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The methods used to measure separately the electronic and lattice heat conductivities κe and κg in a metal are reviewed, and it is pointed out that care is necessary in interpreting the results in view of the underlying assumptions. The equations given by Wilson for κe and for the electrical conductivity σ are used to plot the theoretical values of the electronic Lorentz ratio Le = κe/σT as a function of T, both for the monovalent metals and for a model metal with 1·8 × 10−2 conduction electrons per atom, which is taken to represent bismuth sufficiently accurately for this purpose. Curves for κe and κg as functions of T are given in both cases, and these, together with a comparison of the observed Lorentz ratio and Le, show that in the monovalent metals κg is unimportant at any temperature, but in bismuth it plays a major part at low temperatures, in agreement with experimental conclusions. Quantitatively the agreement is good for copper and, as far as the calculations go, reasonable for bismuth.
Scattering of lattice waves at the boundaries of single crystals (including insulators) at temperatures of a few degrees absolute is shown to be consistent with the experiments of de Haas and Biermasz on KCl and to be responsible for the rise in thermal resistance in this region as suggested by Peierls.
The assumption in the theory of electronic heat conduction that the lattice energy distribution function has its thermal equilibrium value is examined in an appendix. The conclusion is that it should be satisfactory, though the proof of this given by Bethe is seen to be inadequate.
* E.g. Gruneisen, and Reddemann, , Ann. d. Physik (5), 20 (1934), 843.
* Eucken, and Neumann, , Zeit. Phys. Chem. 111 (1924), 431.
† Reddemann, , Ann. d. Physik (5), 20 (1934), 441.
‡ Wilson, A. H., The theory of metals (Cambridge 1936), referred to as I.
* Mott, and Jones, , Properties of metals and alloys (Oxford 1936), pp. 213, 317.
† Proc. Cambridge Phil. Soc. 33 (1937), 371 referred to as II.
* Ann. d. Physik (5), 4 (1930), 121, also 5 (1930), 244 and 12 (1932), 154.
† Sommerfeld, and Bethe, , Handbuch der Physik, 2nd ed., vol. 24, pt 2, pp. 545 et seq.
* Inst. Physical and Chemical Research (Tokyo), 34 (1938), 194.
* Wilson II, equation (17).
* Thompson, N., Proc. Roy. Soc. A, 155 (1936), 111.
* Kohler, , Ann. d. Physik (5), 31 (1938), 116.
† Gruneisen, and Goens, , Zeit. f. Physik, 44 (1927), 615.
‡ Physica (2), 1 (1933–1934), 929.
* Lees, , Proc. Roy. Soc. A, 80 (1907), 143; Handbuch der Metallphysik, 1, 378.
† de, Haas and Biermasz, , Physica (2), 3 (1936), 672.
‡ Loc. cit. p. 871; Reddemann, loc. cit. p. 444.
* E.g. Wilson I, p. 202.
* Loc. cit. p. 547. In his equation (42·10) corresponding to (18) the term hνK 2/q 2E does not appear and the energy denoted by C is to be replaced by 
in the present notation.
† Ann. d. Physik (5), 3 (1929), 1055.
* Loc. cit. (1929); Ann. Inst. H. Poincaré, 5 (1935), 177.
† Phil. Mag. 19 (1935), 989.
* Bethe, loc. cit., obtains a limit 
of that given by (31), due to neglect of the transverse waves.
* Physica (2), 2 (1935), 673 and 1 (1938), 47.
† Loc. cit. (1929).
‡ Physica (2), 4 (1938), 320.
* E.g. Wilson I, p. 202.
† Cf. Wilson II, equations (3), (8), (19), where the term in b(|z|) does not appear since b(z) is supposed to be zero.
* Loc. cit. II.
* Wilson, loc. cit. II, equation (11).
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