﻿678 Sir J. J. Thomson : Further Studies on 



member of the pair in front of the plane is equal to 2nyjl; 



hence the energy transferred by this pair is ~ ~r—. Thus, 



giving y all possible values, we find that ihe total amount of 

 energy transferred across the plane ZZ through the collisions 

 of all the electrons in the chain is 



nl RdO _ . . 



= 94. ~T7 when n is large. 



Thus if there are q chains per unit volume, and if v is 

 their average velocity, the energy transferred across unit 

 area per second is 



nl ,-, d6 



In making this rough estimate of the transference of 

 energy _, we have supposed that the transference occurred only 

 when the electron was in closest proximity to the atom. 

 The process by which the electron first loses energy to the 

 atom and regains it again by a transference of energy 

 along the chain will begin before the electron reaches its 

 shortest distance from the atom and go on after it has passed 

 it ; the result of this will be that at each passage of an electron 

 past an atom the transference of energy may be very con- 

 siderably greater than that in the case we have considered. 

 We must therefore suppose that the transference of energy 



at each collision is not £ -— but a multiple of this, viz. 



ey me 



2n dx ' 

 where e is a number greater than unity which depends on 

 the law of force between the electron and the atom. This 

 will make the transference of energy across unit area per 

 second equal to 



where q is the number of chains per unit volume and v the 

 velocity of a chain. Hence K, the thermal conductivity of 

 the metal, is given by the equation 



K= — eidqv'R 



= g 4 efplv~R. 



