Mr Gamphell, Discontinuities in Light Emission. 313 



the 'events' are independent, or very nearly so, for in general each 

 radiator sends its radiation into one beam and not into both. On 

 the first theory the mean fluctuation of the difference should be 

 zero: on the second the square of the mean fluctuation should 

 be the sum of the squares of the fluctuations of either beam 

 separately. 



§ 5. The application of these ideas to experiment was 

 attempted in the following way. The intensity of the beams 

 was measured by means of the photo-electric current which they 

 excite in the alloy of sodium and potassium in a high vacuum. 

 It seems reasonable at the outset to suppose that each train of 

 radiation emitted by a single radiator, when it falls on the alloy, 

 liberates a number of electrons which is, on the average, the same 

 for all radiators and independent of the total intensity of the 

 beam, i.e. the number of such trains emitted in a given time. If 

 this assumption be true, then the difference between the photo- 

 electric currents due to the two beams will be a function of the 

 difference in the number of trains of radiation constituting the 

 two beams, and measurements of the fluctuations of this difference 

 will enable information to be deduced as to the independence of 

 these trains. The fluctuations were measured by Meyer and 

 Regener's method of observing the readings of an electrometer, 

 the quadrants of which were connected to the two ends of a high 

 resistance through which the current passed. 



§ 6. Before proceeding to detail the experimental methods it 

 will be well to consider the theory a little more closely : if this 

 order had been adopted in the first instance much time would 

 have been saved. 



The main result of the previous paper* may be stated as 

 follows. Let Xt be the average number of events which happen 

 in a small time t, and let x be the deviation of that number 

 from its mean value during the time r : let 



0=f{t) (1) 



represent the motion of the indicator of the measuring instrument 

 at alHnmes t subsequent to the happening of one of the events, 

 and drp'^ the square of the mean deviation of the indicator from 

 its mean position for all times T from the moment of starting the 

 observations, where T is a time long' compared with the time 

 constants of the measuring instrument. Then it is shown that 



eT"=a;'/T.I f'(t)dt (2). 



Jo 



§ 7. We have first to calculate x^. The ' events ' in our case 

 are the liberation of individual electrons. Our fundamental 



* Campbell, loc. cit. 

 VOL. XV. PT. IV. 21 



