24 Dr. N. Bohr : Theory of Decrease of Velocity of 



degree the conditions on p. 20 are satisfied in the case in 

 question. For V = l*75 . 10 9 , we get 



x= ,E^M + m) =1 . 6>10 _ 10 and V /a=0-8.10-*. 

 V 1VJ m 

 We see that the first condition is amply satisfied. We have, 

 further, that the maximum value to be assumed for the 

 quantity p on p. 20 is about 10 -8 , i. e. the " radius '' of a 

 hydrogen molecule ; we thus get the maximum value to be 



assumed for ~ equal to about 0*1. As the corrections due 

 to finite values for (~ , as mentioned on p. 20, are propor- 

 tional to the square of this quantity, we must, therefore, 

 expect them very small in the considered case. 



It may here be remarked that the above value for V/n 

 shows that the effective limit, mentioned on p. 12, for the 

 action of the electrons on the velocity of the particles, for 

 hydrogen and for particles of the velocity considered is about 

 8 times the radius of the molecules ; for /H-tsljs of velocity 

 near the velocity of light the limit in question would be more 

 than 100 times the radius of the molecules. 



We see that the absorption of «-rays in hydrogen can be 

 satisfactorily accounted for by assuming the same number of 

 electrons per molecule and the same frequencies, as those 

 assumed in order to explain the refraction and dispersion in 

 this gas. It may here be mentioned, that if w r e assumed 

 that the hydrogen molecule contained more than two electrons, 

 the theory shows that the frequencies of the other electrons 

 must be extremely high, as the absorption due to them, after 

 the above calculation, cannot amount to more than about 

 10 per cent, of the absorption due to the two electrons con- 

 sidered. Thus assuming that the molecule contains further two 

 electrons, we get that n for them must be at least of the order 

 of magnitude of 10 18 ; a value for n which seems difficult to 

 reconcile with experiments on characteristic Rontgen rays 

 (comp. later, p. 26). If we adopt Rutherford's conception 

 of the constitution of atoms, we see that the experiments on 

 absorption of a-rays very strongly suggest, that a hydrogen 

 atom contains only one electron outside the positively charged 

 nucleus. 



Helium. 



For helium there is no measurement of the absorption 

 coefficient for different velocities ; the only experiment with 

 this gas is a determination by Adams * of the range in 



* E. P. Adam?, Physical Review, xxiv. p. 113 (1907). 



