ARTICLES 595 



is operative within molecular range, it will be impossible to 

 obtain individual values characteristic for each substance. 

 The molecules are held in certain mean positions by the opera- 

 tion of the local molecular field, and at any temperature below 

 the fusion-point, the thermal energy consists partly of trans- 

 lational and partly of rotational oscillations. At the fusion- 

 point, the molecular field ceases to have any directing effect 

 on the molecules, and the amplitude of the rotational oscilla- 

 tions has grown so great that the crystalline arrangement has 

 been destroyed. This theory has obviously a close bearing on 

 the theory of specific heats of the solid state, and suggests a 

 connection between the latter and the elastic properties of the 

 medium (cf. Debye's theory). Superimposed upon the thermal 

 energy of linear vibrations of the molecules we shall have a 

 rotational term : 



I A I 1 



P e 86 m 



at temperature 0, and the dissipation of the energy of crystalline 

 grouping will give rise just below the fusion-point (or, as Weiss 

 has pointed out, in the case of ferro-magnetics, just below the 

 magnetic critical point) to a small but measurable increment 

 of specific heat. 



Experimentally, such effects have been observed by Nernst 

 and Lindemann. 



Again, the relation between the optical and thermal fre- 

 quencies and the elastic constants of the medium follows at 

 once, since the molecular field, which holds the molecules 

 together and determines the rigidity of the medium, is suffi- 

 ciently strong to cause the electrons to vibrate with optical 



frequencies v, in accordance with the relation v — . Within 



27rm 



an atom the local field may be greater than io 7 gauss ; if it 

 attains a value of io 9 gauss, oscillations of X-ray frequencies 

 could be accounted for. The intermolecular field of io 7 gauss 

 may account for the shift of an absorption band on crystallisa- 

 tion in accordance with the theory of the Zeeman effect. 



Molecular Cohesion in Crystals. — We have seen that the 

 energy per unit volume of a crystalline medium is of the order 

 2 x io 9 ergs (Part 4). This gives a measure of the ultimate 

 tensile strength of the medium. It should be noted that in 

 determining the magnetic induction, which gives rise to this 

 mechanical stress, we must imagine a crevasse, whose gap is 

 small in the mathematical sense, situated between a pair of mole- 

 cules. The true local molecular field would then be deter- 

 mined, whether the medium as a whole is diamagnetic or ferro- 



