150 Mr. E. A. Biedermann on the 



any ordinary circuit the number of moving electric particles 

 is such a large one that the variation of magnetic force 

 is negligible at all points external to the conductor, but 

 within the conductor this is no longer the case. At such 

 points the square of the mean value of the magnetic force 

 is not equal to the mean value of the square of the instan- 

 taneous magnetic force. 



Expression (8) is the result of calculation on the former 

 basis, whilst (7) has been deduced on the latter basis. Hence 

 the two results are not identical. This, the author suggests, 

 is the explanation of the discrepancy. 



Experiment proves, however, that (8), which is in effect 

 the result of integrating over all space the square of the 

 mean value of the magnetic force at a point, correctly ex- 

 presses the mutual energy of two circuits. But (7) is the 

 result of integrating the square of the instantaneous mag- 

 netic force and then taking the mean with regard to time, 

 this being in reality what is done when (7) is substituted 

 for (6 a). It follows that H 2 /87r does not represent the 

 kinetic energy density in the field, if by H is understood 

 the instantaneous value of the magnetic force. 



What, then, may be taken to be the true representation of 

 the kinetic energy densit} r at any given point ? 



Let G denote - £RV cos 6 where R is the electric in- 



c 



tensity in E.S.U. at a point due to any single charge, and 

 6 the angle between the directions of R and the velocity Y 

 of the charge. Then 



G* = (±im r cos0) 2 = X 9r 2 + 211 9r9s , 



where 



£ r =*K r V r cos0 p , <V=,&c. 



Referring the system as before to axes with origin at e iy 

 and having the line joining e l9 e 2 for ,2-axis, we have 



1 i 

 Pi = ?3 frs* + v 2 y + w 2 (z - r) } . 



• 9. 



