308 ■ REPORT— 1901. 



The definite character of the arrangement of the pal-ts in the individual 

 unit he expresses thus : ' The geometrical arrangement of the constituent 

 atoms is the same round the centre of gravity of each molecule.' He 

 adds : 'This last hypothesis is necessary for the explanation of the 

 phenomena of isomerism.' * As a result of the rigidity, or fixed relation- 

 ship, which Bravais attributes to the parts of his molecule, the arranging 

 process of crystallisation is regarded by him as partly consisting in the 

 rotation of the molecules in such a way as to bring about their uniform 

 orientation. - 



In his .study of homogeneous assemblages of points Bravais used the 

 mathematical conception of a coincidence movement (the Deckheicegung 

 of German authors), which is now so universally employed in studying 

 the symmetry of a system of points. He supposes each point of a 

 plane of points to consist of two which coincide, and then regards one 

 set of points as movable, the other set as fixed. A movement of the 

 former set which brings it to coincidence with the latter, point by point, 

 but which shifts the position of some or all of the movable points, is a 

 coincidence movement.'' His method practically consists of a study of the 

 possible varieties of axes of symmetry and the possible ways in which they 

 can exist in a .system whose various parts can be derived from each other 

 by movements of translation. 



The parallelepiped al nature of the assemblage results from tlie fact 

 that it possesses movements of translation as one sort of coincidence 

 movements ; the classification of assemblages according to their symmetry 

 is eflfected by considering the various ways in which their parts may be 

 derived from each other by a second sort of coincidence movement — 

 rotation about axes of two-, three-, four-, or six-fold symmetry, which 

 alone are possible in such an assemblage. 



The most general form of coincidence movement is a screw spiral,* 

 but such a movement is not employed by Bravais, and, indeed, had not 

 been introduced at this period. 



Bravais,'' like Haiiy, Delafosse, and Frankenheim, attempts to make 

 cleavage thro\v light on the nature of the internal symmetry prevailing 

 in certain crystals," and thus to assign particular crystals to a precise type 

 of internal symmetry. Having proved that in the space-lattice some 

 planes of points are more densely packed with points than others, and are 

 at the same time more widely separated from the adjacent parallel planes, 

 Bravais shows how the relative deiisity of the planes may be calculated. 

 He then suggests that there is a connection between the relative density 

 of aggregation of the centres in the diflTerent planes drawn in various 

 directions, and tho predisposition manifested in crystals to select certain 

 plane directions for their boundaries. 



A purely mathematical investigation in taking accouLt of all possible 

 types of internal symmetry naturally does not indicate why one type 

 should be more prevalent than another. To determine this point is 

 difticult ; indeed, it will probably be impossible till the types of internal 



' Etudes CrutalloffrapJdques, -p. 101. For a suggestion that the poles of force to 

 which polarity is due a'e the constituent atoms delinitely placed with resi^ect to one 

 another see ibid., p. 19i. - Ibid., p. 197. 



^ Juurn. de l'£coli'. Pohjtecluiique. 1850, xis. pp. 3, 2(5, 32, 57, 98. Cf. Snhncke's 

 detiuitioii of ' Deckung' in Enticicheliuig einer Thcorie der Krystallstructur, p. 28. 



" See below, p. 311. 



" Etudes CTistallograj)Mqucs, p. 202. " Ihld,, p. 1G7, 



