﻿358 Mr. F. C. Toy on the Theory of the 



But if x\a is the fraction of grains which are changed, 

 F 1 = xja ; 



or, denoting log a/ (a — x) by A, we have 



A = N . 



Thus the same form of curve should be obtained when N is 

 plotted against the intensity as is obtained when A is plotted 

 against the same variable. The form of this curve should 

 be an unsymmetrical S, as shown in fig. 2. 



Experimental. 



The first experiment carried out was to determine the 

 relation between A and the light-intensity I for a set of 

 geometrically identical grains, every grain counted being 

 measured, as described in a previous paper (Phot. Jour. 

 192 L, lxi. p. 417). 



Table I. 



Cross-section of grain = 0*98/x, 2 . 



Log I 



(relative). 



X. 



X 



(curve- 

 values.) 



A. 



Log I. 



X. 



X 



(curve 



values.) 



A. 







92-0 



91-5 



2-45 



-0-893 



47-7 



466 



0-62 



-0162 



89-5 



90-0 



2-30 



-1-215 



5-2 



5-2 



0-05 



-0-310 



87-7 



87-0 



2-04 



-1-487 



o-o 



o-o 



o-oo 



-0-572 



74-8 



750 



1-39 



-1-788 



00 



o-o 



0-00 



In the first two columns of Table I. are shown the values 

 of log I and x determined experimentally by exposure behind 

 a neutral wedge, and these are plotted in fig. 3. The values 

 of x given in column 3 are read off the curve in fig. 3, and it 

 is these values which are used in calculating A in column 4. 

 This is the best way of obtaining the A values, since when x 

 is large a very small error in its determination means a very 

 large error in A. The A, I curve, shown by the solid line 

 in fig. 4, is exactly as predicted by the theory. 



We must note here that this is not in agreement with the 

 results of Slade and Higson (Proc. Roy. Soc. 1921, A, xcviii. 

 p. 154) and a previous experiment of the author (ibid. 1921, 

 c. p. 109) to confirm their result. Slade and Higson stated 

 that the relation between A and I can be expressed by the 

 equation 



Arrairi-^ 1 ), 



