THE ARRANGEMENT OF THE ATOMS IN A 



CRYSTAL. 



A GEOMETRICAL problem which has long exercised 

 the minds of crystallographers has recently been 

 solved in a complete and satisfactory manner. The pro- 

 blem is : To ascertain the nature of the symmetrical re- 

 petition in space of its ultimate parts which confers on 

 matter the symmetry shown by crystals. 



Like most other important contributions to exact 

 scientific knowledge the solution is the result of investi- 

 gations carried on by several different workers in different 

 countries, and it has only been brought to its present 

 finality by slow degrees. In a previous article it was 

 shown how the researches of Sohncke in particular supplied 

 the principle by the extension of which the present success- 

 ful solution has been obtained. A crystal was conceived by 

 Sohncke as represented by a system of points so arranged 

 in space that its aspect is precisely the same viewed from 

 every one of the points ; or the property may be otherwise 

 expressed by stating that there are certain movements of 

 translation, or rotation or screw-motion, which can be im- 

 parted to the system without changing its, aspect after 

 they are completed ; this was Sohncke's original way of 

 expressing the fact that a crystal is homogeneous. It 

 was explained in the previous article that the structural 

 theory of Schonflies and Fedorow, which furnishes a com- 

 plete solution of the problem, differs from that of Sohncke 

 by admitting the principle of reflection across a plane, or 

 inversion about a centre, or a combination of the two, as a 

 further possible mode of repetition applicable to a system 

 without changing its aspect. 



Since that article was written Barlow has published an 

 important paper (Zeitschrift fur Krystallographie, vol. xxiii., 

 p. i) in which he applies the principle of reflection or in- 

 version to structures based upon Sohncke's regular systems 

 of points. In this paper, however, the problem is not 



