of Relativity in Electromagnetism. 417 



g l is the unit normal erected on the positive plate of the 

 condenser; (gi Tij) is the cosine o£ the angle which u makes 

 with gj. 



In case the electrons move parallel to the plates the force 

 takes the same form as in the Maxwellian theory. 



§ 3. We will now proceed to consider the energy relations 

 that follow from our principle of relativity. Suppose we 

 have two systems A and B in relative motion. External 

 forces are required to keep the motion steady. We denote 

 the field intensities due to the active system A by E A and Ha, 

 and those due to the active system B by E B and H Bj , where 

 it is understood that E A and H A are measured on B and 

 E B and H B on A. Further, the volume- density of electricity 

 of A is /) A , and that of B is p B . As to the electromagnetic 

 nature of the two systems, we will assume for simplicity that 

 the system A contains only electrical masses, while B contains 

 electrical and magnetic masses. Now remembering that the 

 relative motion of electric and magnetic masses produces 

 forces that are perpendicular to the direction of motion, and 

 hence do not perforin work, we find for the energy change 

 in the element of time : 



dW=dt JJj" pBuE A rf T = ^ fjj p A uE B ^ T . 



By the aid of the equations I. to IV. and by the general 

 rule 



E curl H = div VHE + H curl E, 



we can easily transform this expression and obtain: 



In this equation dg denotes a vectorial element of surface 

 which has the direction of the outward normal. The surface 

 integral vanishes by removing the surface to infinity since 

 radiation is excluded. Thus: 



*w _i £f {Tea*- J^iffiiAir. do) 



We examine now what happens when the external forces 

 which kept the motion steady are removed. Acceleration 

 will set in, and if the inertia of the system B is infinitely 

 larger than than that of A, the latter system alone will be 



Phil. Mag. S. 6. Vol. 13. No. 76. April 1907, 2 G 



