90 
MR. J. a. LEATHEM ON THE THEORY OF THE 
alters the structure of the medium which conveys the light vibrations, but does not 
exei't a direct dynamical effect on these vibrations”; the isotropy of the medium is, 
as it were, destroyed, and rotational terms appear in the fundamental elastic relations 
between displacements and the corresponding forces. This theory, in its valid form 
as regards boundary conditions, has quite lately been formulated for transparent 
media by Basset (‘American Journal of Mathematics,’ vol. 19, 1897, No. 1), and the 
same principles underlie the very different analysis of Goldhammer in his memoir of 
1892 (‘Wied. Ann.,’ vol. 46). Larmor also independently formulated this theory 
in his ‘British Association Report,’ 1893, and more explicitly in ‘Proc. Bond. Math. 
Soc.,’ April, 1893. In his exposition it was shown that the rotational terms in the 
equations connecting electric displacement and electric force are not open to the objec¬ 
tion that they would imply perpetual motions, as they involve only the rate of change 
of the force. The boundary conditions in this theory are of the standard form, 
namely continuity of the tangential components of electric and magnetic force, and 
of the normal components of magnetic induction and total current. It has been 
shown by Basset how the whole scheme may be formulated from a single energy 
function by the principle of Least Action. 
3. In the present paper it is proposed to take the fundamental equations of this 
type of theory in a general form on the lines of Mr. Larmor’s recent papers on 
Electrodynamics, and to develop them so as to obtain the solutions of the problems 
of the reffection of light at the surface of a magnet, and of the transmission of light 
through normally magnetised metallic films. The formulae so obtained will be 
compared with the available experimental results, with a view to ascertaining to 
what extent the theory is in agreement with the facts. The theory involves a single 
magneto-optic constant which in metals may be assumed complex ; we shall try 
whether it is possible, by giving suitable numerical values to the modulus and vector 
angle of this constant, to make the theory account for all the observed phenomena ; 
and if so, we shall ascertain what these numerical values are. If successful we shall 
thus have a formulation of the phenomena in a mathematical scheme, which ought to 
serve as a guide in the elaboration of physical theory. 
In carrying out this programme, I am aware that I shall be going over ground 
which has already been covered to some extent by Goldhammer, and also by Drude, 
but my method will be entirely different from theirs, and I shall be able to use 
important experimental results which had not been published at the time their papers 
were written. 
Notation. 
4. The notation is nearly the same as Maxwell’s : (P, Q, B) is electromotive 
force, {u, V , w ) the total current, { a , h , c ) magnetic induction, cr specific conductivity, 
K specific inductive capacity taken as a pure ratio, c the velocity of radiation; 
{ f '\ g ", h ") corresponds to Maxwell’s total electric displacement; its components 
