122 
PHYSICS: C. BARUS 
It is next in order to consider the possibly observable conditions of the 
(apparent) ether drag. The velocity within the refracting medium of index 
ju is usually written (or follows from the theory^ of relativity) in the form 
c/m . (4) 
where v is the velocity of the medium in the direction, or contrary to the direc- 
tion of the velocity of light c. It remains to determine the average speed of 
the beam along the chord C of figure 1. From the figure 
C = Rd^Yidb = 2 ixh (5) 
whence 
b = 2fjLR V 1 - iuV4 (6) 
In figure 1 let co be the angular velocity of the cyhnder G and dx an element 
of the chord C at a distance p from the axis A. Let the minimum distance 
of this chord from A be h and d its angle with p. 
Then 
dx = p^ CO dt/h, 
if dx is described in the time dt. Hence 
dx/dl = (h^ + x^)/h (7) 
To find the mean speed v along C, we may multiply dx/dt by dx, integrate 
between 0 and C/2 and divide the result by C/2. Thus 
= CO (A + C/m) (8) 
Reducing this equation by (1), (2), (5), eventually 
1 - mV6 
or the mean speed along C may be expressed in terms of co, ii, while v is 
naturally proportional to R and co 
The ratio of the speed in equation 9 (seeing that it is respectively + and — 
for the two interfering rays) to the velocity of light is thus 2v/c. Since these 
rays traverse a path 2C in the rotating cylinder in opposite directions the 
path difference resulting will be 
A P' = (2 VC) 2C = ACv/c = l^A^ 
SO that the path difference for a given ix and co increases with the square of the 
radius, R, of the cylinder or disc. 
But the equation (4) introduces another factor (1 — 1/^^) so that finally 
the path difference is 
