98 THE QUANTUM [vu. 3 
Corresponding to each value of k there will be a certain Bohr 
magneton value, and for each of these we can calculate the 
apparent Weiss magneton number, using the ordinary Langevin 
formula. Thus, in the case k = 1, Weiss would obtain a value 
too great by the factor V3. Instead, then, of five, as we might 
have expected, we shall have p = 5V3, or 87 instead of 5 
Weiss magnetons. In the case k — 2, the method of calculation 
employed by Weiss would give p = 
10 V3 
"W 
or 137, instead of 
10 Weiss magnetons. As an example let us consider the two 
important paramagnetic gases, nitric oxide, NO, and oxygen, 0 2 . 
The values obtained are: 9-20 for NO, and 14-16 for 0 2 . These 
values suggest that in the case of NO we have to deal with one 
Bohr magneton, while for 0 2 the result suggests that we have 
to do with two Bohr magnetons.* * * § Pauli then suggests that 
when the results are calculated in this way we may, in certain 
cases, at least, obtain an integral number of Bohr magnetons. 
This is borne out by other results obtained both for crystals 
and for salt solutions. This point has been dealt with by 
Gerlach f and also by Epstein,£ and we are probably safe in 
concluding that the true unit is the Bohr magneton and not the 
Weiss magneton. Sommerfeld § has pointed out that the 
spectroscopic results dealing with “ multiplets ” lead to magneton 
numbers which support this conclusion, so that it appears certain 
that not only atoms or molecules in gases, but also ions in solu 
tions, tend to take up definite orientations in a magnetic field 
which are determined by quantum conditions. Sommerfeld 
claims that the riddle of the magneton is now solved, the Weiss 
unit being only apparent, the unit of the quantum theory being 
real. 
In later years considerable progress has been made in the 
quantum theory of paramagnetism. || Epstein and Gerlach 
have shown that the susceptibility of paramagnetic salts is 
independent of their being in solution or in the solid state, and 
that ions, whether in solution or in a space lattice, are arranged 
relatively to an external magnetic field in accordance with the 
quantum theory. The theory put forward by W. Pauli in 1920 
* By applying the new quantum mechanics, together with recent 
spectroscopic data for nitric oxide, J. H. Van Vleck claims to have solved 
the difficulties of accounting numerically for the susceptibilities of these 
two gases (Nature, vol. 119, p. 670, 1927). 
| Gerlach, Phys. Zeits., vol. 24, p. 275, 1923. 
X Epstein, Science, vol. 57, p. 532, 1923. 
§ Sommerfeld, Phys. Zeits., vol. 24, p. 360, 1923. 
j| See a useful summary by Tamm, Zeits. f. Physik, vol. 32, p. 582, 
1925.