CONSTITUTION AND TEMPERATURE ON MAGNETIC SUSCEPTIBILITY. 259 



As LOVE points out, the values of these elastic constants for beryl and topaz are 

 remarkable in that they are greater than the corresponding constants in ordinary 

 steel. The values of the elastic coefficients for most of the other substances in the 

 above table are comparable with the constants for steel, and it is considered that these 

 results give very strong evidence in favour of the large intermolecular forcive 

 operative in diamagnetic crystalline media and confirm the suggestion made in 

 Part II., p. 143, that this local forcive is comparable with that in ferro-magnetic media. 



If a crystalline medium be heated, then as long as the crystalline state prevails, 

 rotational vibrations of large amplitude are prevented, so that the specific heat of 

 the crystalline medium is lower than that of the supercooled liquid.* In the latter 

 case, the liquid at low temperatures passes into a rigid gel, and when this is heated, 

 the molecules acquire rotational vibrations gradually until finally the ordinary liquid 

 state is reached, possessing no appreciable rigidity. It is important to note that the 

 molecules are vibrating under a local forcive to which we are ascribing the elastic 

 properties of the medium, and therefore the theory is consistent with the theory of 

 specific heat developed by DEBYE, in which the forces which control the thermal 

 vibrations of the molecules are identical with those which determine the elastic 

 constants of the medium. MADELUNG and SUTHERLAND have similarly suggested 

 that the elastic forces resisting mechanical strain are just those forces which determine 

 the infra-red optical vibrations of the atoms in the solid substance. It has been fou i id 

 possible to calculate the infra-red frequencies from a knowledge of the mechanical 

 properties. In the present researches it has been shown that we can calculate both 

 the optical frequencies! and the mechanical stresses from the local molecular forcive. 

 Within the core of the atom the local controlling force may be more intense, and 

 although such an intense forcive would not be directly operative in determining the 

 state of crystallization, yet it might be responsible for determining frequencies on 

 the ultra-violet side comparable with X-ray frequencies. (See infra, pp. 273 and 278.) 



(4) THE CHANGE OF DENSITY ON CRYSTALLIZATION INTERPRETED AS A MAGNETO- 

 STRICTION EFFECT OF THE MOLECULAR FIELD. 



If we subject a liquid to a magnetic field, a change of volume occurs to such an 

 extent that the internal pressure is reduced by an amount equal to the potential 

 energy per unit volume of the magnetic field. This change of internal pressure (see 

 Part III., p. 91) is 



where 



k t is the susceptibility of the liquid per unit volume, 



X, a constant equal to 1/3, 

 and 



H, the applied field intensity. 



* Part III., p. 94. 



t A. E. OXLEY, ' Roy. Soc. Proc.,' A, vol. 95, p. 58, 1918, and Part III., p. 84. 



