CONTEMPORARY ADVANCES IN PHYSICS, XXVIII 597 



an oncoming particle; it is evident that the minimum kinetic energy 

 permitting of entry will increase with p, starting from neVrr, and rising 

 to infinity as p rises from to r™. The relation between fraction-of- 

 particles-entering-nuclei — call it Pe — and kinetic energy K could be 

 calculated, given specific assumptions about the values of F„ and r„, 

 and the trend of the potential-curve. Without undertaking the calcu- 

 lation, it is easy to see that the vertical rise of what I will hereafter 

 call the "ideal" curve — the curve of probability-of-entry-at-central- 

 impact vs. K — will be distorted into a bending slope, starting, however, 

 at the same critical abscissa neVm. If the sheet of matter is a thick 

 layer, there will of course be a much greater fraction of the impinging 

 particles of which the initial paths point straight toward some nucleus 

 or other, but the fraction achieving entry will not be raised in the same 

 ratio, for the particles going toward nuclei embedded deep in the 

 layer will lose some or the whole of their velocity in passing through 

 the intervening matter.-^ This also will contribute to converting the 

 vertical rise into a gradual bend. Still it does not seem possible that 

 if the ideal curve had such a shape, the experimental ones could rise 

 with so extreme a gradualness as does the one of Fig. 17 or those of 

 Figs. 16 and 17 in the Second Part; for these suggest no sudden be- 

 ginning at all, but rather they have the characteristic aspect of curves 

 asymptotic to the axis of abscissas, as if their apparent starting-points 

 could be pushed indefinitely closer to the origin by pushing up indefi- 

 nitely the sensitiveness of the apparatus. Neither does it seem possible 

 that Vm can be so low as their starting-points imply. 



There is, however, another difficulty: these curves refer not directly 

 to Pe, but to number of transmutations, or to be precise (for precision 

 is essential in these matters) to the number of particles producing 

 transmutations involving the ejection of fragments having certain 

 ranges. Call this number Pt. It is easiest to conduct the argument 

 as though Pt were proportional to Pe — as if an observable transmuta- 

 tion could result only from the entry of a particle through the potential- 

 barrier of a nucleus, and as if the number of transmutations of any 

 special type were strictly proportional to the number of entries, the 

 factor of proportionaHty being independent of K. Yet few assump- 

 tions are less plausible. It is far more reasonable to suppose that the 

 probability of a particle bringing about a transmutation when it enters 

 a nucleus is not invariably unity, but is instead some function /i(J^). 

 It is reasonable also to suppose that a particle passing close to the 

 potential-barrier but not traversing it may yet be able to touch off an 

 internal explosion or eruption leading to a transmutation. Denote 



2^ Contrast the two curves of Fig, 17. 



