﻿Theory of Photographic h\vposure. 259 



which as a whole has been deprived of even a single electron only. 

 It need not lose more than one electron in order to be made entirely 

 developable. According to Professor Joly's original hypothesis * the 

 latent image " is built up of ionised atoms or molecules." In our con- 

 nexion, this does not mean that for every pair of atoms, say Ag Br, 

 there is one electron liberated. Since every grain of silver bromide 

 (as well as of silver chloride) is a crystalline, to wit a simple cubic 

 space-lattice arrangement of Ag and Br atoms t, we may as well con- 

 sider the whole grain as a single molecule. Such a crystalline structure 

 being hit by a light-quantum and deprived of but a single electron, 

 may well become susceptible throughout to the subsequent action of 

 a developer. 



3. With the assumptions just made the question is reduced 

 to a mere problem in probabilities. 



Consider first the ideal case of equal grains. Let there 

 be upon an area S of the photographic plate (feay unit area) 

 N grains. Let a be the size (area) of each of them divided 

 by S, and let n light-quanta impinge upon S, due allowance 

 having been made for those which may be reflected or 

 absorbed by the gelatine. The problem consists in finding 

 the number k of grains hit and (if p = l) affected by this 

 light exposure. 



Roughly, this simple problem can be treated as if -A 7 , k 

 were continuous quantities, in the following way, familiar 

 from many other instances (" mass-law "). At an}^ stage 

 the number of unaffected grains is jST—k, representing an 

 available fraction a(N — k) of the total area S. Thus, if 

 further dn light-quanta be thrown upon S, and if their trans- 

 versal dimensions be negligible as compared with those of 

 the grains %, the corresponding increment of lc will be 



dk = a(]S r — k) dn } 



and since k = for ?i = 0, this gives at once 



k=B(l-e- na ), (A) 



which in fact will presently appear to be correct enough 

 except for the practically unimportant cases of small iV or 

 small JS r —k. 



More rigorously, but provided always that JV at least is a 

 large number §, the required formula can be obtained by the 



* Nature, 1905, p. 308. 



t R. B. Wilsey, Phil. Mag. xlii. p. 262 (1921). 



% An assumption which will be given up in the sequel. 



§ 'Which will be the case if S is taken large enough. Since plates 

 and films in actual use contain as many as ]0 r) grains per cm.' 2 , S can be 

 made as small as one-hundredth mm. 2 , and even less. 



S2 



