Mr, Vince on the 
364 
rn TS— IX = — IX_ = -7-, + —r . omitting the other terms of 
SE 3 4 ST — £K 61 bi 
the feries on account of their fmallnefs. Hence the force 
with which a particle at E is drawn from CB is equal to 
; confequently the effect of this force in a direction per- 
pendicular to ET will be ; hence this force : the 
A u 1 J 
force of the fun on a particle at T :: : ~ 2 :: 3EK 
x KT : ST. Now if P=:the periodic time of the earth, 
the periodic time of a body revolving at the earth’s furface ; 
then the force of the earth to the fun : the force of the body 
to the earth, or the force of gravity, :: p- : p.* and hence the 
force of the fun on a particle at E perpendicular to ET : the 
force of gravity :: 
<# 3EK x KT x p' 
1. 
3. Let v be the center of gyration, and put M=^the quan- 
tity of matter in the earth : then the effect of the inertia of M 
placed at v, to oppofe the communication of motion, is the 
fame as the effect of the inertia of the earth ; and hence, by 
the property of that center, ET 2 : Tu 2 (=*4ET 2 ) :: M : 4 M, 
which is the quantity of matter to be placed at E to have the 
fame effect. 
4. Put /» = the excefs of the quantity of matter in the 
earth above that of its infcribed fphere. Now by Sir Isaac 
Newton’s two firfc lemmas, it appears, that the aCtion of 
the fun upon the fhell of matter, to generate an angular 
velocity about an axis perpendicular to CABD, is juft the fame 
as it would be to generate an angular velocity in a quantity of 
matter equal to 4 tn placed at E. Let us therefore fuppofe the 
fun’s attraction, perpendicular to ET, to be exerted upon a 
3 quantity 
