1 86 
Mr. Vince on the Motion of 
D E F I N I T I O No 
The center of friction is that point in the bafe of a body 
on which it revolves , into which if the whole fur face of the bafe 
and the mafs of the body were collected, and made to revolve about 
the center of the bafe of the given body, the angular velocity de- 
frayed by its friction would be equal to the angular velocity de/lroyed 
in the given body by itsfriflion in the fame time .. 
PROPOSITION III. 
T o find the center of friction. 
Let FGH (fig. 4.) be the bafe of a body revolving about its 
center C, and fuppofe about a, b, c, &c. to be indefinitely 
fmall parts of the bafe, and let A, B, C, &c. be the correfpond- 
ing parts of the folid, or the prifmatic parts having a, b, c, &c. 
for their bafes ; and P the center of fridion. Now it is ma- 
nifeft, that the decrement of the angular velocity muff vary 
as the whole diminution of the momentum of rotation caufed 
by the fridion diredlly, and as the whole momentum of rota- 
tion or effed of the inertia of all the particles of the folid in- 
verfely ; the former being employed in diminifhmg the angular 
velocity, and the latter in oppofing that diminution by the en- 
deavour of the particles to perfevere in their motion. Hence, 
if the effed of the fridion varies as the effed of the inertia, 
the decrements of the angular velocity in a given time will be 
equal. Now as the quantity of fridion (as has been proved 
from experiments) does not depend on the velocity, the effed 
of the fridion of the elementary parts of the bafe a , b , c, &c. 
2 will 
