550 



the sides represent in magnitude the intensity of the incident, reflected, 

 and refracted light in the case of a single plate, and then, leaving 

 the first side and the angle opposite to the third unchanged, multiply 

 the angle opposite to the second by the number of plates ; the sides 

 of the new triangle will represent the corresponding intensities in the 

 case of the system of plates. I say gwasz-geometrical, because the 

 construction cannot actually be effected, inasmuch as the first side 

 of our triangle is greater than the sum of the two others, and the 

 angles are imaginary. 



To adapt the formulae (13), (14) to numerical calculation, it will 

 be convenient to get rid of the imaginary quantities. Putting 



V {(l+r+00 +r-0(l + t-r)(l-r-t)}=, . (15) 

 we have by the common formulae of trigonometry, 



whence, putting 



we have 



e V-ia =cosa + -v/ 1 sma=a Tl . 



It is a matter of indifference which sign be taken : choosing the 

 under signs, we have 



2rsina= V 1A, eV- la =#. 

 We have also 



t It 



no fresh ambiguity of sign being introduced. Putting therefore 



I(l + * 2 -r 2 +A)=:S, ..... (17) 



we have 



eV-i^j. 

 and equations (13) now give 



b m b~ m aa~ l 

 In the case of perfect transparency these expressions take a sini- 



