176 REPORT—1885. 
Thus the wave surface is Fresnel’s, The direction of vibration, the ray 
and the wave normal are shown to be in the same plane, but the direction 
of vibration is at right angles to the ray instead of to the wave normal. 
The assumed conditions f + f; = 0, etc., form a serious objection to the 
——— 
theory as it stands, but on this point it is “capable of modification. The — 
vibrations, of course, are not strictly transversal within the crystal, but 
I am not aware of any experiments which prove that they must be so. 
Of course, if the medium be absolutely incompressible, the displacements 
must be in the wave front, and the theory fails; but the condition of 
stability and the evanescence of the longitudinal wave require merely that 
the incompressibility should be very great compared with the rigidity, 
without being absolutely infinite. 
§ 9. M. Sarrau has considered the peculiar phenomena presented by 
quartz, and shows how on his theory the terms assumed by MacCullagh 
will arise. 
For the crystalline symmetry of such a body, the equations are shown 
to take the form— 
re dv 
a ils oe dy dz 
: ss 
aH g (ve! ai ne 88) ee 
aw v2 
gd Sl ae 2) ae (ngtmis)| 
and it follows that two elliptically polarised waves can traverse the 
medium in any given direction, 
The velocities of these waves are given by 
w=g—5(9-f) sin? 9 + 5/4 @— Aisin 0 
TS (g2 cos? 0+ f, sin? 0) x (g2cos?6—g, sin? 9) ts (14) 
jf, and g, are two constants which are probably very small, and, in that case, 
the squares of the principal velocities at right angles to the axis are ia 
and g, while the squares of the velocities parallel to the axis are given by 
+ mg 
r 
If p, represent the ratio of the axes of the ellipse in the ordinary wave, 
p. that in the extraordinary, then 
Jz cos? 8 — g, sin? 6 (15) 
gz Cos? 0 + 7; sin? 6 f 
7 
P1P2 = 
The major axis of the extraordinary ellipse is perpendicular to the prin- 
cipal plane, that of the ordinary ellipse is in the principal plane, while the 
two waves are polarised in opposite senses. 
$10. DeSt. Venant! criticises the theory in the following points, p being 
the only periodic variable, the equations, he argues, should betreated as if the 
" St. Venant, ‘Sur les diverses maniéres de présenter la théorie des ondes lumi- 
neuses,’ Ann. de Chim. (4), t. xxv. p. 335, 
