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



[The possible bearing of the remarkably straight course of cer- 

 tain plane sections of the y 1 rj 1 D surface on the problem of 

 diminishing the curvature of spectral lines has not been con- 

 sidered because it is not relevant to this paper.] 



Table IV. 



Vi 



D 



Vx 



D 



0° 0' 



0" 



23° 



59' 



28" 



70° 



43' 



52" 



21° 



45' 1" 



10 30 







23 



59 



58 



72 



34 



35 



21 



27 13 



18 10 



19 



24 







38 



76 



40 







20 



55 1 



21 16 



38 



24 







48 



76 



53 







20 



54 57 



22 50 



40 



24 







50 



76 



55 







20 



54 59 



26 51 



18 



24 







39 



76 



56 



16 



20 



55 



30 51 



57 



23 



59 



54 



77 











20 



55 7 



41 6 



50 



23 



53 



29 



77 



30 



5 



20 



58 19 



50 35 



3 



23 



37 



3 



78 



15 



37 



21 



24 43 



60 30 







22 



59 



43 



78 



25 



27 



22 



3 59 



It may not be superfluous to follow the successive positions 

 of the incident and emergent rays around the boundary loci in 

 the actual case of a prism, that is, without reference to a sphere 

 of projection such as is shown in fig. 1. The point of incidence 

 will be considered fixed, so that the incident ray will generate 

 a surface which consists of portions of a cone and of a plane, 

 the incidence face of the prism. Commencing with grazing 

 incidence in a principal plane, the emergent ray will also 

 lie in the principal section and will have the azimuth 7/ = 

 sin -1 [n sin(c— /3)]. This azimuth will be positive, zero, or 

 negative, according as the angle of the prism is less than, or equal 

 to, or greater than, the critical angle respectively. Keeping the 

 incident ray in a grazing position and increasing the altitude of 

 incidence, the emergent ray will have an azimuth w T hich de- 

 creases algebraically, the altitudes of the incident and emergent 

 rays being always equal. [See page 391.] At length, when 

 the incidence altitude equals cos -1 [cot c tan -J/3] the emergent 

 ray will begin to graze the second face of the prism. This is 

 the position of simultaneous grazing incidence and emergence. 

 Also, all of the positive half of the right boundary locus has 

 been passed over. To continue farther, the incident ray must 

 now leave the first face of the prism. As the azimuth of inci- 

 dence decreases, the corresponding altitude must also decrease 

 consistently w T ith the equation 



V, 



COS" 



cot c sin /3 

 cos /3 4- sin y 1 



