336 APPENDIX. 



which, when evaluated, becomes 



(a 2 + V + c 2 ) 2 (//, - pe*) {a 2 (M - pe 2 ) (N- pe*) 



^_ ^ (jr _ 



It thus appears that the velocities of propagation of the two 

 vibrations, whose directions are in front of the wave, are given 

 by the equation 



a 2 T? c* 



the same equation as we should obtain for the determination of 

 the axes of the section of the ellipsoid 



by the plane 



ax + by + cz = ; 



agreeably to equation (10). 



CAMBRIDGE: PRINTED BY c. j. CLAY, M.A., AT THE UNIVERSITY PRESS. 



