THE TRANSFORMATIONS OF ELEMENTS 539 



It is found that the emanations, and many other active 

 products, lose their activity almost completely in a measurable 

 time. From studies of the rate at which the activity is lost, 

 the conclusion is reached that in any one time a certain fixed 

 proportion of the total number of atoms present spontaneously 

 disintegrates. An actual illustration will make this clearer. 

 The activity of any fixed quantity of radium emanation falls to 

 half the initial value in approximately four days. In the second 

 four days it falls to half of this second value, i.e. one quarter of 

 the original. We therefore suppose that the emanation has 

 decomposed to a corresponding extent. In the unit of time 

 chosen, four days, the same quantity, one-half the amount at 

 the beginning of that period, always disappears. Similarly in 

 any other definite period of time a certain quantity, bearing 

 a definite ratio to the original amount, will disappear. Again, 

 at the end of eight days one quarter of the whole amount 

 remains ; at the end of twelve days, one-eighth ; of sixteen days, 

 one-sixteenth. But at the end of infinite time there will always 

 remain some quantity, however small. Similarly in all cases 

 of active matter some remains undisintegrated after infinite 

 time ; the radioactive elements have an infinite life. Though 

 they may have died for all practical purposes at the end of 

 some measurable time, an unmeasurable but definite amount 

 remains. However, it has been shown in Section i (p. 532) 

 that we can always find when half a given quantity of active 

 substance has disappeared. And it is this period which is 

 termed the half-life period of such substances. It varies from 

 four seconds in the case of actinium emanation to millions of 

 years in the case of uranium. 



Another term constantly used is the average life of a sub- 

 stance. In Section 1 the method of calculating it has been given 

 (p. 532). It can be conveniently illustrated by a human parallel. 

 A church filled with people on any fixed date contains a fair 

 assortment of men, women, and children of all ages. If we 

 know the total number of years each person will live after 

 leaving that church we can calculate the average life of the 

 congregation counting from the definite time fixed by that 

 church attendance. This is quite different from the average 

 life of some number of persons from the time of birth of each, 

 which is the basis of the data employed to calculate insurance 

 rates. 



