IN CRYSTALLIZED MEDIA. 



123 



velocities, and in direction the directions of the three corresponding dis- 

 turbances by which a wave can propagate itself in our medium without 

 subdivision. This surface, which may be properly styled the ellipsoid of 

 elasticity, must not be confounded with the one whose section by a plane 

 parallel to the wave's front gives the reciprocals of the wave-velocities, 

 and the corresponding directions of polarization. The two surfaces have 

 only this section in common, and a very simple application of our theory 

 would shew that no force perpendicular to the wave's front is rejected, 

 as in the ordinary one, but that the force in question is absolutely null. 



Let us conceive a system composed of an immense number of par- 

 ticles mutually acting on each other, and moreover subjected to the 

 influence of extraneous pressures. Then if x, y, z are the co-ordinates of 

 any particle of this system in its primitive state, (that of equilibrium 

 under pressure for example,) the co-ordinates of the same particle at the 

 end of the time t will become x', y ', z, where x' y z are functions of x y z 

 and t. If now we consider an element of this medium, of which the 

 primitive form is that of a rectangular parallelopiped, whose sides are 

 dx, dy, dz, this element in its new state will assume the form of an 

 oblique-angled parallelopiped, the lengths of the three edges being 

 (dx), (dy), (dz), these edges being composed of the same particles which 

 formed the three edges dx, dy, dz in the primitive state of the element. 

 Then will 



w -{(&"+ (2)' +(£)"}<*-■*' 



rl 



suppose. 



Again, let 



o = cos < 



(dz') 



dx dx' dy dy' dz' dz 

 dy dz dy dz dy dz 



^mW^Wi 



dx'\* id 11 



T.) + US ' 



m 



Q2 



