320 
MR. J. C. McCONNEL ON AN EXPERIMENTAL INVESTIGATION 
factorily was that of Sarrau. His wave-surface may be obtained from Mac- 
Cullagh’s by making C vary as cos 3 </>. So we must modify equation (11) by intro¬ 
ducing the factor cos 4 (f> into the third term. Calculating from the modified formula 
we obtain the numbers given in the tenth line of the table. The departures from 
constancy can now be explained by errors of less than 1' in the ring diameters, yet 
the numbers still suggest a gradual rise of a — b with <j >. We shall return to this 
point in discussing the results from Plate 3. 
The Bands in Plate 3. 
As cf) increases the correction due to the rotatory term becomes rapidly smaller. 
Thus for the 150th ring in Plate 2 the change in the deduced value of a — b, which 
would be made by simply calculating from the Huyghenian construction, would be 
only one part in five thousand, and it may be readily shown that in Plate 3 it would 
never exceed one part in ten thousand. These figures refer to MacCullagh’s 
theory, and in Sarrau’s expressions the rotatory term is smaller still. By neglecting 
this term the formulae for Plate 3 are greatly simplified. 
We have now 
s' a =a 3 
s" 3 =a 3 cos 3 5 3 sin 3 </>. 
Since the plate is cut parallel to the axis we have for the extraordinary wave 
<£+ t "=90°; 
therefore 
• 0 // / 0 • 9 // 1 73 O //\ • o 
sir t =(r snr t +o^cos^i ) siir i 
and 
, // a/ 1 — a 2 sin 3 l 
cot l = —— -— - ; 
b sm l 
while 
, / a/1 — a 3 sin 3 l 
cot L — V 
a sm i 
But 
R = T sin t (cot l" — cot l) and H=n\ 
therefore 
*X=Tcos t '(£—i). 
or 
7 nob\ 
a — b , . . 
T cos l 
( 12 ) 
In calculating from the observations i was taken to be half the angular distance 
from any band on one side of the normal to the corresponding band on the other side. 
For convenience I will call this distance the diameter. Then l was deduced from i by 
