Now, electro-magnetic experiments show that, excluding magnetic substances, the permeability of all bodies is very nearly the same, and differs very slightly from that of air. The inductive capacity, however, of different bodies is different, and hence the velocity with which electro-magnetic waves travel differs in different bodies.
But the refraction of waves of light depends on the fact that light travels with different velocities in different media; hence we should expect to have waves of electric displacement reflected and refracted when they pass from one dielectric, such as air, to another, such as glass or gutta-percha; moreover, for light the refractive index of a medium such as glass is the ratio of the velocity in air to the velocity in the glass.
Thus the electrical refractive index of glass is the ratio of the velocity of electric waves in air to their velocity in glass.
Now let K₀ be the inductive capacity of air, K₁ that of glass, taking the permeability of air and glass to be the same, we have the result that—
Electrical refractive index = √(K₁/K₀).
But the ratio of the inductive capacity of glass to that of air is known as the specific inductive capacity of glass.
Hence, the specific inductive capacity of any medium is equal to the square of the electrical refractive index of that medium.
Since Maxwell’s time the mathematical laws of the reflexion and refraction of electric waves have been investigated by various writers, and it has been shewn that they agree exactly with those enunciated by Fresnel for light.
Hitherto we have been discussing the propagation of electric waves in an isotropic medium, one which has identical properties in all directions about a point. Let us now consider how these laws are modified if the dielectric be crystalline in structure.
Maxwell assumes that the crystalline character of the dielectric can be sufficiently represented by supposing the inductive capacity to be different in different directions; experiments have since shewn that this is true for crystals such as Iceland Spar and Aragonite; he assumes also, and this, too, is justified by experiment, that the magnetic permeability does not depend on the direction. It follows from these assumptions that a crystal will produce double refraction and polarisation of electric waves which fall upon it, and, further, that the laws of double refraction will be those given by Fresnel for light waves in a doubly refracting medium. There will be two waves in the crystal. The disturbance in each of these will be plane polarised; their velocity and the position of their plane of polarisation can be found from the direction in which they are travelling by Fresnel’s construction exactly.