720 BELL SYSTEM TECHNICAL JOURNAL 



tation which we are here accepting will probably therefore not prove 

 serious. Our approximative formula for x is then as follows: 



X = (*- ^^)-/^^ = - w^ *'(^) = - fr ^ ■ (««) 



and all that remains is to make the step made in every previous case 

 — to determine the last remaining unspecified constant, B, in terms 

 of the total number N of the particles of the assemblage. 



This number N is the sum of A^i and A^o. Ignoring the terms of 

 higher order in //, we have: 



N = 2Lct>iB) (89) 



and this is substantially the equation which was used to determine 

 Sommerfeld's constant A in terms of N; for e^ and 1/A are one and 

 the same. To make this equation identical with (63), or rather to 

 make (63) identical with this one, we must there put 6^ = 2, as we 

 did — this is the reason for having introduced that factor G. 



The procedure is then as follows: put — B for log A in the right- 

 hand member of equation (66) — differentiate it with respect to B — 

 insert into the derivative the value of B obtained by equating to A^" 

 the right-hand member of (66), i.e., the value given in (67) — and 

 substitute into (88). The resulting value for x is this: 



X = 12 (^y\o'n^"moh-'\ (90) 



To pass now to the experiments: is it permissible to suppose that the 

 susceptibility of any metal is due entirely to the electron-gas within it? 

 This is the same sort of uncertainty as confuses the question of the 

 specific heat. Here we have every reason to expect that the magnet- 

 ization of an ordinary paramagnetic metal is a threefold effect, in- 

 volving not only the orientation of the electrons but also the orientation 

 of the atoms, and finally that alteration of the electron-orbits in the 

 atoms which gives rise to diamagnetism. To disentangle these three 

 contributions to the net magnetic moment seems almost beyond the 

 powers of any theory. With the alkali metals, however there is 

 strong evidence that the second may be absent. Spectroscopic data 

 show quite definitely that the magnetic moment of the alkali-metal 

 ion — the atom minus its valence electron — is zero. If every atom 

 in an alkali metal has surrendered its valence electron to the electron- 

 gas, then there will be no orientation of the ions by the magnetic 

 field, and the number of electrons forming the electron-gas will be 



