458 



It tlien occurred to ine that perhaps the spontaneous magnetization 

 of ferromagnetic substances might furnish a still more sensitive 

 criterion for putting the expression given in § 2 for the energy of 

 the molecular rotations to the test. For this the result obtained in 

 § 2 is introduced in § 3 into Weiss's theory for ferromagnetic sub- 

 stances. In doing this it is to be taken into consideration that the 

 energy of the molecular rotations is changed by the presence of a 

 directing field (§ dh). In § 4 the results of a comparison with the 

 observations are communicated. In a further chapter II (Suppl. N°. 326) 

 some general remarks follow, to which the application of the quantum- 

 theory with introduction of the zero-point energy leads, particularl}^ 

 for the state of excited ferromagnetism. Here it should be kept in 

 mind that several of those general remarks are not dependent on 

 the special value which in §§ 2 and 3 is given for the rotatory 

 energy, but follow from the general change of that energy with 

 temperature, such as is given by the formulae of those sections. 

 In how far this is the case for each remark in particular the reader 

 will easily decide himself. 



§ 2. The energy of molecular rotations in the absence of a direct- 

 ing force. If the velocity of the molecular rotations of a group of 

 molecules in a gas is changed, the modification in the motion will 

 be transferred from the centre of disturbance to the other molecules. 

 The same is true for a solid, in which we provisionally suppose the 

 molecules to rotate freely. There is no doubt that for the descrip- 

 tion of the propagation, considered as a molar process, of the 

 disturbance of equilibrium with appropriate simplifying suppositions 

 a differential equation of the same form holds as for the propagation 

 of a wave motion in an elastic medium. 



As also the boundary conditions ') agree with those which are 

 valid for the pi-opagation of a wave motion in an elastic medium 

 (eventually a gas), as regards the rotatory motion conditions of 

 stationary wave motion will be possible which correspond to those 

 which occur with acoustical motions. In particular the number of 

 possible principal modes of vibration with frequencies between v and 

 V -j- dv will be determined by a formula such as equation (3) of 

 Suppl. N«. 30a. 



The molecular rotatory motion in the substance can be resolved 

 into a system of such wave motions. For the determination of the 

 number of these wave motions for a finite number of molecules we 



1) If the molecules can rotate freely at the boundary, a loop occurs there, if 

 their rotatory motion is impeded or strongly damped, a node. 



