652 Scientific Proceedings, Royal Dublin Society. 
absolute ; there will be some difference in the conditions of equili- 
brium because the changes in the operative bails brought about by 
the substitution of one set of inoperative balls for another are — 
not strictly proportionate.’ 
If the presence of the balls which differ in two assemblages — 
whose composition is partially the same, effects any material — 
alteration in the conditions to which the similar balls are exposed 
so as to make them behave quite differently in the two assemb- 
lages, isomorphism will manifestly not be producible by the simi- 
. larity of these bails. In other words, there must be enough 
resemblance between the unlike balls to preclude them from 
disturbing the similarity of conditions requisite to the like balls 
that they may behave sufficiently alike in the two cases. 
If, owing to some difference in the conditions of equilibrium of 
two identical assemblages they are dimorphs, or if two assemblages 
capable under certain conditions of isomorphism or partial isomor- 
phism and intercalation, as just explained, are subject to conditions 
in which similarity of arrangement of their principal centres or 
singular points does not prevail, it is evident that certain layers 
may still display identity or similarity of arrangement in the 
two assemblages and cause the inclination of some principal 
directions to be the same in both, producing isogonism or partial 
correspondence less complete than that above denominated isomor- 
phism, but of the same character. 
And with reference to the intercalation of similarly-orientated 
isomorphous assemblages :— 
Where the supply of material present at a growing surface is 
of various sorts it is evident that the average proportions in which 
the constituents of different kinds are added will depend, not only on the 
proportions in which they occur in the supply, but also on the relative 
rates at which the different kinds are prepared to solidify at any given 
point. If one kind can assume tranquillity more readily than 
another we shall expect the accretion of the former kind to be 
thereby promoted. 
As the mixing of two or more kinds in the same layer may in 
1 This is perhaps expressed more clearly if, instead of balls of different sizes, we 
speak of mutually repellent particles of different kinds (see note 3, p. 580). 
