Intelligence and Miscellaneous Articles. 305 



"We hence easily see that, in the general case where the sphere is 

 moving with component velocities p, q, r, we must take 

 jJ.6 f . _.. , , _a/._ d , . d , ^ d \\ 1 



callins: 



and observing that 



we have 



and then we have 



d , d . d d 



E ' dec 



H= ^4-^X 

 E ^ dz' 

 From these it appears at once that the magnetic effect of the 

 displacement- currents is nil. Tor the components of the magnetic 

 forces a, /3, y are 



_ da _ <m 



dz dy ' 



dx dz ' 

 , = dF_da_ 

 dy dx 

 and x disappears from this, and there only remains the magnetic 

 action due to the current that I have assumed to represent the 

 moving superficial electricity. The effect of this is obviously the 

 same as if the whole quantity of electricity were moving at its 

 centre; and this is the same as Mr. Thomson's result (I. c. p. 236). 



It is to be observed that Mr. Thomson has intentionally omitted 

 the self-induction of these displacement-currents on one another : 

 and it may legitimately be omitted when the motion is compara- 

 tively slow ; but a complete solution of the question would be most 

 interesting. 



It may be worth while remarking, that no effect except light has 

 ever yet been traced to the displacement-currents assumed by Max- 

 well in order to be able to assume all currents to flow in closed 

 circuits. It has not, as far as I am aware, been ever actually de- 

 monstrated that open circuits, such as Leyden-jar discharges, pro- 

 duce exactly the same effects as closed circuits : and until some 

 such effect of displacement-currents is observed, the whole theory 

 of them will be open to question. 



