THE ELECTRIC AKD LUMINIFEROUS MEDIUM. 
737 
any instant half potential and half kinetic, and that there is no loss of energy of the 
light in the act of reflexion, and on the hypothesis that the medium is incompressible, 
the solution of the problem of reflexion as distinct from that of the elastic constitution 
of the medium is immediately derived, for all media which polarize the light linearly, 
without the aid of further knowledge except the law of density and the form of the 
wave-surface. If the density is uniform and the same in all media, the solution is 
that of MacCullagh and Neumann, which is known to be correct in form for 
isotropic (and also for crystalline) media. There is nothing so far to indicate whether 
the vibrations are in the plane of polarization or at right angles to it, but that point 
is soon settled by the most cursory comparison with observation of the resulting 
formulse for the two kinds of polarized light; the vibrations must be in the plane of 
polarization of the light. It remains in this order of procedure, to discover a form 
of the potential-energy function which will lead to the correct form of wave-surface 
in crystalline media, at the same time making the vibrations in the plane of polariza¬ 
tion, and which also will conform to the additional [surface conditions not utilized 
in order to obtain merely the solution of the problem of reflexion ; the discovery of 
such a function, as a result of a precise estimation of what was really required, is 
MacCullagh’s special achievement. 
25. If the aether in crystalline media is of molotropic rotational elastic quality, and 
of isotropic effective inertia the same in all media, all the conditions of the problem of 
actual optical reflexion are satisfied whatever be the degree of its compressibility. 
While, on the other hand, if it is of isotropic elastic-solid quality and aeolotropic 
effective inertia, and there is no elastic discontinuity in passing from one medium to 
another, i.e. if the elasticity is the same in all media, all the conditions are satisfied 
when there is no resistance to laminar compression. It is somewhat remarkable that 
the condition of continuity of the energy assumes the same form in both these cases. 
What happens under more general conditions, or in circumstances of mixed elastic- 
solid and rotational elasticity, or possibly yet more general types of elasticity, we 
shall not stop at present to inquire. [See however § 21.] For the explanation of 
electrical phenomena, MacCullagh’s energy-function possesses fundamental advan¬ 
tages for which none of these other possible optical schemes appear to be able to offer 
any equivalent; it is therefore not necessary to examine whether they can survive the 
searching ordeal of crystalline reflexion. 
Total Rejiexion. 
26. So long as there actually exist the full number of refracted waves, this simple 
mode of solution of the problem by means of rays is perfectly rigorous, and puts the 
matter in as clear a light as a more detailed analysis of wdiat is going on in the 
media; it is not necessary to make any assumption about the character of the incident 
wave, except that it is propagated without change. But the case is different when 
MUCCCXGIV.—A. 5 B 
