PROPERTY 01 



carries a heavy pa m these ] 



- of wlii id the other | the 



from ih' itions of equilibrium, 



';c the vertical plain*, frnn which the parti- 

 by a constant force as th plane of (x, z), ami 



16 as the plane of (y, z) ; take tin- p'.int t< which the 



In, and lei th- 



be vertically downwards. Let x, y, z denote th 

 of the particle in a position of equilibrium, and / tin- 1 

 of the string. Let W be the partieh-, /' the 



constant repulsive force, /MX the force which 

 tauce of the particle from the plane of (;/, z). (''nei-i-. 

 particle displaced into an adjacent position, the co-ordinates 

 of which are x + &x, # + %, z + Bs. Then ly the principle 

 of v' locitics 



" .................. (1); 



the tension of the string has no virtual moment ly Art. 



Also a? + y* + z* = r ....................... (:>) ; 



therefore x8x + y$y + z$z = ..................... 



By (3) we can express B~ in terms of Bx and y; thus (1) 

 becomes 



mi /. Wx ir// 



Therefore fix -- = 0, and 1- - J - 0. 



From the first of these equations we obtain either z = , or 



i.- 

 else x = 0. If we take the former solution we obtain y=- t 



and then x is known from (2) ; thus one position of equili- 

 brium is determined. If we take the solution x = 0, then y 

 and z must be found from tin- equations 



Fz- 



thus another position of equilibrium is determined. 



