360 REPORT— 1893. 



of J. J. Thomson,' that there is some ground for assuming the correct- 

 ness of the equations to which the former method leads ; and those 

 equations may be expressed in the terms of the second method some- 

 what as follows. The electric current is in a dielectric the rate of change 

 of the electric displacement, which is of an elastic character ; in a con- 

 ducting medium part of the current is due to the continual damping of 

 electric displacement in frictional modes : it may thus fairly be argued 

 that the fundamental relation is primarily not between current and 

 electric force, but between current and displacement, while the current is 

 indirectly expressed in terms of electric force through the elastic relation 

 between displacement and force. The equations would then run as 

 follows, (^, rj, ^) being the electric displacement : 



(.,.,z.)=(| + *--)(.S,,4), 



where ^=P-&3Q + 52R; 



4=R-&2P + 6,Q. 



This would make the relation between electric displacement and 

 electric force of a rotational character, owing to the magnetisation. If the 

 medium were not magnetised. Lord Kelvin's argument might be employed 

 for the negation of such a rotational character, on the ground that a 

 sphere rotating in an electric field would generate a perpetual motion ; 

 but as it is the rotation in the magnetic field would generate other 

 electric forces. The frictional breaking down of displacement, viz., con- 

 duction, is known to assume a slightly rotational character, as manifested 

 in the Hall effect. 



Part II. — Correlation of General Optical Theories. 

 MacGullagh's Dynamical Theory of Light. 



21. It has been remarked in this discussion of magneto-optic phe- 

 nomena that a perfectly straightforward mechanical theory of magneto- 

 optic reflexion would be obtained by adding on a uniaxial gyratory part 

 to the energy- function of Lord Kelvin's labile aether.^ The development 

 of such a theory as this, after the manner already indicated, from the 

 single basis of the principle of Least Action, would compare very favour- 

 ably, by the absence of subsequent adjustment and assumption, with any 

 of the foregoing explanations. 



It has possibly been observed that the energy -function of FitzGerald's 

 electro-dynamic analysis considered above is identical except as to 

 surface terms with the energy-function of the labile sether theory, when 

 (S, Tj, C) is taken to denote actual displacement of the medium. The difi'er- 

 ence that, for plane-polarised light, (^, r), C) is in the former case in the 

 plane of polarisation, while in the latter case it is at right angles to that 

 plane, is due, as we shall see, not to the fact that in the electric medium 



the compression - — f.^ + ^ is taken to be absolutely nail, while in the 

 dx ihy dz •' 



labile ajther the pressure is taken to be absolutely null or the medium is 



' J. J. Thomson, ' Recent Advances in Electricity and Magnetism,' 1893, § 412. 

 * Lord Kelvin (Sir W. Thomson), ' On the Eeflesion and Eefraction of Light,' 

 Phil. Mag., 1888. 



