304 
MR. J. C. McCONNEL ON AN EXPERIMENTAL INVESTIGATION 
[When 8=0, R=w\, n being an integer ; as is obvious d 'priori. Now the change 
in the relative retardation necessary to produce a ring gives a fair indication of the 
change in the radius of the ring.*] So for the larger rings, while the displacement of 
the ring in the 45° directions, due to a small error in crossing, is almost nil, the 
displacement in the parallel and perpendicular directions is extremely large. The 
latter, however, is masked by the general obscurity of the brushes. From this it is 
clear that the best position for the plane of polarisation is at an inclination of 45° to 
the plane of incidence. 
It occurred to me, as an objection that might be of importance, that there would be 
some rotation of the plane of polarisation through refraction at the surface of the 
quartz and the surfaces of the lenses, and that putting the plane of polarisation in the 
45° position made this rotation as large as possible. But it is easy to see that if the 
polariser and analyser be turned into the other 45° position the rotation will be in the 
opposite direction. Thus in one case the rings will be slightly too large, in the other 
just as much too small, and by taking the mean of the two the error will be eliminated. 
I have, therefore, taken observations throughout in these two positions of the polariser, 
though no effect of the kind has made itself manifest. 
The first set of observations recorded below were made on a piece of quartz, which 
I will call Plate 1. It has four polished faces, and the section perpendicular to these 
faces has the figure of an equilateral triangle described on a square. The two sides of 
the square adjacent to the triangle were polished faces forming a parallel-sided plate. 
The two other faces were convenient as supplying a definite plane of reference passing 
through the normal to the two plate faces, though they were originally cut for quite a 
different purpose. Each face was about an inch square. The whole piece was 
perfectly clear, and the only flaw was a slight intrusion of contrary quartz into one 
corner. The plate faces were very nearly parallel planes, the error of planitude not 
exceeding 1', and the error of parallelism not exceeding 2'. Measurements of the 
rings were made in two different planes. The plane which is perpendicular to all four 
faces I will call plane A. The plane at right angles to plane A I will call plane B. 
The four polished faces were very nearly in the same zone. 
The observations in plane A were made in the following order. The quartz 
was fixed on the tripod and all four faces set parallel to the axis of rotation of the 
spectrometer in the usual way by means of reflections from the faces. Readings 
were also taken from which I could find the position of the normal to one of the 
plate faces relative to the axis of the telescope for any given readings of the 
telescope and table verniers. The tripod and quartz were then lifted off the 
table, the slit removed from the collimator, the ordinary eye-piece of the telescope 
replaced by the cork containing the low power eye-piece and analyser, the gas- 
flame placed behind the polariser, and the Nicols crossed. The tripod having been 
returned to its old position and the gas-flame exchanged for the sodium-flame every- 
* A.dded May 31, 1886. 
