748 Dr. G. Borelius on the 



Cu, Ag, Au, Al, Pb, and perhaps one form of Ni. On the 

 other hand, the symmetry of the " centred cube " was 

 found to exist in the case of Na, Fe, and Ni, and probably 

 that of the " simple cube " with two atoms connected with 

 each corner in the case of Li. Of the non-regular metals 

 the only one examined as yet is Mg, which shows an 

 hexagonal symmetry. 



We will in the following confine our calculations to 

 metals of the simple type NaCl only. Some of our results 

 will therefore be valid only for metals of the type of the 

 face-centred cube. Many of them, however, will most 

 probably be approximately true for any good conductor. 



For a metal of this simple type the number n of free 

 electrons in the cubic centimetre must be equal to the 

 number n' of atoms, so that 



»-»'=^ (i) 



(N = 6*06 . 10 22 , number of Avogadro, p density, 

 A atomic weight). 



Though it is not a priori probable that this relation 

 will hold throughout for all metals, we will adopt it for 

 our trials, and indeed we shall find as yet no reason to 

 alter it ; some facts rather argue in favour of its general 

 validity. 



After the present paper was nearly finished, an investi- 

 gation of Haber * came to my notice, where he treats the 

 compressibility and the ultraviolet characteristic frequencies 

 of the metals making use of similar assumptions. The last 

 problem was, moreover, treated already in 1911 f. 



§ 3. Optical Phenomena. 



As was first shown by Drude |, the refraction and 



absorption of light in a metal enable us to calculate 



approximately the number of free electrons in it. Schuster § 



and later on, in another way, Drude || have calculated 



n 

 the ratio — , for a number of metals from their optical 



properties. As a result of these investigations, it was 

 found that this ratio is for all good conductors of the 



* F. Haber, Berl. Ber. 1919, p. 506. 



t Verh. d. Deutsch. Phys. Ges. xiii. p. 1128 (1911). 



% P. Drude, Phys. Zeitschr. i. p. 161 (1900). 



$ A. Schuster, Phil. Mag. vol. vii. p. 151 (1904). 



l| P. Drude, Ann. d. Phys. xiv. pp. 725 & 936 (1904). 



