MancJiester Memoirs, Vol. xlviii. (1904), No. 8 33 



assumed to be of the order of a million times greater than 

 for radium, since the radio-activity is about a million 

 times smaller. It will be seen that a fairly complete 

 range of types is known, the average lives varying from a 

 few seconds to a thousand million years. As the average 

 life of a metabolon is increased it will partake more of the 

 nature of a stable element and less of the nature of a 

 transition-form. Consider the case of a mineral like 

 pitchblende, in which there is a parent element A, disin- 

 tegrating at an excessively slow rate through successive 

 transition-forms B, C, D, E, etc., and let the respective 

 rates of change be designated by \^, A^, X,,, etc. A little 

 consideration will show that after radio-active equilibrium 

 is attained, since the amount of each type changing 

 equals the amount produced, the actual amount of each 

 type disintegrating will not depend on its own rate of 

 change, but will be a similar quantity for all the types. 

 The amount of each changing depends only on A^, and is 

 independent of A^, A^,, etc. This is a compensating prin- 

 ciple of great importance. As the rate of change of a 

 metabolon decreases, and its detection in ajty given 

 quantity becomes increasingly difficult, the equilibrium 

 quantity that accumulates correspondingly increases. 

 The radio-activity of each type is expressed by A^ N^, 

 A^ N,^, Xf, Nc, etc., where N^, iV^, etc., represent the actual 

 number of atoms of each of these types present, and it is 

 assumed that an atom of A produces one atom of B, etc. 

 Since in radio-active equilibrium A^ TV"^ = A^ TV^ = A N^, 

 .... it follows that the amount of a transition-form 

 accumulating is inversely proportional to its rate of 

 change, or directly proportional to its average life. 

 Suppose now that B, C, D are rapidly changing types, 

 and that ^ is a very slowly changing type. It follows 

 that when the mineral is separated into its various con- 



