Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/248

 paper by Sir William Thomson, in the November number of the Philosophical Magazine, has opened a new vista in the possibilities of the theory of an elastic ether. Since the general theory of elasticity gives three waves characterized by different directions of displacement for a single wave-plane, while the phenomena of optics show but two, the first point in accommodating any theory to observation, is to get rid (absolutely or sensibly) of the third wave. For this end, it has been common to make the ether incompressible, or, as it is sometimes expressed, to make the velocity of the third wave infinite. The velocity of the wave of compression becomes in fact infinite as the compressibility vanishes. Of course it has not escaped the notice of physicists that we may also get rid of the third wave by making its velocity zero, as may be done by giving certain values to the constants which express the elastic properties of the medium, but such values have appeared impossible, as involving an unstable state of the medium. The condition of incompressibility, absolute or approximate, has therefore appeared necessary. This question of instability has now, however, been subjected to a more searching examination, with the result that the instability does not really exist "provided we either suppose the medium to extend all through boundless space, or give it a fixed containing vessel as its boundary" This renders possible a very simple theory of light, which has been shown to give Fresnel's laws for the intensities of reflected and refracted light and for double refraction, so far as concerns the phenomena which can be directly observed. The displacement in an aeolotropic medium is in the same plane passing through the wave-normal as was supposed by Fresnel,