Energy in the Electromagnetic Field. 1 53 



spherical or not. For 



H'+ff=~(2[RV]) 8 +J(2(RV))s 



C C 



= J 2 {[HV] = +(RV>'}=Jr^, 

 where R now denotes the resultant electric intensity. 



From this it appears that the mass of the system is the 

 same as if each Faraday tube had a mass R 2 /47rc 2 per unit 

 volume, whilst on the basis that the kinetic energy in the 



JH 2 

 — di\ the conclusion arrived at is that the 

 bV 



apparent density of these tubes varies from the above value 

 for motion at right angles to the tubes down to zero for 

 motion in the direction of the tubes. The result arrived at 

 above suggests the possibility of the propagation of dis- 

 turbances other than transverse ones. 



Expression (11) for the energy in the field is easily 

 extended to cover any distribution of electricity whatever 

 the velocities of its elements. Imagine it divided into infi- 

 nitesimal spheres of various sizes. It is easily shown that 

 for a system of spherical volume charges 



m T(H 2 +G-) , 3 v « r * 2 , 9 , ,. 



e<e. 



+ iS -^ < U r U s + V r V * + W r W s) ' 



If p 1 denote the density of the charge (in E.M.U.) in one 

 of the spheres of volume dv^ and therefore of radius 



I 3 



? 



1 O /l 



the coefficient J now entering because %% indicated that 



