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LXXVIIL A Quantitative Relation between the Range of the 

 a. Particles and the Number of Charges emitted during 

 Disintegration. By A. van den Broek *. 



IN 1907 Rutherford f observed that there appeared to be a 

 relation between the period of transformation of a pro- 

 duct and the velocity of the a. rays expelled from it. In 1911 

 Geiger and Nuttall % showed that in the great majority of 

 cases the range of the <x particle increased with the decrease 

 of the period of transformation. Plotting the logarithm of 

 the range of the a particle against the logarithm of the con- 

 stant of transformation, the products of the uranium and 

 radium series lie nearly on a straight line. In the thorium 

 and actinium series again most of the products lie approxi- 

 mately on a straight line parallel with the line showing the 

 relation for the uranium-radium series. As Rutherford § 

 remarks, " The relation found by Geiger is of exceptional 

 interest, for it supplies undoubted evidence that a connexion 

 exists between two of the fundamental magnitudes in radio- 

 active transformation." 



Similar relations were given by Swinne || and H. A. 

 Wilson H. 



Between the velocity of the a rays and the number of 

 charges expelled there appears also to be a similar relation. 

 Plotting the logarithm of the initial velocity of the a particle 

 against the number of charges expelled, the products of all 

 series lie nearly on a straight line. As the values for all 

 series, but not for analogous products in each, are the same, 

 the initial value for each series can be chosen to fit in well. 

 Of course it is not known if these are really the first. 



Two difficulties immediately arise. Firstly, Ra C and 

 Th C (or B) were proved by Fajans ** and by Marsden and 

 Barratt ft to give off two branches of products. It seems, 

 however, that for one branch the relation holds good, while 

 for the other a reversal, and probably a regular one, seems to 

 take place. In this case, on the Ra series one product more 

 for each branch ought to be introduced; for the thorium 

 series, however, more. 



* Communicated by the Author. 



f Phil. Mag. xiii. p. 110 (1907). 



% Phil. Mag. xxii. p. 613 (1911) ; xxiii. p. 439 (1912) ; xxiv. p. 647 

 (1912). 



§ ' Radioactive Substances and their Radiations/ p. 609, Cambridge 

 1913. 



|| Phys. Zeitsch. xiii. p. 14 (1912). 



5T Phil. Mag. xxiii. p. 981 (1912). 

 ** Phys. Zeitsch. x. p. 697 (1909). 

 tt Proc. Phys. Soc. xxiv. p. 8 (1911). 



