IN CRYSTALLIZED MEDIA. 341 



particles is e ; in passing from the plane of .vz - e and in passing 

 from the plane of yx-e", our equation still retains the form 



A" +\ah + ac + bc- {X' + Y' + Z')\ A-abc + aX~ + h Y' + cZ' 



+ 2XYZ=0, 



which is evidently analogous both in its form and mode of derivation 

 from the elimination of P, Q, E to that for determining the three 

 principal axes of a solid: and may therefore be proved in the same 

 manner to give three values of A corresponding to directions at right 

 angles to each other. 



From the form of the equation it is obvious that of the three 

 directions two only correspond to a vibration. 



14. For these two vibrations we shall manifestly have equations 

 of motion analogous to those in other cases. 



The plane in which they lie is called the front of the wave, and 

 the values of A are the velocities of transmission in a direction per- 

 pendicular to the front. 



Let the axes of x,, y,, s,, be the three directions; a;, being that of 

 no vibration, and let them make angles 0,0, v/,,; e^^^v/z^ ; e,<p,x},, witli 

 the axes of x, y, z, respectively. 



Then we must have 



rf^/3. 



= _22(l-§^)3in^Mfi, 

 Vr* r* / 2 ' 



df 



df " \f' f I 



d'y, ^^(1 3Sz',\ ^^^^kSx, 



2 



extending to a,, /3,, 7,, &c. the same meaning as to similar quantities 

 along other axes. 



xx2 



