Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/158

 the aether is indefinitely great compared with that of the transverse waves; for it is found by experiment with actual substances that the ratio of the velocity of propagation of longitudinal waves to that of transverse waves increases. rapidly as the medium becomes softer and more plastic.

In attempting to set forth a parallel between light and the vibrations of an elastic substance, the investigator is compelled more than once to make a choice between alternatives. He may, for instance, suppose that the vibrations of the aether are executed either parallel to the plane of polarization of the light. or at right angles to it; and he may suppose that the different refractive powers of different media are due either to differences in the inertia of the aether within the media, or to differences in its power of resisting distortion; or to both these causes combined There are, moreover, several distinct methods for avoiding the difficulties caused by the presence of longitudinal vibrations; and as, alas we shall see, a further source of diversity is to be found in that liability to error from which no man is free. It is therefore not surprising that the list of elastic-solid theories is a long one.

At the time when the transversality of light was discovered, no general method had been developed for investigating mathematically the properties of elastic bodies; but under the stimulus of Fresnel's discoveries, some of the best intellects of the age were attracted to the subject. The volume of Memoirs of the Academy which contains Fresnel's theory of crystal-optics contains also a memoir by Claud Louis Mario Henri Navier (b. 1785, d. 1836), at that time Professor of Mechanics in Paris, in which the correct equations of vibratory motion for a particular type of elastic solid were for the first time given. Navier supposed the medium to be ultimately constituted of an immense number of particles, which act on each other with forces directed along the lines joining them, and depending on their distances apart; and showed that if e denote.