JAMIX ON METALLIC REFLEXION. 91 



Developing cot 2 « and replacing (a) by its value, we obtain 



2cotStan2«;'= I ^cota (I7.) 



-J cot a 



This formula contains two unknown quantities, 8 and -y, which 



experiment does not make known ; and if we wished to employ 

 it to determine one of the unknowns, it would be necessary to 

 know or to eliminate the other. But we are able, by varying 

 the experiment a little, to bring this equation into a much sim- 

 pler form, and independent of the unknown quantity (8). 



We observe, in fact, that of the two angles (a) and (w'), one is 

 arbitrary. Up to the present time we have polarized the light 

 in an azimuth (90° — a), which we were at liberty to choose at 

 pleasure : we caused the doubly -refracting prism to be turned 

 so as to render the two images equal, and we measured the azi- 

 muth (w'). We may now do the contrary ; that is to say, first 

 place the doubly-refracting prism in an azimuth (w'), constant 

 for all the experiments, but any whatever ; turn the polarizing 

 prism of Nichol, and measure at each incidence the azimuth 

 of polarization (90° — a), for which the two images are equal. 

 Amongst all the values which I might give to (w') I choose 

 w' = 0, that is to say, I place the principal section of the doubly- 

 refracting prism in the plane of incidence. The formula becomes 

 then 



= T cot a 



J ^ I , ' 



-=j cot a 



or 



Y =tan(90°-fi). 



The difference of phase is then eliminated, and we arrive at this 

 remarkably simple result : — 



The ratio of the square roots of the intensities of reflected rays 

 polarized in the plane of incidence and the plane perpendicular, 

 is equal to the tangent of the azimuth of the polarization of the 

 incident ray, for which the two images are equal. 



This method does not yield in accuracy to any of those which 

 we have described already ; it does not employ, in fact, any in- 

 termediate body ; requires only a single reflexion ; allows of the 

 use of a simple light, which removes the liabiUty of error arising 

 from the unequal refrangibility of the rays constituting white 



