﻿V*64 Dr. L. Silberstein and Mr. Trivelli on the 



dart. This gave as the efficient area of a grain, instead of 

 a = 7rr 2 , 



a'=a[l-p/ry. 



Now, exactly the same formula would arise if we assumed 

 that, no matter what the thickness of the light darts (and. 

 whether it is finite at all), a grain is made developable only 

 when the axis of the dart hits it in a point not too near the 

 edge of the target (grain), thus excluding from the total area 

 a boundary zone of a certain breadth p. Such a condition is 

 not altogether fantastic, and one might support it by 

 imagining that if the grain is hit too near its edge, an 

 electron is still ejected and a "centre" of reducibility is 

 produced at the spot, but the wave of development, stopping- 

 dead at the edge, has not such a good chance to spread over 

 the whole grain as when the centre is well within the target. 

 If so, then the empirical principle that a grain is either not 

 affected at all or is made developable entirely would require 

 a qualification, viz., the exclusion of that boundary zone. 

 This alternative, therefore, should and can still be tested. If 

 it is supported by experiment, the original interpretation 

 given to p or a can be abandoned, since it certainly is not 

 very satisfactory. Not that there is anything incredible in 

 the light darts having a finite thickness and a cross section 

 such as one -tenth p? ; so far as we know, they may be trains 

 of waves of even much larger transversal dimensions. But 

 the unsatisfactory point about this interpretation is that it is 

 hard to imagine why the grain to be affected at all, i. e. to 

 have a photo-electron ejected, has to be hit by the whole of 

 that cross section. For, if so, then, unless some light darts 

 have a diameter of the order of 10 ~ 8 cm., no such things as 

 simple atoms or molecules could ever have their electrons 

 ejected by light*. Yet, a grain, as a crystal lattice, may, 

 after all, behave as a single molecule, at least in the present 

 connexion, and the original role attributed to the cross- 

 section of the light darts, though repugnant, may still turn 

 out to be a useful working hypothesis. To ensure the 

 possibility of being fully hit and therefore affected, even to 

 the smallest available silver halide grains, it would be enough 

 to treat a in our formula as the average taken over a 

 sufficiently ample interval of sections down to very small 

 ones. It would be premature to enter into quantitative 

 details of the consequences of such an assumption. But it 

 seems proper to mention even at this stage that an assumption 



* Whereas the photo-electric effect has been obtained with gaseous 

 substances, though not beyond every doubt. 



