MUCELLAYEOUS EX AMPLER. VI 



le resU in equilibrium in a fine groove in the 







at a . the distance of the nar 



the nxi. Also fin-! 



greatest value of a for a pi may 



be a position of equili. 



possesses the following prop. 

 iken and t<-ur triangles formed by jc>. 

 i the an-ular points of the figure, the centres of 

 se triangles 1 circumference of a r 



iiagonals of the quadrilateral are at right 



A square board is supported in a horizontal 



no of them be attached to a 

 must the others be atta< rdcr th:i 



weight which can b<- placed on any part of the board without 



greatest possi 



,ni!ar plate hangs by three parallel threads 

 .t the corners, and supports a heavy particle. Prove 

 reads are of equal strength, a heavier pn: 

 rted at the centre of gravity than at any other 



:C is a trianjjle ; A /', F aro the middle poiots of 

 oppositi //, C respect i is an r p 



d in a givcu ratio at A\ B\ C respeo- 

 lieory orthe centre of gravity that . 

 and 00' meet at a p 



iuely and then placed with its 



a horizontal plane ; prove that when die angle of 



is less than sin ' J f there will be two sections far 



A 



:i on 

 the cone is 



. the equilibrium is neutral, and for intermediate set 

 the cone will fall over. 



1 1. A . lin-liT on an elliptic ease (the semisjcet of 



i are n and b] rests with its n 1 between two 



smooth ii. ined at right angles to eaeh other; 



