H. S. Dhler — Deviation Produced oy Prisms. 403 



Attention will now be directed to the interesting problem of 

 the variation of the deviation at grazing incidence, that is, 

 along the right boundary locus. Formula (38) may be written 



sin \D = % sin P(R t - R 2 ) -y/cos^, 



where 



R t = ^ cos rj l + cot c cot ${3 

 and 



R 2 = y' cos rj 1 — cot c tan %/3. 

 It follows that 



^- = (R i RJ- 1 tan i/> tan Vl (cos 77, - R x R 2 ). 

 Clr) 1 



In general, therefore, stationary values of J9 may correspond to 



Vi = ° 

 and 



cos i7j — lt l R 2 = 0, 



the latter being equivalent to 



cos rj 1 = -J cot c tan /3, 

 which is relation (28). It is easy to show that 

 j^ =i(E> ^J~ 3 csc 2 ^ tan \B\ 4 sin Vl tan Vl sin 2 |Z> + 



JR X R 2 © [© sec 2 \D tan 2 ^ + 2 sin Vl tan ^ + 2 R x R n sec 2 r/Jsin 2 0} 

 where ® = cos 77 x — R x i? 2 , therefore 



= * [1 + (2 tan c — tan /3) cot 2 c cot (3] — 1 ( tan \D = 



drj, 



??i = 



[sin c ^ sin fi esc (2c - 0) - 1] tan \D, 

 and 



/d*D\ 



( tf~V = _ 2 sm2 i^ tan i*> esc 2 £ sec 2 Vl tan 2 ^. 



Assuming £ acute, (^-rj is positive or negative, according 



as tan #> 2 tanc or tan /3 < 2 tanc, hence the deviation at 

 grazing incidence in a principal plane is a maximum when 

 tan $ < 2 tan c, and a minimum when tan ft > 2 tanc. Again, 



when cos 77, = -|cot c tan /3 and rj x ^ 0, (4— r ) is essentially 



\«*7, /e = 



