376 
MR. R, T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 
M O N is the principal plane of the first prism nearly coincident with the plane 
through the optic axes A 0 C. 
FT O L the principal plane of the second prism nearly coincident with the plane 
B O A, so that 0 N is nearly coincident with 0 A. 
MOL the principal planes of the two prisms in the second crystal here treated as 
coincident, inclined at about 60° to B 0 C, and cutting it in a line nearly coincident 
with 0 C. 
Hence 0 M is not far removed from O C. O L is nearly in the plane A 0 B and 
inclined at about 60° to O A or O N. 
The strong fines give approximately the form of the sections of Fresnel’s surface 
by these planes, the dotted lines the results of experiment. 
In the case of the arc N' L the results of theory and experiment agreed closely. 
For the arcs M N, M N / the experiments covered an arc of about 16° from M 
and M'. 
For N L the experiments covered an arc extending from L to about 10° on the side 
nearest to 1ST of the point where the two arcs intersect. 
For M L the experiments extended over an arc of about 70° measured from M. 
Section XI .—Effect of Dispersion considered. 
The theory of dispersion appears to me to afford a more probable explanation of 
these small variations from Fresnel’s construction. 
Fresnel himself remarked (‘ Second Supplement au premier Memoire sur la 
double refraction,’ (Euvres Completes de Fresnel, tom. ii.) that in the case of the 
vibrations which constitute light the radius of the sphere of action of the molecular 
forces brought into play by the vibration is not necessarily very small compared with 
the wave length. 
And, consequently, it is incorrect to suppose that the propagation of each of the 
disturbances of which a vibration is composed is uninfluenced by the disturbances 
which precede and follow it, and that the velocity of propagation is independent of the 
manner in which they proceed and follow it. 
This supposition is the basis of Fresnel’s work on double refraction. 
Let us consider the effect of dispersion in a doubly refracting medium. 
In an isotropic medium the relation between V, the velocity of wave propagation, 
and X, the wave length, is generally allowed to be 
1_ , b , e , o 
V -a+ Y + Y + ’ &C -’ 
a, b, c, &c., being constant, the values of the terms continually decreasing, so that 
except in highly dispersive media we may put p = a ff -~ with sufficient exactness. 
V AY 
