Roijal Microscopical Socldij. 



247 



It will be seen not only that the requisite angle of reflexion 

 from the silver plate has been secured, but that the pure silver 

 thrown down on the highly-polished glass presents a brilliant and 

 even surface, which is effectually preserved from oxidation by the 

 glass on which it is deposited. 



The angles and dimensions of such a prism are easily deter- 

 mined if the index of refraction of the glass employed in its 

 construction be given. 



This will be readily perceived on inspection of the Figure No. 1, 

 in which the dotted line represents a ray of parallel Hght, incident 

 on the lower surface of a prism, to which the line A B is a normal. 

 Let a be the circularly-polarizing angle of the metal employed, n, 

 as usual, the index of refraction, and x the angle sought ; then, as 

 the angle of incidence will be equal to the complement of the angle 



Fig. 1. 



of the prism i^-x\, and the angle of refraction will be equal to 



the circularly-polarizing angle of the metal minus the angle of the 

 prism {a — x), we at once obtain the following relation : — 



COS. X = n sin. (a — x). 



From this equation by an easy transformation, which it is un- 

 necessary to give, we obtain 



tan. X — tan. a sec. a. 



n 



As in the case which we have been considering the metal employed 

 is silver, and the index of the glass used by Mr. Browning in 



