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The peculiar character impressed on light, originally polarized in a plane inclined to that of incidence and reflected from a metallic surface, discovered by Sir D. Brewster, and named by him elliptic polarization, has been since shown to coincide with what, from a different analogy, is termed elliptic polarization in the undulatory theory ; and which is also exhibited by an interposed plate of mica, or by total internal reflexion, as in Fresnel’s rhomb. The most distinct experimental test of the existence of this property and a measure of its amount, is the well-knowndislocation of the polarized rings, seen by a plate of calc-spar and a tourmaline, in light of this kind. And this, as in other similar cases, is represented theoretically by a formula for the intensity at any part of the plate,in the case of the rhomb , forcircular polarization, as in Mr. Airy’s tract on the undula-tory theory (Art. 160.) ; and forelliptic , as in the same author’s paper on quartz. A general formula for the rings in light of all degrees of ellipticity,not restricted by the peculiar conditions of therhomb , has not been hitherto published : but I am in­debted to Mr. Airy for the communication of such a formula, which will be given in the sequel, as leading to some remarkable applications.

V. Observations on certain cases of elliptic polarization of light by reflexion