^70 PROFESSOR POWELL ON THE ELLIPTIC POLARIZATION OF LIGHT 



radii, for the second reflexion to restore plane polarization, at all azimuths of the 

 plane of second reflexion to the first. 



Though the subject of metallic reflexion is still in a condition of great obscurity, as 

 to the mechanical causes to which its peculiar character is referrible, yet the applica- 

 tion of the undulatory theory at least enables us to trace and connect some of its 

 laws, and in the attempt to pursue such an application to some further relations, the 

 nature of my researches may be briefly explained as follows : — 



1. So far as the objects of my former inquiry were concerned, it sufficed to take 

 the formula there employed for the polarized rings in the simplified form resulting 

 from supposing a common coefficient to the two component vibrations ; the plane of 

 original polarization inclined 45° to that of reflexion, and 90° to that of analyzation. 

 With reference however to some of the facts connected with observations at different 

 incidences and azimuths of the polarizer, as well as on other grounds, it seemed 

 desirable to generalize that formula by removing the above-mentioned restrictions ; 

 and I have accordingly here given an expression for the rings in elliptic light of all 

 degrees with general coefficients, and for all positions of the polarizer and analyzer ; 

 which, though without difficulty deducible, has not, as far as I am aware, been stated 

 by any writer. 



2. With respect to the general character of the rings, the slightest observation 

 shows that the distinction between the dark and bright centred systems in plane 

 polarized light, though modified, is not lost, in the lower degrees of ellipticity ; it dis- 

 appears only when the light becomes perfectly circular ; when the distinction is only 

 seen in the changed direction of dislocation. 



When the plane of analyzation is inclined 45° between the rectangular directions, 

 and generally in intermediate positions, the whole appearance is, as it were, distorted ; 

 the dark arcs nearest the centre are situated towards one end of the quadrants, 

 instead of being in the middle ; and in the succeeding rings, though less strongly 

 marked, there is an apparent increase of intensity towards the same end of the qua- 

 drant, owing to a general shade of darkness in the ground towards that side*. Of 

 this appearance, though it must have been constantly seen, as far as I know, no ex- 

 planation has been published. In circular polarization it does not occur. In plane 

 polarized rings the analogous case is that of the well-known system of eight dislocated 

 sectors ; which in ellipticity of lower degrees is combined with, and passes into, that 

 just described. All this is expressed by my formula. 



3. The restoration of elliptic to plane polarized light by means of Fresnel's rhomb, 

 and the determination of the ellipticity by the azimuth of the rhomb, though an 

 obvious process, yet has not, as far as I know, been pursued for any series of metals. 

 Such a set of observations I have accordingly made at the incidence for the maximum 

 ellipticity, for a considerable range of metals, some metallic ores, and other reflecting 

 substances. Also in a few principal cases I have made similar observations at other 

 incidences from 80° up to 30°, at which the ellipticity disappears. 



* See Plate II. fig. 3. 



