152 Mr. E. A. Biedermann on the 



which is identical with (8). Thus, by assuming that the 

 instantaneous kinetic energy density at any point is repre- 

 sented by 5— (H 2 + G 2 ), we should find a correct value for 



OTT 



the mutual energy of two circuits. It is suggested, there- 

 fore, that this may be a correct representation of the instan- 

 taneous kinetic energy density in all cases. The argument, 

 in fact, is identical with that used when we conclude from 

 the theory of point charges of magnetism that the energy 

 density is JL 2 /Sir. In the theory of magnetism, however, 

 H is regarded as constant at a given point (for a static 

 system of magnets) whether without or within magnetic 

 matter, because the latter is treated as capable of infinite 

 subdivision into elements of magnetic moment Idv. 



This is analogous to assuming the moving electricity in a 

 circuit to be continuously distributed throughout the sub- 

 stance of the conductor. In such a case, at any given 

 point, 



G= i $UV cos 6 = iTfpV j g (i) dx dy dz 



the circuit being supposed divided into an infinite number 

 of filaments carrying currents pYda, and the integration 

 extended throughout the conductor. Thus for a uniform 

 distribution of the moving charge throughout each filament 

 of the conductor G vanishes at ail points both without and 

 within the conductor, and H at any point is constant. 

 Actually the charge is not so distributed, and G has a finite 

 and appreciable value within the conductor. 



The value arrived at for the kinetic energy of a system 

 on the above assumption for the energy density leads to 

 some interesting results. 



For a system of spherical surface charges, having a common 

 velocity V both in magnitude and direction, 



2 \ 



T=i2i— + 22 — \V 2 = 



e 2 e e ) V 2 



■w-v, 



where W is the electrostatic potential energy of the system, 

 if supposed at rest in its instantaneous position. This result 

 is perfectly general whether we suppose the charges 



