Mr Campbell, The study of discontinuous phenomena. 129 



the beginning or end of the observed decay curve, and those 

 involving e~** from the end or beginning, according as a is greater 

 or less than p. If a is large, t will be small for the part of the 

 curve over which a is determined, and the term in 7 will be of 

 very little importance. 



All the considerations advanced indicate that a Bronson cell 

 should be chosen with as high a resistance as possible, and an 

 indicating instrument with as short a period as possible. It 

 seems desirable, therefore, to employ a gold-leaf or quartz-fibre 

 electroscope in place of a Dolezalek electrometer. The only 

 objection to the use of such an instrument is that it will be 

 somewhat difficult to determine with accuracy the value of its 



time-constant -, which will be of the order of one second. But 

 a 



it must be remembered that, if a is large compared to p, the terms 



in (21') involving the former quantity are small compared to those 



involving the latter. Moreover, if the movement of the instrument 



is recorded by photography, the value of this quantity may be 



found by a method similar to that employed for measuring the 



constants of an Einthoven string galvanometer. The use of a 



Dolezalek electrometer seems prohibited, since, if it is aperiodic, 



its time-constant will be so great that it will be difficult to make 



the Bronson resistance so large as to avoid an approximate equality 



between a and p. 



§ 11. This elaborate discussion of experimental methods will 

 be worthless unless there is some reason for believing that the 

 method is not affected by some inevitable source of inaccuracy. 

 There seems no reason why the observations should not be taken 

 with very considerable accuracy, and the theory that has been 

 given is, so far as I can see, complete and trustworthy. Let us 

 consider the sources of systematic error which cannot be eliminated 

 by the most careful experimentalist. 



Firstly, there is the Bronson resistance: the current through 

 this instrument is subject to fluctuations which are added to those 

 due to the source observed. These fluctuations can be diminished 

 by using 13 rays in place of a. rays, as the agent of ionisation in 

 the resistance: for though a much larger number of /S particles 

 will be required and the absolute error, measured in number of 

 13 particles, will be increased, the number of ions produced by a 

 /S particle is so much less than the number produced by an a 

 particle that the absolute error, measured in current, is less. But, 

 against the use of /3 particles there is the objection that they 

 cannot, with any convenience, be absorbed completely in the air 

 of the resistance and hence chance fluctuations may arise from 

 changes of temperature, etc. But in any case, the error due to 

 the resistance can be eliminated by calculating the value of the 



