224 H. S. Uhler — Deviation of Rays hy Prisms. 



This formula may be obtained in two different ways. Either 

 the classic relation " cos^D^cos-JD'cos i" may be first 

 demonstrated in the customary manner and then D aud D' 

 may be replaced respectively by tt— J) and it — D', or else an 

 independent proof may be given. The latter plan seems to be 

 preferable because it is more direct, and also since it does not 

 involve a knowledge of a formula of spherical trigonometry, 

 whereas the usual proof does. In other words, the direct 

 method is even more elementary than the indirect. Con- 

 sequently an independent proof of equation (1) will now be 

 presented. 



Fig. 1. 



Figure 1 may serve to define the positive directions of the 

 various angles as well as the symbols for the angles themselves. 

 The use or omission of accents on small letters shall serve to 

 differentiate respectively symbols which refer to angles in the 

 principal section from those which denote angles lying outside 

 of this plane. The path of the ray is AB'EF. The projection 

 of the ray on the principal section is A'B'C'F'. Further, let 

 D symbolize the deviation of the ray from its initial direction 

 AB V to its final direction EF. 



Move the directed lines AB', A'B', EF and O'F', of figure 1, 

 parallel to themselves until they assume respectively the posi- 



