1130 
The magnetic moment of the double molecule will then be 
u, V2, when that of a single molecule is u,. As in the formula of 
LANGEVIN for the susceptibility 
1 np? 
the number of magnetic molecules is now reduced to half its 
original value, the susceptibility is proved to have remained un- 
changed. 
It is only when we take into consideration that the directing 
action of the quadrupoles, though the most considerable one for 
small distances between the molecules, is not the only directing 
influence and that at the same time we must consider the directing 
„action of the external field or that of the action of the magnetic 
dipoles on each other, that we fiud a change in the susceptibility. 
The calculation and discussion of this change will be given in §§3 
and 4 under the assumption that the quadrupolar axis and the mag- 
netic dipolar axis coincide. In $$ 5 and 6 the case will be treated 
in which these axes are perpendicular to each other. 
§ 3. Spherical quadrupolar molecules, having a magnetic dipolar 
moment in the direction of their quadrupolar axis, in a magnetic field. 
We shall suppose the density of the gas to be such that we have 
only to consider pairs of molecules and single molecules, while 
collisions of three or more molecules are so rare that they may be 
neglected. 
In tig. 2 let OA be the direction of the line connecting the centres 
of the two molecules of a pair, which line we shall draw in the 
direction from the second molecule to the first one. Let OQ, and 
OQ, be the directions of the quadrupolar axes of the first and the 
second molecule, chosen in the sense that OQ, and OQ, at the same 
time indicate the directions of the magnetic axes. Then a pair of 
molecules is characterized and its orientation 
with respect to the magnetic field is defined 
by the codrdinates : 
rw. Ps 0. 
Here x may vary between O and a, 
between 0 and 22, while for 7,6,,6, and p 
we may refer to Leiden Comm. Suppl. N°. 
39a § 2"). 
Fig. 2. The potential energy of the pair of mole- 
1) These Proceedings 18, p. 636, 1915. 
