Moving Electrified Particles pas sing through Matter. 27 



to, or at least o£ the same order of magnitude as, the kinetic 

 energy of an electron of velocity just sufficient to excite the 



m 



radiation: putting them equal we get vk = — A 2 . 10 16 , and 



from this v = A 2 . 6*7 . 10 14 . No experiments on characteristic 

 Rontgen rays are made for oxygen, but if we assume Whid- 

 dington's law to hold for this element, and put A=16 in the 

 above expression for v, we get v = l'7 . 10 17 , and accordingly 

 for the frequency n = 27rv=l'l . 10 18 . The agreement as to 

 the order of magnitude between this value and the above 

 value for n', calculated from the absorption of a-rays, is 

 remarkable. 



An estimation of the magnitude of the corrections to be 

 introduced in the formula (4) in case of oxygen, involves a 

 discussion about the relation between the frequencies and 

 the dimensions of the orbits of the electrons in the interior 

 of the atoms ; and must therefore be postponed till the later 

 paper referred to in the note on p. 23. 



For aluminium, tin, gold, and lead, we get in the same 

 manner as for oxygen, by comparing the values in the table 

 on p. 22 with the formula (4) on p. 19, the following- 

 values for r and 2 log (n s . 10 ~ 19 ). 



Substance. 



r. 



-V(l0g*.. 10-19). 

 s=l 



41 



94 



126 



182 



Atomic weight. 



Aluminium 



Tin 



14 

 38 

 61 

 65 



27 

 119 

 197 

 207 



Gold 



According to Rutherford's theory we shall expect values 

 for r equal to about the half of the atomic weight ; we see 

 that this is the case for aluminium, but that the values for 

 r for the elements of higher atomic weight are considerably 

 lower. The values found for X loo- n s are of a magnitude to 

 be expected if the atoms contained electrons of different 

 frequencies varying from the order of magnitude of the 

 frequencies observed by the dispersion in the transparent 

 bodies to that of the characteristic Rontgen rays. It must, 

 however, here be remarked that the magnitude of the cor- 

 rections to be introduced in the formulae (4) must be expected 

 to increase with increasing atomic weight of the. substance 



