ON OPTICAL THEORIES. 241 
rinciple laid down in the former paper! would require that this should 
be mw, not Mw, as he points out, remarking that the equation given is only 
true under certain restrictions, and, in fact, he shows that for vibrations 
in the plane of incidence the continuity of Mw is inconsistent with the 
energy equation, at least unlessb=0. The energy equation gives— 
dw, 
dt 
and this form is assumed for the rest of the work. 
Expressions are then found for the difference of phase between the 
reflected, refracted, and incident beams, and for their relative intensities, 
and these are compared with theory on the assumption that the con- 
stant b vanishes, and that M,=M,. The results of the comparison are 
satisfactory ; but this, however, can hardly be said for the principles 
from which they are deduced, while the difficulties we have already 
alluded to as to the negative value for the real part of the square of the 
refractive index remain in their full force. 
M, Wy) = Mw, as bor 
(81) 
Chapter IV.—Tuerory or Sir Wituiam Tomson. 
GENERAL CONSIDERATIONS. 
§ 1. The lectures of Sir William Thomson delivered last year at 
Baltimore have developed a new interest in the theories now under con- 
sideration. After discussing at some length the elastic solid theory and 
throwing much light on it, and on the meaning of the twenty-one 
coefficients of Green’s theory, he points out its unfitness to explain the 
phenomena, and then proceeds to work out the consequences of a special 
form of reaction between the ether and matter; this he illustrates in his 
own inimitable manner by his mechanical model of the ether within 
a transparent body. This mechanical model consists of a number of 
concentric hollow spheres. ach sphere is connected with the one 
Within it by zigzag springs, and in the centre there is a solid mass 
connected also by springs with the shell next to it. The dimensions of 
these shells, which represent the matter molecules, are supposed to be 
small compared with the wave length. The interior molecule will have 
| #number of periods of vibration depending on the number and nature 
of the Spring connections, on its own mass, and on the masses of the 
shells, The springs are supposed to be massless. The shell molecules are 
distributed through the ether in very large numbers, and the outermost 
shell is connected with the ether. 
It is further supposed that the forces arising from the springs are 
proportional to the relative displacements of the centres of the shells, and 
that the ether acts on the first shell with a force proportional to the 
relative displacement of that shell and the ether surrounding it, so that, if 
& be the ether displacement, z,, x, those of the shells, m, /47”, m,/4a?, ete. 
their masses, the equations of motion are, 
y 2. 
iat qa 1 E—m) — One, — 2) 
a 88 Os (4-20) a(n —2,) 
(82) 
2 Voigt, Wied. Ann. t. xix. p. 900. See above, p. 239. 
1885. R 
