Chap. XLII.] 



EQUILIBRIUM. 



501 



particles of a solid body can therefore be compounded 

 into one resultant acting through one point in the 

 body. That point is the CENTRE OF GRAVITY. We 

 see also from this that the attractive force of gravity 

 depends upon the number of particles of the body, 

 and that it is directly proportional to the mass of the 

 body. Weight, then, depends upon mass. The centre of 

 gravity may be experimentally determined for a body by 

 suspending it from one point by a string which is pro- 

 longed, and has a small weight attached. The vertical 

 line is thus obtained. The body is next suspended 

 from another point. The point of intersection of the 

 vertical lines is the centre of gravity. The centre of 

 gravity of a line is its middle, of a circle its centre, 

 of a parallelogram the place of intersection of its 

 diagonals. 



Stable and unstable equilibrium. When 

 a body is in equilibrium, the force of gravity acting 

 through the centre of gravity is 

 opposed by another force equal in 

 amount and opposite to it in di- 

 rection, acting through the same 

 point ; or when it is not opposed 

 by a single force, but by several 

 forces, the resultant of these forces 

 must act from the centre of 

 gravity. Suppose a plate of wood 

 BCD Fior 212) whose centre of 





., . Hi. Fig. 212.-Stable and 



gravity, as experimentally deter- unstable Equilibrium. 

 mined in the way mentioned, is G. 

 It is evident that if the plate be supported by a pin 

 passed through G, on which, however, the plate is free 

 to turn, it will remain in equilibrium in whatever posi- 

 tion it is placed. Let the plate be supported by a pin 

 at A, directly above the centre of gravity, it will remain 

 in equilibrium, and, if moved to one side or another, 

 will return again to its former position. For the 



