352 R. W. G. Wyckoff— Crystal Structures of 



fleeting planes. Again the large majority of the planes 

 which appeared in the first order region had one even and 

 two odd indices according to the third set of axes (as 

 chosen for calcite). This second transformation was 

 here required for the same reason as previously given for 

 calcite. The fundamental lattice is again r )h and conse- 

 quently the space group is either D 5 3d or D 6 ^. D\ ({ and 

 special case (/) of D\ a were eliminated as with calcite and 

 the expression proportional to the intensity of reflection 

 for the single remaining special case, since (g and h) are 

 identical, is like the previous equation, if Ma is substituted 

 for Ca. 



In the present instance many more planes were found 

 which reflect only oxygen atoms than appeared on the cal- 

 cite plates. Typical planes are given below : 







No. of 





No. of 



Plane 



Eelative Spacing 



Curve 

 (fig. 16) 



Plane 



Relative Spacing Curve 



021 



.436 



1 



531 



.206 3 



311 



.326 



5 



342 



.202 6 



421 



.254 



2 



610 



.196 6 



250 



.244 



2 



641 



.173 4 



764 



.222 



1 



533 



.157 7 



151 



.212 



8 



751 



.148 7 



241 



.208 



6 



913 



861 



.145 7 

 .130 8 



On these curves (fig. 16) there are three positions at 

 which all the planes would have an appreciable amplitude, 

 one at either side of u = 1/4 and one about 0.3 = u. The 

 value of u = 0.23 is improbable from a number of con- 

 siderations. For instance, the spectrometer measure- 

 ments 33 point to the value of u being appreciably greater 

 in the case of rhodochrosite than with calcite. Also, if 

 wjias this position, the appreciable reflection by the plane 

 131 is not compatible with the very favorable conditions 

 which obtain for planes following curve 6. For similar 

 reasons the position about 0.30 is equally improbable. A 

 reflection from the plane 443 which has a large amplitude 

 for u = 0.30 but only a slight one for u = 0.27 was not 

 found although the plane was in a good position to give a 

 reflection. The appearance of plane 861 in spite of its 



33 W. L. Bragg, op. eit. 



