Rays in Crystals "with one a?id t-JooAxes of Double Refraction. 3 



ray was at first the least possible, for example, to the left, 

 and then the least to the right, so that the angle described 

 by the telescope was always exactly the double of the angle 

 of deviation. 



The black lines of which I measured the deviation were 

 those marked B, C, D, E, F, G, H by Fraunhofer. I did not 

 put the prism into the position of least deviation for each 

 individual ray, but put it into this position for one. I measured 

 the double deviation for this one and the others, leaving the 

 prism immoveable, which renders the observation more easy 

 and more accurate. 



The indices of refraction are easily calculated by this me- 

 thod of operating. The angle which the incident ray makes 

 with the anterior face of the prism being =90° — jr, the angle 

 of the refracted ray with the same face = 90°— 2;, the deviar 

 tion = A, the angle of the prism = s, and the index of re- 

 fraction = ??, we have 



sin X =■ n .smz 

 sin {A + s — x) = n . sin (e — z). 



If the prism is at the minimum of deviation for a certain 

 ray, we shall have for it x = ^ ( A + ?) and z z=\e. Hence 



sin i A + e 



n = -. — J . 



sin \ £ 



For another ray whose deviation in the same situation of the 

 prism is = A — 8, and whose index of refraction is = «', we 

 shall have 



sin ^ ( A + ?) = "' sin z' 

 sin (A (A + 0-8) = "' sin (e-s')- 

 and making 2' = ^ e + ^, we obtain 



sin ^ (A -f- £ — 8) .cos ^ 8 = ?i' sin \ £ . cos ^. 

 cos |( A + £ — 8) , sin I 8 = ?^' cos | £ . sin \. 

 And consequently, 



tang ^ = tang \ 8 . tang \ £ . cot ^ ( A + £ — 8). 



Having calculated by this formula the value of the angle ^, 

 we obtain 



, ^ sini(A + £) 

 sin(i£ + ?) • 



Section 1. — Refraction in Crystals wit/i one Optical Axis. 



\. Rock Crystal. — Two prisms of the crystal were cut in sucli 

 a manner that the edge of the prism was parallel to the axis 

 of crystallization, and consequently the two rays lollowcd the 

 law of simple reliaction. The prism was put into such a po- 



V>2 



