M PUB. 



* fixed to a i the 



real! in mil position*. 



A cycloid. 



iiniforro square board in capable of motion in a 

 il plane about a hinge at one of its angular p* 



hed to one of the nearest angular points, and 

 pasaing over a pi illy abo\ .tige at a distance 



the iil rU a * 



> the weight of tin- boari 



positions of equilibria- :uiuo whether they are re- 



spectively stable or unsta 1 



\vosmall sin ;* of equal v >n a 



fixed elliptical wire ol major a\ lical, and 



are connected by a string passing over a smooth peg at the 



us; prove that the rings will rest in whatever poai- 



snmll heavy ring slides on a smooth wir 

 ve whoae pin tical, and is connect* 



a fixed pull plane of the curve 



with another wrijlit which hangs freeh -f the 



it the ring may be in equilibrium in any position. 



A conic section having it* focus at the pull v. 



lx>ard bo placed, so that iu plane ia 

 \vo pegs which arc in the same horizontal plane, 

 quilil.riuin it' the.-**- \*z* be at ti 



icters. What arc the limit* 

 between the pegs mu \<red or fall short 



ttition of equilihriiim maybe possible? 

 .: the equ . is 



hoao centre of gravity coincides 



with in- at the vorti-x, n-*U on a rough 



w that the equilibrium is stable or un- 



stnl.le according as the value of 8 (\ - .rhcn x and y 



vanish, ia positive or negative, x and y being co-ordinatee o( 



