x] RADIO-ACTIVE PROCESSES 303 
particles per second, the increase of the number dn in the time dt 
is given by 
dn = qdt — Xndt — andt, 
dn 
ek ol 
or 
The same equation is obtained when no emanation escapes, 
with the difference that the constant X%+a is replaced by 2. 
dn 
"dt 
When a steady state is reached is zero, and the maximum value 
qd 
f n is equal to —*—. 
E70 1s ea ie ae 
@) 
If no escape takes place, the maximum value of n is equal to \ 
The escape of emanation will thus lower the amount of activity 
: : r : 
recovered in the proportion Lae If m is the final number of 
emanation particles stored up in the compound, the integration of 
the above equation gives a= L—e Atae, 
0 
The curve of recovery of activity is thus of the same general 
form as the curve when no emanation escapes, but the constant 
X is replaced by X+ a 
For example, if a= = 1/463000, the equation of rise of activity 
Mr}. n : : : 
is given by a 1—e-*’, and, in consequence, the increase of 
ny 
activity to the maximum will be far more rapid than in the 
case of no escape of emanation. 
A very slight escape of emanation will thus produce large altera- 
tions both in the final maximum and in the curve of recovery of 
activity. 
A large number of experiments have been described by Mme Curie 
in her These présentée a la Faculté des Sciences de Paris on the 
effect of solution and of heat in diminishing the activity of radium. 
The results obtained are in general agreement with the above view, 
that 75 per cent. of the activity of radium is due to the emana- 
tion and the excited activity it produces. If the emanation is 
wholly or partly removed by solution or heating, the activity of 
