Vil] | CONTINUOUS PRODUCTION OF RADIO-ACTIVE MATTER 189 
ionization current 7, after the active product has been allowed to 
decay for a time ¢, 1s given by 
OF 
% 
e mare 
where 7 is the initial saturation current and 2» the constant of 
decay. 
Now the saturation current 1s a measure of the total number 
of ions produced per second in the testing vessel. . It has already 
been shown that the « rays, which produce the greater proportion 
of ionization in the gas, consist of positively charged particles 
projected with great velocity. Suppose for simplicity that each 
atom of active matter, in the course of its change, gives rise to 
one projected a particle. Each @ particle will produce a certain 
average number of ions in its path before it strikes the boundaries 
or is absorbed in the gas. Since the number of projected particles 
per second is equal to the number of atoms changing per second, 
the number of atoms n which change per second at the time ¢ is 
given by 
UG e-t 
No 
2 
where 7, 1s the initial number which change per second, On this 
view, then, the law of decay expresses the result that the number 
of atoms changing in unit time, diminishes according to an ex- 
ponential law with the time. The number of atoms N, which 
remain unchanged after an interval ¢ is given by 
w= | sage 
t 
to 
Ni i 
Thus a= GM eae rns sates ana (1), 
0 
or the law of decay expresses the fact that the activity of a pro- 
