594 



Example^). Let a point move to and fro free from forces in a 

 Inbe closed on either side. Let a re|)ulsive tield of force arise and 

 increase infinitely slowly in the middle of the tnbe. At last a moment 

 comes when the point with its store of kinetic energy cannot get 

 any longer throngh that "wall", and only moves to and fro in one 

 lialf of the tube. If this field of force is. of infinitely small extension, 

 the kinetic energy of the motion is the same at the end as at the 

 beginning ; the frequency on the other hand is twice the value, for 

 the path has been halved. Accordingly the original motion has split 

 up into two distinct separated branches during the adiabatic influencing. 



§ 3. An example may illustrate the way in which the "adiabatic 

 relation" I may be applied. This example refers to the extension of 

 Planck's assumption (5) from resonators vibrating sinusoidally to 

 rotating dipoles. 



A fixed dipole may be suspended so that it can revolve freely 

 lound the 2-axis. Parallel to the .r-axis a very strong directional 

 field is made to act. We first consider infinitely small oscillations 

 of the dipole. The angle of rotation may be denoted by q, the cor- 

 responding moment (moment of inertia X angular velocity) by p, 

 the frequency of the oscillation by \\. According to Planck's 

 assumption (2) the image point {q, p) of such a dipole can lie 

 nowhere else in the [q, p)-plane than on certain ellipses, which 

 belong to the quantities of energy 0,hi\, 2hv^, .... and for which 

 therefore : 



T\ h h h 



We have namely (sinus vibration!): 



^=1^ w 



The infinite number of points of rest and equilibrium : 



p = ^ = 0, . ± 2rr, =b 4rr, ± 6rr, 



belong to the value of the energy f = 0. 



Some congruent ellipses, wiiich have these points (5) as centres, 

 belong to the value f =: nlti^. 



We now consider an adiabatic influencing of such an initial 

 motion of the dipole by an infinitely slow change of the orientating 

 field of force, and eventually also of the moment of inertia. In this 

 way it is possible to convert the infinitely small oscillations into 



1) Mr. K;. Herzfeld gave this example on the occasion of' a discussion. 



