THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
819 
in comparison with the work done by electric forces; just as was to be anticipated 
from § 117, where it has been shown that to produce a comparable motional effect 
very great velocity of translation or rotation of the molecule is requisite, not the com¬ 
paratively small velocity of movement of the elements of the medium caused by a 
wave passing over it. 
This amounts in fact to asserting that it is only the electric inertia of the molecules 
that affects the electric waves. Their material inertia is quite a different and secondary 
thing from the inertia of the aether on an electric theory it can have no direct 
influence on the radiation. 
It seems clear also that if the molecules, in their relations to the aether, behave as 
systems of grouped electrons, their presence cannot disturb the fluidity of that 
medium, so that the foundation given above (§ 28) for MacCullagh’s dispersion 
theory remains valid. 
123. Let us contrast the merits of this view of dispersion with those of the type 
of theory in which it is ascribed to imbedded ponderable molecules. It has been 
shown,! that for an elastic-solid theory (or aiiy theory treated by the method of 
rays, § 22) to give an account of the observed laws of reflexion at the surfaces of 
transparent media, the inertia may be supposed to vary from one medium to another, 
or else the jigidity, but not both. Thus, setting aside the latter alternative for 
other reasons, the molecules must act simply as a load upon the vibrating sether; 
this requires that their free periods must be very long compared with the period of 
the waves, which is a very reasonable hypothesis. But if the optical rigidity is 
absolutely the same for all media, we are hound to explain not only the dispersion, 
but the whole refraction, by the influence of the inertia of the load of molecules; 
thus to exjflain dispersion we have to take refuge in Cauchy’s doctrine of simple 
discreteness of the medium. 
Now let us formulate the problem of wave-propagation in a discrete medium of 
this kind. It will be a great simplification to consider stationary vibrations instead 
of progressive undulations ; let us therefore combine two equal wave-trains travelling 
in opposite directions, and so obtain nodes and antinodes. We may imagine the 
continuity of the medium severed at two consecutive antinodes; thus the problem 
before us is to find the gravest free period of a block of the medium, forming half a 
wave-length, with its imbedded molecules. To represent in a simple manner the 
general features of this question, let us take Lagrange’s problem of the vibrations 
of a stretched cord with n equidistant beads fixed on it. This will be a sufiicient 
model of the case now in point, where the molecules act simply as a load; but if we 
are to consider possible influence of their free periods, so as to include anomalous 
dispersion as well as ordinary dispersion, we must also endow the beads of the model 
* Of. Lord Kelvin, ‘ Baltimore Lectures on Molecular Dynamics,’ 1884, Lecture xx, 
t Lord Rayleigh, ‘ Phil. Mag.,’ Aug., 1871. 
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