152 



them, as for instance in the case of diamond, where the second spec- 

 trum was completely cut out, --requires a number of conditions 

 to be fulfilled, before the arrangement adopted really explains the 

 diffraction-phenomena observed in every special case. l ) 



More particularly the face^centred space-lattice of cubic symmetry, 

 so closely related to the most closely packed arrangement, appears to 

 be of high importance for the internal structure of cubic crystals. Thus 

 in the case of zinc-sulphide, the zinc-atoms are arranged in such a face- 

 centred cubic lattice, while the sulphur-atoms are disposed through 

 the system in such a way that they occupy the centres of half the 

 number of the eight smaller cubes in which the greater face-centred 

 cubes of the zinc-atoms may be imagined to be subdivided; in this 

 case two of these smaller cubes must never be adjacent to each other. 



When the zinc- and the sulphur-atoms in ZnS are all substituted 

 by carbon-atoms, the structure of diamond is obtained, such as it 

 must be with respect to the experimental results met with in the 

 study of its crystals. That there, contrarily to what was observed 

 in the case of ZnS, the spectre of the second order (f = 2 x 2?r) 

 is completely cut out in the reflection at the octahedron-faces, is 

 explained by the fact that the alternating layers all consist of identical 

 atoms, the amplitudes a and a' of both oppositely directed secondary 

 vibrations being therefore equal in this case. The waves reflected 

 under this difference of phase will therefore totally destroy each 

 other, which was not the case when they were emitted by alternating 

 layers of zinc- -and sulphur-atoms. 



With respect to the structure of diamond it may be remarked 

 that the whole arrangement is such that each carbon-atom is sur- 

 rounded by four others, placed in the corners of a regular tetrahedron, 

 the centre of which is occupied by the first named carbon-atom. 

 This arrangement is in striking agreement with the suppositions 

 once made by Van 'tHoff and Le Bel with respect to the direc- 

 tion in space of the four valencies of the carbon-atom in general. 



Recently Debije 2 ), by means of his most ingenious method of 

 observation; studied the structure of graphite, and of other allotropic 



*) The question may be rised: can the supposed structures be the only true 

 ones, excluding every other possible arrangement? According to Barlow (Proc. 

 Roy. Soc. London, 91. 1. (1915), the possibility of other explanations as given 

 by Bragg, seems to be undeniable. 



2 ) Private communication to the author. The paper considered will be 

 published within a short time. 



