CONTEMPORARY ADVANCES IN PHYSICS 73 



interval is precisely the same, whichever atom one chooses to consider 

 and whenever the instant at which one chooses to let the given time- 

 interval begin. I will quote a passage from Poincare ^^, taking only 

 the liberty of writing 'nucleus' where he wrote 'atom.' "If we 

 reflect on the form of the exponential law, we see that it is a statistical 

 law; we recognize the imprint of chance. In this case of radioactivity, 

 the influence of chance is not due to haphazard encounters between 

 atoms or other haphazard external agencies. The causes of the 

 transmutation, I mean the immediate cause as well as the underlying 

 one {la cause occasionnelle aussi bien que la cause profonde) are to be 

 found in the interior of the atom [read, in the nucleus] ; for otherwise, 

 external circumstances would affect the value of the coefiicient in the 

 exponent. . . . The chance which governs these transmutations is 

 therefore internal; that is to say, the nucleus of the radioactive sub- 

 stance is a world, and a world subject to chance. But, take note! to say 

 'chance' is the same as to say 'large numbers' — a world built of a 

 small number of parts will obey laws which are more or less com- 

 plicated, but not statistical. Hence the nucleus must be a complicated 

 world. . . . " I shall make no further allusion to theories of radioactiv- 

 ity.i7 



The constant t may be interpreted as the time-interval during which 



e — \ 

 the fraction Q (or approximately 0.632(2) of any initially-present 



quantity Q of the substance would undergo its change. It is greater 

 by the factor l/loge2 (or approximately 1.44) than the half-period 

 of the substance, the interval (designated by T) during which one 

 half of the initially extant atoms are transmuted. It is also the 

 average duration of the life of a single atom. All of these statements 

 may be proved without difficulty from the formula (1). From the 

 similarity between (1) and (2) it follows that the rate at which trans- 

 mutations occur in an unreplenished sample of a radioactive substance, 

 and the rate at which rays shoot out of such a sample, and the intensity 

 of all the effects which the rays produce, vary exponentially with time; 

 and the constant T which is the half-period for the extant quantity of 

 the substance is likewise the half -period for all of these. The constant 

 T likewise has the same meaning for them all, and so does its reciprocal 



16 Oerrneres Pensees, pp. 204-205; he credits Debierne with the idea. 



" Further and very valuable evidence that the transmutations of individual atoms 

 are governed by the "laws of chance" operating within their own nuclei is furnished 

 by the variations or fluctuations {Schwankungen) of the numbers of alpha-particles 

 emitted from a sample of any radioactive substance in consecutive equal time- 

 intervals very short compared with the half-period of the substance {v.i.). These 

 are precisely analogous to the fluctuations in thermionic emission known by the name 

 of "Schroteffekt" {Introduction, p. 10). Consult an article by K. W. F. Kohlrausch 

 in Ergebnisse der exakten Naturwissenschaften, 5 (1926). 



