Relative Activities of Radio-Products of Thorium. 357 

 particle by I, then dI=idZ, and therefore 



(14) 



*/o 



where K is a constant. The facts jnst considered indicate 

 that the ionization of equal numbers of alpha particles is not 

 directly proportional to the respectiA'e ranges, as Boltwood 

 suggested. In a radioactive series if each atom of each alpha- 

 ray product gives one and only one alpha particle upon dis- 

 integrating, then for equilibrium proportions of the products 

 of the series, each product will give rise to equal numbers of 

 alpha rays per second. In such a case the relative activities 

 of various products will be proportional to the # power of 

 their ranges. In Table V., column three, are given values 

 of KR 2 ' 3 , K being so chosen that the value of the expression 

 is unity for lit. 



Table V. 



Product. 



Ran ge. 



KR 23 - 



Calculated ; Observed 

 Activity. Activity. 



P.c. of total 

 alplia-ray 

 Activity. 



Th 



2-58 



3-67 



4-1 



5-0 



5-4. 



86 



4-8 



0-79 

 100 



ros 



1-23 

 T29 

 1-76 

 1-20 



0-79 



11-4 

 14-4 

 15'5 

 17-6 

 18-6 



22-5 



Rt 



100 



I 3-60 



J 



] 56 



100 

 3665 



1-540 

 •025 



ThX 



Em 



A 



! c, 



Co 



B+D 



Now we have found in Section II. that the activity of 

 B + d-f Co -f-D compared witli the equilibrium amounts of 

 ThX + Ein + A gave the value t v = 0*427 ; and in Section III. 

 that the activity of ThX 4- Em 4- A + B + (J 1 -+- C 2 + D compared 

 with the equilibrium amount of Rt gave the value ?/ = 5'*23.. 

 From these results it follows that the activity of B + CiH- 

 C 2 + D is 1*565 times that of Rt, and also that the activity of 

 ThX + Em 4- A is 3*065 times that of Rt. A small correction 

 must be made on account of the beta-ray activity of B and D. 

 We found that this activity was 1*6 per cent, of the total 

 activity of B + C, + C 2 + D for our electroscope. The alpha-ray 

 activity of Oi + C 2 is therefore 1*540 times that of Rt, while 

 the beta-ray activity of B + D is 0*025. These observed 



