584 
deduced by means of the adiabatic hypothesis the quantum hypo- 
thesis DeByr gives for the values or ff da dp for non-harmonic 
vibrations. *) 
Let us suppose that an electric dipole with the electric moment 
a, and the moment of inertia a, can rotate about the Z-axis.*) An 
orientating field of the intensity a@, may act parallel to the z-axis. 
As coordinate may be chosen the angle over which the dipole has 
turned. 
If we begin with very great values of a,, a, and also of a,, then 
we may regard the vibrations as injinitesima/ also for considerable 
values of the energy with which they are excited: a resonator of 
PrarckK. By letting a, and a, decrease infinitely slowly we can pass 
reversibly adiabatically to vibrations of finite amplitude, finally 
reversing the pendulum. If then the moment of inertia is kept 
constant, while the orientating field decreases to zero, we finally 
obtain molecules on which no force is acting and which therefore 
are rotating uniformly. For all these adiabatically related motions 
the adiabatic invariant 
rf 
zE dqdp 
Yv 
is thus necessarily confined to the original values o, h, 2h.... It 
for the uniform rotation with frequency rv this is identified with 
the number of complete rotations of the dipole per second: 
eee EA EN 
while it is taken into consideration that 
STER nt ot) eee 
it is therefore required that p can have no other values than 
REN, 
Tt Ae . . e . e (17) 
Remark: The considerations given above must still be completed, 
especially with a view to the difficulty, that during the adiabatic 
change the singular, non-periodic motion is passed, which forms the 
1) P. Desur. Zustandsgleich. u. Quantenhyp. (“Wolfskehlwoche” TEUBNER 
1914) § 3. 
S. Bocgustawsky. Pyroelektricität auf Grund der Quantentheorie. Phys. Z.schr. 
15 (1914) p 569 gl. 3. 
*) Comp. the treatment and application of this example in communication B§ 2 
and C § 3, and especially see the figure in C § 3. 
