﻿the Electron Theory of Solids. 677 



will lose — -7- units of energy, and this will have to be 

 An dx ^ J 



supplied from the chain ; since part of the chain is now on 



the left-hand side of the plane, some of this energy will come 



from this part, and will not be transferred across the plane. 



The energy coming from the part of the chain to the right 



will be transferred across the plane ; the ratio of the length 



of chain to the right of the plane to the length of the chain 



is (/—2c)//. We suppose that this fraction of the whole 



energy comes from the part of the chain to the right, and so 



is transferred across the plane. Thus the transference of 



energy due to the second collision of the front electron is 



R/ dd l-2c 

 An do? I 



Now consider the second collision of the electron at the 

 rear of the chain. 



IT) Jfj 



This electron will by the collision receive -r- — units of 



J An dx 



energy, and as there are a large number of electrons in the 

 chain practically the whole of this must be given out again 

 by the chain. If it is given out uniformly from all parts of 

 the chain, since the length of the portion to the left of the 

 plane ZZ is 2c, the amount of energy given out in this region, 

 which is the amount transferred across the plane ZZ, is 



m de 2c 



An dx ' I ' 



Thus at the second collision of this pair of electrons the 

 energy transferred across the plane is equal to 



IR dd I -2c lRd0 2c 

 An dx ' I An dx I 



__l]id0 



An dx y 



the same as that transferred at the first collision. We can 

 see that this must be true of all the collisions; and as there 

 are n of these before the chain gets right across the plane, 

 the total amount of energy transferred across the plane by 

 the collision of this pair of electrons is equal to 



mdo 



4 dx' 

 For a pair of electrons at a distance y from the centre of 

 the. chain, the interchange of energy at each collision with an 



atom is &- -^ — , and the number of collisions with one 

 tn dx 



