312 Mr Campbell, Discontinuities in Light Emission. 



should show interference, but it is difficult to explain why two 

 beams should interfere when they come originally from a ' single 

 source/ and should not interfere when they come originally from 

 ' different sources.' For, on this view, in both cases they really 

 come from different radiators. Accordingly it appeared that con- 

 siderable value would attach to any experiment which should 

 indicate, by means of observations other than those of optical 

 interference, whether the two beams, into which a beam from a 

 single source of light is divided by interference methods, are to be 

 regarded as coming from the same or from different radiators. 



§ 3. Now the theory recently given by Schweidler*, and applied 

 to radioactive processes by Kohlrauschf, by Meyer and Regenerj, 

 and by Geiger§, provides a very powerful method of investigating 

 any discontinuous process. Schweidler showed that if any effect, 

 of which the magnitude can be measured, is due to the random 

 occurrence of a finite number of independent events, then the 

 magnitude of the effect will not be constant, but will show fluctua- 

 tions about a mean value, and that from the magnitude of the 

 fluctuations the number of independent events can be calculated. 

 Further, if the magnitude of the sum or difference of two effects 

 so constituted is measured, the square of the mean fluctuation of 

 the sum or difference is the sura of the squares of the mean 

 fluctuations of the two effects, if, and only if, the events which 

 constitute one event are wholly independent of those which 

 constitute the other. If, on the other hand, there is complete 

 correlation between the events constituting the two effects, the 

 mean fluctuation of the difference will be zero. In a recent 

 paper II , which will be quoted frequently below, I have en- 

 deavoured to investigate closely the application of this theory to 

 experiment. 



§ 4. Suppose, then, that by some means we can measure the 

 intensity of a beam of light in such a way that the total intensity is 

 the sum of the intensities of the radiations' from the isolated radia- 

 tors of which the source is composed. Let us split up the beam from 

 a ' single source ' by one of the ordinary interference methods and 

 measure in this way the difference in the intensity of the resulting 

 beams, adjusting the arrangements so that the mean difference is 

 zero. If the older theory of radiation is correct, there is complete 

 correlation between the ' events ' which constitute the two beams : 

 when a radiator sends light into one beam, it also sends it into 

 the other. But if the newer theory of the radiation is correct, 



* Schweidler, Congres Internal, a Liege, 1904. 



t Kohlrausch, Wien. Ber. 1906, p. 673. 



J Meyer and Eegener, An. Ph. xxv. p. 757. 



§ Geiger, Phil. Mag. April 1908, p. 539. 



II Campbell, Proc. Camb. Phil. Soc. xv. 1909, p. 117. 



