300 
MR. J. C. McCONNEL ON AN EXPERIMENTAL INVESTIGATION 
It will be well to give at this point some idea of the relative magnitudes involved. 
The difference between the equatorial radii is about -oooth part and the distance 
between the sheets at the extremity of the axis 20 o 00 th part of the radius of the 
sphere. My determination of the distance between the sheets should not at any 
rate be in error by more than one part in 500 at 4° from the axis, one part in 1000 
at 12°, and one part in 2000 at a considerable distance from the axis. Of that, 
though by no means a complete investigation of the form of the wave-surface, these 
observations must be admitted to be a severe test. For if one wave-velocity were 
to be changed while the other remained the same, the change would be indicated 
even though it should only amount to ^“oVootF part of the whole velocity. Indeed 
near the axis 8 ~oooooo^ 1 part would be sensible. 
The theory of the formation of the rings requires some consideration. Take a 
wave-front of the plane polarised incident light. By the refraction at the first 
surface it is resolved into two wave-fronts which are polarised in a manner dependent 
on the constitution of the crystal, and which travel with different velocities. Each 
of these on refraction at the second surface gives rise to a wave-front polarised in a 
manner somewhat different from its own. Let the emergent wave-front due to the 
extraordinary wave be B and the other A. Then B and A are parallel. If B be in 
advance of A by an integral number of wave-lengths, A will be coincident with a 
wave-front exactly similar to B, and in the same phase. But we cannot say that, 
therefore, the combination of these two will be exactly similar to or even polarised 
in the same manner as the incident wave-front, for there has been loss of light by 
reflection at both surfaces, and this has affected A and B differently. 
The consideration of the refractive effects is greatly simplified in our case by the 
circumstance that the optic axis lies in the plane of incidence. Thus the principal 
axes of the ellipses of vibration of the waves in the quartz lie respectively in, and 
perpendicular to, the plane of incidence. 
We will assume at present that the action at the surface produces no retardation 
of phase. Let us first suppose that the incident light is plane polarised and the 
vibration lies in the plane of incidence. This linear vibration on entering the crystal 
gives rise to two elliptic vibrations; and we may, I think, safely assume that, if the 
relative retardation amount to an integral number of wave-lengths these two 
elliptic vibrations will give rise on emergence to a single linear vibration also in 
the plane of incidence. For we may consider the components of these two elliptic 
vibrations perpendicular to the plane of incidence as due to two equal and opposite 
linear vibrations of the incident light. These two linear vibrations would suffer 
equal reductions at the first refraction, and equal reductions at the second refraction, 
so after both refractions they would again neutralise each other. It is indeed 
probable that the difference in the angle of refraction of the two waves would 
affect the amount of light lost by reflection, but it would be to a negligibly small 
extent. Thus the emergent light will be sensibly plane polarised. 
