316 
MR. J. C. Me CORNEL ON AN EXPERIMENTAL INVESTIGATION 
Again the axis lay 18' above the plane of measurement, so a chord of the circular 
ring was measured instead of the full diameter. On this score the following corrections 
had to be added 
2' 
On the whole I had to add 
H' 
i' 
r 
3/ 
4 
2 
ir 
1 2 
1' 
2 
0' O' 
3/ _il' 
4 L 2 
Secondly, for the measurements in plane B. 
Now a=18' only, so the corrections on this score are negligible. In this case the 
plate was tilted till the apparent position of the axis in air lay in the plane of 
measurement. So i was no longer the radius of the rings in air and i consequently 
had to be altered. To allow for this I had to add to the successive diameters 
u 1/ 1/ 1' A' 1/ 
2 3 3 3 3 3 2 
The corresponding corrections for Plate 2 would be infinitesimal. 
The Large Rings. 
Since MacCullagh’s theory will be found to be in tolerable agreement with the 
measurements obtained for the larger values of (f>, it is convenient to take it as a basis 
and discuss later what modifications would make the agreement more perfect. 
MacCullagh starts by assuming the equations of motion 
d 3— A 1 
dt 2 dz^ dJ , x 
>.(5) 
d^n dSj d^ v ' 
dt 2 * dz 2 ^ dz 3 - 
where rj are the displacements parallel to x, y at any time t, and the axis of 2 is the 
wave normal. 
Also 
A—cr 
B=« 3 cos 3 Ir sin 3 cf) 
C is a constant. 
From these equations we get the wave-surface 
(s *_ A)(s3 _B)= 4 AV.(7) 
which has three sheets ; the third sheet, however, corresponds to an index of refraction 
ol about 40,000 ; so for physical purposes we need not consider it. 
