INTO THE FORM OF THE WAVE-SURFACE OF QUARTZ. 
313 
indicating the change in P x or P 3 corresponding to 1' in the diameter. So we see 
that P 3 comes out as a constant within the limits of experimental error except for the 
first ring in Plate 2. It was for this reason that I made a special set of measurements 
of the first ring in Plate 2 with a very bright light. The values obtained in three 
different positions of the analyser and plate were 13° 36§', 13° 34§', and 13° 37', mean 
13° 36', mean temperature 22-|°. This gives precisely the same value, 15‘220. 
Plate 1 also gives a decided drop in P 3 for the first ring which is barely within the 
limits of error above assigned. Now a change of x oV oth in the value of p employed 
in the calculation would alter P 3 by '0275 for the firstring in Plate 2, and by ’0344 
for the first ring in Plate 1. Thus a decrease of two parts in the thousand in the 
value of the rotation would bring the deviation of P 3 from the constant value well 
within the limits of error. The other rings are much less dependent on p ; thus the 
same change in p would in the second ring only increase P 3 by '0086. The most 
extended observations on the rotation are those of Soret and Sarasin (‘ Comptes 
Pendus,’ tome 95 (1882), pp. 635-638, &c.). By the method of Fizeau and Foucault 
they obtain for Di 2173°, for D 3 21'69°, mean 2171°; while by direct observation 
with sodium light they obtain 2173°. I have calculated from the mean of these 
2172, applying the temperature correction which is an addition of ‘00324 for each 
degree rise of temperature. The deduction of two parts in a thousand will bring 
the value down to 21‘6 8°. Another, and, in my opinion, better explanation of the 
peculiar result from the first ring will be given later on. 
Omitting the first ring my observations give P 3 a constant value of 15‘30;p‘01. 
We have to examine how this agrees with the values assigned by the theories. 
Cauchy gives 
P 2 =~^=15‘351 
where a and b are the wave-velocities at right angles to the axis. 
Lommel gives 
Kettler gives 
Sarrau gives 
P a =pA^^ =15 . I78; 
1 — rr la a l \ 
a + la—b 
2 2b « 2 A 
15‘486 ; 
p_?+?«_=»=15-306. 
la a 2 A 
The discrepancy between Cauchy’s value and the observed value is outside any 
probable errors of observation. It corresponds to a change of 4' in the diameter of 
the 7th and 11th rings. Such an error seems out of the question. Lommel and 
MDCCCLXXXVI. 2 S 
