138 



afterwards, the results to which they have come differ in many 

 respects appreciably from those obtained by means of the more 

 objective diffraction-method of Bragg, and because further 

 research must therefore 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 of some simply constituted oxides of bi- 

 valent metals also. We are namely here dealing with the relatively 

 simple case of the symmetrical marshalling of equal spheres. These 

 considerations may be useful afterwards also from another point 

 of view. 



18. It is a well-known fact that the elements crystallise in 



a. Fig. 119. b. 



Cubic Assemblage of Equal Spheres. 



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 close- 

 packed arrangements of equal spheres. *) 



The cubic (tetrahedral) arrangement will be clear from fig. 119 a 

 and b. It has all symmetry-elements of the holohedral class of the 

 cubic system (K H ). The centres of the spheres, the points of 

 contact between the spheres, and the centres of the octahedral 



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

 of Edinburgh 16. 693. (1889). 



