k;//(7« exposed to Polarized Light. 185 



upon the common surface of the two media at the polarizing 

 angle of that surface, when the angle of refraction at the first 

 surface is equal to the tangent, or cotangent of the polarizing 

 angle, according as the refractive power of the film is less or 

 greater than that of the body upon which it rests. 

 Hence we have 



and 

 and 



. ., 1 1 



sin v= — or — r, 

 m m 



tan i' = — Tj or cot t = —r, 



and m' = 



when a ray incident at 90° is polarized at the second surface, 

 or falls upon it at the polarizing angle. 



These formulfe enable us to discover between what limits 

 of refractive power the second disappearance of the rings can 

 take place, and consequently what substances we should em- 

 ploy in order to observe it. In this manner we obtain the 

 Ibllowing results for the mean rays of the spectrum: — 



Tr I c t Values of - , or m. 



Values ot»j. V^jC—l 



3-000 1-061 



2-500 1-090 



2-000 1'154- 



1-900 1-176 



1-800 1-202 



1-700 1-236 - 



1-600 1-281 



1-554 1-307 



1-508 1-336 



1-500 1-341 



1-400 1-428 



1-336 1-508 



1-307 1-554 



Tlie limits, therefore, between which the s^coMf/ disappearance 

 of the rings can take place are 1'554, the index iov quartz a.n<X 

 Jlint glass, and 1-307, the index for ice. But though the 

 range is very limited, it nevertheless includes a considerable 

 variety of solid and fluid bodies. I have omitted the indices 

 of Tabasheer, and the fluids produced by the compression of 

 gaseous bodies, because, though their refractive powers are 

 beneath 1307, they cannot be used in the present inquiry. 



