﻿Quantum Theory of Photographic Exposure, 963 



the fifth rows contain the percentage numbers of clumps 

 affected calculated by (12) with <r = 0*097 and 



(I.) n =2^L 0-286 per ^ 



and (II.) n=^?=0'143, 



respectively, and the fourth and the last rows those observed. 

 The last but one column refers to clumps of 12 and 32 grains, 

 and the fact that almost all of these have been affected 

 G/ob8. = 100) gives an additional score of verifications of the 

 theory (though in the case of (II.) the observed " 100 " sets 

 in somewhat too soon). 



Grains in Clump 2 



3 



4 



5 



6 



7 



8 



9 



10 



11 . 



.. 33 



a 1-73 



3-03 



4-88 



6-2 



7 4 



8-6 



9-8 



11 



12 



13 . 



..>25 



""Uobn. 21 



44-2 



64-3 



743 



81-0 



85-9 



89-7 



92-4 



94-2 



95-5 . 



.. 99'8 



57 



63-8 



74-5 



87-5 



96 



97 



97 



965 



100 . 



.. 100 



TT locale. 15 ' 3 

 "'-bobs. 13 



25-3 



41-2 



49-3 



564 



62-6 



679 



73-5 



75-9 



78-8 . 



.. 95-7 



376 



42-3 



53 



66 



82-5 



86-5 



(?) 



89-4 



100 . 



. 100 



The agreement, although in general not so close as in the 

 previous case, is certainly satisfactory and in three or four 

 instances even remarkably good. Notice especially the case 

 of four-grain clumps which show perfect agreement in all 

 three exposures, the calculated and observed values in the 

 original exposure (cf. first paper) having been 87*3 as against 

 87*1, and now 61*3 and 41*2 as against 63*8 and 42*3. 

 Almost the same is true of the five-grained clumps. But in 

 general the agreement is good enough throughout the array 

 of clumps *. 



4. Notwithstanding the good agreement and the consistency 

 of these three sets of results with regard to the values of n 

 and cr, some critical remarks must now be made about the 

 meaning of the latter parameter. It will be remembered 

 from the first paper that a or 7rp 2 was originally introduced 

 as the (average) "cross-section" of the light darts, and p as 

 their equivalent semi-diameter, and the mathematical role of 

 this finite diameter was fixed by assuming that a grain is 

 made developable only when it is " fully " struck by a light 



* The outstanding- discrepancies being- attributed mainly to the 

 uncertainty of the (average) sizes a of the clumps and perhaps also to 

 disregarding- the effect of tne finite range of a within each class of clumps. 

 How this finite breadth of the classes can be taken into account will be 

 shown presently. 



