136 Ml' Campbell, The study of discontinuous pheiiomena. 



insulated. But Geiger adds all his fluctuations together, whatever 

 the time of observation, as if they were comparable. 



Accordingly it appears to me that Geiger's expectation of 

 obtaining a result even in approximate accordance with that 

 predicted by other work was justified only if he had a large 

 false insulation leak.' If there is such a leak, then Geiger's 

 method is reduced to that of Meyer and Regener, and all observa- 

 tions at more than a certain distance from the moment of 

 insulation are comparable. The existence of an insulation leak 

 would also explain that the 'time of swing of the needle' (o| sees.) 

 is so much smaller than that which is found with most Dolezalek 

 electrometers : for the period between two peaks might then 

 depend, not on the vibrations of the needle, but on the period 

 of decay of his quasi-' Bronson -resistance.' But, if this suggestion 

 is correct, he neglected totally the real time of swing of his needle. 



(3) As a minor point we may note that Geiger, attempting 

 to use von Schweidler's theory, puts j A' | = \/Ni. Correctly 



I A' I = A / — - for one source of rays and 2 a/ — for 2 inde- 

 pendent sources (error about 20 ''/J. The quantity which should 

 be equal to '^Nt is v A'^. As I have pointed out, it seems 

 impossible to find a complete expression for the value of | A' | 

 in terms of N and the instrumental constants. 



In view of these sources of error, it is difficult to avoid the 

 conclusion that the close agreement found by Geiger between 

 prediction and experiment was mainly fortuitous. 



In conclusion I must offer my best thanks to Mr G. H. Hardy 

 for his invaluable help in §§ 5 — 8 : the main principle of the 

 argument is his rather than mine ; to Sir J. J, Thomson, who 

 has pointed out several errors in the original calculations; and 

 also to Mr T. H. Laby, whose acute criticism first turned my 

 attention to the subject and aided greatly in the attainment of 

 clear ideas. 



Summary. 



§§ 1 — 3. A slight modification and generalisation of von 

 Schweidler's theory of the fluctuations in the emission of rays 

 by a radioactive substance. 



§§ 4 — 7. A consideration of the theory of Meyer and Regener's 

 experiment based on von Schweidler's work. 



§§ 8 — 12. Application of this theory to experimental arrange- 

 ments. 



§§ 13 — 17. The theory of Geiger's experiment in the same 

 direction. 



