INTO THE FORM OF THE WAYE-SURFACE OF QUARTZ. 
321 
the relation sin i=a sin i, and a — b determined from the formula (12). But now the 
question occurs, what value must be given to n. In Plate 2 n was easily determined 
for the first ring, and therefore for all the rest, by a rough calculation from the known 
rotatory power. But in Plate 3 n is so large that tolerably accurate values of the 
constants are required to distinguish between one integer and the next. Indeed, 
without the observations on Plate 2, I should have been unable to decide between 
five or six different integers. However with the aid of these observations the 
difficulty disappears. Using the value a—b — ’0037935 in equation (12) I obtained 
for the second band, reckoning from the normal, after correcting for temperature, 
310*91, so I concluded that the true value was 311. 
Fig. 3. 
Perhaps the best evidence on this point is supplied by the diagram, fig. 3. In this 
diagram the ordinates represent a — b — ‘003780, while the abscissae are the values of 
(f>. The small circles are got from Sarrau’s theory, the crosses from MacCullagh’s. 
lor <£> 50° where the two theories agree there are two lines of small circles. The 
upper line is obtained on the supposition that w = 311 for the second band, the lower 
line on the supposition that n= 310. 
The diameters obtained in four sets of measurements are given in Table IY. The 
first line gives the number of the band reckoned from the normal. The seventh the 
resulting values of a — b, omitting the decimal point and two ciphers, and the eighth 
the change in a—b corresponding to 10' in the diameter, omitting the decimal point 
MDCCCLXXX VI. 2 T 
