162 The Aether as an Elastic Solid. 



of the aether are supposed to vanish, and the vibrations of the 

 aether are supposed to be executed parallel to the plane of 

 polarization of the light ; in the other theory, the initial stresses 

 are not supposed to vanish, and the aether- vibrations are at 

 right angles to the plane of polarization. The two investigations 

 are generally known as Green's First and Second Theories of 

 crystal-optics. 



The foundations of both theories are, however, the same. 

 Green first of all determined the potential energy of a strained 

 crystalline solid ; this in the most general case involves 27 

 constants, or 21 if there is no initial stress.* If, however, as is 

 here assumed, the medium possesses three planes of symmetry 

 at right angles to each other, the number of constants reduces 

 to. 12, or to 9 if there is no initial stress; if e denote the dis- 

 placement, the potential energy per unit volume may be written 



fo \2 ("be \ 2 fr\f \ i \ (ffo \2 /f)p \2 /a/, N 



+ $} * () 1 + ** ft) + (I) + (I 



fty*. 



7 ty tz 9 



sf3e y 3g, 

 * 4/1 ;? + s- 



2</ \dz ty 



* 



dx 



The usual variational equation 



= - [[f 



* For there are 21 terms in a homogeneous function of the second degree in six 

 variables. 



