02 Scientific Proceedings, Royal Dublin Society. 
(6), when the assemblage produced is only imperfectly homogeneous, 
may be paralleled by some phenomena of diffusion. 
VI.—Breaking up of an assemblage into two or more distinct 
assemblages; an effect resembling the disentangling of the 
separated atoms or complexes which commonly follows a chemical 
decomposition, and also resembling the crystallizing out of a con- 
stituent from a liquid or partially-liquid mixture. 
VII.—Exchange of the constituents of two or more assemblages 
so as to constitute fresh assomblages; an effect which finds a 
parallel in the re-arrangement or re-distribution which is one of 
the features of double chemical decomposition. 
The object kept in view throughout will be, not so much to 
ascertain with precision what particular relations between the parts 
lead to the formation of particular arrangements, as to show broadly 
that relations are conceivable which will lead to the production of 
the variety of results above enumerated as a direct physical con- — 
sequence of closest-packing carried out under the conditions 
indicated. 
As to the connexion between actual phenomena and the proper- 
ties of the artificial systems obtained in the way here described, I 
would say that so large a number of resemblances can hardly be — 
regarded as all of them mere coincidences, although some of them ~ 
may be, and that we are therefore justified in concluding that some ~ 
mechanical causes akin to those here traced are actually operating — 
in nature. | 
I.—Symmetrical arranging of parts, converting a fortuitous 
assemblage into a homogenous assemblage, and subsequent 
preservation of the homogeneity by the application of the 
ties; an effect which, since crystals are homogeneous 
structures, resembles that arranging of the ultimate parts 
of a body and stereotyping of the arrangement which 
constitute crystallization. 
(A.) Formation of homogencous assemblages when the balls, or 
mutually-repellent centres, are all of one kind. 
The simplest case is that presented when the balls are all 
similar and independent of one another. 
When this is so, it is not difficult to show that the relative 
