MECHANICS. 61 



the sum of the products of all the masses into their 

 distances from the plane, divided by the sum of the 

 masses. 



a. As a single body may be regarded as a system of 

 particles, this proposition applies to such bodies, and 

 is therefore universal. 



If the bodies be A, B, C, D, &c. and their perpendi- 

 cular distance from a given plane a, b, c, d, &c. x 

 the distance of the centre of gravity from the same 



plane, x = 



. + B + C + D. 



111. The effect of any number of bodies to pro- 

 duce motion about a given point, is the same as 

 if those bodies were united in their common centre 

 of gravity. 



112. When a heavy body is at liberty to move 

 about a fixed point, it cannot come to rest till its 

 centre of gravity is either the highest or the lowest 

 possible. 



A body cannot rest on any base, unless a perpendicu- 

 lar to the horizon from its centre of gravity fall with- 

 in the base. 



The centre of gravity of plain figures, and of solids, 

 may be found by the foregoing propositions. A few 

 of the simplest and most elementary of these prob- 

 lems may serve as examples. 



113. 



