Atmospheric-Electric Observations, 1915-16 393 



emanation content. This determination, which necessitates a careful analysis of the 

 curves obtained by plotting rj against the time, is carried out at Washington, and is based 

 on principles which will be clear from the following: 



THEORY OF DETERMINATION OF EMANATION CONTENT OF THE ATMOSPHERE. 



In attempts to calculate the amount of emanation in the atmosphere from an experi- 

 ment depending on the collection of the active deposit, it is customary to assume that only 

 radium A is deposited, although, of course, the fact that this radium A subsequently 

 decays to radium B, and radium C on the wire is taken into account. It is to be remem- 

 bered, however, that radium B and radium C are also deposited, and it turns out, in fact, 

 that the decay curves for the active deposit can not be satisfactorily explained by supposing 

 them to arise entirely from the radium A deposited. It might be thought that the products 

 radium A, radium B, and radium C, in the present experiment, would be deposited in pro- 

 portion to the equilibrium amounts present in the atmosphere, so that it would be an easy 

 thing to calculate the shape of the decay curve from the theoretical constants of the 

 substances. It must be remembered, however, that the A, B, and C products combine in 

 part with the negative ions in the air, and to different extents, depending on their decay 

 periods. Those particles which so combine naturally lose in the experiment their power 

 of being deposited. Thus, in the equation of the decay curves in terms of the known 

 radioactive constants, there must appear 3 constants, to be determined from the shape of 

 the experimental curve, and representing the numbers ria, rit,, and ric of positively charged 

 atoms of radium A, radium B, and radium C per c. c. of the atmosphere. \Vhen the value 

 of Ua has been determined on the above lines, and in the manner to be described in greater 

 detail below, the total number of atoms of radium A per c. c. of the atmosphere, including 

 those atoms which have lost their charge, may be approxmiately determined by multiplying 

 the value of Ua by the correcting factor (l+an_/X^),^ where a is the coefficient of recombi- 

 nation of ions, and n_ the number of negative ions per c. c. of the atmosphere. Thus if E 

 is the number of atoms of radium emanation per c. c. of the atmosphere, and X^ the decay 

 constant of the emanation, we have 



E\E = \A(l+o.^)na (6) 



Of if Q be the weight of radium with which the above amount of emanation would be 

 in equilibrium, and if X^ is the decay constant of radium, we have 



Q=^njl + a-^) (3.7X10-='2) (7) 



where 3.7X10""^ represents the weight of an atom of radium. 



Such a procedure neglects any thorium emanation which may be present ; but in view 

 of the short decay period of thorium emanation there is small likelihood of the existence of 

 any appreciable amount of this element far from land. It is also to be remarked that the 

 time of deposition in the present experiments is so short that in any case the shape of the 

 decay curve is mainly determined by the radium emanation. 



'.See J. Salpeter, Wien. Ber., vol. 118, p. 1163, 1909, and vol. 119, p. 107, 1910. 



