﻿268 Dr. L. Silberstein on a Quantum 



the spatial properties of light-quanta it would be utterly 

 unjustified either to deny or to assert that their lateral 

 dimensions are at all comparable with those of a silver 

 halide grain (of the order of one-tenth up to several 

 microns) *. If, by way of illustration only, p is propor- 

 tional to a power of \, say p = b\ K , the only condition for the 

 existence of a maximum of $(X), and therefore of sensitivity, 

 will easily be found to be k>0. If this be satisfied, the 

 maximum will occur at a wave-length \ m given by 



increasing with the diameter of the grain and bearing to X 

 the fixed ratio 



^=(2*;-r-iy/\ 



As a matter of fact, the maximum sensitivity is known to shift 

 (by two or three hundred A.U.) towards the red by making 

 the grain coarser. But thus far too little is known of the 

 quantitative aspect of such an effect to entitle one to con- 

 sider the above equation as anything more than an illustrative 

 example. The precise form of the function p = p(\) can only 

 be derived from spectrographs experiments followed by 

 microscopic grain counts, or if arrived at by a guess, has 

 to be verified by them. Such experiments are now in 

 preparation in this laboratory, and their results will be 

 reported in due time. A shift of the maximum sensitivity 

 towards the red or the infra-red can, of course, be brought 

 about by a function form more general than a mere positive 

 power of the wave-length. 



6. Generalities, and 'preliminary account of experimental 

 tests. — The chief and most immediate consequence of the 

 proposed theory is the essential dependence of the propor- 

 tionate number of grains affected, k/J¥, on the size a of the 

 grain, viz., the rapid increase of the former and, therefore, 

 of " the speed " of an emulsion with the latter. Now, it has 

 been known for a long time that (cceteris paribus) the speed 

 increases notably with the size of the grain, and we shall 

 see from the experiments to be described presently to how 



* According to E. Marx, Annalen der Physih, xli. pp. 161-190 (1913), 

 the volume of a light-parcel, which according to him is only a u concen- 

 tration place " within a continuous distribution of energy, is proportional 

 to X 4 and amounts for D-light to almost 8.10 -7 cm. 3 , which even with 

 a length of 10 cm. (200,000 D- waves) would still give a section area 

 8.10" s cm. 2 , just of the order of about the average grain area. There is, 

 of course, nothing cogent about Marx's estimate, yet the matter is not 

 without interest. 



