MECHANICS. 



tion by the weight F hanging from B. The ra- 

 dius of the sphere r, its weight W, and that of the 

 hody F heing given, it is required to find the ve- 

 locity which the point B acquires in one second, 

 or the force by which it is accelerated. 



The momentum of inertia computed for the sphere, 



o 



is v r 5 , and therefore the accelerating force at 

 ^ 



Bis Fy3 -&_= F - .. As 2.^ 



Fr 2 +A*-r* F-f-^^r 3 



is the solidity of the sphere, if W be substituted 



F 

 for it, the above expression becomes - '- - . 



F +1 *W 



4f 

 Therefore F -{- ^ W is to F, as the force of gra- 



vity to the accelerating force at B, the equator of 

 the sphere. 



. If the motion, instead of being produced 

 by a body hanging from the sphere, and partaking 

 of its velocity, were communicated by the impulse 

 of a body F, moving with a given velocity c, in the 

 direction of the tangent at B, and striking against 

 the radius produced, the velocity communicated 



ni 15F - C 

 would be -j-^-- 



The solution of the two last problems might be deri- 



ved from the supposition, that the whole mass was 



3 collected 



