108 Bumstead and Wheeler — Radio-active Gas. 



Let 



A = ionization produced by the gas at any instant. 

 E = " " " excited activity. 



I = observed ionization. 

 So that I = A + E. 



As a result of the regular decay of the activity of the gas 

 itself we have 



A= Ae 



— Kt 



Assuming that we have only one kind of excited activity, 

 its rate of production is proportional to the quantity of gas 

 present, i. e. to A ; and its rate of decay is proportional to E, 

 so that 



J = aA.«~«* - XE (1) 



Taking t = as the time when the gas is introduced into the 

 cylinder, the solution of this equation is 



E = ^{ e~ Kt - e-A 



and the total observed effect is 

 1= A 



.{K-y^-x^l ^ 



As we have seen, k— 0*0074 when t is measured in hours, and 

 \=1*36 gives an exponential rise of excited activity not greatly 

 different from that observed in figs. 4 and 5 ; so that during 



the first two .or three hours e~ Kt is nearly equal to unity, and 

 we have approximately 



I=A„-il- 



1 ] + s^ 1 -*-*) \ w 



The curve expressed by (2) differs from (2') in that its asymptote 

 is not a horizontal straight line but the curve, 



and within the time considered this is sensibly an inclined 



« ci 



straight line which is shown in figs. 4 and 5 ; — - is the ratio 



of the excited activity, after equilibrium has been attained, to 

 the activity of the gas. 



After three or four hours e~ ^ is negligible in comparison 



with e~ so that we have sensibly 



1 -^+si)r^ < 3 > 



