1913-14.] Path of Ray of Light in Rotating Solid. 
69 
VIII. — The Path of a Ray of Light in a Rotating Homogeneous 
and Isotropic Solid. By E. M. Anderson, M.A., B.Sc. Com- 
municated by The General Secretary. 
(MS. received November 3, 1913. Read January 19, 1914.) 
The path of a ray of light in irrotationally moving media was first 
investigated mathematically by Fresnel, who showed that to account for 
the observed phenomena it is necessary to suppose that, the aether being 
fixed, the medium imparts - — — of the amount of its own motion, resolved 
in the line of the refracted ray, to the advancing disturbance. This 
conclusion is also a necessary consequence of the modern Theory of 
Relativity, which, while holding that, with reference to axes with regard 
to which the medium is stationary at any point, the speed of light depends 
only on the refractive index, for any other system leads to the above result. 
Using this formula, it is possible to calculate the path of a ray of light 
in a rotating homogeneous and isotropic solid, when the velocity produced 
by rotation is small compared to that of light itself. We shall first 
consider the case of a body rotating about an axis fixed in space, and at 
right angles to the line joining two points A and B, through which we 
will suppose the path to pass. If r be the distance of the disturbance 
at any moment from this axis, and cp the angle made by the ray with 
the direction of r produced ; if further co be the velocity of rotation, and 
c the speed of light ; then the total velocity of the ray is 
c wr sin 4> (/jl 2 - 1) 
