INTO THE FORM OF THE WAVE-SURFACE OF QUARTZ. 
309 
with a magnifying glass, and when the quartz was interposed each pin’s head was 
brought up into contact with its image in the surface of the quartz. Care was of 
course taken to set the plate of quartz at right angles to the length of the callipers. 
This gave the thickness of Plate 1, 1'0885 inch or 27'65 mm., of Plate 2, '7865 inch 
or 19'977 mm. 
These are probably correct within ^UcToth inch. If I had measured Plate 3 in the 
same way I might have got an error of ToVdtl 1 part in the ratio of its thickness to 
that of Plate 2. Now it was the ratio that I was anxious to get accurately, for, as 
will appear below, I was more interested to see whether a — b would come out from my 
calculation a constant, than to find out what might be the value of that constant. I 
had arranged that Plate 3 should be of nearly the same thickness as Plate 2. If 
then I could get an accurate value of the difference between them, it would supply 
an accurate value of the ratio. This difference was measured with a spherometer 
reading to '001 mm. The plate was laid on three steel points firmly fixed into a 
table. The three legs of the spherometer rested on a mahogany block clamped to 
the table. Each leg had been pressed gently into the wood to make a small pit, and 
I found that the spherometer could be lifted off and replaced several times, and yet 
give the same reading. I found the difference of thickness to be '275 mm. within 
'002 mm. Thus I obtained the ratio correct to Toooodh part. 
III. —Calculation and Discussion of Results. 
It is convenient to discuss the observations on small values of </> separately from 
the others. Near the optic axis the additional separation of the sheets of the wave- 
surface, due to the rotatory property, has to be treated as of magnitude comparable 
with the separation given by Huyghens’ construction, both being very small. While at 
a little distance from the axis the Huyghenian separation is greatly increased, and the 
additional portion sinks to the magnitude of a small correction. Thus for each case a 
special formula of approximation is appropriate. The boundary may be drawn at 
(f)= 12°, though either formula will do for some distance on either side of this 
boundary. 
The Small Rings, 
In my former paper I calculated the radii of the various small rings OH Mao 
Cullagh’s theory and compared their values with observation. In order to compare 
the observations with other theories the results will now be presented in a different 
form, and it is convenient to introduce a quantity D to denote the number of wave¬ 
lengths by which one wave lags behind the other in air after the light has traversed 
normally a plate of quartz 1 mm. thick, the normal to whose faces makes an angle c/j 
with the optic axis. Let R denote the retardation actually observed when the light 
