314 Litellujence and Miscellaneous Articles. 



Por our value of H, 



V (it (Iv 

 With insulators C=0, consequeullvj) = 0, y"= — .v ; so that then 



and both energies are tlieu always present in equal quantity. 

 With a conductor, on the contrary, 



or 



Sjt^ {dxj Stt [dt J'^ STTfi U-V dt J "^ T dt +^' -^ / ' 



or, if we denote by A the last term on the right, which is always 

 positive, 



T=E+A; 



consequently T is always greater than E. 



To calculate for our case T, E, and A and the sum of the two 

 energies (T + E= W), we notice that they are periodic functions of 

 t with the period r. Hence we put the quantity e-P'^='U, and 

 form its mean \'alue bv integrating from to r and dividing by r • 



then, putting for shortness ^ — = -, we get : — 





A=^'^- 



A2 



a 



The difference A between T and E must doubtless be ascribed to 

 the occurrence of currents in the medium. Let us consider the 

 limiting cases. 



I. The body is a perfect insulator; C is then =0, 6=p=0, 

 U=l; consequently 



T= — 



A=0, 

 W=E+T=:^. 



