132 Mr Campbell, The study of discontinuous phenomena. 



If their absolute value accorded well with that deduced from other 

 work it can only be because p was small compared with a: but, 

 for all they say, p might have been less than a, or, still worse, 

 equal to a. 



Meyer and Regener also introduce a curious correction by 

 extrapolation for the capacity of their electrode system. I should 

 have thought that it was obvious on general grounds that the 

 value of A^ was independent of the capacity as shown by (21), for 



both Ot and {Ot'^Y are inversely proportional to the capacity. 

 They extrapolate for zero capacity: but, surely, if the capacity is 



zero the fluctuations must be infinite and the value of -^ infinite. 



If extrapolation is to be used at all, it would appear to be more 

 reasonable to extrapolate for infinite capacity: such a process 

 reduces the term in p (equation (20)), which they neglect, to zero 

 — but unfortunately it reduces all other terms in the same ratio. 



Lastly, Meyer and Regener, in estimating the average value 

 of A^ divide SA^ by n — \, and not by n, where n is the total 

 number of observations. There seems to me a confusion here 

 with the determination of the probable error of a variable given 

 by a set of dependent equations from the 'residuals' of those 

 equations after the probable value of the variable is substituted. 

 But there seems to be no quantity analogous to 'residuals' in the 

 case we are considering: the mean fluctuation is simply pro- 

 portional to the mean 'error' in N. 



Geiger's method. 



§ 13. We will now proceed to the discussion of Geiger's method, 

 in which no Bronson resistance was used, but the current due 

 to one a ray source balanced by another current, opposite in sign 

 and, on the average, equal in modulus, due to another source. 

 The deflection of the needle is the algebraic sum of the deflections 

 due to the two sources. 



If we consider only one source, the equations corresponding 

 to (8) and (5), giving the deflection of the needle at all times 

 after one or m particles respectively^ have been emitted from that 

 source, can be found directly from those equations by putting 

 p = 0. Hence, using the same notation as before, 



e = A.e-'^' + B^e-^' + P^ (24), 



Where ^^ = 0/7 ^^ = ^^ «3^ ' ^^^'^^^i:^' 



and dT = tlZ^ {A,e--'>-' + B,e-'^*r' + p^) (25) 



= 2;:;'^i^(0(Bay) (26). 



