C 6 4 ] 
Of the mean motion of the moon's apogee, accord- 
ing to Sir Ilaac Newton. 
The rule given by Sir Ilaac Newton, in the 9 feCtion 
of his firlt book, is to this purpofe: Tab. Fig. 3. 
1. That, fuppoiing the common law of attraction, 
and that a central body T attracts the body P, revolving 
round it in an orbit nearly circular, with a force as 
unity ; if to this be added a conftant force, whofe 
ratio to the former is expreffed by r; then the angu- 
lar velocity of the body P, in an immoveable plane, 
will be to its angular velocity, reckoned from the 
apfis of its orbit, in the fubdupiicate ratio of 1 -f-c to 
i-j -ac, or as f/' tf- to unity. And therefore, if A 
i4-<k 
reprefents any arc deferibed by the revolving body in 
an immoveable plane, A x If will be the cor- 
r 1 -fc 
refponding arc in its orbit, reck on’d fr om the apfis. 
And their difference A x — » will be the 
1 
grefs of the apfis. 
But if the force of the central body T is diminifhed 
by fome conftant force as c, then the fign of c is 
changed in thefe ex preflions ; and the direCt motion 
of the apfis will be Ax 1 — (/ 
2. And hence, if fome foreign variable force, added 
to, or fubtraCted from, the central force of attraction, 
produces a given motion of the apfis , retrograde or 
direCt ; it is eafy to find a conftant force as r, which 
fhould fi^ fume motion. 
3. T- 
