Bootru—On Fresnel’s Wave Surface. 383 
Similarly, the equation may be written 
RK? + mnngns = 0, 
where £& stands for 
Ce +t ee? +e (ery +2?) -7 (+e), 
B/C-e+y/@—b'+ a/ &=8, 
with corresponding values for 2, %, %- In short, Q is the quadric 
factor of Ce and R& of a, 
dz dat 
Once more the equation may be written 
and 7, for 
S?+ pip2psyu = 0, 
where S stands for 
OP +0)? +0 (C +0) +O (G+ 0 )e — 206%, 
and p, for 
£0. /B—C+ybS C-— 0 +20/ a’ — b’, 
with corresponding values for p2, ps, ps. If we omit the terms in 
W of the fourth degree in 2, y, s, then the remainder is nearly the 
value of S with the sign changed. In short, if we had four vari- 
ables, x, y, , win Wso as to make it homogeneous in these variables, 
then S is a factor of a 
dw 
It is considered important by some writers on Physical Optics* 
to determine the equation of the cone whose vertex is the centre of 
the ellipsoid of elasticity, and whose base is one of the circles in 
the case 
jee + Uppal = 0. 
Its equation is, by the foregoing principles, written down thus: 
[ee + Py + ese +b (e+ y’ +2) | P(e -e) 
Gy PEG Pe / Pe) ee aa). 
on simplification, this becomes 
C(P-C)?+0(ae-e)y+e(a—-v)# 
—a#3(¢ £a\/ Gao) (a? = 6°) (8 — c*) ¢)= 
1 See Bassett, Physical Optics, Art. 116, p. 123. 
