120 Mr Gam'phell, The study of discontinuous phenomena. 



that the probability is the same whether the parts of t are adjacent, 

 so that T is continuous, or whether they are scattered at random. 



Now the occurrence of the NT events correspond to the 

 s trials, and the events A and B correspond to the falling of one 

 of the NT events respectively within or without r. Hence 



NT = s, p = ^, g = l-J. 



Then if observations are taken over <t periods, each of length T, 

 and if Nt + Xi, Nt -\- X2, . . . Nt + 00^ are the number of the events 

 which happen within the period r is the 1st, 2nd, ... o-th observa- 

 tions, we have proved that 



^^ = NT.^.{l-^^ 



If we make t small compared to T, we have 



'^ = Nt (1). 



In the particular case of radioactivity, T is the time over 

 which the activity of the substance suffers no appreciable decay : 

 the NT events are the breaking up of NT atoms. If, then, we 

 had some instrument which would indicate the number of atoms 

 which break up during any period r short compared to T, we 

 might discover the value of N by taking a sufficient number of 

 observations and equating to Nr the sums of the squares of their 

 deviations from the means or ' fluctuations.' An electrometer 

 connected to an ionisation vessel which could be exposed for a 

 known time to the action of the rays from the substance would be 

 such an instrument. But it must be noted that, though the 



absolute value of the mean * fluctuation ' Jx^ = \/Nt can be made 

 as large as we please by increasing the period t, the ratio of that 

 value to the value of the whole number of rays emitted during 



^/Nt 

 the period t is equal to „ and decreases with an increase of r. 



Numerical calculation shows that (unless Rutherford and Geiger's 

 method of magnifying the effect due to a single ray is employed) 

 no value for t can be found for which the mean fluctuation exceeds 

 the probable error in the measurement of the value of the total 

 current. 



Accordingly all who have attempted to apply von Schweidler's 

 theory have employed some balancing method by which the mean 

 total current is reduced to zero, so that the fluctuations become 

 fluctuations about the zero and only their absolute magnitude 

 need be taken into account. These may be made as large as is 

 desired by an increase in N and r. Geiger and, before him. 



