ON THE STRUCTURE OF CRYSTALS, 335 



as the most general form of cell belonging to such partitioning. The 

 fourteen walls of this cell are not necessarily plane.' 



Most of his papers cited below relate to the equilibrium of molecular 

 systems, and will therefore be more properly considered later in con- 

 nection with that branch of the subject. A discussion of the relation- 

 ship between the three aspects of the problem of crystal structure — ■ 

 namely, homogeneous assemblages of points, partitioning of space, and 

 close packing of similar bodies — forms, however, an important part of 

 the 'Boyle Lecture' published in 1894.2 



The assemblages of points considered by Bravais and Sohncke may be 

 replaced by solid bodies in contact with each other, or by close-fitting 

 cells ; so also, in the more general case, the Fitndamentalhereiclie of 

 Schonflies may be occupied by points, by solid bodies, or by portions of 

 solid bodies. Lord Kelvin considers these problems on the basis of the 

 Bravais assemblage, and treats very fully of the partitioning of space 

 into identical sameway-orientated cells. His definition of homogeneity is 

 therefore more limited than that of the writers subsequent to Bravais. 

 Thus he says : ' The homogeneous division of any volume of space means 

 the dividing of it into equal and similar parts, or cells, all sameways- 

 oriented. If we take any point iu the interior of one cell and corre- 

 sponding points of all the other cells, these points form a homogeneous 

 assemblage of single points, according to Bravais' admirable and import- 

 ant definition. The general problem of the homogeneous partition of 

 space may be stated thus : Given a homogeneous assemblage of single 

 points, it is required to find every possible form of cell enclosing each of 

 them subject to the condition that it is of the same shape and sameways- 

 oriented for all.'^ 



The manner in which the physical and morphological properties of a 

 substance may be represented by a geometrical cell-partitioning is 

 illustrated by Lord Kelvin's elegant model of quartz described in the 

 Boyle Lecture.'* 



Among the systems studied by Lord Kelvin are those of atoms endued 

 with inertia and held in equilibrium by Boscovichian attractions and 

 repulsions. •' As a possil^le structure for an ice crystal, for example, com- 

 posed of Boscovichian atoms, according to this principle, a system is 

 proposed consisting of two interpenetrating space-lattices of rhombohedral 

 symmetry.'' 



William Barlow, again, in a paper entitled ' A Mechanical Cause of 

 Homogeneity of Structure and Symmetry geometrically investigated,' '' 

 has given numerous examples of the manner in which stacks of close- 



' ' On Hoitioo:eneous Division of Space,' Ptoc. Roy. Soc, 1894, Iv. pp. 1_16 ; ' On 

 the Division of Space with Minimum Partitional Area,' Phil. Mag., 1887, ser. 5, xxiv. 

 pp. 503-514 ; ' The Molecular Constitution of Matter,' Proc. Boy. Soc. £din., 1889, 

 xvi. pp. 693-724. 



« ' The Molecular Tactics of a Crystal,' The Second Boyle Lecture, 1894, Oxford. 



» Proc. Roy. Son., 1894, Iv. p. 1. 



* P. 52. Cf. also ' Piezo-elcctric Property of Quartz,' PJiil. Mag., 1893, ser. 5, 

 Xxxvi. pp. 331-340. 



* 'The Elasticity of a Crystal according to Boscovich,' Phil. Mag., 1893, ser. 5, 

 xxxvi. pp. 414-430, and Proc. Roy. Soc, 1894, liv. pp. 69-75. 



* ' On the Molecular Dynamics of Hydrogen Gas, Oxygen Gas, Ozone, Peroxide of 

 Hydrogen, Vapour of Water, Liquid Water, Ice, and Quartz Crystal,' Report Brit. 

 Assoc, 1896, pp. 721-724. 



' Proc. Boy. Bub. Soc, 1897, viii. pp. 527-690. 



