6S . LECTURE Vir, 



vertical in any two positions in which the body is at rest. Thus, if we sus- 

 pend a board of an irregular form from any two points successively, and mark 

 the situation of the vertical line in each position, we may find by the inter- 

 section the place of the centre of gravity: and it will appear that this in- 

 tersection will be the game, whatever positions we employ, (Plate III. 

 Fig. 39.) 



The consideration of the degree of stability of equilibrium is of material 

 importance in many mechanical operations. Like other variable quantities, 

 the stability may be positive, negative, or evanescent. ''jTbe^ Equilibrium is 

 positively more or less stable, when the centre of gravity would be obliged to 

 ascend more or less rapidly, if it quitted the vertical lirte: the equilibrium is 

 tottering, and the stability is negative, when the centre of gravity would 

 descend if it were displaced; but when the centre of gravity coincides with 

 the centre of motion, or when its path would be a hoiizontal right line, the 

 equilibrium has been called insensible, but may more properly be termed neu- 

 tral, and the body will rest in any position, without tending either to tall, or 

 to return to its original situation. It is obvious that the centre of gravity 

 cannot move, without descending, when it is vertically over the fixed point, 

 nor without ascending, when it is immediately below it ; so that in the one 

 case the equilibrium is tottering, and in the other stable. Hence we may 

 Understand the reason of fixing the moveable handles of a vessel of any kind 

 at its upper part, in order that the centre of suspension may be always above 

 the centre of gravity. If they be fixed too low; the vessel will be liable to 

 overset, unless there be sufficient friction to retain it in its proper situation. 

 (Plate III. Fig. 40.) 



An oval surface, placed on a horizontal plane, is capable of a stable equili- 

 brium, when it rests on its side, or on the extremity of its lesser axis, and of 

 a tottering equilibrium, when it stands on the extremity of its greater axis. 

 13ut the equilibrium of a circle or a sphere is always neutral, foi', when dis- 

 turbed, it neither recovers its first position, nor deviates further from it. A flat 

 body, resting ort a'sphere, will have its equilibrium tottering or stable, accord- 

 ingly as its centre of gravity is more or less than the semidiamcter of the 

 sphere above the point of Contact. (Plate III. Fig. 41, 42.) 



