6 Mr. J. Satterly on the Amount of Radium 



J he Correction for the Growth of Radium Emanation 

 in the Charcoal. 



As explained above, deductions must be made from the 

 observed leaks given by the gas passed into the testing vessel 

 for the leak due to the emanation generated by the charcoal 

 itself since the last heating. 



If at a heating the charcoal is completely deprived of its 

 emanation and then the tube is closed up and left to itself, 

 the emanation will gradually accumulate, the equation of the 

 production being 



I, = I„(1 -er"), 



where I^=the amount in existence at time t, 



T = the amount in existence after an infinite time, 

 e =the base of the natural logarithms = 2*71828 . . . ., 



and X= the radioactive constant of radium emanation. 

 Taking the time for radium emanation to decay to half 



value as 3*858 days *, we have, using the nomenclature of 



Rutherford, 



and since 



T = 3*858x 86400 sees.; 

 XT = log e 2 = -693, 

 X = 2-083 xl0~ 6 sec.- 1 . 



Therefore the equation for the production of emanation in 

 the charcoal is 



I t = I (l-^-2-083xlO-6 X ^ 



where t is in seconds or 



i ( =i (i-«-> 8 °<), 



where t is in days. 



From this equation, and taking the value of I as 100, the 

 following table has been calculated f. 



Table I. 



t (days). 



1. 



3. 



4. 

 513 



5. 

 59-3 



6. 



7. 



10. 



82-7 



25. 



27. 



CO . 



J t 



165 



41-7 



660 



71-6 



98-9 



992 



100 





The reason why these particular values of t were chosen 

 will be seen later (Table II., p. 8). 



* Kolowrat,Ze Radium, July 1909, and Curie, ibid. Feb. 1910. 

 + Tables suitable for these calculations will be found in Kolowrat's 

 paper mentioned above. 



