374 Miss H. Brooks on the Decay of the Excited 
The excited activity on a negatively charged conductor is 
due to the deposit on it of positively charged carriers*, one 
of the decomposition products of the emanation. The initial 
increase after a short exposure, it has been pointed outf, 
can be explained if it be assumed that a double change takes 
place after the positive carriers have been deposited on the 
electrode. If the first of these changes be unaccompanied 
by the production of rays, while the second gives rise to rays 
which ionize the gas, then for a very short exposure the 
radiation from an active body will continue to increase as 
the first change proceeds, reach a maximum when most of 
the matter deposited has undergone the first change, and 
then gradually decrease as the second change takes place. 
That the initial rise in the radiation is to be observed only 
for short exposures is to be expected since, after a long ex- 
posure, the decay of the radiation as a whole more than 
compensates for the increase due to the primary change in 
the radioactive particles deposited in the last few hours of 
exposure. This increase after removal lasts only a few hours 
for the shortest exposures, thus the primary change must be 
completely effected in that time. 
These two changes each follow an exponential Jaw with 
the time, and may be represented by the equation Ns=Noe-™, 
where N; represents the number of particles present un- 
changed after an interval ¢ and N, the original number. 
Let A,=coefficient of the primary change, 
and... As= »» secondary ,, 
then, if the plate is exposed to the emanation for one second 
and mo particles are deposited, the number of particles dq 
which have undergone the first change but not the second at 
a time ¢ after removal is given by 
7+ Mnry ay L 
al ope waa 
B= seal ) 
Now if the rod is exposed for a time ¢, the corresponding 
number of particles g; which have undergone the first change 
at the time of removal is given by , 
gt=nof (t)dt+m{f (dt)}dt+ ..... no f (t)dt 
=|, J (t)dt. 
-* Phys. Zeit. no. 10, 1902. 
+ E. Rutherford, ‘ Radioactivity,’ p. 27. 
