the Index of Refraction. 107 



vations now described, it is necessary to determine the incli- 

 nation of the horizon glass to the optical axis of the telescope. 

 This may be done by directing the telescope to a distant lamp, 

 and then moving the index slowly until an observer at the 

 lamp, with his eye near the flame, sees its image reflected from 

 the index-glass. The angle indicated must then be noted ; 

 and to avoid as much as possible the effect of parallax, the 

 index-glass should be covered, with the exception of a narrow 

 portion over its centre ; and the observer at the lamp should 

 look through a hole twice as far from the flame as the centre 

 of the index-glass is from the axis of the telescope. The angle 

 indicated is double the complement of the inclination of the 

 horizon-glass to the line of coUimation.* 



The index of refraction is then calculated by means of the 

 following formulae : — 



Let & = the angle of the prism ; 



3 = the deviation of the refracted rays ; 



a = the inclination of the horizon-glass to the line of 

 collimation ; 



<p — the first angle of incidence ; 



9'= the first angle of refraction ; 



•v|/= the angle of emergence ; 



>(/'= the second angle of refraction ; and, 



_ !^!Li the index of refraction. 

 Then the following relations are easily obtained : 



Hence ^ + ■+ = ^ + 5, and ^ — •v|/ = '3' + 3 — 2a— ^: 

 From the law of refraction sin ^ = ^a sin (p' and sin -^ = 



,, J j.r o sin ^' — sin -vt' sin ^ — sin \l 



fjj sin -vp' ; and, therefore, - , , . „ = . -^ , . T . 



^ ^ ' ' sin f' + sin r^ sin ^ + sin >// 



Hence tan J (^' — -v^') = tan \{<p — '^) cot ^ (^ + •4') tan ^ 

 (<p' + +'). 



* This may be rendered definite by a pair of cross wires at the focus of the 

 eye-piece, which the images should be made to intersect both in finding the devia- 

 tion of the refracted ray, and the inclination of the horizon-glass to the line of 

 collimation. The latter is a constant angle ; and will not require to be re-de- 

 t€rmined at every new experiment. 



