INTO THE FORM OF THE WAVE-SURFACE OF QUARTZ. 
303 
crossing for all the observations given below was performed with a gas-flame placed 
edgeways behind the polariser. This gave ample accuracy. 
[Added May 31, 1886.— Probably the lenses had some slight doubly refracting 
power, so that each turned the plane of polarisation through a small angle depending 
on its azimuth. In the present case however this effect was a matter of indifference, 
as I was measuring the angles of incidence, for which the emergent light from the 
quartz was polarised similarly to the incident light. In the larger rings, it is true, 
the quartz produced a considerable lateral displacement of the light, so it no longer 
passed centrically through the two object glasses. But in the larger rings the effect 
of any small error of crossing might, as will be seen shortly, be completely neglected.] 
The plane of polarisation was inclined at 45° to the plane of incidence. If we look 
at the appearance presented in the polariscope when the two Nicols are crossed, we 
see that all the rings are circular, and though the inner rings are tolerably uniform, 
the outer rings are crossed by dark brushes in directions parallel and perpendicular to 
the plane of polarisation. These dark brushes have the effect of making the rings 
very ill-defined, so that on that account alone it would be impossible to get a 
satisfactory measure of the 15th ring if the plane of polarisation were parallel to the 
plane of incidence. If now we rotate the analyser slightly we see the rings dilate, 
but not uniformly. The dilatation is much more rapid in the direction of the brushes. 
The rings cease to be circular and become four-cornered. This phenomenon was 
observed and explained by Sir George Airy (Camb. Phil. Trans., vol. 4, p. 85). 
It is an easy deduction from his formula for the intensity at any point of the field 
that the value of II for the darkest part of the ring when the Nicols are not 
accurately crossed is given by 
2 R.7T 
sm —— 
2 sin S 
sin 27 
in the direction of the brushes, but by 
. 2 \inr 
sin - 
A. 
2 sin 8 sin 2y 
in directions at 45° to the brushes. Where It is the relative retardation, 8 is the 
small angular error of crossing, and tan y is the ratio of the axes of the ellipse of 
vibration of either wave, tan y being less than unity. The following figures will give 
some idea of the values of y. For sodium light when— 
<f>= 1° Y = 43° 53' 
<f>= 5° y= 23° 0' 
(f> = 10° y = 7° 21' 
<f>= 20° y 1° 55' 
< i i being the angle between the wave normal and the optic axis. 
