on Radioactive Change. 581 



projected particle will in general produce a certain definite 

 number of ions in its path, and the ionization current is 

 therefore proportional to the number of such particles projected 

 per second. Thus 



n - 6 ' 



where n t is the number projected in unit of time for the time 

 t and n the number initially. 



If each changing system gives rise to one ray, the number 

 of systems .N* which remain unchanged at the time t is 

 given by 



N,= ( n,.dt=^e- 



= 1 "' 



The number N initially present is given by putting t = 0. 



N. = ? 

 and ^ = e-^. 



The same law holds if each changing system produces two 

 or any definite number of rays. 

 Differentiating 



dt =~ X ^ 



or, the rate of change of the system at any time is always 

 proportional to the amount remaining unchanged. 



The law of radioactive change may therefore be expressed 

 in the one statement — the proportional, amount of radioactive 

 matter that changes in unit time is a constant. When the 

 total amount does not vary (a condition nearly fulfilled at the 

 equilibrium point where the rate of supply is equal to the 

 rate of change) the proportion of the whole which changes 

 in unit time is represented by the constant X, which possesses 

 for each type of active matter a fixed and characteristic value. 

 Xmay therefore be suitably called the " radioactive constant/ 3 

 The complexity of the phenomena of radioactivity is due to 

 the existence as a general rule of several different type- of 

 matter changing at the same time into one another, each type 

 possessing a different radioactive constant. 



§ 5. The Conservation of Radioactivity \ 



The law of radioactive change that lias been deduced holds 

 for each stage that has been examined, and therefore holds 



