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



By comparison with the formula? (7), p. 23, we now get 



T (log {n . 10 ~ 19 ) +0*59) = -17, 



S-l 



2 (log(n, .10- 19 ) -0'18)= -61. 



Prom this we get at first by subtraction 



r. 0-77 = 14 or r = 18. 



According to Rutherford's theory of atoms we should 

 expect 16 electrons in an oxygen molecule. The agree- 

 ment between this value and the above value for r is very 

 satisfactory. 



From the above we get further 



Tlog(n,.10- 19 ) = -58. 



s=l 



From experiments on dispersion * we have that an oxygen 

 molecule contains 4 electrons of frequency 2'25 . 10 16 ; we 

 get, therefore, 



Tlog(72 5 .10- 19 )=-58 + 4.6-l=-31. 



s—5 



If we for the present assume that the other 12 electrons 

 supposed contained in an oxygen molecule have equal 

 frequencies n f , we get 



log (n'. 10" 19 ) = -2'8, and n' = 0'6 . 10 lS . 



We know very little about the higher frequencies in 

 oxygen, but we can get some estimation of what we should 

 expect, from experiments on characteristic Rontgen rays. 

 Whiddington f has found that the velocity of an electron 

 just sufficient to excite the characteristic Rbntgen rays in an 

 element is equal to A . 10 8 cm./sec, where A is the atomic weight 

 of the element in question. The energy possessed by such 



11% 

 an electron is — A 2 . 10 16 . According to Planck's theory of 



radiation we further have that the smallest quantity of energy 

 which can be radiated out from an atomic vibrator is equal 

 to v . k, where v is the number of vibrations per second and 

 k = 6'55 . 10~ 27 . This quantity must be expected to be equal 



* C. & M. Cuthbertson, loc. cit. p. 166. 



t R. Whiddington, Proc. Roy. Soc. A. lxxxv. p. 323 (1911). 



