THE ELECTRIC AHD LUMTHIFEROUS METHUM. 
730 
The results obtained for metallic reflexion are however found to suffer, when 
compared with observation, from several serious defects ; the real part of the quasi- 
index of refraction becomes negative, which is sufficient to prevent any stable self- 
subsisting medium from acting in this manner ; wdiile on transmission through certain 
metallic films there is a gain of phase of the light compared with vacuum, when there 
ought, according to the equations, to be a loss. 
Optical Dispersion in Isotropic and Crystalline Media. 
28. In order to make our luminiferous medium afford an explanation of electric 
and magnetic phenomena, it will he necessary to assume its potential energy to 1)e 
wholly rotational, therefore quite Independent of compression or distortion. When 
bodies are displaced through it, its motion will then be precisely that of a continuous 
frictionless incompressible fluid, and therefore no rotational stress will be thereby 
produced in it. 
The phenomena of optical dispersion require us to recognize a dependence of the 
effective elasticity of the medium on the wave-length of the light; for we are bound on 
this theory, in the absence of sympathetic rotational vibrations of the atoms, to take 
the effective density of the primordial medium to be the same throughout all space. 
The dependence of the elasticity on the length of the wave can only arise from the 
presence of a structure of some sort in the medium, representing the molecular 
arrangement of the matter, whose linear dimensions are comparable with the wave¬ 
length of the disturbance that is propagated through it. The actual motion will now 
be of a very complicated character ; but the fact that a wave is propagated through 
without change, in certain media (those which are at all transparent), shows that for 
the present purpose it is formally sufficient to average the disturbance into a 
continuous differential analysis, and thus take it to be a simple one as if there were no 
molecular discreteness, but with an effective elastic modulus proper to its wave-length. 
The expression for the potential energy of the medium will thus have to be of a 
form that will vary with the wave-length, while it is still a quadratic function of 
differential coefficients of the displacements ; therefore we must now assume it to 
involve differential coefficients of higher order than the first. This mode of 
formulating the problem is what is led up to by the transparency of dispersive 
media i.e. by the permanence of type of simple waves travelling through them, and 
by the rotational character of the optical elasticity which is quite distinct from that 
of the molecular web, and, we may assume, of a different order of magnitude. It need 
excite no surprise if in extreme circumstances, involving near approach to equality 
with free periods of vibration, it is insufficient. 
29. Now if the medium is to be thoroughly and absolutely fluid as regards non- 
rotational motions, i.e. if a vortex-atom theory of matter is to be part of the theory 
of the jether, this potential-energy function must be such that no work is done by 
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