H. S. TJhlev — Deviation Produced, by Prisms. 419 



While the incident ray is changing its position in the manner 

 just indicated, the emergent ray will persist in a grazing posi- 

 tion with ever decreasing altitude. Finally, when the azimuth 

 of incidence attains the value sin -1 [n sin (/3— <?)] both rays will 

 again lie in the principal plane and the positive half of the left 

 boundary locus will have been generated. This process may 

 be continued for all possible negative altitudes until the entire 

 boundary surface shall have been traced out. However, it is 

 not necessary to consider negative altitudes in detail because a 

 principal section constitutes a plane of symmetry. The pre- 

 ceding results are made concrete by the data in Table V, for 

 which /3=20° and n=l-5. Throughout this table the values 

 of y 2 ' correspond to grazing incidence, y 1 = 90°. The left 

 boundary values can be read off by reversing the ray ; that is, 

 by considering y/ as —90° throughout and by changing the 

 signs of the angles in the second column. The values thus 

 obtained represent y, when grazing emergence is maintained. 

 Incidentally, the corresponding data for D and i^are given. 



Table V. 



±Vx 



7/ 



D 



E 



0° 0' 



0" 



33° 



52' 



10" 



36° 



7' 



50" 



36° 



7' 50" 



6 



22 



33 



43 



26 



36 



4 



12 



36 



16 34 



16 37 



53 



32 



43 



30 



35 



39 



43 



37 



16 30 



26 



43 



30 



56 



39 



34 



57 



51 



39 



3 21 



35 52 



50 



27 



53 



17 



33 



50 



53 



42 



6 43 



46 39 



12 



22 



29 



43 



32 



6 







47 



30 17 



57 



45 



13 



43 



50 



29 



45 



11 



56 



16 10 



65 59 



16 















26 



59 



43 



70 







72 38 



31 



-20 











24 



21 



26 



90 







74 35 



49 



-30 











* 23 



28 



46 



100 







76 1 







-40 











22 



49 



59 



110 







77 2 



43 



-50 











22 



23 



22 



120 







76 46 



27 



-60 











22 



7 



49 



130 







78 15 



37 



-70 











22 



2 



42 



140 







78 32 



21 



-80 











22 



7 



49 



150 







78 37 



49 



-90 











22 



23 



22 



160 







The properties of the lines which bound the domains char- 

 acterized by the conditions 



(3 = 2c, cos §/3 = cot c sin -J/3, and • tan (3 — 2 tan c 



will now be discussed. The most important portions of these 

 lines are shown in fig. 8. Unlike the preceding diagrams, this 

 figure is perfectly general, that is. it does not depend upon 

 special values of the prism angle or of the index of refraction. 



