122 Mr. L. Simons on the Beta-Ray Emission from 



the paths of the electrons emerging from the gaseous atoms, 

 shown in 0. T. R. Wilson's cloud experiments, do not vary 

 continuously from a maximum downwards, whilst to be com- 

 pletely satisfied, the photo-electric equation requires that each 

 X-ray spectral line shall be accompanied by a corresponding 

 /3-ray spectral line. 



The X-ray spectrum of an element is invariable except in 

 that the lines of shorter wave-length may be entirely absent 

 if the incident waves are of longer wave-length ; on the 

 contrary, the /3-ray spectrum will vary completely with the 

 wave-length of the incident radiation. Assuming that the 

 photo-electric equation does apply, we have 



l<mv 2 = Jiv — id, 



where \mv L is the kinetic energy of ejection of a /3-particle 

 from an atom within which the potential energy of the 

 particle is iv and Jw is the quantum of incident energy. 

 The energy w is that which was radiated by the atom 

 during the previous binding of the electron, and equals * 

 (hv K + hv L + etc.) if the electron occupied a "K" ring, or 

 (/if L +...) if it occupied an "L" in the parent atom. 

 Assuming that the X-rays are absorbed in quanta and that 

 it is not a necessary condition that every atom taking part 

 in the absorption should return at once to the stream the 

 maximum possible quantity of X-radiation, we should obtain 

 groups of electrons of speeds v ]} v 2 , v s etc., emitted from an 

 element S when X-rays of frequency v fall upon it, given by 



\mv x 2 = hv- s (7iv K + Jw L + hv M + . . . ) 



lmv 2 2 = hv — s {hv L i-hv M + ...) 



hmv B 2 = hv — B {hv M +...), 



etc. 



These groups constitute the /3-ray spectrum varying with v. 



v i >v 2 >v J . 



* Bohr, Phil. Mag\ ser. 6, vol. xxx. p. 412 (1915) gives a discussion 

 of what should constitute the quantity in the brackets. Apparently his 

 conclusions lead him to one, viz., the first term in the brackets, but he 

 produces evidence from the separate work of Moseley, Kossel, and 

 Barkla for the inclusion of all the terms as they appear here and in 

 subsequent expressions. Throughout this paper 1 have followed the 

 latter method, but at the conclusion it is shown that a better agreement 

 with the theory can be obtained amongst the results if we assume that 

 the energy required to remove a U K" electron to a point of zero 

 potential with no kinetic energy =/*t; K , the atom readjusting itself 

 subsequent to the removal. (See also O. W. Richardson, 'Electron 

 Theory of Matter,' p. 509 (1916).) 



