THE ELECTRIC AHD LUMINIFEROUS MEDIUM. 
243 
inertia from attaining Q^ny sensible velocity before the force is reversed; so that in 
neither way can the propagation of electric displacement across the medium be 
sensibly affected by the presence of the molecules. The formula shows, however, 
that the damping effect of conductivity usually persists to higher periods than the 
simple refracting effect of the excited vibrations. 
The theoiy of dispersion would assume a simpler form if the molecules were 
systems vibrating about positions of equilibrium, instead of about states of steady 
motion. In that case the coefficients Cjg, Cjg, .... are null: the restoring forces, 
proportional to the velocities, to which these belong, are in fact Introduced by the 
steady motions, and may be named, after Lord Kelvin, motional gyrostatic forces; 
they evidence themselves by causing slow processional oscillations. The positional 
gyrostatic forces, or centrifugal forces proper, are merged in T — W along with the 
forces arising from the potential energy.* When these motional forces are absent, 
we have 6 ^ = — Ajp^) and similarly, so that ; and 
as before, in a transparent medium, (K' — 1)/(K' + 2) = | Si?/. Thus the 
values of g^, g., . . . . g„ are in this case all positive; so that, if this represented the 
facts, the fragments of a horizontal spectrum, with red on the left, would after 
further refraction by a prism of anomalous material with its edge horizontal and 
uppermost, all slope upwards from left to right. On the other hand, each change of 
sign from positive to negative among the successive values of g^, g-z, ■ . . . g„ would 
give two fragments of the spectrum which would be curved back so as to be highest 
and lowest respectively near the middle, while a negative following a negative would 
imply slope upwards from right to left. According to Kundt’s law the index is 
abnormally great on the lower side and abnormally small on the upper side of an 
absorption band; and if this generalization is universally valid, it will follow that 
9 i> i/ 2 , ... . g,, are actually all positive. 
31. It is thus fundamentally desirable on various grounds to obtain Information as 
to how the signs of these quantities depend on the gyrostatic coefficients ; in 
particular because the present theory of gyrostatic molecules is a very wide one, and 
lor example includes as a limiting case the hydrodynamical vortex atoms of Lord 
Kelvin, in which the constitution is purely gyrostatic but the number of degrees of 
freedom is infinite. It will be convenient for this purpose to change to new 
coordinates of which -p . . . . _j_ is one, say the one with suffix unity : 
and to choose them semi-normal, so that the potential energy is represented by a 
character, compared with ordinary molecular encounters, is in keeping with the rapid disintegration 
and evaporation of metallic plates under its influence. It is conceivable that the long-continued 
Becquerel radiation from fatigued phosphorescent substances arises in like manner from very sudden 
release cf their molecules into new groupings, in the course of their gradual return to a natural or 
unfatigued configuration. 
* The periods of small free vibrations, and the amplitudes of small forced ones, would not be affected 
by reversal of all the gyrostatic momenta in the system: in fact this reversal would just change the 
s)'stem into its optical image. ” 
