THE QUANTUM 
[VII. 2 
to assume that the changes in orientation are brought about 
by the processes by which temperature equilibrium is maintained, 
that is primarily by collisions between the molecules. 
Langevin* assumed the molecules of the gas to be small 
magnets of equal magnetic moment M. Before the application 
of the magnetic field H the axes of the magnets are assumed to 
have a random distribution, but this uniform distribution of the 
axes is slightly disturbed by the action of the field. In the 
final state of the system a condition of statistical equilibrium 
is reached in which two tendencies balance one another; these 
are the tendency to set in a particular direction under the action 
of the field and the tendency to set equally in all directions as 
the result of thermal agitation and collisions. Langevin assumes 
that the law of distribution in the final state is the same as that 
which governs the density of a gas acted on by the force of gravity. 
The result of the mathematical investigation is to give for the 
resultant magnetic moment I of the N molecules considered 
I = NM^coth# -i) 
7:8 
MH 
where a — , k being Boltzmann’s constant and T the abso- 
Rj i. 
lute temperature. 
Since NM is the saturation value of the magnetic moment, 
we denote it by I 0 , and then we have 
I 0 ^coth a — ^ 
At ordinary temperatures, even with the highest field available 
a will be very small, and it will be sufficiently accurate to retain 
the first term in the expression for I, giving 
1 0 a I 0 MH 
— = - - 7 :10 
3 3kT ' 
Consequently the magnetic susceptibility I/H is given by 
MI 0 NM 2 
3^T 3*T 7 
In applying this formula we must be careful to take N as the 
number of molecules per unit volume, or per unit mass, according 
as we wish to find the volume susceptibility or the specific 
susceptibility. When we are dealing with the gram molecule 
(1 mole) of gas we find 
NM 2 N 2 M 2 „ TO 
X = -r~- = • • • • 7: 12