348 THE FORMS OF CELLS [ch. 



already formed. Each particle would seem to be influenced only 

 by the particles in its immediate neighbourhood, and to be in 

 a state of freedom and independence from the influence, either 

 direct or indirect, of its remoter neighbours. So Lavoisier was 

 the first to say. And as Kelvin and others later on explained 

 the formation and the resulting forms of crystals, so wo beheve 

 that each added particle takes up its position in relation to its 

 immediate neighbours already arranged, in the holes and corners 

 that their arrangement leaves, and in closest contact with the 

 greatest number*; hence we may repeat or imitate this process of 

 arrangement, with great or apparently even with precise accuracy 

 (in the case of the simpler crystalhne systems), by piling up spherical 

 pills or grains of shot. In so doing, we must have regard to the 

 fact that each particle must drop into the place where it can go 

 most easily, or where no easier place offers. In more technical 

 language, each particle is free to take up, and does take up, its 

 position of least potential energy relative to those already there: 

 in other words, for each particle motion is induced until the energy 

 of the system is so distributed that no tendency or resultant force 

 remains to move it more. This has been shewn to lead to the 

 production of plane surfaces f (in all cases where, by the hmitation 

 of material, surfaces must occur); where we have planes, there 

 straight edges and solid angles must obviously occur also, and, if 

 equihbrium is to follow, must occur symmetrically. Our pihng up 

 of shot to make mimic crystals gives us visible demonstration that 

 the result is actually to obtain, as in the natural crystal, plane 

 surfaces and sharp angles symmetrically disposed. 



* Cf. Kelvin, On the molecular tactics of a crystal, The Boyle Lecture, Oxford, 

 1893; Baltimore Lectures, 1904, pp. 612-642. Here Kelvin was mainly following 

 Bravais's (and Frankenheim's) theory of "space-lattices," but he had been largely 

 anticipated by the crystallographers. For an account of the development of the 

 subject in modern crystallography, by Sohncke, von Fedorow, 8chonfliess, Barlow 

 and others, see (e.g.) Tutton's Crystallography, and the many papers by W. E. Bragg 

 and others. 



t In a homogeneous crystalline arrangement, symmetry compels a locus of one 

 property to be a plane or set of planes ; the locus in this case being that of least 

 surface potential energy. Crystals "seem to be, as it were, the Elemental Figures, 

 or the A B C of Nature's workmg, the reason of whose curious Geometrical Forms 

 (if I may so call them) is very easily explicable" (Robert Hooke, Posthumous Works^ 

 1745, p. 280). 



