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266 EXCITED RADIO-ACTIVITY [CH. 
time is supposed to include the effects of different kinds of 
radiation emitted during the succession of changes which may 
occur. 
The number of ions produced per second after a time ¢ by the 
active particles deposited for the first short interval of exposure is 
given by gn, f (t) dt. 
The number JV; of ions produced per second at the time ¢ by 
the radio-active matter deposited during the interval ¢ is given by 
a 
M,= 7 | 
A steady state is reached when the rate of supply of fresh ions 
per second by the addition of the radio-active material is balanced 
by the rate of diminution of the production of ions by the excited 
radiation as a whole. This steady state is reached after a long 
interval of exposure, and the maximum rate of production of ions 
NV, is given by 
F(t) dt. 
0 
N,= gn | f(t) dt, 
/ 0 
and 
t 
t) dt 
Ni en ) 
7 — px ; 
No | roa 
0 
If the curve of decay of the excited activity for a very short 
exposure is plotted with the ionization current as ordinate and — 
time as abscissa, as in Fig. 51, the values of these integrals are at 
once determined from the experimental curve by measuring the 

area included between the curve and the ordinates erected at the 
points corresponding to the time limits of the integrals. 
The curve of rise of excited activity can thus be deduced from 
the decay curve and vice versd. 
N,, the rate of production of ions due to the excited radiation, 
after removal from the emanation for a time ¢,, 1s given by 
rt-+ty 
NG = 9M, F(t) dt, 
Jt 
if t is the time of exposure. 
