Closing Years of the Nineteenth Century. 463 



Consider now the case in which there is conduction of heat 

 without conduction of electricity. The flux of energy will in this 

 case be given by the equation 



W--*** 



K 



where K denotes the thermal conductivity of the metal expressed 

 in suitable units ; or 



3ma da 

 W = - K.-^ -j-- 



2q dx 



If it be assumed that the conduction of heat in metals is 

 effected by motion of the electrons, this expression may be 

 compared with the preceding; thus we have 



and comparing this with the formula already found for the 

 electric conductivity, we have 



7 W ' 



an equation which shows that the ratio of the thermal to the 

 electric conductivity is of the form T x a constant which is the 

 same for all metals. This result accords with the law of 

 Wiedernann and Franz. 



Moreover, the value of q is known from the kinetic theory of 

 gases; and the value of e has been determined by J. J. Thomson* 

 and his followers ; substituting these values in the formula for K/y, 

 a fair agreement is obtained with the values of K/y determined 

 experimentally. 



It was remarked by J. J. Thomson that if, as is postulated 

 in the above theory, a metal contains a great number of free 

 electrons in temperature equilibrium with the atoms, the 

 specific heat of the metal must depend largely on the energy 

 required in order to raise the temperature of the electrons. 

 Thomson considered that the observed specific heats of metals 

 are smaller than is compatible with the theory, and was thus 



* Cf. p. 407. 



