Motion of Electrons in Solids. 



781 



from the application o£ Drude's equations to visible light : 

 4t the number of free electrons in a metal is equal to the 

 number of atoms, or exceeds that number not more than three 

 times." Or. if n is the number of atoms per unit volume, 

 N=jdw, where p lies between 1 and 3. Assuming as we do 

 that the electrons have energy appropriate to the temperature 

 of the body, the law of Dulong and Petit sets the upper 

 limit 22 to the value of p for all metals, and a still smaller 

 upper limit for those metals for which the atomic heat is less 

 than 6*5 (e. g. for platinum, atomic heat =6*29, corresponding 

 limit for p assigned by specific heat is 2*1, our limit for p is 

 2''d, Schuster's limit for p is 1*91). When the limiting value 

 for p is found to be close to the limit allowed in this way 

 by the specific heat, the inference is that almost all the heat- 

 energy of the substance may reside in its free electrons. In 

 such a case (if any such exists) the atoms must form an almost 

 stationary network of obstacles through which the electrons 

 move. We shall return to this later (§ 23). 



Kirchhoff's Law. 



13. Let medium 1 be air and medium 2 be metal. Let a 

 beam of radiation of frequency p be incident on the boundary 

 AB of the media, bounded by cones of angles 6 Y and 6 X + d6\ in 

 medium 1, and passing into medium 2 between cones 6 2 and 

 s +d0 2 . 



Fig. 1. 



If K l3 Ko are the inductive capacities of the media, and C 

 the velocity of radiation in vacuo, we have the equations 



~by __ B/9 = K, dX 

 By ds C dt 



&c. 



