36o SCIENCE PROGRESS 



An even more striking illustration of the difficulties involved in 

 Kopp's notion is afforded by the isomorphism of potassium and 

 caesium sulphates. Passing from the former to the latter salt, 

 there is an increase in molecular volume of about 30 per cent. ; 

 according to Kopp, the whole increase is due to the greater 

 atomic volume of caesium compared with that of potassium. If 

 this were so, on substituting potassium by caesium, the attainment 

 of a stable equilibrium of the atomic forces, such as is indicated 

 above, would involve so great a distortion that the crystalline 

 form of caesium sulphate would necessarily diverge widely from 

 that of potassium sulphate. But, on the new hypothesis, since 

 caesium has the same valency as potassium, the volumes of the 

 caesium, sulphur and oxygen atoms in caesium sulphate would 

 be in the same ratio as those of potassium, sulphur and oxygen 

 in potassium sulphate ; and as a consequence close similarity of 

 crystalline form in the two salts would be anticipated. In fact, 

 but for some reservations which the authors of the new theory 

 have found it necessary to make, the two substances should be 

 crystallographically identical : it is necessary to call attention 

 to these reservations in order to prevent misunderstanding of 

 their conception. 



In the first place, it is not to be supposed that the volumes of 

 the spheres of influence of the atoms stand precisely in the ratio 

 of the whole numbers by which we represent valency. These 

 whole numbers do not exactly represent the relative atomic 

 valencies or volumes of the spheres of influence of the atoms of 

 the elements ; the idea of the existence of residual valencies has 

 gradually forced itself upon the minds of chemists and just as 

 no two elements appear exactly to satisfy each other in 

 combination, in the same way it is probable that no two spheres 

 of atomic influence of different elements are exactly displaceable 

 the one by the other.^ All so-called univalent elements are not 

 precisely equivalent; and observed crystallographic facts show 

 that their atomic spheres of influence must differ to some small 

 extent in volume. Secondly, it must be borne in mind that 



' It might be remarked here that if valency expresses a volume relation, it can 

 hardly be expected that nature would construct spheres of influence of atoms of the 

 various elements in the strict volume relation of i : 2 : 3 : 4. Much rather would it 

 be anticipated that the volume of any specific element would be any value up to 4 

 and that the fundamental valency is merely the nearest whole number to the 

 volume referred to a univalent sphere as unity. 



