17t! J. C% Sanderson — Probable Influence of the 



between the activity with the pump running and the activity 

 when the air was at rest was due to the thorium emanation. 

 It i> easily seen that all the thorium emanation is drawn from 



a sphere whose radius R = y -±-=5 = 23'5 centimeters, where 



' 4 7rl 



q = cuhic centimeters per second drawn by the pump (50); T, 

 the number of seconds required for thorium emanation to decay 

 practically completely (420); and P, the volume of air per cubic 

 centimeter of the earth or sand ("366). This is the radius of the 

 sphere from which all the air is drawn in seven minutes and 

 any emanation originating beyond this sphere will entirely 

 decay before reaching the electroscope. Since the tube was 

 driven into the soil a distance equal to about six times the 

 radius of this sphere, no variation in the concentration of tho,- 

 rium emanation was to be expected. The radium emanation, 

 on the other hand, with its longer half-value period, was drawn 

 from a sphere of relatively enormous size, but, in standardizing 

 the radium, the underground air current was never running 

 for lengths of time aggregating to more than twenty minutes 

 and in this time all the air was drawn from a sphere of only 

 about 32 centimeters radius. 



Let n be the amount of thorium emanation in equilibrium 



per cubic centimeter of the earth. Then -^- is the amount of 



emanation per cubic centimeter of underground air, and this 

 will be its concentration whether at rest or in motion, until it 

 leaves the earth to enter the tube. If Tc J is the total volume of 

 the brass tube and all connections, up to the ionization chamber, 



Tc 



— - is the time taken to reach the ionization chamber and the 

 ( 1 



pi, AfCi 



concentration will there have the value — e~ ~„ , where \ is 



■p 1 ~ 



the decay constant for thorium emanation. The time taken to 



h 

 pass through the ionization chamber is — -, where k 3 is the 



volume between the inlet and outlet. The activity measured 

 is proportional to the mean concentration of the emanation in 

 its passage or 



t « 







