nutting: absorption of light 323 



1 — 7ii Gi. In other words the absorption and transmission coeffi- 

 cients are respectively the probabilities of being stopped and of 

 being passed. 



In the second layer let the corresponding quantities be nz and 

 a2, in the third n^ and as and so on. For brevity call the product 

 rii «: = Ai, etc. Now the only manner in which a ray may pass 

 thru all layers is to pass each layer separately hence the probabil- 

 ity of passing all layers is the continued product 



(1 - Ar) {I -A,) .... (1 _ A J ^ T^ (1) 



of the probabiUties of passing each separate layer. This is the 

 transparency of the whole sheet. The corresponding absorption 

 Bm is the complementary quantity 



Bra = l -T^ (2) 



It may be noted that the absorption of the whole is not the 

 product {Ai Ao . . . A^) oi the probabilities of absorp- 

 tion in the various layers since the action is not alike in all layers, 

 a ray may be passed by several layers to be stopped in another. 

 The above product {A1A2. . . A2) is the probability of pos- 

 sible stoppage in all layers, i.e., the probability per unit area of 

 a continuous train of grains lying one behind the other, thru all 

 the successive 7n layers. In fact, if the value of Tn, in (1) be 

 written in (2), multiplied out and grouped according to the num- 

 ber of ^'s multiplied together, then each group gives the proba- 

 bility of 2, 3 . . . m grains overlapping. 



In the special case of all layers alike in number and size of 

 grain, the transparency of all m layers will be 



Tn. = (1 - A)- (3) 



since in (1) Ai = A2, = . . . = Am- This corresponds to 

 Beer^s Law in ordinary optics. 



Photographic density D has of late years been precisely defined 

 by the relation 



D ^ - logio T (4) 



T being the transparency in the sense used above. The value of 

 Tin in either (1) or (3) may be substituted in (4) according to 



