of a Stream of Light passing through a Crystalline Plate. 83 

 4. Keturning to the general equation (i), write 



A' = cos sin x? A = cos cos x cos w sin sin w, 



B' = sin sin x B = sin cos % cos w-j-cos sin w, 



C' = cos x, C = sin x cos w. 



Then the equations between which.jp has to be eliminated become 



! . . sin A 2 /6 3 \ /c 2 \ / sin A 2 c 3 \ a 3 \ 



A' + A- - --1 )(- a -l + B' + B 

 \ v / \p~ I \f I \ v 



~ 



sin i\* fa* \ fb z \ 

 + C'+C- ---!--!= 0. 



\ i' / \p- / V / 



1 3 sin 



and since 



3 



/. . sin A 3 /^ _. sin A 2 /' _ sin A 2 sin 2 ^ 1 



f A r *+A - + B^+B - -f-lCn-fC - = n*+ = , 

 v } \ v / \ v I tr jr 



the result of the elimination becomes 





and multiplying out and arranging the terms, this equation may be 

 written 



sn 



7 sin i . I sin~ i. , /_ sin i _ sin 3 i\ 



'-* 3+ ( c +^-H n - 2 ( 6 '--+^-^-) 



^-=0.. . (ii), 



where 



XA'iV 



~, 



61 ~ "SA^I^" ' 3 ~ x ~ "" 73 " 2 " 



/2 /--c 3 ) 



' *' 



