166 F. K Wright — Transmission of Light through 



9 



c . . . . 



— , r sm r (— « ai sin </> cos r — a 23 cos y + a a , sin y sin r) 



Wherein 



„ . 47r" 2ir / x' sin r + z' cos »• 



C = — A =5 COS -==- t 



T 9 T \ q 



similarly from (14) 



9\i „ 



-pr-^- = — (J cos y cos r 



9*v . 



w = C sm y 



-71-5- = (J cos v sin r 



St- 



Substituting the values from these last two sets of equations 

 in (10), we obtain the two equations 



— cos i//= 2 (— # l2 sin if/ cos r— a 33 cos »^ + a 23 sin \p sin ?•) and 



sin r 

 sin y = — j— (— -a ]3 sin i/* cos r—a 73 cos i/' + « 33 sin y sin r) — 



cos r ... 



— j— ( — a n sin i// cos f— a ia cosi// + a 13 sin i/< sin r) 



which, on rearrangement, become 



(a) cos y (q* — « 22 )=sin y (a 13 cos r— a 33 sin r) (15) 



(J) cos y" (a 12 cos r— « 23 sin /•) = 



smy" (j 2 — a 33 sinV— a n cosV + 2a 13 sin r cos r) 

 By division of 15 (a) by 15 (5) an expression results which is 

 free from y" ; 



{q i —ci^)(q l — a n cosV— a 33 sinV + 2a 13 sin r cos r)= (16) 



(a 13 cos p— a 23 sin r)' 

 and which reduces to 1 



[a l -2aJgr+(a a -k 1 )tg'r][a i , + {a i -Jcyff^]= (16a) 



K,-«.,^» , ) , (1 + ^V) 



if & be substituted for the constant value -r 2 — which, by reason 



sin r * 



of the sine law of refraction, is equal, for all possible waves, to 



q 

 ~—. where q is the velocity of light in the isotropic medium 



enveloping the crystal and i the angle of incidence. By means 

 of this standard formula, which can be derived in different 



1 G. Kirchhofr, Tiber die Eeflexion und Brechung an der'Grenze Krist. 

 Medien, Berliner Akad. Abh., 1876.— Th. Liebisch, Neues Jahrbuch, II, 191, 

 1885. 



