ON OPPICAL THEORIES. 193 
fectly reasonable way, leads to results agreeing very closely with experi- 
ment, while Cauchy’s method of treating the pressural wave requires 
an unstable condition in the ether. 
Inanother paper Lord Rayleigh! considers the problem of reflexion at 
the confines of a medium of variable density. The incidence is supposed 
to be normal, and in, the particular problem solved completely, the density 
is supposed to vary as the inverse square of the distance from a fixed plane 
parallel to the surface. This variable medium extends between the two 
planes x= 2,, =, and the density is constant on the other sides of 
these planes, and it is shown that if the thickness of the variable layer is 
not very different from the difference in the wave lengths in the two, then, 
for the case in which the two media are air and glass, the reflexion will 
be excessively small. 
§ 5. The paper by Kirchhoff? in which the problem of reflexion and 
refraction is considered has been already referred to. The theory there 
given is, in its results, nearly the same as those of Neumann and 
MacCullagh. 
The ether is not treated strictly as incompressible, though it is 
supposed that only transverse waves are propagated, and therefore that 
the equation 
du , dv , dw_ 0 
dx dy dz 
is satisfied without the coefficient A becoming very large. These trans- 
verse waves falling on the interface of the two media would tend to set 
up longitudinal vibrations. Some surface action, however, is supposed to 
go on over the interface, the result of which is to quench these vibrations 
and the condition that this surface action should involve neither loss nor 
gain if energy is formed. This, with the three equations implied in the 
continuity of the displacement, makes four conditions from which the 
intensities and planes of polarisation of the reflected and refracted waves 
can be found. 
The theory differs from MacCullagh’s merely in recognising the 
possibility of the existence of the normal waves, and then accounting for 
their absence by means of some unknown surface action. It is not astrict 
elastic solid theory, nor does it attempt to explain of what nature the 
surface forces are which quench the normal waves. The formule to 
which it leads are identical with MacCullagh’s,? and do not offer an 
explanation of the change of phase observed by Jamin. It can hardly 
be looked upon, therefore, as a satisfactory explanation of the phenomena, 
nor can we regard Kirchhoff’s principle, as the fundamental hypothesis 
is called by various German‘ writers, as one which may replace the true 
surface conditions of an elastic solid. 
Chapter V.—Meratuic ReErexion. 
§ 1. Various experimenters—and among them Brewster, MacCullagh, 
Briot, Airy, Neumann, De Senarmont, Jamin, Quincke, Wernicke, and 
Conroy—have investigated the optical effects produced by metallic re- 
} Lord Rayleigh, Proceedings of London Math. Soc. vol. xi. No. 159. 
? Kirchhoff, Abh. der Konigl. Akad. xu Berlin, 1876 
% See Glazebrook, ‘On the Reflexion and Refraction of Light,’ Proc. Camb. Pril. 
Soc. vol. iii. p..329. 
* See Ketteler, Voigt, etc, 
1885. () 
