320 MR. J. C. Me CONNEL ON THE FORM OF THE WAVE-SURFACE OF QUARTZ. 
band to band becomes smaller as we go further from the axis, and I took as an 
approximation that the darkest point would divide the sensibly dark region in the 
same ratio as the band itself divides the distance between the two neighbouring bands. 
Here was the mistake. For the sensibly dark region is that part of the band where 
the intensity of the light falls below a certain fixed value, and the intensity of the 
light obviously varies approximately as the square of the small angular distance from 
the point of total extinction. It might then be expected that this darkest point 
would lie practically at the middle of the sensibly dark region. This opinion was 
confirmed by a closer examination, with the aid of Sir George Airy’s formula, for the 
intensity of any point of the field. 
By the removal of those corrections the discrepancies I obtained between theory 
and observation would be reduced one-half, and the remainder may be easily accounted 
for by the imperfection of the polished faces. I knew that the rings would not be 
much altered by curvature of the faces; for when the incidence is nearly normal, a 
slight deviation of the path through the quartz does not materially increase the length 
of the path, so I contented myself with noticing in the measurements with the callipers 
that the faces appeared tolerably parallel and plane. Lately, however, I examined 
the crystal again, and optical tests showed that the curvature of the faces was quite 
sufficient to explain the discrepancy of some 5' between theory and observation. 
