268 EXCITED RADIO-ACTIVITY [CH. 
Let us suppose, for example, that a body has been exposed for 
a long interval in a vessel containing a constant quantity of the 
radium emanation. The excited activity in the body will have 
reached a maximum value when the rate of supply is balanced by 
the rate of change. Suppose this body is removed and an exactly 
similar body immediately substituted. The sum of the excited 
activity on these two bodies will at any time be the same as on 
the single body before removal. If this were not the case, there 
would be a change in energy of the radiations from the radio- 
active system, as a whole, purely by removal of one body and 
substitution of another. This is contrary to the general experi- 
mental fact that the processes occurring in radio-activity are 
independent of control, and that the radiation from a system in 
radio-active equilibrium remains constant. 
Thus if /; = intensity of radiation from the excited body at any 
time t after removal. 
I, = intensity of radiation from the new body exposed 
under the same conditions for a time tf. 
Then J, + J; =J, where J, is the initial activity on the removed 
body. 
/ 
EER TE , ; é 
Thus 1——" =~, which is the same relation that has been 
If, If 
developed from other considerations. 
These results are particular cases of what may be termed the 
“conservation of radio-activity,’ which is discussed in detail in 
section 196. 
175. Theory of successive changes. It has been pointed 
out that the excited activity produced in a body exposed for a very 
short interval in the presence of the thorium or radium emana- 
tions does not decay according to a simple exponential law. In 
the case of a body excited by the thorium emanation, the activity 
increases for a few hours, passes through a maximum where the 
activity is five to six times the initial value, and then slowly decays 
in an exponential law with the time, fallmg to half value after 
a further interval of 11 hours. After the maximum is reached, 
