MAGNETISM 
vii. 3] 
97 
magneton of Weiss is an empirical, and not a mechanistic 
deduction, and the experimental evidence in favour of such a 
unit is not sufficient to demonstrate its existence with any 
certainty. The Weiss magneton is convenient for the expression 
of atomic moments, but it is more than doubtful whether it 
is a true physical unit. 
The Bohr magneton is, as we have seen, about five times 
as large as the Weiss magneton. There appears, then, to be a 
contradiction between the results of the quantum theory and 
the empirical results obtained by Weiss. Considerable light has 
been thrown on this problem by the work initiated by Pauli * 
who, for the first time, applied the principle of spatial quantizing 
to the individual magnetic molecules. According to Langevin’s 
theory, for a paramagnetic gas the product of the specific mag 
netic susceptibility and the absolute temperature is a constant, 
determined by the product of M 2 /R and the average value of 
cos 2 0. 
M 2 
*T = -^-cos 2 0. 
Here we have M as the magnetic moment of the gram atom, R 
is the gas constant for the same mass of gas, and 0 is the angle 
between the magnetic axis of a gas molecule and the direction 
of the magnetic field. Langevin assumed d to be continuously 
variable. The average value of cos 2 0 when all positions are 
regarded as equally probable, is found to be When, however, 
we adopt the point of view of quantization in space, only certain 
particular positions of the electron orbits which constitute the 
magnetons are possible. These favoured positions are deter 
mined, as we have seen previously, by taking cos 0 = 
Rt Rr Rr R 
When k is equal to unity, all the orbits are perpendicular to the 
lines of force, and in this case the average value of cos 2 0 is 
obviously 1. When k = 2, we must have either cos0 = or 
cos0 = 1, part of the orbits being perpendicular to the lines of 
force, part of them being at an angle of 30 0 to the lines of force. 
Consequently, 
COS 2 0 = f[i + (I) 2 ] = t 
In the general case, in which there are k equally probable positions, 
we find, 
In the limit, when k tends towards infinity, this reduces to 
Langevin’s formula. 
* W. Pauli, Phys. Zeits., vol. 21, p. 615, 1920.