Mr Campbell, The study of discontinuous phenomena. 117 



The study of discontinuous phenomena. By Norman 

 Campbell, M.A., Fellow of Trinity College, Cambridge. 



[Bead 22 February 1909.] 



§ 1. The application by Kohlrausch* by Meyer and Regenerf 

 and by GeigerJ of von Schweidler's theory§ of the discontinuities 

 in the emission of rays by a radioactive substance to the measure- 

 ment of the charge carried by an a particle opens up a new and 

 most important field of physical research. The ingenuity of the 

 method must always give great interest to their work, but it has 

 lost much of its immediate importance since Rutherford and Geiger|| 

 have measured the same quantity by the more direct and probably 

 essentially more accurate method of counting the number of particles, 

 one at a time. The justification of the lengthy discussion of von 

 Schweidler's method which is given in the following pages is two- 

 fold. In the first place, it is believed that the discussion by the 

 four authors first named of the principles according to which their 

 observations should be interpreted is neither exhaustive nor com- 

 pletely devoid of error, and that a more thorough discussion will 

 enable the results obtained by von Schweidler's theory to rival in 

 accuracy those attained by Rutherford and Geiger. In the second 

 place, it should be remembered that radioactivity is not the only 

 discontinuous process which we study. The trend of modern theory 

 is everywhere to replace by discontinuity the continuity which was 

 the basis of the science of the last century. Any method which is 

 especially applicable to discontinuous processes is certain to be 

 fruitful of results in every department of investigation, and any 

 considerations which can be advanced in the elucidation of such 

 a method are not devoid of value ; at the present time I am 

 engaged in an attempt to apply the method to a totally different 

 form of ionisation current. 



I 2. It will be desirable first to put von Schweidler's theory 

 in a slightly more general and a somewhat more accurate form. 

 The author of that theory used in his calculations Bernoulli's 

 integral of probability. Now the use of the integral calculus in 

 this case is open to the objection that it assumes that the number 

 of possible cases, the probability of which is considered, is so large 

 that it may be regarded as infinite. But the essential feature 



* Wien. Ber. 1906, p. 673. + An. d. Phys. xxv. p. 757. 



+ Phil. Mag. April, 1908, p. 539. § See Kohlrausch, loc. cit. 



II Proc. Roy. Soc. A. 81, p. 191. 



