Velocity of Swiftly Moving Electrified Particles. 5^5 



It will be seen that the correction is very small unless V 

 is very near to the velocity of light, since in other cases the 

 two last terms will approximately cancel each other out. 



§ 4. Comparison with measurements on a rays. 



In the former paper it was shown that the formula (5) in 

 ■section 1 gives values which are in close agreement with the 

 measurements on absorption of « rays for the light elements 

 hydrogen and helium, if we assume that the atoms of these 

 •elements contain 1 and 2 electrons respectively, and if for 

 the characteristic frequencies we introduce the frequencies 

 determined by experiments on dispersion. It was also shown 

 that an approximate agreement with the measurements of 

 the absorption in heavier elements could be obtained by 

 assuming that these elements, in addition to a few electrons 

 of optical frequencies, contain a number of electrons more 

 rigidly bound and of frequencies of the same order of mag- 

 nitude as those determined in experiments on characteristic 

 Rontgen rays ; the values deduced for the number of electrons 

 were in approximate agreement with those calculated on 

 Sir E. Rutherford's theory of scattering of ex. rays. In this 

 section we shall therefore only consider tho new evidence 

 obtained by later more accurate measurements. 



Since the velocity of a. particles is small compared with 

 the velocity of light, we have T=JMV S . From (5) we 

 therefore <ret 



g-K,f(logV»-£Slog»+K,), . (19) 



where 



v 4™ 2 E 2 N , „ f / kMm 



Ki= ,, ai 



1 mM 



,, , / kMm \ 

 K ' =1 °g Ur«E(M+ OT ) j 



This expression depends on two quantities characteristic for 

 the different substances, i. e the number of electrons in the 

 molecule n, and the mean value of the logarithm of the cha- 

 racteristic frequencies of the electrons -SWy. The latter 



n ° 



quantity determines the characteristic differences in the 

 '" velocity curve/' i. e. the curve connecting corresponding 

 points in a (a?, V) diagram. In the former paper formula (19) 

 was compared with values for dV/d.c deduced from the 

 measurements. Since the quantity directly observed is the 

 value of V corresponding to different values of x, it is simpler 



2Q2 



