602 Dr. N. Bohr on the Decrease of 



This gives 



A(H /3 )= — (l-/5 2 )-IA/9. 



On the theory of relativity we have further 



T = c 2 m((l-/3 2 )-*-l); 

 from this we get 



AT = c 2 my9(l-/3 2 )-i A/3 (25) 



We have consequently 



AT = e/3A(Rp) (26) 



From (18) we thus have, putting E = e and V/c- = /3, 

 2iremAx*r /£VNwA#\ ' /1-/3 2 



^>-^r ? w 



47T^ 2 



Except for very high velocities the variation 

 factor will be very small, and we shall therefore, according 

 to the theory, expect A(JB.p) to be approximately proportional 

 to /3~ 3 . The third column of the table contains the values 

 for /8, and the fourth column the values for /3 3 A(H/>). It 

 will be seen that the values in this column are constant 

 within the limit of experimental errors. 



Putting n=13 and using the value - S log v = 39*0 



calculated from experiments on a rays, we get from (27) 

 for an aluminium sheet 0*01 gr. per cm. 2 



/3 = 0-6 0-7 0-8 0-9 0*95 

 J3 Z A{K P )= 40 41 42 44 46 



Considering the great difficulty in the experiments and the 

 great difference in mass and velocity for a and ft rays, it 

 appears that the approximate agreement may be considered 

 as satisfactory. The mean values for A(Hf)), calculated 

 from the formula (5) in section 1, would be about 1*3 times 

 larger for the slowest velocities and would increase far more 

 rapidly with the velocity of the /3 rays. 



Measurements of the decrease of velocity of ft rays in 

 sheets of metals of higher atomic weight are more difficult 

 than with aluminium on account of the greater effect of the 

 scattering of rays. Danysz found that the rate of decrease 

 of velocity was approximately proportional to the weight 

 per cm. 2 of the absorbing sheet. Since the number of 

 electrons in any substance is approximately proportional to 



