$6 



Mr. ViNCE on the Motion of 



DEFINITION. 



The CENTER of FRICTION ts that point in the bafe of a body 

 on "which it revolves, into which if the ivhole fur face of the bafe^ 

 and the mafs of the body were coUeSfed, and made to revolve about 

 the center of the bafe of the given body, the angular velocity de- 

 ftroyed by its fridiion would be equal to the angular velocity dsHroyed. 

 in the given body by itsfriciion in the fame tirne^ 



PROPOSITION III. 



T^ofind 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 theprlfmatic parts having a, b, c, &c. 

 for their bafes ; and P the center of fri6lion. Now it is ma- 

 nifeil:, that the decrement of the angular velocity muft vary 

 as the whole diminution of the momentum of rotation caufcd 

 by the friction diredily, and as the whole momentum of rota- 

 tion or efFe(fl of the inertia of all the particles of the folid //?- 

 verfely ; xht former being employed in diminifhing 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 efFe6l of the friction varies as the effe£l of the inertia, 

 the decrements of the angular velocity in a given time will be 

 equal. Now as the quantity of fridlion (as has been proved 

 from experiments) does not depend on the velocity, the etFe(5t 

 of the fridlion of the elementary parts of the bafe a, b, c, &c. 

 2 will 



