1904] The Chemical Dynamics of Photographic Development. 457 



Now, the chemical equation for development with ferrous oxalate 



is probably Ag + Fe (C 2 4 ) 2 = Ag + Fe (CA) 2 , i.e., one silver ion is 



(met.) 



converted into metallic silver. The velocity equation will then be 



dx/dt = KC/Ag C/FeOx. 



C Ag may be reckoned as constant on the above view of the 

 instantaneous adjustment of the equilibrium, as solid AgBr is present. 

 If we assume a layer of constant thickness, 8, in which diffusion takes 



place, then there will diffuse into the reaction-layer S- (a - x) dt of 



reducer in the time dt, where A is the diffusion coefficient of the 

 reducer, a its initial concentration, and x equivalents of AgBr have 

 been reduced. If x be very small compared with a, the total concen- 

 tration, this becomes S a.dt, and the velocity of development is 



given by dx/dt = KS, where S is the surface of the solid phase, and 

 K = A.a/8. Now the existence of a maximum and fixed quantity of 

 developable AgBr is proven by the experiments detailed above. We 



shall distinguish the amount of this by (AgBr) and in the course of 

 the reaction it varies from (AgBr) to 0. The surface S, therefore, also 



varies from </> (AgBr) to O. Now, the microscopic examination of the 

 photo-film shows that it consists of a number of very fine AgBr grains 

 embedded in gelatine. This, and the fact that the emulsion absorbs 

 light, according to the law I/I = e~ m * where m is the mass of haloid, 



allow us to substitute for S = <f> (AgBr), S = p (AgBr), i.e., the 



surface is directly proportional to the mass of AgBr at any time, and 

 therefore to its optical density. The optical density D of the latent 



image (AgBr) must equal D x , the density reached on ultimate develop- 

 ment, while, obviously, the density of the (AgBr) at any time, t, equals 

 DOO "~ D, where D is the density of reduced silver at the time, t. Hence 

 dD/dt = KS = K (D^ - D), which gives on integration 



losr = K. 



If this formula be written D = D 00 (1 - -*), it will be seen to be the 

 same as Hurter and Driffield's, when e~ K = a, but it has been obtained on 

 quite general grounds, free from hypothesis, as to the nature or dis- 

 tribution of the developable haloid. 



* A fine-grained heterogeneity may be treated formally as a solution, cf. Bredig, 

 " Anorganische Fermente," Leipzig, and Bodenstein, < Zeit. f. Physik. Chem.,' 



49, p. 42, 1904. 



