306 
MR. J. C. Me CORNEL ON AN EXPERIMENTAL INVESTIGATION 
upon the following expedient. I fixed a small piece of silvered glass on to one 
side of the plate so as to be approximately in the same zone as the four faces 
and approximately perpendicular to the axis in air. I first fixed it in its place 
with soft wax, adjusting it with my eye at the telescope, and then secured it 
firmly by pouring in electrical cement behind it. After this was attached, it 
was only necessary to bring its normal into the plane of measurement to secure 
that the diametral chord was being measured. Plane B then may be defined as 
passing through this normal and being approximately perpendicular to plane A. 
The first ring was considerably broader and less sharply defined than the 
others ; yet in obtaining the diameters recorded in the tables below I have relied 
on a snaffle reading of each side even of the first ring. For durinff a long course 
of preliminary measurements I had found, that two readings of the first ring 
would seldom differ more than though I could not be confident that the true 
reading lay within If of either. It seemed in fact to be easier to bring the 
needle back to the same point in the band than to make sure of that point being 
the middle of the band. To obtain real accuracy I relied on varying the conditions 
as much as possible. Thus the four sets of measurements recorded in Table I. 
were made on four different days with different positions of the polariser, analyser, and 
plate of quartz. 
I also made a number of measurements of the larger rings in Plate 1, but these, 
I regret to say, have proved to be useless. The formulae, which are compact enough 
when the plate is cut truly perpendicular to the axis, become hopelessly complicated 
when the deviation of the axis has to be introduced. Since the deviation of the 
axis was small I tried approximations, carrying them as far as the squares of 
the deviations in the two directions. But the discrepancy between the results 
for plane A and for plane B seemed to indicate that the cubes also should have 
been included. 
I then determined to obtain a new plate in which the deviation of the axis should 
be negligibly small. I selected a good piece at Hilger’s and got him to cut it 
roughly at right angles to the axis. I then set it up on the spectrometer, determined 
the magnitude and direction of the error, and sent it back to Hilger to be recut. By 
repealing this process, getting it recut no less than four times, I at length attained my 
object. This plate I will call Plate 2. It was perfectly clear and free from maccling. 
The two polished faces were good planes about 30 mm. square, and inclined at an 
angle of about 1The two planes through the normal and parallel to the sides of 
the square I will call plane A and plane B. The error of the axis was about (V 
parallel to plane A and about the same parallel to plane B. This I found was small 
enough to be negligible throughout. The thickness was about 20 mm. only. 
The first ring had nearly the same diameter as in Plate 1, but it was produced 
by a retardation of three wave-lengths instead of four. Owing to the smaller thick¬ 
ness the bands were broader and further apart than before ; but I do not think this 
