283.] POTENTIAL. I73 



These are the direction cosines of the force f(r) with which the 

 mass m at Q(x' r , y l ', 2') attracts the mass I at P(x, y, z). The 

 components of this force are, therefore, 



, , 



dx dy d 



These expressions show that there exists a function 



of which the components of the force at P are the partial deriv- 

 atives : 



X - 



283. The potential 



at a point P for a given system of masses is a function of the 

 co-ordinates of the point P. , If this function be known, the 

 attraction at any point P produced by the given masses can at 

 once be found ; for the components of this attraction are 



v dV T/dF 7 dV 



^l = -, Jr = , / = 



dx dy dz 



Hence, 



dV=Xdx+ Ydy + Zdz. 



If the function V be equated to any constant F 1? the result- 

 ing equation 



v=v l 



represents a surface that is the focus of all points at which the 

 potential of the given masses has one and the same value F r 

 Such a surface is called an equipotential surface, or a level, or 

 equilibrium smface. 



