772 
DR. OLIVER LODGE ON ABERRATION PROBLEMS. 
General Arithmetic of a Shift. 
43. It may be convenient for easy future reference to write down the meaning of 
any observed reversible shift under given circumstances. 
An odd number of reflexions must be used if the light is to be sent many times 
round, hence triangles and pentagons are excluded. An even number of reflexions 
has the advantage that it makes the paths of the two half-beams identical and not 
merely parallel {cf fig. 8 ) ; but it does not seem readily feasible to get the light round 
more than once with an even number of reflexions. The square or hexagon are there¬ 
fore the natural figures for the path of light. Take a square, whose side is a, as the 
mean path of the light. Then its perpendicular distance from the centre of rotation 
is ^ a ; and it is the perpendicular distance which is important, for, since the velocity 
of light at any point P has to be resolved perpendicular to the radius vector, we get 
precisely the same tangential component everywhere as exists at the point M. 
M 
Let the disks revolve with angular velocity w, and let the shift of the middle band 
be X band-widths of a particular wave-length X. Then, if the light goes n times round 
each way, with velocity v, 
x\ \ak()) 
8na V 
where h is the fraction of the velocity of matter which is imparted to the ether 
between the disks, the quantity to be determined by observation of x. 
Thus 
k _ \v _ 4 X 10^ 
X n(oa~ 
The limit of speed of a given material (see § 34) is given by something like 
hence the limiting value of hjx, observable by this method, is 
4 X 20y 
na 
\/ (2T/ • 
