EFFECTS OF MOLECULAR DISSYMMETRY 263 



Repulsive Forces. 



Of course the attractive forces in matter must be balanced by equal 

 repulsive forces. Very little has been definitely known about these forces 

 except that they vary inversely with some very high power of the distance 

 between molecules. In the past in the kinetic theory it has been usual to take 

 into account these repulsive forces merely by assuming that the molecules 

 behave like infinitely hard elastic spheres which is equivalent to assuming 

 that the force varies inversely with an infinite power of the distance. 



In order to account for the compressibility of solids Born and Lande "^ 

 have shown that definite exponents for the repulsive force must be as- 

 sumed. Thus in the case of halide salts of the alkalis such as NaCl, KI, etc., 

 he showed that the compressibility of the solid salts indicated that the re- 

 pulsive force varied inversely as the loth power of the distance between 

 the ions, while the attractive force varied inversely as the square of the 

 distance in accord with Coulomb's Law. Born ''''* also attempted to show 

 that the inverse loth power law for repulsion could be deduced by assum- 

 ing that the electrons in the ions were arranged with cubic symmetry as at 

 the corners of a cube. This attempt, however, must be regarded as a failure 

 for two reasons, ist. The method of mathematical expansion used is not 

 legitimate when applied to distances as short as those between ions in 

 salts, and 2nd, Born assumed that the cubical ions were all oriented so that 

 their edges are parallel. This kind of orientation would be unstable under 

 the forces assumed. If the atoms should become oriented in response to 

 the forces acting, the repulsive force would disappear and would be re- 

 placed by an attractive force which would act in addition to the force 

 between the ionic charges. 



Such orientation of ions as Born assumes may very possibly exist in 

 solid crystals from causes which he does not discuss, but this orientation 

 cannot be the cause of the repulsive forces which determine the com- 

 ,pressibility, since the elimination of the orientation by melting the salt does 

 not greatly alter the density or the compressibility, whereas by the reason- 

 ing of Bern's theory the repulsive forces, being then unbalanced, should 

 cause a complete collapse of the structure. 



Thus we cannot regard Born's theory as one that throws anv light on 

 the cause of the repulsive forces. 



Debye,^ however, has recently developed a theory which seems to in- 

 dicate the nature of the repulsive forces. It depends essentially on the 

 orbital motions of the electrons within the atoms in accord with Bohr's 

 theory, whereas Born in his calculations had assumed that the electrons 

 acted as if stationary. Debye assumes that the conditions imposed by the 

 quantum theory determine the size of the electron orbits and the frequency 

 of rotation in these orbits. Thus the electric field around an atom or 



