Atmospheric-Electric Observations, 1915-16 395 



This neglects the ionization due to the ^-rays and 7-rays in the ionization chamber; but 

 such ionization is small in view of small range of action available, in the chamber, for these 

 rays. 



If we multiply the product of the quantities W and rj, as defined in the specimen com- 

 putation on page 400, by a factor h, to allow for the fact that some of the a-particles do not 

 travel the whole of their range in the ionization chamber, we have 



r,Wh = \^N^p+\cNcr+^cNcr+\cNcr (13) 



In so far as the fractional loss of ionization depends, in part, on the range of the a- 

 particles, the quantity h theoretically depends upon the ratio of the amounts of ionization 

 from the A and C products, and this ratio varies with the time. In practice, however, 

 since the radium A decays to half its activity in about 3 minutes, practically the whole of 

 the measurements depend upon the ionization by radium C. Thus, in the calculation of /;, 

 which will be explained later, the range has, as an approximation, been taken as that of the 

 radium C particles. This does not, of course, imply that, at the end of a few minutes, the 

 influence on the shape of the decay curve, of the radium A deposited, is lost, for the radium 

 A produces radium B, and this, while it produces no ionization, slowly grows into radium C 

 If we now substitute in (13) the values given by (8), (9), (11), (12), putting in the 

 values of the constants X^, Xs, and Xc in the coefficients of the exponentials; and if we 

 further note that the quantities njW , ns/W, and iic/W represent respectively the 

 quantities ria, n,,, and n^, i. e., the numbers of atoms of radium A, radium B, and radium C 

 in the atmosphere, we find 



■n=r)i-]ry]2+r}3 (14) 



^^^^•^ /ii7i = n,(1.92e-V+5.36e-^B'+4.98e-M)Xl0^ (15) 



/i772 = n6(4.76e->^B'-4.21e-V)XlO^ (16) 



/»j3 = n,(1.56)e-MxiO^ (17) 



Theoretically, the values of njh, rit/h, and njh can be obtained from 3 points on the 

 experimental curve. Such a method of determining the constants is, however, somewhat 

 laborious, and not very satisfactory in the present case. If, however, the curves for t/i 

 and 7)1 are plotted with arbitrary values of njh and nt,/h, it turns out that, for both curves, 

 the slope is practically zero at t = 1,320 seconds. Thus, the whole of the slope of the experi- 

 mental curve at this point is due to 173, and consequently at i= 1,320 seconds we have, using 

 (14) and (17), 



^=_^(1.56)e-i32ox,xiO^ 



which serves to determine njh, since Xc is known. The curves may thus be simplified into 

 curves involving only curves of the types tji and 1)2, and the values of njh and n„/h may be 

 more satisfactorily determined. When n^ has been obtained, the emanation content may 

 immediately be deduced from equation (7). 



The quantity h was obtained from the following considerations: Suppose Pds repre- 

 sents the number of a-particles which, coming from an area ds of the foil, are initially shot 

 out within unit solid angle. The total ionization to be expected from these a-particles is 

 Prds, if they traveled their full range in air. The ionization to be expected, under the same 

 conditions, from all of the a-particles emitted from the element ds would consequently be 



Io = 4irPrds (18) 



Now half of the a-particles never succeed in leaving the metal foil, since they are shot 

 directly into it, and of the 2irPds particles which do leave the foil, a number strike the wall 

 again before completing their range. 



