236 Lord Kelvin on Magnetism and Molecular Rotation. 



If v = co , cases (a) and (b) cannot occur ; and in cases (c)> 

 (d) we see by (8L) that J = ao ; that is to say, the whole 

 energy is carried away by the equivoluminal waves. If v is 

 very small in comparison with u, we find that although J is 

 infinite in cases (a) and (c), it is zero in cases (b) and (d). 

 This to my mind utterly disproves my old hypothesis* of a 

 very small velocity for irrotational wave-motion* in the undu- 

 latory theory of light. 



XXIII. Magnetism and Molecular Rotation. J >/ 

 By Lord Kelvin, P.R.S.E.] 



§ 1. /CONSIDER the induction of an electric current in an 

 V.7 endless wire when a magnetic field is generated 

 around it. For simplicity, let the wire be circular and the 

 diameter of its section very small in comparison with that of 

 the ring. The time-integral of the electromotive force in the 

 circuit is 2AM, if A denote the area of the ring and M the 

 component perpendicular to its plane, of the magnetic force 

 coming into existence. This is true whatever be the shape of 

 the ring, provided it is all in one plane. Now, adopting the 

 idea of two electricities, vitreous and resinous, we must 

 imagine an electric current of strength C to consist of currents 

 of vitreous and resinous electricities in opposite directions, 

 each of strength ^C. Hence the time-integrals of the opposite 

 electromotive forces on units of the equal vitreous and resinous 

 electricities are each equal to AM. 



§ 2. Substitute now for our metal wire an endless tube of 

 non-conducting matter, vitreously electrified, and filled with 

 an incompressible non-conducting fluid, electrified with an 

 equal quantity, e, of resinous electricity. The fluid and the 

 containing tube will experience equal and opposite tangential 

 forces, of each of which the time-integral of the line-integral 

 round the whole circumference is eAM, if the ring be a 

 circle of radius r ; and the effect of the generation of the 

 magnetic field will be to cause the fluid and the ring to rotate 

 in opposite directions with moments of momentum each equal 

 to eAMr, if neither fluid nor ring is acted on by any other 

 force than that of the electromagnetic induction. Their 

 angular velocities are therefore eAM/nc, eAM/rw', and their 

 kinetic energies are ^e 2 A 2 M 2 /w, ^A^M^/io', where iv, w r 

 denote the masses of fluid and ring respectively. 



§ 3. Suppose now for simplicity in the first place, the ring 



* " On the Reflexion and Refraction of Light," Phil. Mag. 1888, 

 2nd half year. 



t Communicated by the Author ; having been read before the Royal 

 Society of Edinburgh, July 17, 1899. 



