508 The Rev. S. Haughton on some new Laws 



is not peculiar to M. Cauchy's fonnulse, but that Mr. Green's 

 formulae (subject to a modification which I have suggested) ex- 

 plain the facts at least as well as M. Cauchy's. 



Since writing the paper just mentioned, I have had an oppor- 

 tunity of trying many experiments with an apparatus similar to 

 that used by M. Jamin, and fully described by him in pp. 271- 

 276 of the memoir already quoted. To avoid repetition, I refer 

 the reader to M. Jamin's description, and shall proceed at once 

 to a description of the new facts which I have been fortunate 

 enough to ascertain. 



It occurred to me, on reading M. Jamin's memoir and repeat- 

 ing some of his experiments, that it would be instructive to 

 ascertain the position of the major axis of the reflected elliptically- 

 polarized light, and to tabulate the ratio of the axes of the ellipse 

 for different conditions of incidence and azimuths of incident 

 plane-polarized light. I accordingly investigated formulae for 

 the position and ratio of axes in terms of the quantities measured 

 by direct experiment. The details of this investigation are given 

 in the next section, and the details of the experiments in the 

 following. 



The method followed by me is purely experimental, and inde- 

 pendent of any theory as to the nature of light ; by following 

 this method rigorously, and faithfully adhering to the results of 

 observation, I have succeeded in establishing the following facts 

 or laws, which, so far as I am aware, are new, and are certainly 

 interesting. 



Law I. That if plane-polarized light be incident on a trans- 

 parent reflecting body, and the angle of incidence be gradually 

 increased from 0° to 90°, the ratio of the axes of the reflected 

 elliptically-polarized light diminishes from infinity at 0° to a 

 minimum attained at the principal incidence, and increases again 

 to infinity at 90° incidence. 



Law II. That this minimum ratio of axes diminishes as the 

 azimuth of the incident plane-polarized light (or angle made by 

 its plane of polarization with the plane of incidence) approaches 

 a certain value, which can be ascertained, and which I shall call 

 the Circular limit. 



Law III. That w^hen the azimuth of the incident plane- 

 polarized light reaches this value or limit, the reflected hght is 

 circularly polarizedy and the ratio of axes is unity. 



Law IV. That for azimuths of incident plane-polarized light 

 greater than this limit, the minimum ratio of axes increases, be- 

 coming greater as the incident azimuth departs from the circular 

 limit. 



Law V. That when the azimuth of the incident light is less 

 than the circular limit j the axis major of the elliptically-polarized 



