MOLECULAR ARCHITECTURE 349 



particles through space on parallel lines, partly to the shape 

 of the particles. The theory was based upon the law that the 

 distinguishing properties of a crystal depend upon the direction 

 in which the property is determined and are alike in parallel 

 directions whilst internally the conditions are similar at all 

 points. Bravais showed that identity of environment and of 

 orientation of the particles involved the distribution of these 

 particles in the regular manner premised by the theory. A 

 mental picture of a space-lattice {Raiungitter) whose figure is 

 indicated by the distribution of the particles may be formed 

 by imagining space partitioned by three sets of parallel planes 

 into similar and equal parallelopipedal cells, the planes of each 

 set being equidistant ; the space-lattice consists of the points 

 of intersection of the cell edges. In the most general case the 

 edges of any one cell will be unequal and none of the angles 

 will be right angles. The space-lattice then corresponds to 

 a low type of symmetry in crystals. 



The necessity for assigning a lower degree of symmetry 

 to the particles than to the space-lattice marked by their 

 arrangement, in order to obtain the hemihedrism or partial 

 symmetry observed in some crystals, arose from the fact that 

 no space-lattice of mere points displays symmetry of this 

 nature, e.g., every space-lattice of mere points possesses centres 

 of symmetry and is therefore incapable of representing a 

 case in which no centre of symmetry is present. 



The objection to Bravais' theory is its lack of generality ; 

 whilst all the kinds of crystal symmetry observed can be 

 represented by means of his flocks of particles, a number of 

 forms of homogeneous structure which also display the 

 symmetry of crystals are not represented by his method or 

 only imperfectly. 



In Bravais' work we see the presentation of the perfected 

 methods of a number of previous workers ; indeed the 

 importance of his work consisted almost entirely in giving 

 precision and completeness to conceptions already put forward 

 by his predecessors. Much the same remark may be made 

 regarding the achievements of Sohncke, who gave to crystallo- 

 graphers in an acceptable form the important generalisation 

 based on the Bravais method which led to a mathematically 

 complete definition of homogeneity of structure exactly corre- 

 sponding to the facts regarding crystal symmetry. 



