314 Mr Campbell, Discontinuities in Light Emission. 



assumption states that the number of electrons liberated is pro- 

 portional (at any rate for a given intensity of the light) to the 

 number of light disturbances falling on the cell. If N is the 

 average number of such disturbances striking the cell in unit 

 time, ft) the average number of electrons liberated by each light 

 disturbance, then 



Xt = Ncot (3). 



The fluctuations of X, which are measured by x^ arise (1) from 

 fluctuations of N and (2) from fluctuations in co. The introduc- 

 tion of ft) allows for all changes of the absorption of the light in 

 different parts of the optical train, and for all differences in the 

 state of the cell and the manner of the incidence of the light 

 upon it. Then, if f and i] are the deviations of Nt and oo respec- 

 tively from their mean values during any very short time r, we have 



(Xt + x) = {Nt+^)(co + v) (4), 



and OS = Nrr] + ^Q) + ^7] (5), 



and "^ = [N^'t)^ + f ft,2 + |2^2 + 2Nt7]^co + Wrrf^ + ^^wrj] . . .(6). 



It will be assumed that ^ and rj are wholly independent, hence 

 V^> ff^ ^^d ^'rf are all zero, since t) and f are zero. Also, since 

 T tends to the limit zero, NH'^ is infinitesimal compared to a. 



Therefore ^=P(w2-|-7f) (7). 



As was proved in the previous paper, 



J^ = Nt .....(8). 



Hence '^- = N {w'' + t)'') r (9). 



§ 8. (9) gives the result when we are considering a single 

 beam falling on a single cell and measuring the fluctuations of 

 that cell as Meyer and Regener* measured the fluctuations of a 

 single source of a rays. Let us now consider a second cell (the 

 quantities referring to which are distinguished by dashes) and 

 measure the fluctuations in the quantity X — X', where X = X'. 

 In this case t) and 77' are independent and it will be assumed that 

 ^2 _ ^'2. ^ g^^(j ^' QTj-Q dependent or independent according as the 

 two beams of light are dependent or independent in the sense 

 which has been discussed. Then it is easy to show that, if x 

 now represents the fluctuations in {X — X')t, 



x'=2N{co' + ^')t (10) 



if the beams are independent, or 



-'^"=2N^'t (10') 



if the beams are dependent. 



* Meyer and Eegener, loc. cit. 



