CONTEMPORARY ADVANCES IN PHYSICS 71 



uranium II sufifers a dual alpha-ray disintegration, about 97 per cent 

 of the atoms transmuting themselves into ionium and the other 3 per 

 cent into the mysterious substance uranium Y which is always found 

 mixed with uranium, and which is known to emit beta-rays and hence 

 to pass over into an isotope of element 91 which may well be protactin- 

 ium, the first known member of the actinium series. On following 

 out these presumptive transformations in Fig. 1 the reader will see that 

 they would lead to the actually-observed result; but that is not quite 

 the same thing as proving that the observed result is attained in just 

 that way. The branching may occur elsewhere in the posterity of 

 uranium; or the observed constancy of the ratio of actinium to radium 

 in the rocks may mean that actinium and its family all descend from a 

 separate isotope of element 92, not concerned in the production of 

 radium. Much light would be shed upon this question if someone 

 would only determine the atomic weight of even one member of the 

 actinium sequence — an achievement which would settle at once those 

 of all the others, and is most eagerly awaited. 



Having dealt with the filiation of the radioactive substances, having 

 specified the substance from which each is born and the substance to 

 which it gives birth, and the sort of particle which is emitted in each 

 process of transmutation, it remains to specify the rates at which the 

 transmutations occur, and the speeds of the particles which are emitted, 

 and the wavelengths of the quanta of radiation which sometimes come 

 out also, and how many there are of these. The fundamental assump- 

 tions of the theory of radioactivity, which the experiments have sus- 

 tained, require that in a transmutation only one alpha-particle or 

 one beta-ray be emitted from the nucleus of one self-transmuting atom ; 

 but there is no such limitation upon the radiation-quanta, nor upon the 

 electrons incidentally ejected from the circumnuclear family. 



The rate of transmutation of every radioactive substance, so far as 

 we know, is governed by the famous exponential law which signifies 

 that equal fractions perish in equal times — that if one were to take a 

 sample of the substance and determine the quantities extant at two 

 instants an hour apart, and also those existing at two other instants an 

 hour apart, and at any number of pairs of instants separated by inter- 

 vals of one hour, then the mutual ratios of the two measured values of 

 all those pairs would be the same. Half of any sample of thorium C 

 transmutes itself in one hour; half the remainder in the next hour; half 

 the remainder in the next hour, and so forth ad infinitum (or, to speak 

 more carefully, up to the limit of the observations). 



This law is described by the following formula relating the quantity 

 Q of the substance existing at any time /, and the quantity Qo existing 



