288 On R*j "ruction, Reflexion, and Extinction. 



negative values of z, by all the vibrators contained in the 

 plate. I£ this effect be represented by E*, we have by (7) : 



E* r = -29ranN[~P C dz^- hz *+<*-* «K 



" z 



+ Qf rfso^+^o+^-^o)]! . . (19) 



From this we easily obtain, making use of (12), (14), (15), 



[be +1^6^- (be -±y~6 



■' • "^2jnbZ /h„ i^^ — i/zbZ y ~ y 



The last application that we shall make of the results 

 obtained is to investigate the intensity of the transmitted 

 beam of light. We begin by calculating, at a point M past 

 the plate (z>Z), the cumulative electric effect that arises 

 under the influence of our system of vibrators. By means 

 of (7) we get the result 



2wN r v , Q - - . /A P 1 



\_i(bc+l) i(bc — 1) 



+ \i(bc-l) i(bc+l)) e J * * [ J 



The effect of: the vibrators in the plate is thus to increase by 

 the quantity (21) the component along x of the electric field 

 of the incident wave (1) conceived to pursue its course un- 

 disturbed. Accordingly, for the complete expression of the 

 actual electric field at the point M past the plate, we have 

 with use of (11), (14), and (15) : 



4/>cA (1) e^-«(~~-Z)+<l 

 (be + iye inbz -(bc-l) 2 6- 



ii . i\2jnbZ /; 1/ ,_1 \2~ — inbZ' ' * v~'"v 



It may serve as a confirmation of the legitimacy of the 

 method employed to mention that (21) and (22) are in 

 accord with the results which it is customary to obtain by 

 the aid of certain assumptions respecting boundary con- 

 ditions. While constructing our argument we have 

 convinced ourselves that, on the view here advocated, 

 boundary conditions could be altogether ignored. 



