§ 4 Double Refraction of Light Explained by the Wave Theory
The two elements of rapidity of propagation, both of sound and light, in any substance whatever, are elasticity and density, the speed increasing with the former and diminishing with the latter. The enormous velocity of light in stellar space is attainable because the ether is at the same time of infinitesimal density and of enormous elasticity. Now the ether surrounds the atoms of all bodies, but it is not independent of them. In ponderable matter it acts as if its density were increased without a proportionate increase of elasticity; and this accounts for the diminished velocity of light in refracting bodies. We here reach a point of cardinal importance. In virtue of the crystalline architecture that we have been considering, the ether in many crystals possesses different densities, and different elasticities, in different directions; the consequence is, that in such crystals light is transmitted with different velocities. And as refraction depends wholly upon the change of velocity on entering the refracting medium, being greatest where the change of velocity is greatest, we have in many crystals two different refractions. By such crystals a beam of light is divided into two. This effect is called double refraction.
In ordinary water, for example, there is nothing in the grouping of the molecules to interfere with the perfect homogeneity of the ether; but, when water crystallizes to ice, the case is different. In a plate of ice the elasticity of the ether in a direction perpendicular to the surface of freezing is different from what it is parallel to the surface of freezing; ice is, therefore, a double refracting substance. Double refraction is displayed in a particularly impressive manner by Iceland spar, which is crystallized carbonate of lime. The difference of ethereal density in two directions in this crystal is very great, the separation of the beam into the two halves being, therefore, particularly striking.
I am unwilling to quit this subject before raising it to unmistakable clearness in your minds. The vibrations of light being transversal, the elasticity concerned in the propagation of any ray is the elasticity at right angles to the direction of propagation. In Iceland spar there is one direction round which the crystalline molecules are symmetrically built. This direction is called the axis of the crystal. In consequence of this symmetry the elasticity is the same in all directions perpendicular to the axis, and hence a ray transmitted along the axis suffers no double refraction. But the elasticity along the axis is greater than the elasticity at right angles to it. Consider, then, a system of waves crossing the crystal in a direction perpendicular to the axis. Two directions of vibration are open to such waves: the ether particles can vibrate parallel to the axis or perpendicular to it. They do both, and hence immediately divide themselves into two systems propagated with different velocities. Double refraction is the necessary consequence.