186 The Rev. 8. Haucuton on the Equilibrium and 
this curve will evidently cut the oval, whose semiaxes are —= 7 if N be intermediate 
in value between L and M3; supposing, therefore, that m is the mean of the three 
quantities, L, M, N, the ellipse in the plane (., z) will cut the branch of the oval, 
whose semiaxes are we and in the other coordinate planes it will lie, in one 
M 
case, completely outside the oval; and, in the other case, completely inside the 
oval. Hence there are always at least four singular points on the surface of 
wave-slowness ; whether there be more singular points will depend on the rela- 
tive magnitude of a, B, c, compared with L, m, N; if we assume (as seems probable 
from its being true in homogeneous solids) that a, B, c are greater than L, M, N, 
4 ] ] 1 ers. Ae 
then the ovals whose semiaxes are aR Ve We will lie completely inside both 
miley 1 
the ellipses and the other ovals, whose semiaxes are equal to — ES 
Vi VM VN 
surface of wave-slowness will therefore consist of three sheets ; one, whose semiaxes 
1 1 lies 4 sonal 
are Va lialet WG isolated, and lying inside the other two sheets ; and the other 
two sheets, having four points in common, like Fresnel’s wave-surface, and piercing 
1 1 
the axis of x in the points Weak ade the axis of y in = 
1 ] 
Vi) VM 
I shall now proceed to discuss some particular cases of the motion, and to 
5 Way and axis of z in 
Vi 
explain the phenomena which arise from the existence of nodes in the surface of 
wave-slowness. 
Let a plane wave move through the body, perpendicular to z; the auxiliary 
ellipsoid becomes, in this case, 
M2’ + ry? + cz’? = 1 
because /= 0, m=0, n= 1; hence the three possible vibrations of the mole- 
cules will be parallel to the axes of symmetry, and two of them will lie in the 
wave-plane at right angles to each other, and the other will be perpendicular to 
the wave-plane; and the three velocities of propagation will be proportional to 
