Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/196

 the ambiguous sign being determined according as the circular polarization as right-handed or left-handed.

Substituting in the above differential equations, we have

or

Since 1/l denotes the velocity of propagation, it is evident that the reciprocals of the velocities of propagation of a right-handed and left-handed beam differ by the quantity

from which it is easily shown that the angle through which the plane of polarization of a plane-polarized beam rotates in unit length of path is

If we neglect the variation of c, with the period of the light, this expression satisfies Biot's law that the angle of rotation in unit length of path is proportional to the inverse square of the wave-length.

MacCullagh's investigation can be scarcely called a theory, for it amounts only to a reduction of the phenomena to empirical, though mathematical, laws; but it was on this foundation that later workers built the theory which is now accepted.