99 



i has only a vertical plane of symmetry, perpendicular to the 

 ice of the crystal-plate. 



quartz the basal section has only a ternary axis perpendicular 

 it. the section (1010) has no symmetry-elements whatever per- 

 mlicuhir to its plane, and the section (1210) has only a binary-axis 

 T)>< nclicular to it. 



In ctilcite the basal section has a ternary axis and three planes 

 '! -vmmetry, all perpendicular to it; the section (1010) possesses 

 vertical plane of symmetry perpendicular to its surface, and the 

 ( ti(>n (1210) has a binary axis perpendicular to its plane. 

 The Ront gen-radiation however has in all circumstances a centre 

 t in version. Thus, if this symmetry-centre, according to the thesis 

 ibove explained, be added to the symmetry-elements of the three 

 stals considered, the symmetry of the calcite will not appear to 

 Iter, because calcite has itself such a centre of symmetry already, 

 if we remember (p. 15) that the combination of a binary axis 

 id a symmetry-centre has as a consequence always the existence 

 a symmetry-plane perpendicular to that axis, and vice versa, - 

 will be evident that in quartz there will be produced three planes 

 : symmetry by the addition of the symmetry-centre mentioned, 

 /hich planes are all perpendicular to the binary axes already present, 

 id thus will bisect the angle between both the others, at the same 

 time passing through the ternary axis of the crystal. 

 In the same way in the turmaline-crysta\ three binary axes per- 

 mdicular to the existing vertical symmetry-planes will be produced 

 >y the addition of the symmetry-centre, and of course these axes 

 bisect the angle between every pair of successive planes of 

 symmetry. The symmetry of both kinds of crystals thus will evi- 

 mtly be changed into the same as that of calcite (Z)?). The result 

 therefore that the Ront gen-patterns obtained in all three cases 

 show the same symmetry, as if they originated from three crystals, 

 /ery one of which possesses the symmetry of the group D%. 

 If the sections parallel to (0001), (lOH)), and (T2lO) are traversed 

 >y a thin pencil of Ront gen-rays exactly perpendicular to their 

 surfaces, the result will be that the patterns obtained 

 with a crystal-plate parallel to (0001) will show a ternary axis 

 and three symmetry-planes perpendicular to the plane of the 

 photographic plate; 



with a crystal-plate parallel to (lOU)) will show a single vertical 

 plane of symmetry perpendicular to the photographic plate; 



