304 REPORT — 1901. 



symmetry, and supplied a method by which the thirty-two classes might 

 have been deduced. 



About the time of Hessel's discovery an important change of method 

 was introduced by Seeber,' who did not, like Haiiy, consider the form of 

 the constituent particles, but confined his attention to the relative situa- 

 tions of the centres of these particles. According to him the molecules, 

 which he supposes always to be arranged to form a parallelepipedal net- 

 work, are separated from each other by intervening spaces. Much the 

 same ideas were shortly afterwards put forward by Delafosse,^ who, like 

 Seeber, regarded crystals as consisting of molecules regularly arranged in 

 this manner, but not in contact. The following quotation shows that 

 the latter uses the property of cleavage merely as an evidence of the 

 existence of uniform internal symmetry : — 



' Indeed, from the possibility of a cleavage in one particular plane 

 direction, we can only conclude that the molecules of the crystal, con- 

 sidered as material points, are distributed on a series of parallel pianos ; 

 if there are two more cleavages in two new directions we deduce, as a 

 probable consequence, that the molecules must be situated in a uniform 

 and symmetrical manner, having their centres of gravity at the points of 

 intersection of these series of parallel planes, and thus present . . . the 

 picture of a lattice with parallel figured meshes. The molecules make up, 

 indifferent directions, rectilinear and parallel threads, in each of which their 

 centres of gravity are equidistant. Those threads on the same plane are 

 at equal distances from one another. . . . What Haiiy considers as the 

 dimensions of this hypothetical molecule are nothing more than the inter- 

 vals which separate the real molecules in the directions of the edges or 

 axes of the primitive foi'm.' ^ 



Wollaston ■* while, like Hooke, suggesting the presence of spherical 

 molecules, had already remarked that, in place of the sphei-es, mathe- 

 matical points endowed with forces of attraction and repulsion can be 

 postulated ; Brewster,^ Dana,'' and Forster " employed very similar 

 conceptions. 



We see, then, that while speculations as to the forms of the ultimate 

 particles are soon lost sight of, the geometrical idea which survives and is 

 held in common by various investigators is that crystal structure consists 

 in the similar repetition throughout space of identical units tvithout regard 

 to their shape or constitution. The question of the form of the ultimate 

 units of crystals, however interesting, has no essential place in a general 

 investigation which seeks to discover the various ways in which ultimate 

 parts may be uniformly repeated, i.e., an inquiry into the various types of 

 homogeneous structure. The purely geometrical investigation is one 

 which takes no account of the nature of the physical and chemical 

 characters of crystals, but nevertheless it is one of the greatest impoi't- 

 ance even from the physical and chemical point of view, as will be seen 

 subsequently. 



' 'Versuch einer Erklarun^f des innern Baues der festen Korper ' in Gilbert's 

 Anndleit der Physik, 1824, Ixxvi. pp. 229-2iS. 



2 ' Eecherches sur la cristallisation consideree sous le* rapports physiques et 

 mathematiques,' J/t'w. ^rc'.<ewi!£V.s par divers savants a V Acadim. Koy. do Stienc.de 

 VInst. de France., 1843, viii. pp. 641-690. 



3 Ibid., p G49. 



* Phil. Trans., 1813, pp. 51-63. * lUd., 1830, pp. 87-95. 



6 Sillimau's Amerlcnn Journal, 1836, Series 1, ssx. pp. 275, 296. 

 ' PUl. Mag., 1855, Series 4, s. pp. 108-115. 



