﻿676 Sir J. J. Thomson : Further Studies 



on 



greater than 2c, lost far more than this, so that energy must 

 be transmitted along the chain to A to bring its energy up to 

 its proper value. Thus when the electrons are connected 

 together in chains, the transference of energy is not confined 

 to the energy carried by the electrons when they are crossing 

 the plane ; each collision made by an electron in the chain 

 will, until the whole of the chain has passed the plane, result 

 in the transference of energy across the plane ; if the chain 

 is long this second type of transference may far exceed in 

 magnitude that which would occur if there were no 

 collisions. 



We shall now proceed to find an estimate of the trans- 

 ference due to the collisions. 



Let us take the electrons in the chain in pairs, the con- 

 stituents of a pair being equally distant from the centre ; let 

 this distance be y. Then, as the chain moves along, one of 

 the constituents of the pair has energy corresponding to a 



temperature y -j~ above, the other constituent the energy 



dO 

 corresponding to the temperature y-p below the temperature 



of its position. If ^R6 is the energy corresponding to one 

 degree of freedom at the temperature 6, this excess or defect 



of energy of an electron will be „ — R — . We shall suppose 



that at each collision of an electron with an atom the energy 

 of the electron is restored to the value corresponding to its 

 position. 



Let us begin with the electrons at the beginning and end 

 of the chain. We have seen that the first collision of the 

 front electron after passing the plane results in the trans- 

 ference of -j- j- units of energy across the plane. The 

 collision made by the electron in the rear will result in its 

 gaining — ~ units of energy ; this will have to be given 



up by the chain, but inasmuch as all the chain is on the right 

 of the plane ZZ, the energy will be given off in tnis region 

 and will not be transferred across the plane. 



Thus the first collision of this pair of electrons transfers 



4:n dx 



units of energy across the plane. 



Let us now consider the next collision. The front electron 



