394 J. C. Sanderson — Radio-active Content of 



piece of pressure tubing, and the ionization vessel was con- 

 nected, in turn, to a manometer and filter pump. Pinchcocks 

 were provided between the manometer and the pump, between 

 the ionization vessel and the cylinder and at the top of the 

 cylinder. First the ionization vessel alone was exhausted, the 

 first pinchcock closed and the pressure p x noted. Then the 

 second pinchcock was opened and the ionization vessel and 

 cylinder allowed to come to an equilibrium pressure p which 

 was noted. Finally the pinchcock on the upper end of the 

 cylinder was opened and the whole system came to the atmos- 

 pheric pressure p^ (the gross barometric height), the air 

 passing through the soil. After three hours, the active deposit 

 was in virtual equilibrium with the emanation, and readings 

 of the electroscope were taken (in divisions per minute over a 

 definite part of the scale). 



Determination of the Radium Content. 



Call the volume of the ionization vessel V, and the volume 

 of the cylinder V 2 . Then the porosity P, or the ratio of 

 the volume of the interstices of the soil to the total volume, is 

 given by 



V 2 p-p 



The volume of air in the soil is, of course, P V 2 , and the 

 volume of air, at atmospheric pressure, which enters the ioni- 



p — p 

 zation vessel as it passes from p 1 to p^ is V 2 — — — 1 . Hence 



Pi 

 the number of cubic centimeters of soil from which emanation 



p — p 



, , air entering ionization vessel __ V n — - — — 



is taken equals — - —. — — 7-. x V „ = p„ 



u total air in soil 2 — p~v — 



Let n be the fraction of a gram of radium per cubic centi- 

 meter of the soil, which would account for its free emanation ; 

 then n Y/ is the mass of radium which supplied the emanation 

 in the ionization vessel. If this emanation caused a leak of JN 



n V . 

 divisions per minute in the electroscope, ^ 2 is the mass of 



radium which would cause a leak of one division per minute. 

 But it is known, from the standardization of the electroscope, 

 that the emanation in equilibrium with M gram of radium 

 (from a standard solution of radium bromide) gave a leak of 



M 



A divisions per minute ; whence — r- is the mass of radium 



