﻿of the iLlectroh Theory of Matter.' 613 



whence 



P. = J.-J, = ^fijjog f r dn-l £ logg^}(44) 



and 



« L7-1 Wj ni & ^T J 



Thus the formulae o£ the more complete theory only differ 

 from the formulae of the simple theory, which treats the 



internal free electrons (v x per unit volume) as if they were 



1 C* si 



all alike, by the substitution of — 1 log -7- dn for log v x . 



n ijni dr 

 In the new formulae n Y is the total number of electrons 

 which can become free which are contained by the conductor 

 considered. 



The present theory removes a number of contradictions 

 •with experiment which the simpler theory exhibited. In 

 particular there is no reason to expect any very close 

 connexion between the Peltier effect and the difference 

 in the electrical conductivity of the substances concerned. 

 Koenigsberger and Weiss * have recently shown that the 

 Peltier effect at the junction between a very poor and a very 

 good conductor is not in general of exceptional magnitude 

 and in some cases is in the opposite direction to that required 

 by the simple theory. The present theory requires that not 

 only those electrons which are free, in the sense that they can 

 take part in conveying the current, should be taken into 

 account, but also those which are potentially capable of 

 entering this class by means of the dynamical actions which 

 actually occur. There may be a large number of the latter 

 in the very worst conductors, and there is, so far as I am 

 aware, no way of determining the integrals which occur in 

 (44) except by thermoelectric and thermionic measurements. 

 Similar considerations apply to the large Peltier effect which, 

 as Sir J. J. Thomson pointed out, should, on the simpler 

 theory, be found to occur between the liquid and solid phase 

 at the melting-point. An argument from phase-rule con- 

 siderations may be used to prove the equality of J 1 and J 2 

 for the two phases in equilibrium ; but as I am not sure that 

 such an application of the phase rule is legitimate, I do 

 not wish to press this point at present. At any rate there is 

 no reason to expect a large Peltier effect in this case, and 

 the experiments of Wiedemann, Cermak, and others have 

 shown that any such effect, if it exists, is exceedingly small. 



* Ann. der Physik, vol. xxxv. p. 1 (1911). 



