 
as if the method itfelf were fufficiently exaCt ; but to 
{hew, that if, hereafter, in cafes, where the limits of 
the forces are incomparably narrower, we fhall, in- 
ftead of fumming the momenta , make ufe of a mean 
force determined in a like manner, there is no fenfible 
error to be apprehended. 
8. Hitherto we have confidered the body ground 
which P revolves, as quiefcent ; and it is thus authors 
have always confidered it : altho’ the cafe in nature, 
to 
