123 



(according (o ~ = i l-ii- and /:?.' = 200° K. for silver 100° K.) mul- 

 tiplied by [/T, while above 7'^0 (for various metals above helium 

 temperatures) it seems to become practically nothing. We must 

 therefore adhere to the old formula ^) for calculating the amplitude, 

 or rather, accepting the new formula on account of the more satis- 

 factory- representation tliat it gives in many respects, we must assume 

 that the amplitude of the vibrators tliat comes into consideration for 

 the determination of free path and of the distance between the 

 atomic surfaces (the part of the patii between their old and their 

 new positions, upon which the electrons experience resistance in 

 their movement from one atom to another) ^) is only determined by 

 that part of the energy of the vibrators, which is dependent on the 

 temperature. In addition, in order to explain the existence of the 

 super-conducting state one would have to assume that when the 

 excess of the energy above the zero point energy has fallen to the 

 small value which corresponds to the temperature of the vanishing 

 point, the resistance to the motion of the electrons between the 

 atoms suddenly becomes zero. ") 



In the reasonings of Comm. N". 119 it was assumed that all 

 vibrators in the metal have the same frequency. As the resistance 



^t 

 is mainl}' determined by 6^ ^ one need only assume as the single 



difference between the super-conducting condition and the normal 



that the frequency of the vibrators is say four times higher in order 



to find at tiie vanishing point a micro-residual resistance 10^ smaller 



than the ordinary resistance at the same temperature and at 2° K. 



one which is 10'' times smaller. But against this explanation it may 



be adduced that in order to bring the formula of Comm. N°. 119 



into agreement with the observations at the lowest temperatures the 



frequency has to be taken lower as the temperature falls "). Wien 



1) As Wien does hi his theory. Sitz. Ber. Ak. d. Wiss. Berlin 1913, p. 200. 



-) We may remark that it is not necessary that when an electron jumps over 

 with resistance the whole surplus velocity which it has to propagate should he lost. 



3) Perhaps the distance of the surfaces of neighbouring atoms has tlien become 

 etiual to that of two neighbouring electrons in the same atom (comp. Keesom's 

 paper cited above p. 108 note 1) and the connection of the electrons of two atoms 

 similar to that of the electrons in one and the same atom (comp. the speculations 

 on "atom-fast" compounds in Kamerlingh Onnes and Keesom, Encyclop. d. Math. 

 Wissensch. V 10, Suppl. No. 23 Nr. 57. 



•*) As 1 pointed out at the discussion of the Conseil Solvay (1. c. p. 298) one 

 might suppose considering that the vibrations take place in the system of mutually 

 connected molecules that there are two kinds of vibrations, a longitudinal and a 



