738 Prof. E. Rutherford on the 



a standard solution of radium bromide, prepared by Rutherford 

 and Bolt-wood. For the above electroscope the emanation 

 from 10 — 9 gram of radium gave a movement of the gold-leaf 

 of 11' o divisions per minute. 



An amount of emanation which increased the natural leak 

 by ten per cent, could be detected with certainty, so that the 

 electroscope was capable of showing the presence of 10 ~ 12 of 

 a gram of radium in a solution. Ten times this quantity 

 could be measured with a probable error not more than a 

 few per cent. 



In the experiments to be described later, it will be shown 

 that there was a constant rate of growth of radium in most 

 of the solutions under examination. Since the amount of 

 emanation in the various solutions was determined at irregular 

 intervals, it is necessary to consider how the electroscope 

 readings are connected with the amount of radium existing 

 in the solution at the moment of expulsion of the emanation. 



Let q = amount of radium present initially. 



Let ^ = rate of growth of radium. 



Then after the solution has stood for a time t, the amount 

 of radium present is q + q-t. 



Suppose that the emanation is completely removed after a 

 time t-i since the preparation of the solution, and is tested for 

 the amount of emanation after a further interval t 2 . If a 

 constant quantity of radium is allowed to produce emanation 

 for a time t, it is well-known that the fraction of the equi- 

 librium quantity of emanation produced is l — e~ xt , where \ 

 is the constant of decay of the radium emanation. 



Consequently the amount of emanation present after a 

 time of collection t 1 is proportional to 



(qo + qt^l-e-^ + q I (l — e^^dt. 



The left-hand side of the expression is proportional to the 

 amount of emanation due to the radium present in the solu- 

 tion at the time t l9 while the integral is proportional to the 

 emanation produced by the quantity of radium formed in 

 the interval t 2 . 



After reduction, the amouut of emanation is seen to be 

 proportional to 



[qo+q(ti-^](i-e-^)+ q t 2 . . . . (i) 



This expression is proportional to the observed rate of 

 movement of the gold-leaf, so that knowing q , t l9 t 2 , and X, 

 the value of q may be expressed in terms of divisions per 

 minute of the electroscope. 



In all the experiments to be discussed, the value of q was 



