ON OPTICAL THEORIES. 245 
so that the difference between the squares of the refractive indices will 
be inversely proportional to the squares of the wave length, and this is 
quite contrary to experiment. The question as to whether the theory 
here suggested would lead to Fresnel’s construction is not considered. 
In a later lecture Sir William returns again to the question of what 
becomes of the energy absorbed by the molecules, and of the nature of 
the ether. As to the latter he adopts Stokes’s view, that the medium may 
be perfectly elastic for the small disturbances of a light-wave, executed, 
as they are, in the twenty-million-millionth of a second, and yet be a 
perfect fluid in respect of forces which act, as may be supposed in the 
kinetic theory of gases, for the one-millionth of a second. Now, the 
numerical calculations of Professor Morley, undertaken at Sir William’s 
suggestion, show that the energy given to a system such as described 
tends to become absorbed by the vibrations of lower modes, so that the 
original energy appears as vibrations in which the period may be the 
millionth of a second instead of, perhaps, the twenty-million-millionth, and 
this energy shows itself in the motions which we deal with in the kinetic 
theory of gases, rapid it may be in themselves, but slow compared with 
the light-vibrations. 
§ 3. Metallic reflexion and the quasi-metallic reflexion of such sub- 
stances as give anomalous dispersion are dealt with, and it is shown that 
the phenomena are such as would be produced by making p”, a negative 
quantity, and this is given by values of 7 a little below the critical period. 
Thus the molecular explanation of the great reflecting power of silver 
is that the highest mode of vibration of the molecules with which silver 
loads the ether is graver than the mode of the gravest light or radiant 
heat which has ever been reflected from silver; and if, again, for certain 
modes p? is not negative, but less than unity, it shows that, conformably 
with the experiments of Quincke on gold leaves, we should expect light 
to travel through the medium faster than through air. This forms a 
marked and most important distinction between this theory and others 
which have been given to explain metallic reflexion. For the other 
theories the metallic effects arise from the importance of the viscous 
terms of the form —yduw/dt. 
In an appendix Sir William works out the problem of reflexion and re- 
fraction, following Green and Lord Rayleigh so far as ordinary transparent 
media are concerned. He then transforms Green’s formule for vibra- 
tions in the plane of incidence to the case in which p? is a real negative 
quantity, and arrives at formule expressing, on a strict elastic solid 
theory, the intensity and change of phase in a wave reflected from metal. 
According to this solution we have, if »? = — p? so that v® is positive, 
the values of ® and ¥ given by— 
Y= — »? cos (ax+by +t) +tan ei ad sin (av+ by + wf) 
v2 
v2>—] 
2 2 
¥i= — v? cos (aw+by+ut) —tand Bei (+ ax+ by + vt) 
pees 
2,2 me (RE 
= a = e~* sin (by + wt) ie) 
WY’ = 22" cos (by + wt) 
2 
4 o’ =— ee ee © gin (by ss wt) 
ys 
