328 
MR. R. T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 
Thus the experimental results are represented by a curve, which near the major 
axis agrees with Fresnel’s section, but which, as we go from 6° to 16° away from 
that axis, differs from that section, and lies outside the section. 
This result, viz. : that on going away from the maximum radius vector the curve 
given by experiment should lie outside that given by theory, is exactly that to which 
we have been led by the work for the second prism. 
The cutting of the crystal would not allow of observations being taken near the 
minor axis of the ellipse, in the case of the first prism. 
Of course, it has here been assumed that the sections of the surface of wave 
slowness, by the principal planes, are curves of the same kind; or rather the results of 
experiment lead to that as a fact. 
Lord Rayleigh’s theory needs no further discussion here, for his curve being the 
inverse of an ellipse, always lies outside the ellipse with the same axes, and therefore 
cannot agree with experiment. 
Section IX.— Possibility of an Error in the Position of the Crystallographic Axes 
discussed.—No Section of the Surface of Wave Slowness in Fresnel’s Theory can 
agree with the experimental Results. 
But the possibility remains that there is an error in the determination of the posi¬ 
tion of the faces of the prisms, especially in the second case, with respect to the 
crystallographic axes. 
The probability of any error is small, as the observations were repeated on several 
different occasions with nearly coincident results. 
To make certain, however, let us solve the inverse problem. Having given the two 
values, jji.i, of the radii vectores of the surface of wave slowness drawn in the same 
direction l m n in the crystal to find l, m, n. 
We have as the equation to find v on Fresnel’s theory 
L + -A_ = o 
v~—cr v* — b" v*—c* 
Whence 
1 - v 2 {l 2 {b 2 +c 2 ) +m 3 (c 3 +« 3 ) + n 2 (a 2 +b 2 )} + ZW+mW+nW= 0 
. ’. if i\ v. 2 are the roots of this equation, that is, the velocities for the same wave front 
0 o 707 0 o ■ oqOi 0070 
VyVcf = r fr<r+m^crcr+rrcrtr 
vgNv£=l~{b~+C) + m~ (c 3 + a 2 ) + u 3 (a 3 + b 2 ) 
but n 2 = 1 — m 3 — l' 2 
Whence we get 
W(c 2 -a 2 ) + a%df 2 -lr) = vfvp-Plr 
l 3 (c 3 — a 3 ) + w d(c 2 — Ir) = v{ 2 fi-1’ 3 3 —cr— h 2 
