The Instability of the Homogenous Exemplifying Instability at Large(*)<* The idea developed in this chapter originally formed part of anarticle on "Transcendental Physiology," published in 1857. SeeEssays, Vol. I.> §149. The difficulty of dealing with transformations so many-sidedas those which all existences have undergone, or are undergoing, is suchas to make a definite or complete deductive interpretation seem almost hopeless.
So to grasp the total process of re-distribution, as to see simultaneouslyits several necessary results in their actual interdependence, is scarcelypossible. There is, however, a mode of rendering the process as a whole tolerablycomprehensible. Though the genesis of the re-arrangement undergone by everyevolving aggregate is in itself one, it presents to our intelligence severalfactors; and after interpreting the effects of each separately, we may, bysynthesis of the interpretations, form an adequate conception.
The proposition which comes first in logical order, is, that some re-arrangementmust result; and this proposition may be best dealt with under the more specificshape, that the condition of homogeneity is a condition of unstable equilibrium.
First, as to the meanings of the terms, respecting which some readersmay need explanation. The state of "unstable equilibrium," so namedin mechanics, is well illustrated by a stick standing on its lower end, incontrast with the state of stable equilibrium of a stick suspended by itsupper end: the one instantly losing its equilibrium and the other regainingit if disturbed. But the reader must be warned against confusing the instabilitythus exemplified with the instability here to be treated of. The one shownby a stick on end may be called an external instability, while that whichwe have now to consider is an internal instability. It is not alleged thata homogeneous aggregate is liable because of its homogeneity to be overthrownor deranged by an external force. The allegation is that its component partscannot maintain their arrangements unaltered: they must forthwith begin tochange their relations to one another. Let us take a few illustrations.
Of mechanical ones the most familiar is that of the scales. If they beaccurately made and not clogged by dirt or rust, it is impossible to keepa pair of scales perfectly balanced: eventually one scale will descend andthe other ascend -- they will assume a heterogeneous relation. Could a massof water be brought into a state of perfect homogeneity -- a state of completequiescence, and exactly equal density throughout -- yet the radiation ofheat from neighbouring bodies, by affecting differently its different parts,would inevitably produce inequalities of density and consequent currents;and would so render it to that extent heterogeneous. Take a piece of red-hotmatter, and however evenly heated it may at first be, it will quickly ceaseto be so: the exterior, cooling faster than the interior will become differentfrom it in temperature. And the lapse into heterogeneity of temperature,so obvious. in this extreme case, takes place more or less in the cases ofall surrounding objects, which are ever being warmed or cooled. The actionof chemical forces supplies other illustrations. Expose a fragment of metalto air or water, and in course of time it will be coated with a film of oxide,carbonate, or other compound: its outer parts will become unlike its innerparts. Often the heterogeneity produced by the actions of chemical forceson the surfaces of masses, is not striking, because the changed portionsare soon washed away, or otherwise removed. But if this be prevented comparativelycomplex structures result. In some quarries of trap-rock there are strikingexamples. Not unfrequently a piece of trap may be found reduced, by the actionof the weather, to a number of loosely-adherent coats, like those of an onion.
Where the block has been undisturbed, we may trace the whole series of these,from the angular, irregular outer one, through successively included onesin which the shape becomes gradually rounded, ending at length in a sphericalnucleus. On comparing the original mass of stone with this group of concentriccoats, each differing from the rest in form, and probably in the state ofdecomposition it has arrived at, we get a marked illustration of the multiformityto which, in lapse of time, a uniform body may be brought by external chemicalaction. The instability of the homogeneous is equally seen in the changesset up throughout the interior of a mass, when it consists of units thatare not rigidly bound together. The molecules of a slowly-settling precipitatedo not remain separate, and equably distributed through the fluid in whichthey make their appearance. They aggregate either into crystalline grainsor into flocculi; and where the mass of fluid is great and the process prolonged,these flocculi do not continue equi-distant, but asSemble into groups. Thatis to say, there is a destruction of the balance at first subsisting amongthe diffused particles, and also of the balance at first subsisting amongthe groups into which these particles unite.
The instability thus variously illustrated is consequent on the fact thatthe several parts of any homogeneous aggregate are exposed to different forces-- forces which differ either in kind or amount; and are of necessity differentlymodified. The relations of outside and inside, and of comparative nearnessof the parts to neighbouring sources of influence, imply the reception ofinfluences that are unlike in quantity or quality, or both: unlike changes,now temporary now permanent, being caused.
