318 REPORT— 1901. 



with theoretical considerations relating to systems of regular particles, 

 and the very title of his principal treatise, ' Entwickelung einer Theorie 

 der Krystallstruktur,' shows that he addresses himself rather to establish- 

 ing a physical theory than to the demonstration of a set of purely 

 geometrical propositions. From the geometrical point of view, his 

 investigation constitutes, as has been said, a completion of Camille 

 Jordan's work, already referred to : he has traced the symmetrical features 

 of the various infinite groups of movements described by the latter, and 

 has discovered a number of additional groups which Jordan had over- 

 looked ; ^ so far his work is indisjDutably a mathematical demonstration, 

 not a plausible theory. Jordan's groups of movements constitute purely 

 geometrical configurations, and their symmetrical features are perfectly 

 definite and traceable tvithout postulathig the nature of the stmcture which 

 repeats itself throughout space ; it is not essential to the geometrical 

 reasoning that this structure shall consist of a Sohnckian assemblage of 



Fig. 7. 



o 



discrete particles separated by void spaces ; - its constitution may indeed 

 remain quite undefined, so long as it is capable of the requisite coinci- 

 dence-movements. 



With Sohncke, however, the crystal element is not devoid of a certain 

 hypothetical character, as is shown by his employment of an arbitrary 

 fundamental proposition {G rundsatz)? This asserts that the symmetry 

 displayed by a crystal cannot be lower than that of the point-system, 

 according to which the centres of its elementary particles (KrystaUbait- 

 steine) are arranged. Evidently the effect of such a provision is to insist 

 on the regularity of form of these elementary particles or to treat their 

 shape as a negligible factor. As Sohncke contends that this provision is 

 a physical, not a geometrical, necessity it is obvious that his particles are 

 not mere geometrical space units ; indeed it is always possible so to 



1 EiitKichelnnrj einer Theorie der Knjstalhtriiktur, p. 26. 



- The plausibility of the conception of discrefe particles or centres of force is 

 generally admitted ; the point here insisted on is that this conception is not essential 

 to the geometrical reasoning under review. See Min. Mag., 1896, vol. xi. p. 120. 

 Com p. KrystaUsysteme und KrystaUstructur, p. 237, 



9 Zelts. Kryst. Min., 1892, vol. sx. p. 447. 



