Bartow—A Mechanical Cause of Homogeneity of Crystals. 529 
is that the distance between the centres of two spheres of given 
sizes which touch one another is the same throughout an assem- 
blage of this kind whether the line joining them has in all places the 
same relation to the general symmetry or not. _ This arbitrary feature 
is obviated if, instead of rigid spheres placed against one another 
without pressure, we employ elastic deformable balls differing in 
material as well as in size, and subject the closest-packed assem- 
blage to some uniform compression which flattens the spheres 
at the places of contact. An assemblage thus constituted can be 
regarded as equivalent to a flock of mutually-repellent particles 
occupying the places of the ball-centres, and which is in equili- 
brium ;? provided that repulsion subsists only between near particles 
whose interaction is represented by the effect on one another of 
balls which touch. Hquality of lines whose situations are unlike 
is now avoided, and at the same time the polarity is still that of 
the disposition and not of the forms of the ultimate parts. The 
type of symmetry will not be materially affected by the modification 
referred to. 
In what follows we shall mostly content ourselves with the use 
of the undeformable balls, believing that the changes occasioned 
by using the elastic ones instead, would in all cases be quite 
symmetrical and immaterial so far as type of symmetry is 
concerned. The employment of spheroids or ellipsoids in place of 
spheres appears, as just remarked, to be unnecessary. 
_ For the purpose of imitating two of the principal universal 
properties of molecular matter, the balls employed will be (1) regarded 
as suffering contraction or expansion under change of‘ conditions, 
those of one size, composed of one material, changing at a different 
1 Comp. Note 2, p. 550. 
2 Some simple equilibrium arrangements for mutually-repellent particles of two 
kinds have been suggested by Lord Kelvin, the particles being under a constraint in 
addition to exhibiting repulsion. (See ‘‘ Molecular Constitution of Matter,’’ oe, cit., 
“pp. 699, 700.) 
It is conceivable that the spheres of influence around centres of force of one or more 
kinds found recurring throughout some uniform mass of matter appropriate to them- 
selves distinct portions of space as large as possible as a consequence of the interacfion of 
‘the molecular movements or properties. And if this is the case, we appear to be 
furnished with a system of mutually-repellent spheres of influence whose stable 
equilibrium will be reached when the arrangement is a closest-packed one. 
2R 2 
