102 



parallel to the basal plane (0001), to the prism-face (10TO), and 

 to the face (T2TO) of the second prism. 



In turmaline the basal section has thus a ternary axis and three 

 symmetry-planes perpendicular to it, the section (1010) has no 

 symmetry-element whatever perpendicular to it, while the section 

 (F210) has only a vertical plane of symmetry, perpendicular to the 

 surface of the crystal-plate. 



In quartz the basal section has only a ternary axis perpendicular 

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

 pendicular to its plane, and the section (T2TO) has only a binary-axis 

 perpendicular to it. 



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

 of symmetry, all perpendicular to it; the section (1010) possesses 

 a vertical plane of symmetry perpendicular to its surface, and the 

 section (1210) has a binary axis perpendicular to its plane. 



The Ron t gen-radiation, however, has in all circumstances a centre 

 of inversion. Thus, if this symmetry-centre, according to the thesis 

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

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

 alter, because calcite already possesses such a centre of symmetry. 

 But if we remember (p. 16) that the combination of a binary axis 

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

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

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

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

 which planes are all perpendicular to the binary axes already present, 

 and thus will bisect the angle between the others, passing at the 

 same time through the ternary axis of the crystal. 



In the same way in the turmaline-crystal three binary axes per- 

 . pendicular to the existing vertical symmetry-planes will be produced 

 by the addition of the symmetry-centre, and of course these axes 

 will bisect the angle between every pair of successive planes of 

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

 dently be changed into the same as that of calcite (D D 3 ). The result 

 is, therefore, that the Ron t gen-pat terns obtained in all three cases 

 will show the same symmetry, as if they originated from three crys- 

 tals, every one of which possesses the symmetry of the group Z)?. 



If the sections parallel to (0001), (10TO), and (T2lO) are traversed 

 by a thin pencil of Ron t gen-rays exactly perpendicular to their 

 surfaces, the result will be that the patterns obtained with a 



