which, when evaluated, becomes (a2 + ¿2 + c2)2 (u — pe2) {a2 (M — pe3) (N— pe3) - + b2 (N − pe3) (L -- pe2) + c2 (L — pe2) (M — pe2)} = 0. 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 the same equation as we should obtain for the determination of the axes of the section of the ellipsoid by the plane Lx2 + My2 + Nz2 = 1, ax+by+cz = 0; agreeably to equation (10). CAMBRIDGE: PRINTED BY C. J. CLAY, M.A., AT THE UNIVERSITY PRESS |