274 EXCITED RADIO-ACTIVITY [CH. 
which n, particles were deposited on the body, the number q of 
particles which have passed through the first change but not the 
second is at any time 7’ given by 
NN 
gi Glas 
ary Al (A) 
(See section 174.) 
But, since only the second change is accompanied by rays, the 
intensity of the radiation is always proportional to q the number 
unchanged, 1.e. to nf (E). 
It has been shown in section 174 that; for a very long exposure, 
the activity Z;, after removal for a time ¢, is given by 
(e- dt — e- Mt) 
1,_ |, mroe 
fo [ons dt 

where J, is the initial intensity after removal. Substitutimg the 
value of f(t) and integrating 
Aineg 
aie =Ant re ent 
I, M=%, x, AG 


This is of the same form as the equation of the decay curve 
found by Curie and Danne. Substituting the values A, = 1/2420, 

: Z Wate 
A, = 1/1860, which were found by them, the value of — = “18 43 
1 2 

and of — — x; is 3'3. 
The experimental value found by Curie and Danne for these 
constants was 42 and 3:2 respectively. The agreement between 
the theory and the experiment is as close as could be expected. 
There are thus three distinct changes in the emanation X of 
radium, viz 
(1) A very rapid initial change. Half of the matter changes 
in about three minutes and is accompanied by ionizing rays. 
(2) A slower change, which is not accompanied by ionizing 
rays. Half of the matter undergoes change in 36 minutes. 
