134 Mr Campbell, The study of discontinuous phenomena. 



mechanical integrator which should give the value of \-. — - — rrdx 

 for a wholly irregular curve. 



§ 15. As regards the choice of instruments for this method, 

 the conclusions reached in considering Meyer and Regener's 

 method are still valid. Since p is zero there is no need for 

 considering the relation between the periods of the electrometer 

 and the resistance, but it is still desirable that a should be very 

 large. For there is some uncertainty in the determination of the 

 value of this quantity : since the importance of the terms involving 

 a in comparison with the term Pi^T, which does not involve a, 

 decreases as a increases, it is clearly desirable to make a as large 

 as possible, that is, to use an electroscope with as short a period 

 as possible. 



On general grounds Geiger's method seems less satisfactory 

 than that of Meyer and Regener for observations on phenomena 

 for which both methods are, in principle, equally applicable. But 

 it is easy to imagine circumstances in which Geiger's method 

 would, and Meyer and Regener's would not, be applicable : for 

 instance, the object of the experiment might be to detect dis- 

 continuity in the difference between two sources, and indeed 

 I am engaged at present in endeavouring to conduct such 

 experiments. It is desirable, therefore, to consider Geiger's 

 method a little more closely. 



I 16. It must be pointed out that the theory of Geiger's 

 method which has just been elaborated does not represent any 

 practicable experimental conditions. It is impossible to reduce 

 the quantity p accurately to zero. In the first place, there is 

 always an ' insulation leak,' which acts like a Bronson resistance 

 and sets a limit to the deflection which the indicating instrument 

 will attain when acted upon for an infinite time by a finite current. 

 But this leak can (though with great difiiculty) be made so small 

 that values of T can be chosen such that aT is very large and 

 pT is very small. In such a case Geiger's method could be applied 

 according to the theory just given. But, in most of the cases to 

 which the method is likely to be applied, there is also an ' apparent 

 insulation leak,' which is a far more serious matter. It must 

 be remembered that no ionisation current is really perfectly 

 'saturated.' A condition can often be attained ia which an 

 increase of the acting potential difference from 1000 to 2000 volts 

 does not increase the current by more than O'OOl of its value, but 

 this does not prove that an increase of 1 volt in the p.d. may not 

 cause an increase of one millionth in the current. And a change 

 of one millionth may be extremely important when we are 

 concerned with the minute differences in the magnitudes of two 



