137 



cannot be said to be very hopeful. But this general and, from a 

 mathematical point of view, highly finished theory certainly remains 

 of interest, as being the final and exhaustive solution of the special 

 mathematical problem concerning the regular arrangement in dis- 

 continuous and homogeneous systems. 



14. In the preceding paragraphs we repeatedly had occasion 

 to point out that the most general properties of space-lattices and of 

 regular structures, were just those, by which crystals are also cha- 

 racterised. Crystalline matter behaves in many respects as a physical 

 medium of continuous structure ; but for a number of physical pheno- 

 mena, as for instance with respect to its cohesion-, and growth-pheno- 

 mena, with respect to its influence on a thin pencil of R on t gen-rays 

 travelling through it, etc., it exhibits an undeniable discontinuous 

 character. The validity of Hauy's law for space-lattices, the corres- 

 pondence of the values for the periods of eventually occurring sym- 

 metry-axes in regular systems of the kinds mentioned above, and 

 the circumstance that all possible regular structures as deduced in 

 the modern structure- theories belong to exactly the same 32 classes, 

 to which also crystals may be reckoned, are all facts which give 

 the conviction that an explanation of crystallonomical phenomena, 

 presupposing an analogous internal structure for crystals such as 

 those dealt with in the above, will certainly be successful. 



It was precisely for this purpose that in the middle of the nine- 

 teenth century Bravais began his famous studies on space-lattices. 



With great acumen and in a most ingenious way he developed 

 these views gradually for the explanation of the most important 

 properties of crystalline substances; later on his methods were 

 followed with admirable success especially by French authors for 

 the explanation of a great number of physical phenomena; and it 

 cannot be denied that Bravais' simpler and more transparent 

 ideas have been far more effectual for the development of the science 

 of crystalline matter, than those concerning the more general, but 

 incomparably more complicated regular arrangements of Sohncke, 

 Von Fedorow and Schoenflies. Another cause of this is also the 

 particular fact, that up to now there had been no method available 

 which allowed in any concrete case the making of a definite choice 

 between the numerous structures possible in the same crystal-class. 

 In most cases it remained, therefore, merely a question of personal 

 preference, which grouping of particles an observer wished to attribute 

 to the crystal-species under investigation; and it is conceivable 



