552 Mr. vince’s Invefigation of the 
the momenta, arifing from the magnitude of the bo- 
dies, their diftance from the center of rotation and ve- 
locity conjointly, remain the fame after the flroke as 
v x CD 4 x P . v x CA 4 x0 
before, we fhall have PxVxDC = 
v x CB* x B 
', and therefore v 
CG + CG 
P x V xDC x CG 
CG 7 ~ P x OC- + AxAC 2 + BxBC- 
■■ ■ ■ - F x - r - x CG ; hence if p be fuppofed an elaftic body, 
A-fBxCG + PxDC 1j - 
we fhall have 
for the velocity of the 
A+BxCG+PxDC 
center of gravity after the ftroke, in ipfo motus initio, 
PROP. IV. 
determine the motion of the bodies after the firgl infant , 
or when they are left to move freely by themf elves . 
The writers on mechanics, from confidering the 
equality of motion on each fide the center of gravity, 
when a body revolves about that point, have inferred, 
that if a body had a projectile as well as a circular mo- 
tion communicated to it, the center of gravity Would 
continue to move in a right line, as that point would 
not be difturbed by the rotatory motion : yet, as, in 
the cafe we are now confidering, the bodies begin to re- 
volve about a different center, it may be proper to exa- 
mine more accurately into this matter, and to fhew from 
what 
