MOLECULAR ARCHITECTURE 361 



different elementary atoms in a structure behave differently as 

 regards the volume changes which they undergo under 

 varying conditions, such as changing temperature. Again, the 

 absolute magnitude of the sphere of influence of a particular 

 atom changes in passing from one compound to another ; for 

 instance the oxygen and sulphur atoms cannot occupy the same 

 absolute volumes in caesium sulphate as in potassium sulphate. 

 The hypothesis states that in any particular compound the 

 volumes of the spheres of influence of the constituent atoms are 

 very approximately proportional to their valencies. 



The problem of multiple-valencies has always proved a 

 stumbling-block to every theory of valency ; but even this 

 difficulty yields to the new method of treatment. Another 

 geometrical property of close-packed assemblages of deformable 

 spheres explains the fact that when an element increases its 

 valency it does so in steps of 2 units. The property in question 

 may be illustrated as follows : Suppose that a number of sets of 

 spheres of influence each of total volume ni can be removed 

 homogeneously from an assemblage and that into each of the 

 cavities thus formed be squeezed a sphere or spheres of total 

 volume {nt + 1); then it is found that another sphere of 

 volume I must be introduced into each cavity in order that 

 close-packing may be restored without remarshalling. In 

 general, if the volume of the substituting sphere be {ni -f- n), 

 further spheres of volume n must be introduced into the 

 structure to restore close-packing. To give a concrete 

 example, ammonium chloride must be regarded as derived 

 from the ammonia assemblage by inserting into this an atom 

 of valency i, a gap being thus produced in the assemblage 

 which can be filled only by a second monovalent atom. It is 

 thus possible to give a hitherto unexampled explanation of this 

 singular atomic property of matter. In the case however of 

 elements which appear to possess valencies differing only by 

 one unit (cf. molybdenum, which forms the chlorides M0CI2, 

 M0CI3, M0CI4 and M0CI5), it can be assumed that the volume 

 of the sphere of influence of the atom lies nearly midway 

 between two whole numbers and that the element may form 

 a close-packed assemblage with either the smaller or the 

 greater number of univalent atoms, or with either number 

 plus 2. The phenomena of multivalency are therefore not incon- 

 sistent with the interpretation of valency as a volume relation. 



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