Bartow—A Mechanical Cause of Homogeneity of Crystals. 689 
modify at every part of an assemblage any subsisting arrangement 
of the particles in such a way as to produce closer-packing, until 
an arrangement is reached which gives at every part the closest- 
packing attainable. For while the most obvious way of describing 
closest-packing is to say that it consists in getting the greatest 
possible number of certain bodies into a given space, if, instead of 
making the nwmber we make the size variable, we can define it as 
the packing of the largest sizes of a number of bodies of certain 
patterns into a given space, e.g., if the balls contained in a bag all 
swell uniformly the bag will be closest-packed when the maximum 
enlargement of the balls has taken place. And the effect of the 
hypothetic repulsions in making the particles get as far from con- 
tiguous particles as possible, can be regarded as equivalent to the 
swelling of spheres described about the latter as centres. 
As only the repulsions between near particles are operative, 
each part of the assemblage affects other parts not in immediate 
proximity to it only so far as its changes affect the general pressure, 
or set up travelling waves of fluctuating pressure; and although no 
doubt, in most cases, the united effect of the particles everywhere 
packing as close as they can will be to make the assemblage, as a 
whole, ultimately occupy the least space possible under a given 
pressure,' this is not necessarily the case always when we are 
dealing with assemblages the movements of whose particles are 
gradually becoming restricted in the manner defined.” 
The effect referred to, which we may call the law of closest- 
packing, may be stated concisely thus. 
Every assembly of mutually-repellent particles whatever, which 
Julfils the above definitions, will continually approximate to, or strive 
after, that relate arrangement of the particles composing tt in which 
it has come at every part to occupy a minimum space under a given 
general pressure, or average repulsion between the particles. And 
this will be true whether the assemblage is capable of ultimate 
stable equilibrium or not, and even if the disturbances referred to 
are such as to undo what is accomplished of closer-packing as fast 
as it is achieved. 
1 See No. 5 in the above list of Data. 
2 Compare conclusions as to bent and branched crystals, p. 568. 
