228 H. S. Uhler — Deviation of Hays hy Prisms. 



it is obvious that D cannot be a function of i x . Hence, the 

 cosine formula again leads to false conclusions. 



In order to test the accuracy of the algebraic work which led 

 to equation (3) as well as to get a concrete idea of the varia- 

 tions of D and D\ with i x , the numbers in the following- 

 table were worked out for the special case where a'— 60° and 

 n=l m 65. The data in the second column were obtained from 

 equation (2). The numbers in the third and fourth columns 

 were found by substituting the corresponding values of D' 

 from the second column in equation (1) and in " cos |-D — 

 cos iD\ cos i" respectively. All the angles in the third 

 column were also worked out from formula (3). The abso- 

 lute agreement of all the values of the true D obtained by 

 these two independent modes of calculation verifies equation 

 (3). The last row of the table exhibits the superior limits of 

 the angles for minimum deviation. The first and fifth col- 

 umns taken together show the obliquity of the incident ray. 



ii 



Do 



Do 



"Do" 



|3'i=i(D' + a') 



0° 



51° 10' 37" 



A ; 51° 10' 37", 



51° 10' 37" 



55° 35' 18".5 



± 5° 



51° 34' 57" 



51° 22' 19" 



52° 28' 40" 



55° 47' 28"'5 



+ 10° 



52° 49' 54" 



51° 58' 7" 



56° 14' 6" 



56° 24' 57" 



± 15° 



55° 1' 46" 



53° 0' 17" 



62° 6' 37" 



57° 30' 53" 



± 20° 



58° 22' 54" 



54° 33' 21" 



69° 45' 36". 



59° 11' 27" 



± 25° 



63° 15' 56" 



56° 45' 45" 



79° 0' 19" 



61° 37' 58" 



± 30° 



70° 24' 58" 



59° 54' 29" 



89° 55' 13" 



65° 12' 29" 



± 35° 



81° 35' 0" 



64° 42' 35" 



103° 20' 34" 



70° 47' 30" 



± 40° 



105° 23' 7" 



75° 4' 45" 



124° 40' 17" 



82° 41' 34" 



40° 44' 5" 



120° 0' 0" 



82° 1' 28" 



135° 28' 21" 



90° 0' 0" 



The conclusion to be drawn from the preceding argument 

 is that either the formula "cos -|D=cos -J-D' cos i" must be 

 replaced by sin %D= sin -J-D' cos i 1 or that the cosine formula 

 may be retained, but, when the latter alternative is followed, 

 the various writers should state explicitly, and lay special 

 Stress upon, the fact that the D and the D' of the cosine rela- 

 tion are the supplements of the corresponding deviations as 

 involved in the other equations of the subject. We think 

 that, for sake of consistency and to avoid confusion of symbols, 

 the formula sin %D= sin -JD' cos i t should be introduced in 

 the text-books in place of the cosine equation. 



Sloane Physical Laboratory, Yale University, 

 New Haven, Conn. 



