RECENT STATISTICAL THEORIES 



709 



through the observable range of temperatures. Indeed, in calculating 

 electrical resistance and certain other properties of metals, one may 

 use the mean values of the various powers of v which are tabulated 

 in {72a). There are however other properties of metals, thermal 

 conductivity for instance, for the estimation of which it is not sufficient 

 to assume that the mean values of the powers of v are always the same 

 as at absolute zero, and one must derive more nearly approximate 

 values for them; for these however I refer the reader to Sommerfeld. 



0.5 



I ■ ■ M^^ I 



0.95 



Fig. 1 — Graphs of the Fermi distribution-function / plotted against e/lV-: as 

 independent variable, for an electron-gas having 6.5 • 10'- particles per cc, at 

 temperatures zero (rectilinear curve) and 1500° K. (rounded curve). The value of 

 Wi is 6 equivalent volts. 



In practice, the values of W; are rather astonishingly great; no less, 

 for example, than 5.6 equivalent volts for silver, 5.7 for tungsten, 

 6.0 for platinum. Obviously they depend on the compactness of the 

 lattice, being greater the more closely-packed the atoms are. In 

 potassium and sodium the atoms are relatively widely spaced, and 

 the corresponding values of Wi are about 2.1 and 3.2 in equivalent 

 volts. 

 46 



