Moving Electrified Particles passing through Matter. 



23 



From the formula (-4), p. 19, we get, putting 



* = 4-65.10- 10 , E = 2e, e/m=5-31.10 17 , E/M=l'46.10 14 , 



and N = 2'59.10 19 (at 76 cm. and 20° C), 



for 



V = 1-35. 10°, ^=4'42.10 6 % (log Oz s .10" 19 ) +0-59) ) 

 and for )- (7) 



V=l-75.10 9 , ^-=2-03. 10 6 2 (log (» s .10- 19 ) -0-18) J 



UiU s—l 



From experiments on the refraction and dispersion in 

 hydrogen, and the discussion of these experiments according 

 to Drude's theory, C. and M. Cuthbertson find that a hydrogen 

 molecule in its normal state contains 2 electrons of frequency 

 n=2'21.10 16 *. 



Putting r = 2 and « 1 =n 3 =2*21.10 16 in the above formulae, 

 we get 



for V = T35. 10°, f^=-4-9.10 7 , 



Ix 



and 



for V=l'75.10 9 . ^ = -2'G. 10 7 . 



ax 



These values are in close agreement with the values for 

 in the table on p. 22, i. e. respectively 



CLiC 



<IV dV 



V-=-5-4. 10 7 and =-2'7.10 7 . 



ax a. r 



The small differences between the calculated and the 

 observed values are not greater than was to be expected, as 

 the values calculated, on account of possible experimental 

 errors hi the entering constants, are not certain within more 

 than about 10 p.c. We shall further here examine to what 



* C. and M. Cuthbertson, Troc. Roy. Soc. A. lxxxiii. p. 166 (1909); 

 see also Drude, Ann. <J. Phys. xiv. p. 714 (1904). (The agreement with 

 Drude's theory is, however, not quite satisfactory, as the number of 

 electrons works out somewhat less than 2. A probable explanation of 

 this fact seems to be that the frequency of the electrons is not the same 

 for displacements in all directions, a circumstance not to be expected in 

 a system which has at most one axis of symmetry, t. e. the axis of the 

 diatomic molecule. This question will be discussed in a later paper ; 

 for the present we shall use the above value for n, as the influence on 

 the result of the correction in this value, w r hich will follow from the 

 discussion referred to, will not be greater than the inevitable errors due 

 to the uncertainty in the other experimental constants entering into the 

 calculations.) 



