While seeking for a good elementary illustration of Hamilton's general methods in optics, the author was led to consider, from a somewhat novel point of view, the path of light in a medium whose refractive index is a function of the distance from a plane. This is, at least approximately, the case of the peculiar atmospheric arrangements to which are due the phenomena of Mirage, so long as the curvature of the earth can be neglected.

A considerable improvement in the usual theoretical treatment of this subject was introduced by Professor J. Thomson in 1872, and afterwards developed by Professor Everett in Phil. Mag., 1873.

The main feature of this improvement is the study of the curvature of the ray in terms of the rate of change of refractive index in the medium.