370 THE DEEP SEA 



If No is the number of atoms of R at time to, and N is the number 

 now present, the age t of the system may be calculated from the 

 fundamental equation : 



N/No = e-^' (1) 



Let us note that a knowledge of N alone does not suffice for a 

 calculation of t. In other words, if we have a system containing a 

 radioactive isotope R and know only the amount of this isotope 

 present in the system, we cannot calculate the age of the system. 

 We need to possess further information prior to doing this. 



Practically all methods of measurement could be included into 

 one or the other of the three types; 



1. Either No or only N / No is known. Generally, N /No is known 

 because R has one, or several, stable isotopes, and its isotopic 

 abundance in the external medium is known at the time of sepa- 

 ration of the system. The age of the system can be calculated 

 directly from equation (1). The carbon-14 method is of this type. 



2. R is transformed, either directly, or indirectly into a stable 

 nuclide, S. The ratio of the concentrations of R and S actually 

 present in the system allows the age to be calculated from the 

 equation: 



S/R = (e^'- 1) 



This is valid only under certain conditions, conditions which we 

 shall not discuss here. This type of method includes most of the 

 classical methods: Pb/U, Sr/Rb, A/K, and He/U. 



3. R is a member of a radioactive family, and is transformed 

 into another radioactive nuclide R', with a shorter life. If, at the 

 moment of formation, to, of the system, only R is included in it 

 and no R', the ratio R'/R will increase from its initial value of 

 zero up to its maximum value upon attainment of radioactive 

 equilibrium between R and R'. Since the actual ratio R'/R is 

 known, the age t of the system may be deduced by using the 

 equation : 



R'/R = (1 - g-'O 



on condition that T » T' . The method lo/U is of this type. 

 Some particularly interesting applications exist because two of 



