STABLE AXD UNSTABLE EQt . 



AOA'-O, a\A'-<f>. 



r body (Unplaced by rottimg on the 



arc A A' *= arc a 

 therefore ? - r. 



Al * fX 



fore 



^ r ~ 



is stable able according as 



: less orgrea j- . 



r surface be concave instead of oemtez, it may 

 be shewn in the same way that the equilibrium is stable or 



;&sAG is less or greater than -^ . 



results of til is Article will hoM when : 

 />AE arc not circles; r and It will then r the 



iture of T mi'l low. 



i->wer surface is pi un- 

 stable equilibrium Ad must be less than r. 



- in the first case, or - ' in the 



/< -f T -r 



second case, the equilibrium has been called tier thU 



case, n t n will hnve to be made to < 



whet hr : or unstable. Suppose, 



a portion of n paraboloid rests in neutral 



i.iiiun with its vertex in contact with a horizontal plane, 



