Oct. 4, 1921 dorse y: radioactive quantity 385 



When the unit is the r these coefficients become 



X2 X3 X3 Xi Xi X2 



^ " (X2-Xl)(X3-Xl)' ^" (Xl-X2)(X3-X2)' ^" (Xi-X3)(X2-X3)' 



In these the symmetry is perfect. 



A name for the quantity r would be most useful when curves similar 

 to those given by Rutherford as figures 102, 103, 110 {Radioactive 

 substances and their radiations) have to be plotted. The ordinates of 

 these curves are proportional to the number of r's of the several ele- 

 ments, and to the sum of these r's. If the alpha particles from each 

 element are equally effective in producing the effect measured, the 

 total effect is proportional to the sum of the r's and on this assump- 

 tion the ordinates are proportional to the "activities." In lieu of a 

 name for the quantity r the ordinates are labeled "activities," and the 

 assumption is explained in the text. Were there a name for the quan- 

 tity r the ordinates could be so marked and no assumption would be 

 required. 



It has been shown how the weight of an r of any element can be 

 computed. Consequently there is no serious difficulty in determining 

 the number of r's contained in a given amount specified in grams; 

 or conversely. In the portion of the radium family comprised between 

 ionium and radium-C, both inclusive, the elements are now actually 

 measured in terms of r, which in this region may be regarded as merely 

 an abbreviation of the oft recurrent phrase "amount that is in equili- 

 brium with one gram of radium." Beyond these branch points a 

 factor depending upon the branching ratio must be introduced. Sev- 

 eral methods are available for determining the value in r's of a radio- 

 actively defined amount of an element of another family. If a chemi- 

 cally pure salt of known composition either of this element or of another 

 genetically related to it and not separated from it by a branch point 

 has been prepared, we can determine at once the value of \N for a 

 gram of that element. The ratio of this to k will be the number of 

 r's in a gram of that element, and likewise in such amounts of its 

 derivatives as can exist in equilibrium with a gram of it. Or the num- 

 ber of alpha particles emitted per second by the material considered 

 or by an equilibrium amount of a related element might be determined. 

 This number divided by 3.72 X 10 ^'^ (the value for one gram of radium, 

 i.e., the quantity we have denoted by k) will be the number of r's in 

 the quantity considered, unless more than one alpha particle is emitted 

 during a single transformation of an atom; this can be determined by 

 suitable observ^ations. 



