208 30 



also dependent on the form of tlie ionisation chamber. I have therefore preferred 

 comparing tlie emanation in the liot spring gases with the emanation evolved by 

 a known quantity of radium per second. In this way the unit of emanation 

 becomes independent of the shape of the ionisation chamber, because the known 

 quantity of emanation is measured in exactly the same way as that which it is 

 desired to determine. It is taken for granted in this, as in every other case where 

 measurements of emanation are to be made, that the ionisation is proportionate to 

 the emanation, other conditions being equal. 



As the unit of radium emanation, I have adopted the amount of emanation 

 evolved per second by the radium in one gr. uranium in natural minerals. A similar 

 used by unit is Boltwood ' in his researches of some American hot springs. 



In order to obtain the value of a„, in the proposed unit, I dissolved about 

 0.1 gr. uraninite from Joachimthal in dilute nitric acid. The solution was put 

 into a bottle that could be made airtight. Then the solution was freed from 

 emanation by boiling, and the bottle closed. The radium contained in the solu- 

 tion incessantly evolves emanation, which is stored up in the bottle. After standing 

 three or four days, the emanation evolved is completely removed from the solution 

 by pumping and boiling, and the emanation thus collected is introduced into the 

 ionisation chamber, where it is measured in the ordinary way. 



According to two analyses, for which I am deeply indebted to Cand. polyt. 

 V. Farsöe, the uraninite used in these experiments contained 23.8 "/o uranium. If 

 p gr. uraninite are dissolved, the radium in the solution evolves per second 0.238 p 

 emanation units. On this basis, and by making proper allowance for the decay of 

 the emanation, the amount, q, of radium emanation in the solution at any given 

 time, may be calculated. Of the emanation q, the fraction aq is transformed every 

 second; here, the transformation coefficient a is, according to Rutherford and 

 SoDDY", computed at 2.16x10-''. Then with respect to the solution, the total 

 increase of the emanation in the infinitesimal interval dt, is given by the differ- 

 ential equation, , 



^1^ dt = 0.'23Hpdt— oqdt. 



Hence we get by integration, 



0.238/) , ,, _,,, 

 q = - -4- Ce "'. 



I/. 



By letting q = when / = 0, we get the integration constant, 



^ ^ _0.238p 

 « 

 Therefore, 



0.238/),, „. 



In this formula the transformation coefficient a = 2.16 x 10-^, e the base of the 



1 Amer. Journ. Sei. IS. .S78, 1904. 



- See Rutherford: Radio-activity 2. ed. 1905, p. 247. 



