138 The Aether as an Elastic Solid. 



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 dis- 

 covered, no general method had been developed for investi- 

 gating 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 Marie 

 Henri Navier* (&. 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. ISTavier 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 



* Mem. de 1'Acad. vii, p. 375. The memoir was presented in 1821, and 

 published in 1827. 



