ON THE ACTION OF MAGNETISM ON LIGHT. 353 



that due to conduction. But at the interface between two media 

 the transmission of energy without accumulation on the surface requires 

 that, the axis of x being assumed normal to the interface for the moment, 

 in addition to the continuity of (/3, y) the tangential magnetic force, we 

 must have continuity in 



The tangential electrical force is therefore to be taken discontinuous • 

 and the author enters into explanations to minimise the repugnance which 

 may be felt to such a hypothesis, their gist being that the part of the 

 electric force derived from the relations of the system itself must be con- 

 tinuous, but the part imposed from without need not be so. 



The weak point in this determination of the boundary conditions is 

 the fact that, as the extra terms are supposed to have their origin in a new 

 term in the energy, this term ought to have been included in the reckon- 

 ing befoi-e we can draw any conclusions from the flux of energy across 

 the interface. 



The equations of propagation are, for periodic motions in which 



-^ =—=.—ir — „, 01 the type 

 dt T cW ^^ 



K f7 

 where K' is the complex quantity -r-^.+ir, and where, when the axis of 



47r n,t, 



X 



_ is normal to an interface, the quantities above mentioned are to be con- 

 tinuous across it. The vector (a, ft, y) is in the wave-front of the undu- 

 lations for, the magnetic permeability being constant, 



^ + ^1 + ^=0. 

 dx dy dz ' 



and it is in the plane of polarisation. 



These equations may also be variously expressed in terms of other 

 vectors, e.g., of (P, Q, R) which is in the plane of the wave-front and 

 transverse to the plane of polarisation, or of 



fp. ciq , dR \ 



The magnetic rotation is here to be explained by the single real 

 vector coefficient (b^, b.^, 63) ; and the same value of this coefficient is in 

 fact found to give a fairly good account of the various circumstances 

 attending the rotation of the plane of polarisation in magnetic reflexion 

 by iron and nickel, while it is also of the same order of magnitude as 

 would correspond to Kundt's measures of the rotation produced by 

 transmission through a thin film of iron. 



14. A theory published a few months before by Goldhammer ' goes, 

 on the other hand, on the assumption that the eff'ect of the mao'netic field' 



' D. A. Goldhammer, ' Das Kerr'sche . . . Phiinomen,' Wied. Ann., slvi 1892 p 71 



1893. i';" ■ 



