ARRANGEMENT OF MOLECULE CENTRES 141 



Fig. 29. 



a, I, and c, the axial distances to the lengths of a, b, and c. 



The condition that the arrangement round, e. g., point 4 



should be similar and parallel to that 



round i is satisfied by choosing the point 5 



in a direction and distance from 2 parallel 



and equal to b. In the same way 6, 7, 



and 8 are arrived at, and so an elementary 



parallelepiped completed. This may then 



be developed into a regular point system 



(Fig. 30) by extending the line a to an 



equal extent, to obtain a new point, and 



so on. Such an arrangement of molecule 



centres would reproduce the relations of a crystalline 



figure 1 . 



If, now, the bounding faces of the crystal are planes in 

 which molecule centres are contained, they may pass either 

 through 2, 3, 4 or through i, 2, 3 or through i, 2, 4 or 

 through i , 3, 4. With any other 

 choice, such as 3, 5, 6, the law 

 of rational indices obviously 

 holds, since each index cor- 

 responds to a row of points 

 starting from i with a definite 

 number of steps between them. 



3- 



Relations of Symmetry 

 in Crystals. 



Just as a crystal is not cap- 

 able of assuming any form, 

 so the relations of symmetry Fig 30p 



of these forms are restricted, 



and from the above fundamental law of geometrical 

 crystallography Hessel and Gadolin deduced all the 

 actually observed relations. We cannot give the deduction 

 here in full 2 , but it may be shown how the law of rational 



1 Groth, Physikalische Krystallograplde, 3rd ed., 1894, p. 248. 



2 Ibid., 1. c. p. 311. 



