JBoltwood — Life of Madium. 495 



2*41 Xl0 14 £, when the value of e is expressed in electromag- 

 netic units, the number of a particles expelled per second by 



one gram of pure radium free from products is equal to 2 ^ ' 9 . 



]STow assuming that the disintegration of the radium atom is 

 accompanied by the expulsion either of (1) a single a particle 

 having a mass equal to that of a helium atom and bearing 

 twice the charge of a hydrogen ion, or of (2) two a particles of 

 a mass equal to half that of a helium atom with a single ionic 

 charge, the number of atoms in one gram of radium disinte- 

 grating per second is given as 4'1 X 10 10 per second, or 

 12*7 XlO 17 per year. Taking the total number of atoms in one 

 gram of radium as 3*6 X 10", the . fraction disintegrating per 

 year is equal to 3*5 XlO" 4 and the half-value period is approxi- 

 mately 2000 years. The latter is about 77 per cent of the 

 maximum estimate on the basis of the measurement of the 

 charge carried by the a particles. 



Owing to the relative uncertainty as to the exact values of 

 many of the quantities used in the above calculations, it is not 

 to be expected that the results obtained by the different 

 methods will at best give more than the approximate order of 

 the rate of the change taking place in radium. 



The amount of emanation produced by one gram of radium 

 is also a measure of the rate of disintegration of radium. The 

 results obtained by Ramsay and Soddy from measurements of 

 the volume of the emanation produced by known amounts of 

 radium salts were in fair agreement with the quantities to be 

 expected from the rate of change indicated by Rutherford's 

 early calculations.* Quite recently, however, Cameron and 

 Ramsay have publishedf an account of the results of some 

 similar experiments which they interpret as indicating that 

 the rate of change of radium is much more rapid than has been 

 generally supposed, and on the basis of these results they have 

 calculated that the fraction of radium disintegrating per day is 

 l - 162XlO -5 , which corresponds to only 163 years for the half- 

 value period. 



Theory of Present Experiments. 



It follows from the disintegration theory, that in any system 

 of radio-active substances, consisting of a parent element A 

 and a series of successive disintegrating products, B, C, etc., 

 when the relative amounts of products have reached their 

 highest possible value and a state of radio-active equilibrium 

 has been attained in the system, the number of atoms of the 

 parent substance disintegrating in unit time is exactly equal to 



* Radio-activity, 2d edition, p. 458, 1905. 

 f Jour. Chem. Soc, xci, 1266, 1907. 



