306 Prof. W. H. Bragg on the Structure oj 



Let a be the length of the edge of the cube containing 

 one molecule, that is to say the volume per molecule put 

 into cubic form. The specific gravity of the crystal is 5*2 

 approximately, its molecular weight is 3 X 56 + 4 X 16 = 232, 

 and the weight of a hydrogen atom is 1 # 64 x 10~ 24 . 



Hence a 3 x 52 = 232 x 1*64 x 10" 24 , 



a 3 = 73-2 X 10- 24 , 



a = 4'18A.U. 



The length of a face diagonal of such a cube is 5*92 A.U. 

 and the length of the cube diagonal is 7'25 A.U. A cube 

 containing eight molecules has twice these dimensions. 



There is a clear connexion between these dimensions and 

 the spacings of the planes which we have calculated. We 

 may state it simply in the following form : — 



The spacing of: the (100) planes is a quarter of the edge 

 of a cube containing eight molecules, the spacing of the 

 (110) planes is a quarter of the face diagonal of such a cube, 

 and the spacing of the (111) planes is a third of the cube 

 diagonal. 



Now this is exactly what has already been found to be 

 true of the diamond, atoms of carbon replacing molecules of 

 Fe 3 4 *. We conclude, therefore, that magnetite has funda- 

 mentally the same structure as diamond, a molecule in the 

 magnetite corresponding to an atom in the diamond. 



It has been suggested by Barlow (Proc. Roy. Soc. xci. 

 p. 1) that such, arguments as this are ambiguous, and that 

 atoms lying on any of the cubic space lattices may be shifted 

 in a manner which he describes without the fact being 

 betrayed by the X-ray spectrometer. This is not the case, 

 however. The moves which he describes will, amongst 

 other things, introduce a periodicity into the spacings of 

 the (110) planes which is twice as great as before. If such 

 a periodicity existed, it would be detected at once by the 

 existence of a spectrum at half the normal glancing angle of 

 the first order. 



The structure described above, so long as each molecule 

 is represented by a point, has all the full symmetries of 

 Class 32. 



We have now to place the atoms in the molecule : in doing 

 which we are guided by two requirements. 



(1) The symmetry must not be degraded. 



(2) The relative intensities of the spectra of different 



orders must be explained. 



* ' X-rays and Crystal Structure ' (G. Bell and Sods, 1915), pp. 102-6. 



