9 6 
THE QUANTUM 
[vii. 3 
energy. The application of the quantum theory was also con 
sidered by Gans * and by Weyssenhoff.j The latter made use 
of Planck’s second quantum hypothesis, and assumed a single 
degree of freedom for the magnetic element, which was treated 
as a magnetic dipole with a fixed axis of rotation. 
Reiche $ developed a theory of paramagnetism in which the 
problem was regarded as one of two degrees of freedom, the 
axis of rotation being free and not fixed. By employing the 
differential equations of Jacobi and Hamilton he deduced a 
somewhat complicated expression for the molecular susceptibility, 
which may be written in the form : 
X 
5tt 2 M 2 KN ¿t' + ASo 
Where S 0 = ^ 
-cm2 
4/f 5 
S = ' S y [ *ne~ an ' 1 , and a 
7 :12 
k 2 
8ji 2 KkT 
2 h{n 2 — i)’ 
K being the moment of inertia of the magnetic element. Tables 
for the numerical evaluation of % are given in his paper, but 
care must be taken, as pointed out by S. J. Barratt,§ to distinguish 
between the molecular and the specific susceptibility. When 
this point is attended to, the values for the susceptibility at high 
temperatures given by the quantum theory are in agreement 
with those found from the classical theory of Langevin and Weiss. 
The quantum theory gives a satisfactory representation of the 
variation of susceptibility with temperature. 
We have seen in Chapter III that in studying the molecular 
susceptibility of magnetite, Weiss concluded that the magnetic 
moment of the molecule was always a multiple of a unit which 
may be called the magneton. Later Weiss noticed that the 
magnetic moments at saturation of iron and nickel at low 
temperatures were very nearly in the ratio of whole numbers, 
viz. ii : 3, and came to the conclusion that atomic magnetic 
moments are multiples of the same fundamental unit. The 
value he found for this unit in 1911, reckoned per gram atom, 
was: , 
M w = ii23’5 C.G.S. units. 
Thus at 20 0 on the absolute scale iron contains 11 magnetons, 
and nickel contains 3 magnetons. From measurements on 
solutions Weiss later on deduced a slightly larger value for the 
magneton, 1126 C.G.S. units, which he considered more accurate. 
Nevertheless magneton numbers are generally expressed in terms 
of the older unit. It must be clearly understood that the 
* Gans, Ann. d. Physik, vol. 50, p. 163, 1916. 
f Weyssenhoff, Ann. d. Physik, vol. 51, p. 285, 1916. 
X Reiche, Ann. d. Physik, vol. 54, p. 401, 1917-8. 
§ S. J. Barratt, Ann. d. Physik, vol. 77, p. 98, 1925.