ON OPTICAL THEORIES. 233 
and hence, m(e+a)_ 4a'x? 
[SS e ? 
cs nr2m 
m+r—- 
Aer? 
_X being the wave length in air and N the refractive index. 
The complete value for A is— 
—. .a@(u—U) d?(u—U) d*(u—U) - 
A=>-r Sas Oa +a! i AL n(u—U) . (57) 
and in the above equation (56) U has been treated as small compared 
with w. 
We see thai the first and last terms are those given by the theories 
of Ketteler and Helmholtz respectively; Voigt’s more general theory 
includes them as particular cases. The first and third terms occur in the 
theory developed by Boussinesq, which is also included in Voigt’s. 
In a further paper, in reply to some criticisms of Lommel, who argues 
that a wave propagated through the molecules of the medium must be a 
sound-wave, and that therefore the matter motion which affects the trans- 
mission of light must be intra-molecular not inter-molecular, Voigt 
shows,! by taking the matter motion into account, that the velocity of wave 
propagation in a mcdium constituted as supposed will be given by a 
quadratic equation. One root of this quadratic will be comparable with 
the velocity of light in this medium, the other with that of sound; while 
the ratio of the energy of the matter to that of the ether in the light- 
motion is the reciprocal of the same ratio in the sound-motion. 
Voigt’s theory applies only to perfectly transparent media, and its aim is 
to show that the optical properties of all such media can be explained on 
an elastic solid theory by considering the mutual reactions of two 
mutually interpenetrating elastic media. The author does not touch the 
problem of absorption, because for that purpose we require to deal with 
the molecular motion to which, in his opinion, heat effects are due, and 
these lie outside the domain of elastic solid theories. He does, however, 
deal with double refraction, circular and elliptic polarisation, and the 
yarious problems connected with reflexion and refraction. Most of these 
haye been treated of also by Lommel and Ketteler. 
Chapter II.—Dovsite Rerraction. 
We will consider first the problem of double refraction. All three 
explain it in a similar manner. Within a crystal the action of the 
matter particles on the ether will depend on the direction of vibration, 
and some or other of the constants of the theory will be functions of this 
direction. It is assumed that the ether remains isotropic, and that there 
are three axes of symmetry, which are taken as those of the co-ordinates. 
§ 1. Lommel? in his theory treats the constant we have denoted by 
@ as a function of the direction. /3?, which determines the action 
between ether and matter, and y?, on which the frictional effects depend, 
1 Voigt, ‘Zur Theorie des Lichtes,’ Wied. Ann. t. xx. p. 144. 
? Lommel, ‘ Theorie der Doppelbrechung,’ Wied. Ann. t. iv. p. 55. 
