ON THE ACTION OF MAGNETISM ON LIGHT. 355 



and its first differential coefficients, and continuity of the electrostatic 

 potential. 



15. The equations of Drude may be subjected to an important trans- 

 formation which will bring them into line with another class of electrical 

 theories. If in them we write 



and take (P', Q', B,') as the electric force instead of (P, Q, E.), we may 

 preserve unaltered both of the fundamental circuital relations. The first 

 one is clearly preserved ; and so will be the second one if the relation 

 between electric current and electric force is taken to be that derived by 

 substitution from 



This leads to a relation of type 



U^rdi J \ ^dt ^ dtj' 



which differs from the structural relation assumed by Goldhammer, but is 

 of the same class. When this transformation is made, Drude's boundary 

 conditions become simply the ordinary ones which express that the 

 tangential components of the electric force and the magnetic force are 

 continuous in crossing the interface ; the difficulty as to discontinuity in 

 the tangential electric force does not now occur. 



The special type of this relation which is assumed by Goldhammer is 



dP /K d , \-^ , dv dw 



d? /K cZ , \-' , dv dw 



in which he asserts that ^i, p.^, jj^^ are each, owing in some way to their 



K' d 



origin, of the form + 0-', so that they are complex constants of 



47r dt 



which the real and imaginary parts are, for the case of light-waves, of 

 the same order of magnitude. He had previously rejected the coef- 

 ficients (A-i, X2. ^3) of the Hall effect as being for light- waves negligible in 

 comparison with those retained, although the purely imagioary part of a 

 coefficient of type ^ must have the same character as they have, irrespec- 

 tive of magnitude. It is, perhaps, difficult to see any reason which 

 would give pi'obability to this assumption that the coefficients of type jx 

 are complex quantities whose real and imaginary parts come to be pre- 

 cisely of the same order of magnitude. 



16. A general formal development of the equations of the electro- 

 magnetic theory, which is necessarily wide enough to take account of all 

 possible secondai'y phenomena, such as dispersion and circular polarisa- 



A A 2 



