Bartow—A Mechanical Cause of Homogeneity of Crystals. 685 
B, are places of most open or loosest packing, then it is evident that 
the following reciprocal relation between the two assemblages may 
be looked for:— 
When two parallel exchanges of the kind above referred to are 
effected between a third assemblage and the two kindred assem- 
blages respectively, the balls newly arriving in A are likely to fill 
the blanks whose positions correspond to points already occupied in 
B, and the same balls newly arriving in B are likely to fill the 
other kind of blanks corresponding to points already occupied in A, 
and if in the assemblages formed the influence of the newly-arrived 
balls predominates, the result will be that the new assemblage 
formed from 4 will resemble B, while that formed from B will 
resemble 4. And this will be the case whether or no the original 
balls whose positions were different break away and are expelled 
by the action of the principle of closest-packing, 7. e., whether the 
re-arrangement is of the nature of a metathesis or a synthesis. 
It is perhaps interesting to notice that if the positions of the 
balls thus exchanged are singular points they will, when occupied, 
probably be the centres of the respective groups, and as a conse- 
quence, the parts of the assemblages turned towards the centres of 
the groups in the one will be found turned towards the outer 
boundaries of the groups in the other related assemblage. 
A resemblance to the effect above described is found in the 
behaviour of the isomeric acids, fuwmaric acid, and maleic acid, the 
former combining with bromine to produce bromo-maleic acid, and 
not a derivative of fumaric acid—and the latter, in conjunction 
with the same element, forming bromo-fumaric acid. 
It is easy to see that if two assemblages are related in the way 
just described and intermixture of either of them with some third 
assemblage effects the transformation to the form of the other, this 
intermixture need not necessarily be followed by a linking in of 
the new constituent, as in the case just treated of, and if there is no 
such linking in, avery small quantity of the third assemblage may, by 
travelling about effect the transformation of a large quantity of whichever 
of the two assemblages is less stable into the more stable form; there 
will also be the converse transformation, but naturally the one 
named will predominate. . 
Resembling this we have the fact that mere contact with some 
