ON OPTICAL THEORIES. 179 
Lord Rayleigh further assumes the medium to be absolutely incom- 
pressible, so that ¢ is zero and A is infinitely large, p remaining finite ; 
this, of course, leads to the fourth equation— 
du , dv , dw _ 
ae ae Ont ; ‘ ; (18) 
And from these equations the equation to the surface of wave slowness is 
shown to be i : : 
l m n 
yz + 72 ; + 7 = 0 : : (19) 
a? b2 c 
This, however, is not Fresnel’s surface, and experiments of a very 
high! degree of accuracy have shown that the wave surface in a 
erystal is very approximately indeed Fresnel’s surface, and of course 
this is fatal. But, as we shall see in the next section, according to all the 
theories yet proposed based on the mutual reaction between matter and 
ether, the first and most important effect of the matter is to alter the 
apparent density of the ether in the way here supposed. The mutual 
d*u 
reaction, it can be shown, will introduce terms of the form hae into the 
C 
equations, and & may conceivably depend on the direction. 
§ 14. Equations of motion practically the same as Lord Rayleigh’s 
are given by Boussinesq, Lommel, Ketteler, and Voigt, and the question 
arises, Are these equations incompatible with Fresnel’s wave surface ? 
Lord Rayleigh has, of course, proved that they are if the equation 
du dw dw —0 
expresses an absolutely necessary condition ; but it is not difficult to show 
that if, instead of the above equation, we put 
Didi Naw. oh dat 9 
adx  b? dy Pr le é : ; Spi: 
then the wave surface will be Fresnel’s, the direction of vibration will be 
normal to the ray, and will be in the plane containing the ray, the wave 
normal, and an axis of the section of the ellipsoid a?2? + b2y? + c2z2 = 1 
by the wave front, and while the velocity of propagation will be inversely 
proportional to the length of this axis. 
Assuming equations of the same form as Lord Rayleigh’s (17), we have 
to determine the pressural wave given by p= poei'@*™+™-V9 the equation 
2 2 2 
—p) = BM, | N (5 = + pm (=-1) nee (3-1) \, 
~where UW = AOget(lz+ my +nz-V), etc,, 
and this, on Lord Rayleigh’s assumption of JA + mu + nv = 0, reduces to 
AL | yum , wm 
Po = tB6,V? { aa se Te + oth . . . (21) 
’ See Stokes, Proc. Roy. Soc. vol. xx. p. 443; Abria, Anv. de Chi mie; Glazebrook, 
Phil. Trans. Pt. I. 1879; Kohlrausch, Wied. Ann. t. vi. p. 86; t. vii. p. 427. 
N 2 
