﻿Characteristic Curve of a Photographic Emulsion. 355 



so that the number of active nuclei increases also. Secondly, 

 the sensitivity of every nucleus may not be the same, so that 

 as the intensity of the light is increased, nuclei become 

 operative which are unaffected by lower intensities, and 

 again the total number of active nuclei increases with the 

 intensity. 



We will consider only the case of grains in the form of 

 thin plates as they occur in high-speed emulsions. Eggert 

 and Noddack (Preuss. Akad. Wiss. Berlin. Ber. 1921, xxxix. 

 p. 631) have recently measured photometrically the fraction 

 of the incident light which is absorbed by an ordinary 

 commercial photographic plate, and have found it to vary 

 with the different plates from about 4 to 12 per cent, for 

 violet light, for which the amount of light absorbed is near 

 the maximum. Now, these plates contain several layers of 

 grains, so that a very extreme upper limit to the fraction of 

 light absorbed by a single grain is, say, 20 per cent. Thus, if 

 there is an increase in the incident intensity of the order of 

 20 per cent., the intensity of the light transmitted through a 

 grain will be equal to the intensity incident before the 

 increase took place. Thus, if all nuclei are equally sensitive, 

 a change in the incident intensity of the order of 20 per 

 cent, will cause a difference in the number of active nuclei 

 from zero to some fixed maximum, so that the characteristic 

 curve can only function over a range of intensity such that 

 the ratio of its extremes is of the order of 1*2 : 1. As will 

 be shown later, for the steepest characteristic curve plotted 

 this ratio is about 25 times as much as this, so that as an 

 appreciable factor in determining the increase of nuclei 

 with intensity the first assumption is untenable. We have, 

 therefore, to assume that all the nuclei are not equally 

 sensitive. 



Since these nuclei are all formed in the same emulsion, 

 most of them will have a sensitivity near the average value 

 for the whole, and there will be a few which are very 

 sensitive and a few which are very insensitive. There will 

 be none which will respond to zero intensity, and none so in- 

 sensitive that it takes an infinite intensity to affect them. 

 We therefore expect the curve showing the relative number 

 of nuclei R having any given sensitivity I to be of the 

 general form shown in fig. 1. The exact mathematical form 

 of this curve is immaterial at present, but it will be similar 

 in general form to that obtained by Clerk Maxwell for the 

 distribution of velocities between the molecules of a gas. By 

 similar reasoning to his, the number of nuclei (Nj) which 



2 A2 



