746 Dr. Gr. Borelius on the 



Further, the agreement between the experimental measure- 

 ments of the K-series spectra and the theoretical values of 

 Debye and Kroo shows that the inverse square law still 

 holds at the K ring. In the case of platinum the radius of 

 the K ring is about 10 ~ 10 cm. 



Thus, measured from any point in the region between 

 3xl0" 12 cm. and 10" 10 cm. from the nucleus of a heavy 

 atom like platinum, the charge is equal to the atomic 

 number and the law of force is the inverse square. We 

 may therefore conclude that no electrons are present in the 

 region between the nucleus and the K ring. 



I wish to thank Sir Ernest Rutherford for suggesting 

 this work, and for his interest and advice throughout its- 

 progress. 



LXXXV. On the Electron Theory of the Metallic State. 

 By G. Borelius, Ph.D.* 



§ 1. Introduction. 



THE well-known theory, founded by Riecke and Drude r 

 and worked out in its further consequences by 

 Lorentz, Bohr, and others, assumes the conducting electrons 

 to be freely moving among the atoms of a metal, and to have 

 the same mean kinetic energy as gas molecules at the same 

 temperature. These assumptions gave, as a first striking- 

 result, a deduction of the laws of Wiedemann and Franz 

 and of Lorenz. However, other consequences of the theory 

 cannot be said to agree very well with experimental facts. 

 There is, for example, no probable ground for the cha- 

 racteristic dependence upon temperature found for the 

 electric and thermal conductivities in pure metals ; without 

 the addition of the most improbable assumptions, it gives a 

 wrong idea of the magnitude of the thermoelectric pheno- 

 mena ; the specific heats observed require the number of 

 free electrons to be very small compared with the number 

 of atoms, whereas optical phenomena require these numbers 

 to be of the same order of magnitude ; in the Hall pheno- 

 menon it gives us directly only negative signs, though both 

 signs are actually observed, and so forth. 



All these facts have caused J. J. Thomson f, W. WienJ r 



* Communicated by the Author. 



t J. J.Thomson, 'Corpuscular Theory ' (1907) ; Phil. Mag. vol. xxx. 

 p. 192 (1915). 



.+ W. Wien, Berl, Ber. 1913, p. 184. 



