674 Scientific Proceedings, Royal Dubiin Society. 
balls, or mutually-repellent particles, the arrangement is the 
closest-packed possible, and this assemblage is brought in con- 
tact with another differently-constituted assemblage which is 
also in this condition, and 7f an intermingling of the assemblages 
enables the balls, or particles, to pack still closer, then it is evident 
that in obedience to the principle of closest-packing, the two 
assemblages will combine to form a single assemblage.’ 
The process will commence at the boundary where the two 
assemblages touch, and they will gradually interpenetrate one 
another.” 
If closest-packing is reached in a homogeneous arrangement, 
the resulting compound assemblage will, under sufficiently favour- 
able conditions, be homogeneous, and therefore display one of the 
thirty-two kinds of symmetry proper to crystals ;* if not it will be 
amorphous. 
The two assemblages will ultimately combine in the propor- 
tions in which they pack closest, and if there is an excess of one 
of them over the quantity requisite for this combination, the 
excess Will remain uncombined.* : 
Moreover, it is not necessary to suppose that all parts of any 
considerable portion, either of the constituent assemblages before 
the combination, or of the resultant assemblage afterwards, reach a 
condition of equilibrium simultaneously ; the combination will still 
take place if disturbances are occurring which prevent any great 
continuity in either time or space of the symmetrical arrange- 
ments towards which the principle of closest-packing is continually 
urging the mass. We may have, instead of very perfect homo- 
geneous assemblages whose continuity is unbroken over a con- 
1 The conditions are taken to be uniform throughout 'the mass. If they are not 
we may have closest-packing reached in one kind of arrangement at one place, in 
another kind at another. 
2 This is better understood if we take mutually-repellent particles and not balls. 
Compare note 1, p. 549. 
3 Zeitschr. f. Kryst., 23, p. 1. 
4 While the mass remains fluid there will be no hard and fast boundary between 
the combined and uncombined portions thus produced; particles at the edge of the 
combined portion will continually fall out of combination again, while, to compensate 
this, particles at the edge of the uncombined portion will become combined ; there may 
also be transitioual combinations. See below, p. 680. 
