354 EEPOET— 1893. 



is to produce a temporary structural change in the' medium. In the 

 ordinary case of an isotropic medium 



eo that in periodic motion for which — ^ - we have 



at r 



- (P, Q, E) = f—+iaTJ (u, V, «') = ^ («, ^, H say, 



in which the complex part of the coefficient, involving cr, represents the 

 effect of conductivity. This is now replaced by a wider relation : in the 

 general crystalline medium he proposes the form 



dP 47r , , , , du , dv dw 



dQ 47r , . , , dv , div du 



dt K'2 ^ ^^ dt ^^ dt ^^ dt 



cZR 47r , . , , dw , du dv 



in which ^j, n^, ps are assumed to be complex. 



When the period r/27r is very great the last terms, involving 



— (w, V, iv), exert no appreciable effect, and so may be left out of account : 



at 



the vector coefficient (X,, Xj, X3) which is left is the representative of the 

 Hall effe(;t. When the period r/27r is very small, as in the case of light- 

 waves, the rotational coefficient (/Xj, /k.,, /^s) is preponderant, and the other 

 one (X|, X9, Xg) may bo neglected. We may also leave out of account the 

 slight double refraction represented by the coefficients ju^., fjy, fi., as these 

 are in nowise rotational. Thus, for an isotropic optical medium, the 

 structural relation which connects electric force with electric current 

 would reduce to the form 



cZP 47r , dv dw 



'dt'=K'''^f''dt-^'dt 



dO 47r , dw du 



f?R 47r , du dv 



dt=-K''"+^'Jt-^^dt'' 



in which Goldhammer takes (/ui, /xg, 1^3) to be complex (unless the medium 

 is transparent) and proportional to the intensity of the imposed magnetic 

 field. This structural relation between magnetic induction and magnetic 

 force is supposed to remain unmodifiable in form by magnetic or other 

 disturbance. But it is not easy to understand the manner in which the 

 relation is introduced into the equations of electro-dynamics, and the 

 analysis to be given pi-esently leads to a different result. The bodily equa- 

 tions are expressed in terms of Maxwell's vector-potential ; they are the 

 same in form as Drude's equations expressed in terras of magnetic force ; 

 and the boundary conditions assumed are continuity of the vector-potential 



