H. S. Uhler — Deviation Produced by Prisms. 391 



Z N x ON a = /3 — angle of prism, 

 ZNjOP^aj = " " incidence, 1st face, 

 ZNJOS =a/= " " refraction, " " 

 /N 2 OS =a 3 = " " incidence, 2d " 

 Z N 2 OQ =a 2 '= " " emergence, " " 

 Z QOP =1)— deviation of oblique ray, 

 ZqOp = E — " " projected ray, 



ZpOP = v i 

 Z sOS =17/, V = altitudes, 

 ZqOQ = r, 9 ' 9 ) 



Z xt^ S =7)/ ' U azimuths. 



ZN.Oq =7 2 'J 

 Angles will be counted positive when generated by a right- 

 handed rotation about the axis OH. Also, the only angles in 

 the above list which may exceed \ir and still correspond to 

 physical reality are ft, D and E. [For further details of fig. 

 1, see p. 407.] 



/3 = y/-y 2 0) 



#= ri -y/-/3 < (2) 



Since the prism is surrounded by the same medium 



V* = Vi: 



This fact was noted by Bravais as earl} 7 as 1845. He says :* 

 "... ce qui nous donne cette premiere loi de la refraction 

 oblique dans les prismes 'Le rayon emergent et le rayon 

 immergent sont egalement inclines sur le plan de la section 

 principale.' ,: Consequently the triangle QPH is isosceles, and' 

 hence 



sin-JZ) = sin -%E cos rj x (3) 



This relation was used by Bravais for the case of minimum 

 deviation. He gave 



" sin ^A = sin \D cos H" 



on page 83, loc. cit. Since, in general, cos rj 1 <C 1 relation (3) 

 shows that 



D<E. 



In spite of this obvious inequality, several modern authors 

 write, with Heath, 



cos \D = cos ^Ecos rj^ 



* A. Bravais : Journal de l'Ec. Polytechn. 18, 30 e Cahier, p. 79, 1845. 



