the Spinel Group of Crystals. 315 



atoms in order to make these alterations, which we do by- 

 making the tetrahedra at A and B point towards each other 

 and putting 4a = 7r. The oxygen terms in the formula then 



7VTT 



become simply 8 X 16 cos— : or, in the different orders 



-128 0+128 -128 +128 



Combining these with the effects due to the iron atoms we 

 get the calculated series 



-34 96 -190 240 -190 96 34 464, 



which has the proper rise and fall, though the maximum is 

 actually at the 4th instead of between the 3rd and the 4th. 

 The 8th is large as it should be. It is too large in fact : 

 but that need not trouble us because the spectra of high 

 order seem to diminish even faster than the inverse square 

 of the order. At this stage the plus and minus signs have 

 no significance. 



When a is put equal to j the structure becomes much 



simpler. The two oxygen tetrahedra round A and B in 

 fig. 2 should be supposed to grow until the two corners on 

 the line AB pass each other and finally lie each on a face of 

 the other tetrahedron. The oxygen atoms then all lie on 

 two planes. When a model is made it is seen that each 

 trivalent iron atom lies at the centre of a regular octahedron 

 of oxygen atoms and each divalent at the centre of a tetra- 

 hedron of oxygen atoms. The (100) planes consist of Fe 2 4 

 planes having the spacing 2 07 A.U. interleaved with Fe 

 planes. This makes the second order spectrum more intense 

 than is normally the case and agrees with experiment (see 

 fig. 1). The (110) planes may be looked on as consisting of 

 Fe 2 2 planes of spacing 2*94 A.U. interleaved with Fe0 2 

 planes. The near equality of these two kinds of plane will 

 readily account for the fact that the first (110) reflexion is 

 so very small (fig. 1). 



The results for spinel MgAl 2 4 work out in exactly the 

 same way, though it looks as if the oxygen tetrahedron was 

 not quite so large. But these details may be left to be 

 discussed hereafter. 



