Ix] EXCITED RADIO-ACTIVITY 269 
the activity decays at the normal rate observed for bodies exposed 
for a long interval in the presence of the thorium emanation. 
The increase of activity with time cannot be ascribed to a 
possible occlusion of the radio-active matter in the pores of the 
substance and a gradual passage to the surface after removal ; 
for it has been found that a very thin sheet of aluminium foil, 
which absorbs very little of the radiation, exhibits the same effect 
as a solid plate. The effect is, however, similar in some respects 
to the increase of activity with time observed in a closed vessel in 
which the radium emanation has been introduced. This is known 
to be due to the production from the emanation of radio-active 
matter, which is deposited on the walls of the vessel and adds its 
radiation to that of the emanation proper. In a similar way the 
activity of Th X increases for the first day after separation from 
the thorium, and this is ascribed (see section 190) to the produc- 
tion of excited activity in the mass of the Th X. 
The most probable explanation of the initial increase of activity 
with time, observed for the excited activity produced by the thorium 
emanation, is that there are two successive changes occurring in 
the emanation X of thorium after the deposit of the active matter 
on the surface of the body. 
The theory of these secondary changes will now be considered. 
Let n, be the number of radio-active particles deposited on the 
body during the exposure to the emanation. The exposure is 
supposed to be so short that only a very small proportion of the 
particles have undergone change during the time of exposure. 
These particles are supposed to undergo change in an exponen- 
tial law with the time, and the product of the first change to 
break up again according to the same law, but at a different rate. 
Let A,, A. be the constants of the first and second changes respec- 
tively. After removal for a time ¢, the number n of particles 
remaining unchanged is given by 
D= Ty OO 
the number which change in the time d¢ at the time ¢ is given by 
Ame * dt. 
Some of this number at once begin to go through the second 
