324 MR. J. C. Me CORNEL ON AN EXPERIMENTAL INVESTIGATION 
Thus the value •0037043 falls within each pair of limits. The last line of each list 
gives the results from the first ring obtained with the use of Soret and Sarasin’s 
value of the rotation. Thus the sudden drop of P 3 for the first ring, which was the 
most striking eccentricity of the observations on the small rings, is explained at once 
by the more general form of Sarrau’s theory, without the necessity of assuming an 
error in the rotational coefficient. 
Of course we have had to assign an arbitrary value to Jc. But the form of the 
correction, viz., h cot 2 <£, was fixed by the theory, and was exactly the form that was 
required, giving, as it does, the correction for </>=4° 24' some thirty times as great as 
that for <£= 53°. 
We have now compared Sarrau’s theory and the MacCullaoh group of theories 
with observation for all our values of </>. With regard to the remaining three, 
Cauchy has given, so far as I know, no general expression for the wave-surface, while 
Lommel and Kettler are so widely at variance with the Huyghenian construction 
that I have not thought it worth while to make a detailed comparison. 
I find, however, that the values of a — b deduced on Kettler’s theory from my 
observations would differ by about 3 parts in 1000 for </>=60° and </>= 85°, whereas 
according to the Huyghenian construction they agreed within 1 part in 6000. 
We conclude, then, that out of the nine theories we have examined the only one 
which agrees with observation is that of Sarrau, and that to make the agreement as 
perfect as possible we must choose his constants, so that 
8 TT 9 -a 2 g. 2 (g l — f x ) = •0 0 0 0 3 3 (a 2 — 6 2 ) 2 X 2 
or 
<7r—= 1'07 g,. 
IY.—Values of the Constants employed. 
I have used Rudberg’s values for a and b, viz., 
a= -647593 
b— ‘643799. 
Mascart gives 
a= -647573 
6= *6 43756 
I have taken \= -00058920 mm. This is the mean of Angstrom’s values for Di 
and 1> 3 . 
Fizeau has given coefficients of the expansion of quartz with temperature along the 
axis and at right angles to it. He also measured the change of a and b with 
temperature. These are so small as to be negligible in the present case except for the 
