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BELL SYSTEM TECHNICAL JOURNAL 



at any other time /o (provided that no replenishment of the supply is 

 taking place!) : 



Q = Qg exp 



(1) 



Furthermore the rate dQjdt at which the substance is being transmuted 

 at any instant is related to the amount Q existing at that instant as 

 follows : 



jr\lJt Q ^0 / to — t 



dQ/dt = — — = — -^ exp 



(2) 



These formulae contain only a single constant characteristic of the 

 substance. Nothing simpler could be desired. A phenomenon that 



120 140 160 



Hours 



180 200 220 340 260 280 300 



Fig. 2, Decay-curve of radium E (R. F. Curtiss) 



(Being plotted on logarithmic paper, the graph of the exponential law is a straight 

 line.) 



can be described by a formula involving only one constant which has 

 to be varied to distinguish one case from another is a rare gift of 

 nature. 



While the equations (1) and (2) are naturally valid whatever the 

 unit in which we choose to measure Q, it is desirable as a rule (and 

 necessary, in comparing the radioactivity of different substances) to 

 express Q either in gramme-molecules, or in actual numbers of atoms. 

 In some places I shall use iV as a symbol for Q measured in the latter 

 manner. 



The exponential law is a law of chance. It may be expressed by 

 saying that the chance of an atom disintegrating within a given time- 



