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.