498 Boltwood — Life of Radium. 



the powdered material, with the activity of the emanation from 

 a solution containing a known amount of radium. 



The solutions of ionium were sealed up in glass bulbs and 

 the radium emanation present was determined from time to 

 time by boiling off the gases in each bulb and measuring the 

 activity of these gases in an electroscope. The radium ema- 

 nation obtained in this manner is a measure of the amount of 

 radium present in the solution at any time, but for short 

 periods of accumulation is not directly proportional to the 

 actual amount of radium contained in the solution."" 



If a freshly prepared solution of ionium free from radium 

 is sealed up and radium is .produced at a constant rate, then at 

 the end of t days the amount of emanation present in the solu- 

 tion is proportional to 



q A ( ) 



when q is the amount of radium produced per day expressed 

 in terms of its equilibrium amount of emanation and X is the 

 constant of change for the emanation, the day being taken as 

 the unit of time. The ratio of the amount of emanation in 

 the solution at the end of t days, to the amount of emanation 

 in equilibrium with the total quantity of radium then present 

 would be equal to 



or 



qt- 



-!c 





1 - 



qt 



■e ). 



Thus at the end of four days, for example, taking X as 

 0*178, the value of the ratio would be 



i 



(1 - -49) = 0-286, 



•712 



viz., the amount of emanation present would be 0286 the 

 amount in equilibrium with the radium in the solution. 



If a quantity of radium q is present in the ionium at the 

 start, then the proportion of its equilibrium amount of emana- 

 tion which will accumulate in the solution in the time t will 



be equal to q (l — e~ ). The total amount of emanation 

 at the time t will then be equal to 



?o(l-*~V^[l-~0-^)]- 



* The general mathematical considerations which apply in this case have 

 been discussed and developed by Eutherford. Phil. Mag., xiv, 733, 1907. 



