269 



and accoi'dingly the resulting value of tan -y will be real, and 



therefore the disappearance of the rings possible, only when 



cos(6 + 9') and cos(0' + 6") are of opposite signs ; i. e. when 



the angles of incidence on the two surfaces are, in the one 



case greater, and in the other less, than the polarizing angle. 



The media at the two sides of the plate, therefore, must 



have different refractive powers. 



Again, the phases of the two portions of the reflected 



beam, and which are polarized respectively in the plane of 



incidence and in the perpendicular plane, are given by the 



formulas, 



zi'(l — M^) sin a 



tana' 



tan a" = 



w(1 + m'2) + M'(l + M'')cosa' 

 w'{\ — w"^) sin a 



w{l 4- w'^) -{-w'{[-^iv-) COS a 



The phases, a' and a", are consequently in general different, 

 and therefore the resulting light will be, in general, eUijiti- 

 cally polarized. The author entered into some developments 

 connected with this part of the subject, which does not ap- 

 pear to have been noticed by Sir D. Brewster in the course 

 of his experimental inquiries ; and he concluded by stating 

 the important bearings which it may possibly have upon the 

 phenomena of elliptical polarization by metals. 



Professor Lloyd having, in the preceding communication, 

 thrown out the idea that the elliptical polarization of metals 

 might possibly be identified with that which is produced 

 by a thin film on the surface of a reflecting body. Pro- 

 fessor Mac Cullagh took occasion to observe that an analo- 

 gous, but far more general, hypothesis had occurred to 

 himself some years ago, among the various conjectures by 

 which he had sought to account for the remarkable dif- 

 ference between the action of metals and that of trans- 

 parent media in reflecting light. In his theory of crystalline 

 reflexion he had found it allowable to suppose that the 

 change in the elasticity of the ether, in passing out of 



