192 REPORT—1885. 
if x’ be the angle of refraction for a normal wave produced by a trans- 
verse wave incident at an angle ¢, then, with the notation of Lord Ray- 
leigh’s paper, sin? y= sin? @, and hence x is imaginary unless is 
less than sin“'(n/m). That is to say, if m be infinitely large, the effects 
of the pressural wave are entirely confined to the surface, and, indeed, 
for this total reflexion, if we may so call it, of the pressural wave to 
take place, it is practically not necessary for the ratio of n to m to be 
zero. If, for example, n/m=1/100, there will be total reflexion if ¢ is 
greater than 0° 35’, and for so small an angle of incidence as this the 
component of the vibration normal to the surface on which the pressural 
wave depends would be too small to produce a measurable effect on the 
transmitted light. 
If we put A,,/N’ = py, then py is the refractive index of the medium 
for the normal vibrations, and we have for p 
ee 
0 
Now, it was shown, first by Haughton,! and then by Kurz, that the 
expressions (39-41) agree with experiment very closely if M or p be 
treated as a constant to be determined by experiment, and if we suppose 
p to have the form just given, then for sulphuret of arsenic, for which 
p= 2-454, according to Jamin, y= 1083. Green, going further into the 
mechanism of the motion, has shown, however, that on a strict elastic 
solid theory we must have \,,/X’’=A/N and po=p. The last conclusion 
Hisenlohr calls ‘ durchaus unhaltbar,’ and in this he is right if he means 
that it does not agree with experiment, but wrong if he means that there 
is a flaw in Green’s theory. The suggestion that » and jy may be 
different is due to Haughton,” but the reasons he has assigned for it have 
been shown by Hisenlohr to be invalid. Lord Rayleigh has suggested 
others which have great weight, and the importance of which will be 
more clearly seen when we come to consider some recent theories based 
on the mutual reaction between matter and the ether. The large quan- 
tities m and m’ are, in Lord Rayleigh’s paper, eliminated from the equa- 
tions by means of the relations 
m(a’? + 6?) =De?, 
m! (a,'? + 6?) = D’e?, 
D and D’ being the densities of the ether in the two media. 
Now, in the pressural wave we are only concerned with a layer of 
ether close to the bounding surface, and Lord Rayleigh’s suggestion is 
that, although the transverse vibrations are affected nearly in the same 
way as if the transition were instantaneous, it may not be so for the 
surface waves, and that therefore we may put D/D’ = p,? where po is less 
than ». There are, I think, even stronger reasons for supposing jy and 
p to be different to be derived from the theory I have already referred 
to, which will be developed later. 
Thus the papers of Lord Rayleigh, Lorenz, and Hisenlohr show, con- 
clusively, that Neumann and MacCullagh’s theory is inadmissible, and 
that Green’s strict elastic solid theory, when slightly modified in a per- 
1 Haughton, Phil. Mag. (S. 4), vol. vi. p. 81; Kurz, Pogg. Ann. t. eviil. 
2 Haughton, Phil. Mag. (S. 4), vol. vi. p. 81; Hisenlohr, Pogg. Ann. t. civ p. 346. 
