The Aether as an Elastic Solid. 1 43 



On the basis of these equations, Cauchy worked out a 

 theory of light, of which an instalment relating to crystal-optics 

 was presented to the Academy in 1830.* Its characteristic 

 features will now be sketched. 



By substitution in the equations last given, it is found that 

 when the wave-front of the vibration is parallel to the plane 

 of yz, the velocity of propagation must be (h + G)% if the vibration 

 takes place parallel to the axis of y, and (g+ G)$ if it takes place 

 parallel to the axis of z. Similarly when the wave-front is 

 parallel to the plane of zx, the velocity must be (h + H)% if the 

 vibration is parallel to the axis of x, and (/+ H)^ if it is parallel 

 fo the axis of z\ and when the wave-front is parallel to the 

 plane of xy, the velocity must be (g + /)* if the vibration is parallel 

 to the axis of x, and (/ + /)* if it is parallel to the axis of y. 



Now it is known from experiment that the velocity of a 

 ray polarized parallel to one of the planes in question is the 

 same, whether its direction of propagation is along one or the 

 other of the axes in that plane: so, if we assume that the 

 vibrations which constitute light are executed parallel to the 

 plane of polarization, we must have 



/+#=/+/, ff + I = g+G, k + H=h+G; 

 or, G = H=L 



This is the assumption made in the memoir of 1830 : the theory 

 based on it is generally known as Cauchy' s First Theory ;( the 

 equilibrium pressures G, H, /, being all equal, are taken to be zero. 



Tf, on the other hand, we make the alternative assumption 

 that the vibrations of the aether are executed at right angles to 

 the plane of polarization, we must have 



* Mem. de 1'Acad., x, p. 293. 



In the previous year (Mem. de 1'Acad., ix, p. 114) Cauchy had stated that the 

 equations of elasticity lead in the case of uniaxal crystals to a wave-surface of 

 which two sheets are a sphere and spheroid as in Huygens' theory. 



f The equations and results of Cauchy's First Theory of crystal-optics were 

 independently obtained shortly afterwards hy Franz Ernst Neumann (b. 1798, 

 d. 1895) : cf. Ann. d. Phys. xxv (1832), p. 418, reprinted as No. 76 of Ostwald's 

 Klassiker der exakten Wissenschaften, with notes by A. Wangerin. 



