﻿264 Dr. L. Silberstein on a Quantum 



grains, so that no better agreement could be expected. 

 The refined experimental tests which are now in progress 

 in this laboratory, and by means of which it is hoped to 

 corroborate the proposed theory, deal, as they should, with 

 separate size-classes of grains. 



But questions concerning the comparison of the theory 

 with experiment will be treated in a later part of the present 

 and in subsequent papers. 



4. Passing next to the case of an emulsion of any type 

 /(a), it can be easily proved that the approximate formula 

 (4) will hold for each class of grains separately. In order 

 to see this it is enough to consider the case of two distinct 

 classes of grains. Thus, let there be N± grains of size a l 

 and N 2 grains of size a 2 spread over the (unit) area S of the 

 plate, and let n light-quanta be thrown upon S. Of these a 

 number m 1 = niV r 1 a 1 will fall on the a r grains and a number 

 m 2 = nN 2 a 2 upon the a 2 -grains. It remains only to be found 

 how many ax-grains will be hit by the m 1 quanta, and how 

 many of the a 2 -grains will be hit by the m 2 quanta. Now 

 each of these is a problem of the kind we have already 

 treated. The number k x of ax-grains hit will be given by 



1 J_ 1 



i^x + iVi-l^ + iV 1 -/r 1 + l- naiJ 



and similarly for the a 2 -grains, so that k x and k 2 will each be 

 determined by the previous formula for k with J\ 7 , a replaced 

 by JSr iy ai, and N 2% a 2 respectively. Similarly for an emulsion 

 consisting of three or more classes of grains. 



Thus, also, for an emulsion of any type /(a), the number 

 of grains ranging from a to a-\-da hit and (if £>=1) affected 

 by n impinging light-quanta will be k a da, where, apart from 

 the correction f 



The total area * of silver halide affected or made developable 

 will be found by extending the integral 



K- 



\akada (8) 



over the whole range of sizes, say from a 1 to a 2 . 



If, for instance, f(a) = Ce~ fl - a , say from a = a 1 to a 2 , where 

 C, ix are constants, as in the case of some films and plates 



* It will he kept in mind that a stands for the " efficient " area of a 

 grain (plate), i.e. for the orthogonal projection of the grain upon the 

 film base. 



