382 



Mr. E. Edser. An Extension of 



These equations are identical with those used by Professor J. ,] . 

 Thomson in his developments of Maxwell's theory.* They express 

 the law that however the electromotive intensity at any place may 

 be modified by the presence of the charged atoms, its line integral 

 round a closed curve will be equal to the rate of decrease of the 

 induction through the curve. 



These equations differ from those obtained by Helniholtz.f 

 7. If a, fi, 7 are the components of the magnetic force, and , r , w 

 those of the electric current, then 



dv dfi } 



= - 



ay dz 



da, d*t I 



4 TTV = - -- -7- 



dz dx 



doc. 

 

 ay 



, 

 (8), 



The current component u will include the total displacement 

 current in the direction of x, i.e., not only that due to the variation 

 of the induced electromotive intensity, but that also due to the 

 continual alteration in position of the atoms throughout the medium. 

 This will be equal to Kpi'4ar. Mr. HeavisideJ has further shown that 

 in order to close the displacement current produced by a charge 5, 

 moving with a velocity v it we must add at the position occupied by </ 

 a current element such that its moment is qi\. Hence in the present 



case the value of u will be given by +2^%, where ^qv x indi- 



4?r 



cates the summation, for unit volume, of the products of the several 

 charges into their respective velocities parallel to the x axis. 

 Hence (8) may be written 



dy dz 



doc. </7 

 dz dx 



(9). 



* l Recent Researches in Electricity and Magnetism,' p. 252. 



f The equations obtained by Helmholtz, besides diifering in sign from the corre- 

 sponding equations of Maxwell, would lead to the conclusion that the displace- 

 ment produced by the charged atoms is circuital. 



J O. Heariside, * Phil. Mag.,' April, 1889. p. 324 ; see also J. J. Thomson, ' Phil. 

 Mng.,' April, 1881, July, 1889 ; also ' Recent Researches,' p. 19. 



