3?6 Mt\ ViNCE on the Motion of 



DEFINITION. 



'The CENTER of FRICTION IS that point in the bafe of a hoiy 



mi which it revolves, into which if the whole furface of the bafe^ 

 mid the majs of the body were collected^ and made to revolve about 

 i'he center of the bafe of the given body, the angular velocity de- 

 ft/oyed by its fridiion would be equal to the angular velocity df/Iroyed-: 

 in the given body by itsfriBionin the fame time. 



PROPOSITION III. 



To find the center of frldlion. 



Let FGIi (fig. 4.) be the bafe of a body revolving about its 

 center C, and fuppofe about a, b, r, &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 prifmatie parts having a^ b, c, &c. 

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

 nifeft, that the decrement of the angular velocity muft vary 

 as the whole diminution of the momentum of rotation caufcd 

 by the fri<£lion dirc^ly, and as the whole momentum of rota- 

 tion or efFe(£l of the inertia of all the particles of the folid in- 

 verfly ; X.\\Q 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 effedl of the inertia,, 

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

 equal. Now as the quantity of fri6tion (as has been proved 

 from experiments) does not depend on the velocity, the efFedt 

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

 2 will 



