ct-P articles with Hydrogen Nuclei. 503 



7. An Attempted Application of the Quantum. 

 Before passing on to the next model, it will be con- 

 venient to consider the matter on quite different lines. 

 Bohr's theory of spectra is based on the idea that of all 

 mechanically possible types of orbit that a system can 

 describe, only a certain number are actually permissible. 

 Might it not be that the nuclei are both point charges, and 

 that the peculiarities of our curves are in some way con- 

 nected with this question of permissible orbits ? Almost all 

 the work on this subject has, of course, been carried out 

 with the elliptic orbits of electrons moving round nuclei ; 

 but Epstein * has discussed the question of hyperbolic 

 orbits — though his method of quantising them appears to 

 the present writer to be of very doubtful validity. In his 

 <3ase the forces were attractive, but we can see no reason 

 why repulsive forces should be excluded. However that 

 may be, a very little calculation shows that there is no help 

 to be found in the quantum theory. For any application of 

 it, on lines at all similar to those used in other work (whether 

 we follow Epstein the whole way or not), must lead to the 

 condition that the angular momentum of the system is a 

 multiple of the quantum. Thus we get the relation 



MpY = nh. 



If we take V = 2 x 10 9 cm. per sec. for fast a-particles, we 

 get p = nx 5 x 10~ 13 cm. Standing by itself, this might 

 conceivably be taken to mean that, when p was less than 

 5 x 10 ~ 13 cm., there could be no deflexion at all, a result 

 something like what is observed. But the argument breaks 

 down completely when variations of V are considered, for 

 the lower the velocity the larger the limiting value of p 

 becomes. So we should get the result that the behaviour at 

 low velocities is even more abnormal than at high, directly 

 contrary to the facts. We must therefore abandon the hope 

 of help from the quantum theory, and explain its non- 

 applicability by saying that that theory is a theory of 

 radiation and that if (as may be the case here) radiation 

 does not occur, quantum principles do not apply. 



8. The Elastic Plate. 



For our next model we take the simplest type of plate-like 

 form that gives a soluble problem. In this a repels II with 

 a force acting according to inverse square of the distance 

 from its centre, but this centre is surrounded by a circular 



* P. S. Epstein, Ann. d. Phys. vol. 1. p. SI 5 (1916). 



2 L 2 



