CONTEMPORARY ADVANCES IN PHYSICS, XXVIII 595 



square force-field. This is the obstacle, or at any rate, a part of the 

 obstacle, which an oncoming proton or deuton or alpha-particle must 

 overcome in order to reach the nucleus and achieve transmutation. 

 One may picture it as a hill, up which the ball must roll to reach the 

 castle at the top — and down which the ball will roll if it starts from 

 the top, shooting outward towards infinity as the fast-flying alpha- 

 particle. 



Now to assume the inverse-square force as prevailing all the way 

 inward to r — would be to postulate a point-nucleus without room 

 for parts or structure, surrounded by a hill of infinite height which no 

 approaching positive particle could climb; all of which is inadmissible. 

 Departure from the inverse-square law is actually shown by some 

 experiments on scattering of alpha-particles which pass very close 

 to the nucleus, and these indications are to be heeded in tracing that 

 part of the curve of Fig. 12 which lies to the right of the maximum; 

 but the maximum itself and the sharp descent to its left are dictated 

 by no such observations, and to postulate them is to make the theory 

 which is now to find its employment and its test. That there should 

 be such a maximum and such a descent is of course the most natural 

 supposition to make. If there are several particles of positive charge 

 which stay for a finite time within the nucleus, there must be something 

 which restrains them from flying away. This something must either 

 be an agency of a type as yet unknown, or else be described by a 

 potential-curve with a maximum at what we may henceforward call 

 the boundary of the nucleus; and the latter assumption is to be pre- 

 ferred till proved unusable. 



Applying classical ideas to this "model" (if the word be not con- 

 sidered too presumptuous) of a nucleus, one is led at once to two pre- 

 dictions, which may be sharply formulated if we adopt symbols such 

 as Vm and r™ for the two parameters indicated on Fig. 12, viz. the 

 "height of the potential-barrier" and the "radius of the potential- 

 barrier" as they are commonly called, the latter being also called the 

 "radius of the nucleus." These are: 



1. If the nucleus emits a particle of positive charge -f 2e, the 

 kinetic energy with which this particle is endowed when it completes 

 its escape cannot be less than 2eVm', consequently, when it is observed 

 that atoms of a certain element emit alpha-particles with kinetic 

 energy Ko, the height of the potential-barrier for that element cannot 

 surpass Ko/2e; consequently, when the force-field about the nuclei of 

 such atoms is explored by the classical method of studying the scatter- 

 ing of alpha-particles projected against a sheet of that element, it 

 must be found that the region of repulsive force, and a fortiori the 



