﻿of Radiation and Line Spectra. 801 



emitting system to which Bohr's theory has been applied 

 with some measure of success, can be immediately deduced 

 from the theory outlined above. The systems which he 

 assumes to emit the hydrogen, helium, and other spectra are 

 characterized, in their steady states, by constant kinetic 

 energy, and by one positional coordinate q. The hypothesis 

 expressed by equations (2) takes, for such systems, the form 



t+ 1 - 



2L j, 



dt = ph 



L=Pf, ...... (20) 



and, since L in these systems is numerically the same as 

 Bohr's * W, we see that (20) expresses Bohr's principal 

 hypothesis. A further assumption made by Bohr is that the 

 energy emitted by an atom, in passing from one steady state 

 to another, is exactly equal to hv ly where v x is the frequency 

 of the emitted radiation. Now according to the foregoing 

 theory, since the energy of the nether vibrations of frequency 

 v must be equal to rhv (equation (17)), where r is a positive 

 integer or zero, it follows that the energy emitted by an 

 atom (like those assumed by Bohr) must be equated to 



r 1 hvi-]-r i 7iv 2 + . . . , .... (21) 



where the r's are integers, not necessarily all positive, and 

 i'i, v 2 • • • are the frequencies of the corresponding sether 

 vibrations. The present theory therefore includes this 

 second assumption of Bohr's as a special case. 



The conclusion that energy emissions to the 9ether are 

 represented by an expression of the form (21), and are not 

 necessarily monochromatic in all cases, receives some support 

 from Prof. Barkla's experimental work on X-radiation f . 

 It is noteworthy that Barkla finds that the energy absorbed 

 from the primary radiation, during the production of the 

 "fluorescent" radiations, is equal to 



per electron emitted, the first term representing the kinetic 

 energy of the emitted electron and v K , v L the frequencies of 

 the " fluorescent'" radiations. 



* N. Bohr, loc. cit. 



t C G. Barkla, « Nature,' 4th Mar. 1915. 



Phil. Mag. S. 6. Vol. 29. No. 174. June 1915. 3 F 



