228 The Mathematical Electricians of the 



This expression for the force between two electric charges 

 was taken by Weber as the basis of his theory. Weber's is the 

 first of the electron-theories a name given to any theory which 

 attributes the phenomena of electrodynamics to the agency 

 of moving electric charges, the forces on which depend not 

 only on the position of the charges (as in electrostatics), but 

 also on their velocity. 



The latter feature of Weber's theory led its earliest critics 

 to deny that his law of force could be reconciled with the 

 principle of conservation of energy. They were, however, 

 mistaken on this point, as may be seen from the following 

 considerations. The above expression for the force between 

 two charges may be written in the form 



where U denotes the expression 



ee'c~ 



Consider now two material particles at distance r apart, whose 

 mechanical kinetic energy is T, and whose mechanical potential 

 energy is F, and which carry charges e and e'. The equations 

 of motion of these particles will be exactly the same as the 

 equations of motion of a dynamical system for which the 

 kinetic energy is 



ee'i* 





and the potential energy is 



To such a system the principle of conservation of energy may be 

 applied : the equation of energy is, in fact, 



m -rr 1 > 6e ' G " 



T + V - ee r + - = constant. 

 2r r 



