INTO THE FORM OF THE WAVE-SURFACE OF QUARTZ. 
301 
Similarly, if the vibration of the incident light be perpendicular to the plane of 
incidence, the emergent light will be also plane polarised. Consequently, if the 
incident light be plane polarised in any plane, the emergent light will also be 
plane polarised, though not necessarily in a parallel plane. Thus, for angles of 
incidence giving a relative retardation of an integral number of wave-lengths, the 
refractive effects are equivalent to a small rotation of the plane of polarisation of 
the incident light. And the same is no doubt very approximately true for neigh- 
boui’ing angles of incidence. This small rotation can, as will appear later on, be 
eliminated by taking the mean of two sets of observations. 
Up to this point, and indeed throughout, we assume that there is no perceptible 
retardation of phase at the surface. Careful observations have been made on glass 
with regard to this point, and the only trace of retardation found was at very high 
angles of incidence, and even that was highly doubtful. There seems to be no reason 
to expect such an effect in crystalline media more than in isotropic, at any rate when 
the rotatory effects are small. In the present case too the rings are very close 
together at the high angles of incidence, so that only a small error would result; e.g., 
at an incidence of 75°, which is the highest incidence I have reached, the error 
in the diameter of a ring produced by a retardation of would be only 
As to any surface retardation connected with the rotatory power, we know from 
measurements of the rotation in plates of different thickness that it is, at any rate, 
very small when the light is incident normally, and passes along the axis. These 
measurements have been made with great accuracy, and no such effect has been even 
suspected. So we have a maximum limit for it, from which I deduce that it could 
only make itself felt slightly in the first ring, in the others not at all. 
II.— The Apparatus and Measurements. 
My previous observations were made with one of Groth’s polariscopes somewhat 
modified, as described in the paper, but since then I have found it a great improvement 
to use instead an ordinary spectrometer. With some slight additions the spectrometer 
became a most efficient instrument for measuring the rings. 
The general arrangement is indicated in fig. 1. The source of light is a Bunsen 
flame in the edge of which is placed a bead of sodium carbonate. The light is 
