IN CRYSTALLIZED MEDIA. 295 



tions 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 abso- 

 lutely nullt. 



Let us conceive a system composed of an immense number 

 of particles mutually acting on each other, and moreover sub- 

 jected to the influence of extraneous pressures. Then if x, y, z 

 are the co-ordinates of any particle of this system in its primi- 

 tive state, (that of equilibrium under pressure for example), the 

 co-ordinates of the same particle at the end of the time t will 

 become a?', #', z, where a?', y', z are functions of a?, 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 



suppose. 



dx'\* fdy'\* 

 ) +{-f- 



j \dzj 



Again, let 



dx_ 

 dy'\ dy dz dy dz dy dz 



M 



V /}/dx'^ ( dy'\^ (d^\(fdx\^ (dy' 

 V \(dy) + (dj) + (cTy) \\(TZ) + (Tz 



* [It will be seen that this remark is not strictly correct, as the surface must 

 necessarily have another common plane section.] 



-|- [Referring to the values of u, v, w given in p. 301, we see that, since the 

 direction of vibration is supposed to be in the front of the wave, we have 



But the force perpendicular to the wave's front is a -r^-+ b r-^ + w-^ } which is 

 equal to e a (aw +bv+ cw), and is therefore null.] 



