to study of the Structure of Crystals. 



135 



positions such that two or more of the general equivalent 

 points have the same position. If, for instance, the 

 coordinates of a point in the unit are such that it lies in 

 a plane of symmetry or on a trigonal axis, two or, in the 

 second case, three sets of coordinates of the most 

 generally placed equivalent points will coincide. In the 

 case of the space group Csh^ (fig. 3) if ^ is made equal 

 to r-A, that is, to one half of the height of the unit prism, 

 then the four equivalent points of the unit occupy ttvo 

 equivalent positions (M coincides with M" and M' with 



Fig. 3. — A portion of the mouocliuic space group Csh^ The point group Ca'^ 

 is placed at the points of the monoclinic lattice T^, as at points A, A,, B, C, 

 etc. OADBGUFE is the unit of structure. M {x y z), M' (x = BD - _^_= 2r^ 

 — X = X ; y= AD — y = 2-y — y = y \ z), M" {x y z), and M. ' ' \x y z) are 

 the eqnivalent points within the unit. 



M'"). Again sodium chloride crystallizes in the holo- 

 hedry of the cubic system. Since there are as many as 

 192 equivalent positions within the unit cube, there would 

 in the most- general case be as many as 192 sodium atoms 

 and an equal number of chlorine atoms in the unit, if all 

 the sodium atoms are alike and if all the chlorine atoms 

 are also alike. X-ray spectrum measurements, however, 

 seem to indicate that but four chemical molecules are 

 associated in this case with the unit cell. If this is true, 

 then, the sodium atoms and the chlorine atoms must 



