Results of Crystal Analysis. IT 



atoms of the other substances. In both cases — for Ti 2 4 as 

 well as for Sn 2 4 — the Zr and Si atoms are to be substituted 

 with the same sort of atoms. This will considerably alter 

 the type of the lattice and make it much simpler. In fact, 

 the metal atoms will be arranged in a prism-centred lattice 

 with sides 2d 10() , 2d m , 2d oi : but in order to^ preserve the 

 analogy with zircon, we shall suppose the lattice formed in 

 the same way from an elementary lattice, a = 4dioo, c = 4rf oi. 



From the equations (6 c) and (6 d) we see that the ratios 

 for the spacings (100) (001) (110) (101) should be un- 

 altered ; but for the face (111) the spacing would in 

 comparison be four times smaller than in the case of zircon,, 

 or the sine of the first-order glancing angle four times 

 as large. 



As a matter of fact this does not occur. 



It is only the spectra corresponding to the orders 

 1, 3, 5, &c. of zircon which have vanished for the (111) face 

 in the case of Ti0 4 and Sn 2 4 , and the spacings have the 

 following ratios : 



-^^ v%v% ■ (8i 



This apparent discrepancy, however, is not fatal to the 

 correctness of the assumed arrangement of the metal atoms ; 

 for as a matter of fact the first-order spectrum for the 

 face (111) in the case of Ti 2 4 and Sn 2 4 is produced entirety 

 by the oxygen atoms. 



§ 6. The Arrangement of the Oxygen Atoms. 



In the case of zircon the observed spacings for all the 

 reflexion planes considered are just the same as we should 

 get from the lattice of Zr and Si without the oxygen atoms r. 

 hence it follows that the arrangement of the oxygen atoms 

 must be determined from the intensity measurements. Only 

 in the case of rutile and kassiterite the maxima of order 1,, 

 3, 5, &c. for the face (111) should be due entirely to the 

 oxygen atoms. 



The problem before us is to arrange the oxygen atoms in 

 the Zr-Si lattice — with four atoms to each pair of (Zr-Si) 

 atoms — in such a way that the distribution of intensities of 

 the reflexion maxima is explained and the crystallographies- 

 symmetry accounted for. 



