The differential equations of Fresnel's polarisation-vector, with an extension to the case of active media

1. In many problems of physical optics it becomes necessary to know the differential equations that the polarisation-vector of a stream of light has to satisfy, and the boundary conditions that subsist at the interface of media possessing different optical properties. These are usually obtained by formulating some theory respecting the character of the ether in the media and the nature of the vibrations in a train of waves, but there is an obvious advantage in directly basing our investigations, if possible, on the known experimental laws of the propagation of a luminous disturbance.