Dr. 0. Halm mi Radioactinium. 171 



film of the active substance and gave the ionization curves 

 obtained with it. 



The success was complete. Immediately after preparation 

 of the radioactinium the a rays were found to be homogeneous 

 and had a range of 1'8 cms. This result showed that only 

 one a ray product, viz. radioactinium, was present. 



Progressive measurements showed the gradual entrance 

 of new kinds of a rays, the most penetrating of which were 

 shown to be due to actinium X. 



If the actinium X was separated the ionization curves 

 showed exactly the same variation with time as before. 



d. Comparison of 'the Exverimental with the Theoretical Curves. 

 (1) a Ray Curves. 



Knowing the period of radioactinium and its connexion 

 with the other actinium products, it is not difficult to deduce 

 theoretically the rise and decay curves, measured by the a 

 and (3 rays, that should be exhibited by raclioactininm. 



We must remember that Ba Act. is the parent of Act. X, 

 which in turn is transformed through the stages emanation, 

 actinium A, and actinium B« 



Let X 1? a 2 be the constants of transformation of radio- 

 actinium and actinium X respectively. 



Let P and Q be the number of atoms of radioactinium and 

 actinium X respectively existing at any time t after the 

 preparation of the radioactinium. Then it is known from 

 Butherford's theory of the successive changes * that 



V = n.e-^\ 

 Q=^L<>-v_*-ai*), 



A.\ — A 2 



■where n is the number of atoms of radioactinium initially 

 present. 



Now the oc ray activity of the radioactinium some time after 

 preparation is due to radioactinium, actinium X, the emana- 

 tion, and actinium B. The period of actinium X is 10*2 days, 

 of the emanation 3'9 sees., of actinium A 36 minutes, and of 

 actinium B 2 minutes. The changes following actinium X 

 are thus very rapid compared with actinium X itself, and we 

 may, for the purpose of calculation, assume without sensible 

 error that the changes succeeding actinium X are instan- 

 taneous. We may therefore include the activity due to these 

 products with that of actinium X. 



Now* the activity It (measured by the electrical method) of 



* Eutherford. 'Radioactivity 



