324 nutting: absorption of light 



conditions. Equations (1) and (4) give the general relation 

 sought between density and the number, size and distribution of 

 grain. 



In all ordinary practice the size and distribution of grain thru- 

 out the film is so uniform that (3) gives a very close approxima- 

 tion indeed. In this case. 



D = - mlog(l - A). (5) 



If further A is so small that the overlapping of grains is negligi- 

 ble, as is the case with low and medium densities, 



D=mA=mna (6) 



The ratio of the mass of reduced silver per unit area to the 

 density (4) is an important quantity, the so-called photographic 

 constant. 



Now the film is m layers deep, hence m n = N is the whole 

 number of grains per unit area. Mass of silver (M), per unit 

 area is then proportional to N and to the average volume of the 

 grains, 



M = cNa '/', (7) 



the constant c involving the specific gravity of the silver and 

 certain numerical factors. 



The photographic constant (P), defined as mass of silver per 

 unit area per unit density, is then 



p M cNa'/' ,- .^. 



P = — = = c\a (8) 



D Na ^ ^ 



if the overlapping of grains is negligible, or is 



p=- , , :^ , (9) 



Slog(l — na) 



without assumptions as to overlapping or uniformity of grain 

 thru the film. 



From these equations it appears thatP, to a first approximation, 

 is independent of N and hence of exposure and development, 

 but that it will vary among different brands of plates in propor- 

 tion to the mean diameter of grain. The first of these conclu- 



