140 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



1 . of the moved 4- ^ E from A 



upon itself ....... l(Wft-W„) 



towards the moved — ^E . . t(V— V) 



towards the motionless -E . . -(— V — W„) 



towards the motionless —-E . t(~^*""^)* 



2. of the moved— -E from B 



z 



upon itself i(Wa~WJ 



towards the moved +^E . . jlV— V) 



towards the motionless — j^E . -7(— V— W^) 



towards the motionless +-E . t(— Wo~V) 



2 4 



Sum-(v + 5^') 



This quantity gives us therefore the maximum of the vis viva to 

 be generated and the quantity of tension gained by electrifying. 

 To obtain, instead of these potentials, more familiar ideas, let 

 us consider as follows. Suppose surfaces to be constructed for 

 which the potential of an electric element, which lies in them, in 

 regard to several other electrified bodies which are present, pos- 

 sesses equal values, and let us call these surfaces of equilibrium, 

 then must the motion of an electric particle from any point 

 whatever of one of them to any point of another of them, 

 always increase the vis viva by the same quantity ; a motion on 

 the surface itself, on the contrary, will not alter the velocity of 

 the particle. Hence the resultant of the whole of the attractive 

 forces of the electricity for every single point of space must be 

 perpendicular to the surface of equilibrium which passes through 

 it, and every surface which is at right angles to this resultant 

 must be a surface of equilibrium. 



