SUCCESSION OF CHANGES IN RADIOACTIVE BODIES. 193 



as that found experimentally by CURIE and DANNE. On substituting the values 

 Ag, X 8 found by them. 



= 4'3, and X = 3'3. 



Xg Xj \l Xg 



Thus not only does the theoretical equation agree in form, but also closely in the 

 values of the numerical constants. If the first as well as the second change gave 

 rise to a radiation, the equation would be of the same general form, but the value of 

 the numerical constants would be different, the values depending upon the ratio of 

 the ionization in the first and second changes. If, for example, it is supposed that 

 both changes give out ft rays in equal amounts, it can readily be calculated that the 

 equation of decay would be 



I, _ '5X 2 



e "* 



Taking the values of X 2 and Xg found by CURIE, the numerical factor e"* 1 ' l)ecomes 

 2'15 instead of 4 '3 and 1'15 instead of 3 '3. The theoretical curve of decay in this 

 case would be readily distinguishable from the observed curve of decay. The fact 

 that the equation of decay found by CURIE and DANNE involves the necessity of an 

 initial rayless change can be simply shown as follows : 



Curve I. (fig. 11) shows the experimental curve. At the moment of removal ot 

 the body from the emanation (disregarding the initial rapid change), the matter must 

 consist of both B and C. Consider the matter which existed in the form C at the 

 moment of removal. It will be transformed according to an exponential law, the 

 activity falling to half in 28 minutes. This is shown in curve II. Curve III. 

 represents the difference between the ordinates of curves I. and II. It will be 

 seen that it is identical in shape with the curve (fig. 5) showing the variation of the 

 activity for a short exposure, measured by the $ rays. It passes through a maximum 

 at the same time (al>out 36 minutes). The explanation of such a curve is only 

 possible on the assumption that the first change is a rayless one. The ordinates of 

 curve III. express the activity added in consequence of the change of the matter B, 

 present after removal, into the matter C. The matter B present gradually changes 

 into C, and this, in its change to D, gives rise to the radiation observed. Since the 

 matter B alone is considered, the variation of activity with time due to its further 

 changes, shown by curve III., should agree with the curve obtained for a short 

 exposure (see fig. 5), and this, as we have seen, is the case. 



The agreement between theory and experiment is shown in the following tables. 

 The first column gives the theoretical curve of decay for a long exposure deduced 

 from the equation 



' = ** e~ x '' ^ e~ v 



*O Xj Xg X^ Xj 



taking the value of X., = 3-10 X 10~ 4 and X 3 = 4'13 X 10" 4 . 

 VOL. cciv. A. 2 c 



