141 



made of analogous trials made by other investigators to elucidate 

 relationships between crystalline forms of different, but closely 

 related substances. Multiplication of axial ratios with other numbers 

 than those following from the directly observed Millerian indices 

 of the occurring crystal-facets, with the purpose of bringing out 

 analogies in form with the crystal-forms of other substances, is a 

 dangerous process. By suitable choice of the multipliers, all desired 

 axial ratios can finally be made comparable with each other. Not- 

 withstanding this, it can be seen from the Bar low- Pope-theory 

 that a certain persistence of a particular type of structure as an 

 element throughout widely differing assemblages, often occurs in 

 the case of substances, which are substitution-products of a same 

 mother-compound; and also, that the structures of two polymorphous 

 modifications of a same substance are geometrically often very 

 simply related to each other. 



It is of no use to study all the cases considered by the authors 

 in the light of these conceptions, nor to mention all the numerous 

 conclusions to which they have arrived, because, as we shall see 

 later, the results to which they have come differ appreciably in many 

 respects from those obtained by means of the more objective diffrac- 

 tion-method of Bragg, and because further research must bring 

 full evidence as to the correctness of the one view or the other. But 

 it may be of interest to say some few words about the crystalline 

 forms of the chemical elements as seen from this standpoint, and 

 also of some simply constituted oxides of bivalent metals. We are 

 here dealing with the relatively simple case of the symmetrical 

 marshalling of equal spheres. These considerations may also be 

 useful afterwards from another point of view. 



18. It is a wellknown fact that the elements crystallise in 

 either the cubic or the hexagonal (ditrigonal) system. Assuming this 

 phenomenon to have some relation to the hypothesis mentioned 

 above, the question may arise whether the crystalline structures of 

 these elements may be considered as most closely packed assemblages 

 of equal spheres? 



Equal spheres can be packed most closely under a general pressure 

 so as to produce a completely homogeneous system in two ways only, 

 which can be differentiated as the cubic and the hexagonal closely 

 packed arrangements of equal spheres. *) 



!) W. Barlow, Nature, 29, 186, (1883); Lord Kelvin, Proceed. Roy. Soc. 

 of Edinburgh, 16, 693, (1889). 



