ROT 



Prttp. If a system of bodies be connected together and supported at 

 tiny point which is not the centre of gravity, r.nd then left to descend by 

 that part of their weight which is not supported ; 2 g multiplied into the 

 sum of all the products of each body into the space it has perpendicular, 

 ly descended will be equal to the sum of all the products of each body 

 into the square of its velocity, g being = &2% feet. (Mr J)au-son t Serf, 

 lergh.) 



A demonstration of this Prop, may be seen in Leybourn's Mathemati- 

 cal Repository. 



Ex. 1. Let a cylinder whose weight = W, moveable about a horizon- 

 tal axis passing through the centre, be put in motion by a weight P at- 

 tached to a string wound round it ; required the force accelerating the 

 body P, and the space descended in t seconds. 



Let s space perpendicularly descended by P, = velocity acquired 

 in the time t t r radius of the cylinder, a- = distance of the centre of 

 gyration from t'.ie centre of the cylinder ; then by the Prop. 



2gXPs = Pi*+ WXt = Pa*-f W X^ 



v |p T^ accelerating force. 



4.v2 



To find s, put c* =. r^- in the leading equation, and we shall have 



Er. 2. A given cylinder with a thread wound round it is suffered to 

 unwrap itself and descend j required the time of its descent through a 

 given space. 



The same notation being retained 



2g X W* - Wt; 8 +Wc* X = WX 



KJC. 3. P and \V are hung over a fixed pviley, to find how /ar F will 

 descend in t", 



