ON OPTICAL THEORIES. 253 
problem which is due to Helmholtz.' This we shall consider later. It was 
also solved by J. J. Thomson,’ so far as the isotropic media are concerned, 
and by Fitzgerald.* 
Some further developments of the theory are given in a paper by the 
author of this report, and read before the Cambridge Philosophical 
Society.* 
In this paper the general equations for the displacement and for the 
magnetic induction in a crystal are given. If a, 6, ¢ be the principal 
velocities given by the equation 
: 1 
—— 
pK, 
etc., then 
Pf _=2 car_ 4 fr of B dg, ~9dh 
mec FAG din a Ginn a) ae 
.» whil 
etc., while @Pa_~» ia 5 Pa, 2a 
ee as ga oa 
d f-qda , 7. db , ~.dc 
Se ee - + 6? — +67 _ : : : 
FAG in dy ie z) (9) 
If a wave of electric displacement 8’, in a direction in which the 
_ inductive capacity is K’, be traversing the medium, the electromotive 
force is 47S//K’ in the direction of displacement, and 47S’ tan y/K’ 
_ along the wave normal, when x is the angle between the ray and the 
wave normal. 
§3. The surface conditions implied by the theory, and used by Lorentz, 
J. J. Thomson, Fitzgerald, and Glazebrook, are that the electric and 
magnetic displacements normal to the interface are continuous, while the 
electric and magnetic forces in the interface are also continuons. 
The formulz obtained are identical with those given by MacCullagh 
and Neumann, electric displacement being substituted for the ordinary 
displacement of the medium. 
The theory has the very great advantage over the ordinary elastic 
solid theory that reflexion and double refraction are both explainéd by 
variations in the same property of the medium, viz. the inductive capacity. 
Variations in its value from medium to medium give rise to reflexion and 
refraction ; variations in different directions within the same medium are 
the cause of double refraction. 
§ 4. The theory has been applied by Lord Rayleigh to account for the 
various phenomena ° connected with the scattering of light by a cloud of 
small particles. These are deduced satisfactorily from the theory on the 
supposition that », the magnetic capacity, is a constant through the two 
media, and that the effects are due to variations in the inductive capacity, 
while, when terms of the second order in A K/K are included, the scattered 
light does not vanish—the incident light being plane polarised—in a direc- 
1 Helmholtz, Borchardt’s Journal, Band lxxii. 
? J. J. Thomson, Phil, Mag. April, 1880. 
’ Fitzgerald, Phil. Trans. 1881. 
| * Glazebrook, Proc. Camb. Phil. Soc. vol. iv. p. 155. 
* Lord Rayleigh, ‘On the Electro-magnetic Theory of Light,’ Phil. Mag. Aug, 1881. 
