The subject of Crystalline Reflexion has been treated by Mr MacCullagh and M. Neumann; but both these writers commence their investigations by assuming that certain equations hold true at the common surface of two media. The object of the present Memoir is to obtain such equations from mechanical considerations. To attain this, the following hypotheses are made:—

1. That common light consists of vibrations, whose plane of motion is continually changing without law, or is indeterminate.

2. That light, polarized in a given plane, consists of vibrations perpendicular to that plane.