of the light being stopped, when the formulae give a reflexion 

 very nearly total. 



The value of S'— S, or the difference of phase, increases 

 from 0° to 1 80°. "When a plane-polarized ray is twice reflected 

 from a metal, it will still be plane-polarized if the sum of the 

 values of ^—8 for the two angles of incidence be equal 

 to 180°. 



It appears from the formulae that when the character- 

 istic X is very small, the value of S' will continue very small 

 up to the neighbourhood of the polarizing angle. It will 

 pass through 90°, when mm— 1 ; after which the change will 

 be very rapid, and the value of 3' will soon rise to nearly 180°. 

 This is exactly the phenomenon which Mr. Airy observed 

 in the diamond. 



Another set of phenomena to which the author has ap- 

 plied his formulae are those of the coloured rings formed be- 

 tween a glass lens and a metallic reflector ; and he has thus 

 been enabled to account for the singular appearances de- 

 scribed by M. Arago in the Memoires (TArcueil, tom. 3, 

 particularly the succession of changes which are observed 

 when common light is incident, the intrusion of a new ring, 

 &c. But there is one curious appearance which he does not 

 find described by any former author. It is this. Through 

 the last twenty or thirty degrees of incidence the first dark 

 ring, surrounding the central spot which is comparatively 

 bright, remains constantly of the same magnitude ; although 

 the other rings, like Newton's rings formed between two ^ass 

 lenses, dilate greatly with the obliquity of incidence, l^is 

 appearance was observed at the same time by Professor 

 Lloyd. The explanation is easy. It depends simply on this 

 circumstance, (which is evident from the table,) that the angle 

 180°— 8', at these oblique incidences, is nearly proportional 

 to cos L 



As to the index of refraction in metals, the author con- 



lectures that it is equal to . 



** ^ cos X 



