366 SCIENCE PROGRESS 



respectively are in the ratio of 4:1, i.e. in the ratio of the 

 valencies of the elements. 



It is worthy of note that the experimental data quoted in the 

 above table were contributed by Krafft a quarter of a century 

 ago and had not hitherto received a satisfactory interpretation. 

 The very close agreement observed between the experimental 

 and calculated values of V is striking testimony to the accuracy 

 of Krafft's work. 



The Architecture of the Crystalline Elements 



It has long been known that the majority of elementary 

 substances crystallise in forms exhibiting a high degree of 

 symmetry, most of them belonging either to the cubic or to the 

 hexagonal system. In fact 85 per cent, of the elements which 

 have been examined crystallise in one or other of these systems. 

 This observation can be readily accounted for by the new theory 

 which regards crystals as homogeneous, close-packed assem- 

 blages of the spheres of influence of the component atoms. In 

 the case of an element we have atoms of but one kind to 

 consider and it can therefore be immediately assumed that 

 their crystals may be adequately represented by close-packed 

 homogeneous assemblages of equal spheres which stand for the 

 spheres of influence of the atoms. Indeed, a suggestion to this 

 effect was made as early as 1883 by Barlow. 



It has been shown independently by the late Lord Kelvin 

 and by Barlow that two modes exist of homogeneously close- 

 packing equal hard spheres. The two modes give assemblages 

 possessing respectively the symmetry of the cubic and hexagonal 

 crystalline systems. Fig. 2 shows a number of spheres packed 

 together to form the cubic assemblage. It may be of interest 

 to the reader to trace out the connection between this assemblage 

 of spheres and one of the 230 homogeneous point systems. 



Suppose space partitioned into cubes by three sets of parallel 

 planes at right angles to one another ; place a particle at each 

 cube corner and at the centre of each cube face and then discard 

 the cubes, leaving only the particles; what remains is one of 

 the 230 homogeneous point systems. Imagine next that each 

 particle expands uniformly in all directions until it touches its 

 next neighbours ; when further expansion ceases, an assemblage 

 of spheres is found to have been formed similar to that in the 

 figure. There is no way of packing together equal spheres more 



