ON THE ACTION OF MAGNETISM ON LIGHT. 359 



Gerald and by Basset ' to calculate tbe circumstances of magnetic re- 

 flexion, without, however, entering into tbe case of metallic media. While 

 recently J. J. Thomson ^ has employed them in an independent discussion 

 of the laws of magnetic reflexion, which corroborates the main conclu- 

 sions of Drude without going so much into detail. In dielectric media 

 Rowland and Basset proceed simply by assuming rotational terms in the 

 expression for the electric force on the analogy of the Hall eSect in 

 metals ; and FitzGerald, as we have seen, deduces his equations from a 

 new term in the energy which repi'esents the linking on of tlie magnetic 

 system. It is shown by J. J. Thomson, in his discussion of Kerr's results 

 on reflexion, that in metals as well as dielectrics it is the time-rate of 

 change of the induction or electric displacement, and not the total 

 electric current, that combines with the magnetic field in the formation 

 of this new term. 



The boundary conditions are determined by FitzGerald and Basset 

 from the hypotheses that the tangential magnetic force shall be con- 

 tinuous, and there shall be no concentration of energy, or g^tasi- Peltier 

 effect, at the interface, subject however in the case of the latter to the 

 same objection as has been appUed above to Drude's use of this principle; 

 while J. J. Thomson arrives at the same boundary conditions by 

 postulating that the part of the electric force which is derived from the 

 system itself must be continuous tangentially, whatever may happen 

 to the part imposed from without. 



20. There are thus two ways in which the magnetic field may aSect 

 the phenomena of light-propagation. The imposed magnetisation is an 

 independent kinetic system of a vortical character which is linked on to 

 the vibrational system which transmits the light- waves ; the kinetic 

 reaction between the two systems will add on new terms to the 

 electric force : these terms are naturally continuous so long as the 

 medium is continuous, but owing to their foreign origin they need not 

 be continuous at an interface where the magnetised medium suddenly 

 changes. At such an interface the other part of the electric force, which 

 is derived from the vibrating system itself, has been assumed to be con- 

 tinuous in the ordinary manner, viz., its tangential components con- 

 tinuous ; the total induction through the interface must of course always 

 maintain continuity. This seems to be the type of theory developed 

 by Maxwell in his hypothesis of molecular vortices ('Treatise,' § 822), 

 and the conditions to which it leads have been applied to magnetic re- 

 flexion by the majority of writers on the subject, including Basset, 

 Drude, J. J. Thomson. But against this procedure there stands the 

 pure assumption as regards discontinuity of electric force at an inter- 

 face. The correct boundary conditions would be derived from the modi- 

 fication of FitzGerald's procedure, which has been explained above. 



The other point of view is the purely formal one contemplated by 

 Lord Kelvin and Maxwell in their discussions of possible rotational co- 

 efficients introduced into tlie pi'operties of the medium by magnetisation. 

 The magnetisation is supposed to slightly alter the structure of the 

 medium which conveys the light- vibrations, but not to exert a direct 

 dynamical effect on these vibrations. 



It would appear from the analysis of Drude. and more particulai'ly 



' A. B. Basset, Phil. Trans., 1891. 



- J. J. Thomson, ' Eecent Researches . . .,' § 408, seq 



