Mr Campbell, The study of discontinuous phenomena. 121 



Kohlrausch, balanced against each other currents due to two 

 independent radioactive sources. Since some doubt has been 

 thrown on Kohlrausch's results by later workers no further reference 

 will be made to them. Meyer and Regener balanced the current 

 from one radioactive source by means of a Bronson resistance, to 

 the terminals of which a compensating potential difference was 

 applied by a potentiometer arrangement. And these two arrange- 

 ments are examples of the only two principles which seem possible 

 in any measurements of this kind. 



But it must be noted that, if a reading of the instrument 

 is taken while the rays are acting, this reading will not indicate 

 the value of the fluctuation at the moment of observation. The 

 instrument has inertia, and its indication at any time is a function 

 of the fluctuations during some finite period preceding the moment 

 of observation. In Geiger's method it might be possible to get rid 

 of the inertia of the needle by removing the sources of rays after 

 a definite period of action and allowing the instrument to take 

 up a steady position before the reading is taken. But we shall 

 see that there are grave practical difficulties in such a procedure : 

 and the method is not applicable to Meyer and Regener's ob- 

 servations by reason of the ' inertia ' of the Bronson resistance. 

 Accordingly the problem before us is to determine the relation 

 between the observed fluctuations, which depend on the constants 

 of the instrument, and the real fluctuations which depend only 

 on the nature of the source. We will consider first the method 

 of Meyer and Regener. 



Meyer and Regener s method. 



I 4. Let a charge E be given to the electrode system when 

 the electrometer is at zero and at rest. If the capacity of the 

 electrode system be G, the resulting potential will be EjC. If 

 the current through" the Bronson resistance is proportional to the 

 potential difference between its terminals, this potential difference 

 will diminish exponentially with the time, so that the potential 

 difference acting on the electrometer needle at a time t after the 

 charge has been communicated is 



EjCe-P' 



where p is a constant depending only on the nature of the 

 resistance. 



Let / be the moment of inertia of the needle, [x the coefficient 

 of damping, k the coefficient of torsion and KV the couple acting 

 on the needle when the p.d. between the quadrants is V. (It is 

 assumed that the deflection 6 is proportional to the steady p.d. 



9—2 



