BarLtow—A. Mechanical Cause of Homogeneity of Crystals. 681 
The attempt made to formulate a general law respecting the 
combining properties of different chemical atoms which shall 
assign to each kind its definite value, or “‘valency,’’ with respect 
to other kinds has, it is well known, met-with but very limited 
success, and it cannot therefore be regarded as surprising that 
among the geometrical properties here traced no general law of 
valency of the various kinds of balls finds a place. It is true that 
in any given combination each kind of the hypothetic balls can, 
when the conditions are given, be seen to have its own proper com- 
bining proportion, but it is not easy to see how the proportion 
observed by a given kind in one combination will be related to 
the proportion observed by the same kind in another different 
combination. 
It is interesting to notice that increase of disturbance will 
diminish the efficiency of the principle of closest-packing, 7.¢., will 
hinder it in availing itself of the compatibility of units for fitting 
close together when appropriately intermixed ; and that resembling 
this we have the fact that increase of temperature diminishes the 
number of chemical bonds of substances capable of combination, 
and weakens their exhibitions of affinity, so that above a certain 
limit of temperature there is no strictly chemical action. Further, 
that change of temperature in the other direction greatly compli- 
cates the chemical effects.* 
In this connection we may call to mind the fact that the sta- 
bility of some of the carbon compounds which produce rotation of 
the plane of polarization is destroyed by a moderate rise of tem- 
perature.” 
Where the interpenetration of two assemblages depends on the 
closeness of packing being increased by the intermixture, it is 
evident that portions of a third assemblage present in one of the 
two assemblages which intermix may occupy some of the inter- 
stices and hinder the process; it may also disturb the symmetry, 
and in this way prove a hindrance. 
In connection with this may be cited the observation of 
Arrhenius, that the presence of a percentage of alcohol in 
1 Compare Bischoff’s ‘‘ Handbuch der Stereochemie,’’ p. 42. 
2 Ibid., p. 87. 
