( 625 ) 



to a field F and a state A of these bodies, the two actions we shall 

 have to consider may be represented by 



(F,, A,) and (F,, .10. 



The first of these is reatlily seen to be 0. Indcetl, the niaji,iietic 

 field, produced by the forces II, thongh modified by the presence of 

 the dielectric ring, is synnnetrical around the axis PQ. Therefore, 

 if tiie periphery of the condenser-plates is nowhere interrupted, the 

 state A^ will consist in circular currents in these plates, without any 

 electric charge. It is impossible that the field F^ should, by its 

 action on these currents, give rise to a couple, since, whatever be 

 the nature of this field, each element of the stream-tubes will only 

 be acted on by a force perpendicular to its length. 



In reality the case was somewhat different, each condenser-plate 

 being cut by a vertical slit. There must have been equal and 

 opposite charges at the edges of each slit and the field F^ must 

 have acted on these charges, in virtue of the electric force existing 

 in it. These forces may howevei- be supposed to have annulled 

 each other, because the distance between the charges on the two 

 edges was very small. 



§ 16. The action {F.-^, A^) is therefore the only one that remains 

 to be considered. Now, in the state A^, the plates of the condenser 

 were the seat of charges, whose amount was modified by the 

 influence of the dielectric ring, and whose alternations were accom- 

 panied by currents in the wire W and in part of the plates them- 

 selves. In so far as they are currents of conduction, i. e. in so 

 far as they consist in a motion of electrons, these currents are evi- 

 dently unclosed. We may decompose the whole sj-stem of them into 

 infinitely thin stream-tubes, the tubes being all thronged together in 

 the connecting wire, and widening out in the plates, at whose sur- 

 faces each stream-tube ends in two elements of surface. 



Let S be one of the stream-tubes, ir the end of it on the outer, 

 and H that on the inner plate, e the charge in G, — e that in H, 



de 



' = it (^^) 



the current in the tube in the direction from H towards 6', and let 

 us consider the action {F^, A.^) only in so far as it depends on this 

 current / and on the charges e and — c. 



In the first place there will be an electromagnetic foree on the 

 tube S, owing to the eurrcnt /. The couple arising from it depends 

 on the course of the magnetic lines of force in the field 7% ; it is 

 most easily found by remarking that its work dui-ing a complete 



42* 



