340 H. M. Dadourian— Atmospheric Radio-acUvity. 



Suppose 

 N = number of atoms of radium emanation in l cc of air 



N x = 





a 



a 





A 



a 



N a = 





a 



tt 





B 



a 



N> 





a 



a 





C 



n 



N' = 





a 



ii 





thorium emanation 



a 



W = 





a 



ii 





" A 



a 



»'.= 





a 



ii 





B 



it 



N'.= 





a 



ii 





C 



a 



n and 



n 



i 



number 



of 



atoms of radium an 



id thorium 



emanation which are transformed per second in l cc of 

 the air. 

 X, \„ X 2 , X 3 , X', X'j, X' 2 , and X 7 3 , = the disintegration 

 constants of radium emanation, Ra A, Ra B, Ra C ; 

 thorium emanation, Th A, Th B, and Th C respec- 

 tively. 



We will assume that each particle of any one of a group of dis- 

 integration products gives rise to a particle of the next product 

 of the group. Then if this group is in radio-active equilibrium 

 the number of the particles which are transformed per second 

 is the same for all the members of the group. Since the air 

 is supposed to be in radio-active equilibrium, 



n = XN = A 1 N 1 = A 2 N 2 == X 3 N 3 ( 1 ) 



holds for the radium group, and 



n'= A'N' = X' 1 S\ = X' 2 N' 2 = X' 3 N' 3 (2) 



for the thorium group. 



The number of atoms of any of the disintegration products 

 present on the negatively charged wire is proportional to the 

 number of particles of the same product present in l oc of the 

 air, provided the wire has reached the state of radio-active 

 equilibrium with the surrounding air. Therefore if we denote 

 the number of particles on the wire of any one of the six pro- 

 ducts by M, with the proper subscript and prime according to 

 the above notation, we can write 



M„ M„ 





M 1 





N, 







N> 



= KM 



N\ 



= KM' 



(3) 

 (4) 



N s N 3 



N' 2 W s 



N 2 = KM 2 , N 3 = KM 3 

 N' 2 = K'M' 2 , N', = K'M' 3 

 Therefore substituting in equations (1) and (2) 



n = AN = K A, M, = K A 2 M 2 = K A 3 M 3 (5) 



n' = A'N'= K'A'.M'^ K'X' 2 M' 2 = K'A' 3 M' 3 (6) 



