303 
MR. J. C. McCOXNEL ON AN EXPERIMENTAL INVESTIGATION 
The above observations relate to values of </> ranging from 4° to 38°. For larger 
values I required a plate cut parallel to the axis. So I had two new faces cut on 
Plate 2, at right angles to the former ones and therefore nearly parallel to the axis, 
forming in fact a new plate, which I will call Plate 3. The two new faces were good 
planes and made an angle of about 2with one another, and not more than 9' with 
the axis. 
In the observations on Plate 3, it was necessary to set all four faces nearly parallel 
to the axis of rotation of the spectrometer table so as to secure that the axis should 
lie in the plane of measurement. The bands were shadowy and indistinct compared 
with those seen in Plate 2. This was only to be expected, for we really have two 
distinct sets of bands due to the two sodium lines. For a given value of <£ the 
retardation is very nearly the same for either line, but if it amounts to 300 wave-lengths 
for D : it will be about 300‘3 wave-lengths for D 3 . Thus the 300th band for wall 
divide the distance between the 300th and 301st bands for D 3 in the ratio of 3 to 7, now 
in the bands observed the retardation ranged from 253 wave-lengths to 312. So it was 
no wonder the bands were indistinct, the wonder was rather that they w r ere measurable 
at all. Fortunately however a large angular error in the measurement of a band only 
produced a small error in the retardation deduced. To take an extreme example, in 
the first band an error of 10' in the diameter only produced an error of y b o oo ^ P ar t 
in the retardation deduced therefrom. 1 took two sets of measurements of these bands 
with the analyser in one position and two sets with it in the rectangular position. 
The 2nd, 5th, 15tli, 30th, and 50th bands were measured in all four sets, the first only 
in the first set, and the 60th only in the two last. On either side of the first band I 
took three readings, the extreme difference between two being 14'. For the second I 
usually took two readings, the extreme difference in one case being 9', the next greatest 
being 5^'. For the fifth in four cases I took two readings, the extreme difference 
being 2^'. But, as will be seen below, these differences are quite eclipsed by those due 
to small differences of temperature on different days. 
Indeed if it was desired to get a very accurate measure of the change of a — b with 
temperature a most powerful method would be to take similar observations to these, 
using a plate of quartz about 70 mm. thick, so that the bands for the two D lines 
would nearly overlap, and thus narrow and sharply-defined bands would be presented 
in the field of view. 
The Measurement of the Thickness. 
The thickness of the plates was measured with a pair of callipers made by Elliott 
Bros. These were fitted with a vernier reading to thousandths of an inch, and the 
graduation was so good that it was easy to divide the vernier divisions into halves 
or even quarters. To avoid any error arising from the jaw faces of the callipers not 
being strictly plane, 1 clamped two pins on to the jaws of the callipers with their 
heads opposed to one another.. The direct contact of the two pins’ heads was observed 
