THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
743 
which violates the condition of fluidity. But the only forms of for an isotropic 
medium, which maintain an invariantive character independent of axes of co-ordi¬ 
nates, and in which each factor involves oidy (f, g, h), appear to be made up of 
MacCullagh’s forms and the form 
(jh /,£ ‘V_\\ 
\dij ^ dzj ^ \dz ^ dx j ^ \dx ^ dy j ’ 
and if the medium is incompressible this new form is identical with the second type 
of MacCullagh. The conclusion thus follows that for isotropic media, the form of 
the potential energy, when we include dispersion and other secondary effects in it, is 
that of MacClllagh, the two forms given by him being in this case identical. 
33. The question now presents itself, whether there is any distinction between the 
two types into which MacCullagh divides possible energy-functions of this kind, 
which will enable us to reject the one that modifies the form of the wmve-surface. It 
seems fair to lay stress on the circumstance that the first of MagCullagh’s types of 
dispersional energy may represent an interaction between the average strain of the 
medium [f, g, li) and the average disturbance of the strain due to molecular 
discreteness, while the other form represents the energy of some type of disturbance 
of the strain which combines only with itself, and is not directly operative on the 
average strain. It would seem natural to infer that a term of the second type would 
have its coefficient of a higher order of small quantities than the ones we are now 
investigating. 
For the most general case of seolotropy, the dispersional energy Wo must be either 
a quadratic function of first differential coefficients of {f, g, h), or else a lineo-linear 
function of [f, g, h) and its second differential coefficients. If the first alternative be 
rejected for the reason just given, there remains a form of which MacCullagh’s is 
the special case in which the second differential coefficients group themselves into the 
operator V^. A reason for this restriction is not obvious, unless we may take the 
form already determined for an isotropic medium as showing that the dispersion 
arises from the interaction of {/, g, h) on [f, g, It); such a restriction is in fact 
demonstrable when we bear in mind the scalar character of the energy-function. 
The Injiuence of Dispersion on Ref exion. 
34. It has been explained that on this theory the mode of formal representation 
of dispersion without sensible absorption, is by the inclusion of differential coeffi¬ 
cients of the displacement, higher than the first, in the energy function. This ma.kes 
the dispersion depend on change of elasticity, and not on any effective change of 
inertia of the primordial medium ; in the neighbourhood of a dark band in the 
absorption spectrum of the medium, absorption plays an important part, rendering 
the phenomena anomalous, and we must then have recourse to some theory of the 
