160 i iv. 



Art. 1)1, the body will not 1)C in equilibrium unless the 

 al through the centre of gravity of the body falls 

 within a polygon formed by so joining tin- joints of contact 

 of the body ami the plane as to include them all and have 

 no rc-cntenng angle. 



<>n a body is suspended from a point round wl< 

 freely, it will n< />// be in 



iht vertical line passing thrwyh the point ofsuspen^' 



For the body is acted on by two forces, its own w -i 

 wliie: rtically through its centre of gravity and 



force arising from the fixed point; for equilibrium these : 

 must act in the same straight line and in opposite directions ; 

 thus the centre of gravity must be in the vertical line passing 

 through the point of suspension. 



1 1. nee if a body be suspended successively from two points 

 the vertical lines drawn through the points of suspension will 

 both pass through the centre of gravity; therefore the point 

 in which they intersect is the centre of gravity. 



If a body le capable of revolving round an axis 

 not vertical it will not rest unless lite centre of ///<///>// 



rtical plane passing through the axis. For the body is 

 acted on by its own Weight and the forces arising from the 

 fixed points ; by Art 87, the moment of the weight round the 

 fixed axis must vanish, this requires the centre of gravity to 

 be in the vertical plane through the fixed axis. 



The student will readily perceive as an experimental fact 

 that there is an important difference 1> on of 



equilibrium in which the centre of gravity is vertically < 

 the fixed point or fixed axis, and that in which it is vertically 

 below it. In the former case, if the body be .-lightly 

 from its equilibrium position and then left to itself, it will 

 begin to recede from its original position. In the latter < 



if me body be slightly disturbed from its equilibrium j.nsition 

 and then left to itself, it will begin to return to its ori _ 

 position. The former position of equilibrium is called uns' 

 r,nd the latter stable. We shall return to this point in 

 Chap. XIV. 



