496 Bollywood — Life of Radium. 



the number of atoms of each successive product disintegrating 

 in the same period. If the number of atoms of the substances 

 A, B, and C is equal to P, Q, and R, respectively, and \„ A 2 , 

 and X 3 are the respective constants of change or fractions of 

 the total amounts of each substauce which undergo change 

 each second, then the relation existing under equilibrium 

 conditions is expressed by 



X,P = A 2 Q = A 3 R 



and the amount of the first product B which disintegrates per 

 second to form the second product C is exactly equal to the 

 amount of B which is produced per second by the disintegra- 

 tion of the parent substance A. This follows from the very 

 assumption of a state of equilibrium, for if the amount of B 

 which disintegrated per second was greater or less than the 

 amount formed in the same interval, the relative proportion of 

 B as compared to A would diminish or increase accordingly, 

 which is contrary to the fundamental assumption. 



If, therefore, it is desired to find the rate of change X 2 for 

 the product B, and for any reason a direct determination of 

 this is impracticable, it is possible to obtain a knowledge of its 

 value by comparing the amount of B formed in a given inter- 

 val from a known amount (P) of A with the amount of B in 



A P 



radio-active equilibrium with P. Thus A 2 = -p-^ , where X L P 



is the amount of B formed per second by P atoms of the 

 parent A. 



Now in the case of radium, owing to its rarity and its slow 

 rate of change, it is not at present possible by direct measure- 

 ments conducted with radium compounds to accurately deter- 

 mine the rate at which disintegration is taking place. The pri- 

 mary uranium minerals, however, represent systems which are 

 certainly of sufficient age for a state of radio-active equilibrium 

 to have been reached by the different products. If, therefore, 

 the parent substance from which the radium is formed can be 

 separated from such a mineral, and the amount of radium 

 produced by this parent can be determined and compared 

 directly with the amount of radium with which it was associ- 

 ated in the mineral, it is possible to obtain a more accurate 

 knowledge of the constant of change of the radium than can 

 be obtained by other methods. 



The constant proportion which has be*en found to exist 

 between the quantities of uranium and radium in different 

 minerals is very conclusive evidence in support of the assump- 

 tion that radium is a disintegration product of uranium, but 

 attempts made to detect the growth of radium in compounds 

 of pure uranium indicated that if radium was produced at 



