( 624 ) 



complete dielectric ring, bounded by a surface of revolution witli the 

 axis PQ. Moreox'er it will be safe to assume that the action on the 

 two bodies which it was sought to observe, did not depend on their 

 relative positions A\itli respect to the wires leading to the condenser- 

 plates, and remained therefore the same, in whatever position the 

 torsion-balance was turned. If this was the case, the action on 

 a body that is the 7i''' part of the ring (being cut out of it by two 

 planes passing througli the axis) must have been the n^^ part of the 

 couple, acting on the complete ring. Consequently, it will suffice to 

 show that the effect is 0, if the experiment is made with a complete 

 dielectric ring. 



^15. For simplicity's sake we shall suppose the condenser-plates 

 to be united by a wire W and their alternating electric charges to 

 be produced by a periodic electromotive force in this wire. As to the 

 currents in the coil, tliey may be regarded as due to electromotive 

 forces of the same period, acting in the windings themselves ; indeed, 

 the action on the dielectrics can only depend on the magnetic field 

 and not on the way in Avhich it is produced. For this same reason 

 it is allowable to ascribe to the windings so small a resistance that 

 they do not carry any appreciable charges. 



Then no other but electromagnetic forces will act on the windings 

 of the coil and these cannot give rise to any couple about the axis 

 PQ, because such forces are perpendicular to the elements of the 

 windings. By the theorem of § 13 the couple acting on the torsion- 

 balance must therefore have been equal and opposite to the moment 

 of rotation, acting on the condenser-plates and the wire W. It remains 

 to show^ that this last moment has been 0. 



I shall denote by I the electromotive forces acting in the connecting 

 wire IF, by II those existing in the windings of the coil, and I 

 shall distinguish by the suffixes 1 and 2 the states arising from these 

 tAvo causes. Let us indicate by A^ the charges of the plates and 

 the currents in these and the wire IF, in so far as they are due to 

 I, and let A, have the same meaning with respect to II ; also, let 

 F^ and F, be the electromagnetic fields excited by the two causes. 

 In each of these fields there will be an electric force b (acting on 

 charges that are in rest), as w^ell as a magnetic force f) ; in virtue of 

 the first, the field will exert a ponderomotive force on the charges 

 of the plates and in virtue of the second on the currents, one of 

 these actions being determined by the first, and the other by the last 

 term in the general equation (VII). If we denote by the symbol {F, A) 

 the couple acting on the plates and the wire, in so far as it is due 



