358 REPORT — 1893. 



rotation can be got out of this relation by assuming the functions <P and 

 ^ to have rotational quality ; though Gibbs himself later on in his 

 memoir qualifies its use by a statement that ' the equation would not hold 

 in case of molecular vibrations excited by magnetic force. Such vibra- 

 tions would constitute an oscillating magnetisation of the medium, which 

 has already been excluded from the discussion.' 



If the rotational quality is simply due to a magnetic field, we may 

 take for brevity the direction of its lines of force to be along the axes of z, 

 and the equations will be 



u^eP — vQ 

 v=tQ + vF 



K d . d 



where f= J~ ju + ^^'j ^^^ ^ is of the form X , +p. The circuital relations 



of types 



, dy dj3 da (ZR (ZQ 



dy dz ' dt dy dz 

 lead to 



2p__^/cZP fTQ ^^_, *t_, ^P_4 ^ 



dx \dx dy dz ) dt dt dt ' 



d^ 

 Thus the rotational operator, instead of being of Maxwell's type ^^21* 



comes out of type ( \—- + v | — 

 •'^ V dt Jdt 



Though a rotational term of this latter type, entering into the rela- 

 tion between current and force, and conjoined with the ordinary equations 

 of electro-dynamics, leads, as we have just seen, to precisely the same 

 scheme as Drude's to explain magnetic reflexion of waves of any single 

 period ; yet in order to take into account Verdet's laws of magnetic dis- 

 persion (in transparent media) the coefficients \ and i' have to be taken 

 functions of the wave-lengths, whereas the coefficients in Drude's form of 

 theory remain constant for all wave-lengths. The relation of Gibbs is 

 competent to give an account of the laws of reflexion and of crystalline 

 propagation for any one wave-length, by altering so to speak the electric 

 inertia of the medium ; and it fails for dispersion simply because the only 

 method it possesses of rendering an account of dispersion is by accepting 

 the observed facts, and making the coefficients functions of the wave- 

 length. Thus we ought not to allow its faihire to agree with magnetic 

 dispersion to tell too much against the mode of explaining magnetic 

 reflexion now under discussion. Yet the fact remains that the scheme 

 embodied in Drude's equations has an advantage in comprehending a 

 wider group of phenomena, and to that extent corresponds more funda- 

 mentally with the mechanism of the action ; while on the other hand it 

 exhibits, especially with regard to the boundary conditions, a more 

 empirical character. 



19. These equations we have named after Drude because his memoir 

 contains by far the most detailed comparison with observation that has 

 yet been made. The same equations, however, had been used by a number 

 of other writers. For transparent media they had beea obtained by 

 Rowland ' as equations of propagation, and they had been used by Fitz- 



' H. A. Rowland, Pftil. Mag., 1881. 



