Results of Crystal Analysis. 79 



This arrangement will be clear by noticing that if a = c 

 the oxygen atoms would be arranged in the corners of tetra- 

 hedra with the Si atoms at the centres. 



None of these arrangements, however, is able to explain 

 the experiments. Thus the types (1), (2), and (3 a) would 

 make the second order spectrum of the face (111) vanish, 

 contrary to observations. 



The question whether the oxygen atoms might be arranged 

 according to (3 b) is of fundamental importance with regard 

 to the properties of the atoms. If the atoms were arranged 

 in this way, the tetragonal lattice could be considered as a cubic 

 lattice compressed in the direction of one of the principal axes, 

 and there would be nothing in the geometry of the lattice to 

 explain its tetragonal form. 



The compression of the lattice would be due to symmetry 

 properties of the centres (atoms), and under the conditions 

 present the atoms would exert a different force in the direction 

 of the tetragonal axis from that in a direction perpendicular 

 to it. 



The arrangement (3 b), however, cannot be accepted 

 although it gives a finite value for the second order spectrum 

 of the face (111) ; but no value of ewill satisfactorily explain 

 the actual intensity-distribution observed. Thus in order to 

 account for the disappearance of the first order spectrum of 

 (111) for rutile and kassiterite, we must put e= — 1/8. With 

 this value of e the amplitude in the case of rutile would be 

 given by the formula : 



Am = 1 + 1*38 cos n -, 



z 



which would give a ratio of the intensity of the first to that 

 of the second order equal to about 16 : 1, while the spectra 

 actually observed are in the ratio 1 : 1. 



In a similar way we can show that we cannot arrange the 

 oxygen atoms round each of the Zr atoms, when the Zr 

 atoms are to take up a central position in groups of four 

 O-atoms. 



Let us then try to associate two oxygen atoms with each 

 Si and Zratom. The O-atoms must be situated on a straight 

 line through the Si or Zr atom considered and at equal 

 distances on both sides of it ; but the distance from a Si 

 atom to the two neighbouring O-atoms may not be equal to 

 the corresponding distance for the Zr atom. 



Then the determination of the lattice under these condi- 

 tions would involve the determination of the two distances 

 (parameters) and the orientation of the lines through the 



