THE TRANSFORMATION OF ELEMENTS 



85 



decomposition takes place, the rate of recombination must be 

 sufficiently rapid to reunite any oxygen and hydrogen formed. 



It has been shown in Part I. that all radioactive elements 

 decompose according to the law expressed by the exponential 

 equation 





-' . ,-m 



(0, 



where v is the original amount (volume, if a gas) v t that at time t y 

 and X is constant for the particular element (0*1795 for radium 

 emanation if time is reckoned in days). It was also shown that, 



100 



10 . 12 14 16 



Time in Days. 



Fig. 4. 



although all the elements have an infinite life, yet their half-life 

 period is quite definite ; and, as has already been mentioned in 

 this paper, Sackur's value for the emanation is 3*86 days. 



The chemical action induced by radium emanation obeys the 

 same law. Thus, if V is the initial volume of gas under observa- 

 tion, V, the volume at time t, and V^ the final volume, then 

 V -V. 



x> 



V, -V, 



S mm e 



-A/ 



(2) 



-jO 



The curves in fig. 4 show the values for (V, — VJ plotted 

 against time, taking (V — V K ) as 100, and the corresponding 

 logarithmic values together with the logarithmic curves for 



