﻿672 Sir J. J. Thomson : Further Studies on 



will on the average probably contain more than 10,000 

 electrons, and their average length would be greater than 

 2.10~ 4 cm. As the average length of the chains varies 

 inversely as the temperature, the average length at 3° Ab. 

 would be greater than "02 cm. and their average velocity 

 less than 10 3 cm. /sec. 



Super- Conductivity. 



The expression for the specific conductivity given by 

 equation (5) is based on the assumption that in a " collision " 

 between an electron and an atom, the energy imparted to 

 the electron by the electric field is given up to the atom 

 during this " collision," so that the electron starts as it were 

 afresh after each collision. For this to happen there must 

 during the collision be a considerable transference of energy 

 from the electron to the atom. The energy of the atoms is 

 due to their vibrations about positions of equilibrium, and 

 the frequencies of these vibrations, according to the experi- 

 ments of Nernst and Lindemann on the variation of the 

 specific heats with temperature, range from 10 12 to 10 13 for 

 the different metals. Now, it follows from general dynamical 

 principles that a collision lasting for a time which is long 

 compared with the time of vibration of a system, will excite 

 very little vibration in the system and communicate very 

 little energy to it. The amount of energy communicated 

 will fall off very rapidly as the ratio of the duration of the 

 collision to the time of vibration increases In a case con- 

 sidered by Jeans, ' Kinetic Theory of Gases,' § 481, the 

 energy communicated to the system was proportional to 

 €~ 2cp , where c is the duration of the collision and p the fre- 

 quency of the free vibration of the system. It follows from 

 this that when the chains of electrons are moving so slowly 

 that the time of a collision is long compared with the time 

 of vibration of the atom, very little energy will be trans- 

 ferred. Our expression for the electrical conductivity was, 

 however, obtained on the assumption that at each collision 

 the excess energy due to the electric field was given up* 

 If, however, the transference of energy is not sufficient to 

 allow of this, the average velocity of the electrons will be 

 greater than that calculated, and the conductivity greater to 

 a corresponding extent. If there were no transference of 

 energy, the average velocity of the electrons and the electrical 

 conductivity would both be infinite. We see then that when 

 the temperature gets so low that the time taken by an 





