First Principles

CHAPTER XIII.
THE INSTABILITY OF THE HOMOGENEOUS. ¹⁶

§ 109. Thus far our steps towards the interpretation of Evolution have been preparatory. We have dealt with the factors of the process, rather than the process itself. After the ultimate truth that, Matter, Motion, and Force, as cognizable by human intelligence, can neither come into existence nor cease to exist, we have considered certain other ultimate truths concerning the modes in which Force and Motion are manifested during the changes they produce in Matter. Now we have to study the changes themselves. We have here to analyze that re-arrangement in the parts of Matter, which occurs under the influence of Force, that is unchangeable in quantity though changeable in form, through the medium of Motion taking place rhythmically along lines of least resistance. The proposition which comes first in logical order, is, that some re-arrangement must result; and this proposition may be best dealt with under the more specific shape, that the condition of homogeneity is a condition of unstable equilibrium.

First, as to the meaning of the terms; respecting which some readers may need explanation. The phrase unstable equilibrium is one used in mechanics to express a balance of forces of such kind, that the interference of any further force, however minute, will destroy the arrangement previously subsisting; and bring about a totally different arrangement. Thus, a stick poised on its lower end is in unstable equilibrium: however exactly it may be placed in a perpendicular position, as soon as it is left to itself it begins, at first imperceptibly, to lean on one side, and with increasing rapidity falls into another attitude. Conversely, a stick suspended from its upper end is in stable equilibrium: however much disturbed, it will return to the same position. The proposition is, then, that the state of homogeneity, like the state of the stick poised on its lower end, is one that cannot be maintained. Let us take a few illustrations.

Of mechanical ones the most familiar is that of the scales. If they be accurately made, and not clogged by dirt or rust, it is impossible to keep a pair of scales perfectly balanced: eventually one scale will descend and the other ascend – they will assume a heterogeneous relation. Again, if we sprinkle over the surface of a fluid a number of equal-sized particles, having an attraction for each other, they will, no matter how uniformly distributed, by and by concentrate irregularly into one or more groups. Were it possible to bring a mass of water into a state of perfect homogeneity – a state of complete quiescence, and exactly equal density throughout – yet the radiation of heat 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-hot matter, and however evenly heated it may at first be, it will quickly cease to be so: the exterior, cooling faster than the interior, will become different in temperature from it. And the lapse into heterogeneity of temperature, so obvious in this extreme case, takes place more or less in all cases. The action of chemical forces supplies other illustrations. Expose a fragment of metal to air or water, and in course of time it will be coated with a film of oxide, carbonate, or other compound: that is – its outer parts will become unlike its inner parts. Usually the heterogeneity produced by the action of chemical forces on the surfaces of masses, is not striking; because the changed portions are soon washed away, or otherwise removed. But if this is prevented, comparatively complex structures result. Quarries of trap-rock contain some striking examples. Not unfrequently a piece of trap may be found reduced, by the action of the weather, to a number of loosely-adherent coats, like those of an onion. Where the block has been quite undisturbed, we may trace the whole series of these, from the angular, irregular outer one, through successively included ones in which the shape becomes gradually rounded, ending finally in a spherical nucleus. On comparing the original mass of stone with this group of concentric coats, each of which differs from the rest in form, and probably in the state of decomposition at which it has arrived, we get a marked illustration of the multiformity to which, in lapse of time, a uniform body may be brought by external chemical action. The instability of the homogeneous is equally seen in the changes set up throughout the interior of a mass, when it consists of units that are not rigidly bound together. The atoms of a precipitate never remain separate, and equably distributed through the fluid in which they make their appearance. They aggregate either into crystalline grains, each containing an immense number of atoms, or they aggregate into flocculi, each containing a yet larger number; and where the mass of fluid is great, and the process prolonged, these flocculi do not continue equidistant, but break up into groups. That is to say, there is a destruction of the balance at first subsisting among the diffused particles, and also of the balance at first subsisting among the groups into which these particles unite. Certain solutions of non-crystalline substances in highly volatile liquids, exhibit in the course of half an hour a whole series of changes that are set up in the alleged way. If for example a little shell-lac-varnish (made by dissolving shell-lac in coal-naphtha until it is of the consistence of cream) be poured on a piece of paper, the surface of the varnish will shortly become marked by polygonal divisions, which, first appearing round the edge of the mass, spread towards its centre. Under a lense these irregular polygons of five or more sides, are seen to be severally bounded by dark lines, on each side of which there are light-coloured borders. By the addition of matter to their inner edges, the borders slowly broaden, and thus encroach on the areas of the polygons; until at length there remains nothing but a dark spot in the centre of each. At the same time the boundaries of the polygons become curved; and they end by appearing like spherical sacs pressed together; strangely simulating (but only simulating) a group of nucleated cells. Here a rapid loss of homogeneity is exhibited in three ways: – First, in the formation of the film, which is the seat of these changes; second, in the formation of the polygonal sections into which this film divides; and third, in the contrast that arises between the polygonal sections round the edge, where they are small and early formed, and those in the centre which are larger and formed later.

The instability thus variously illustrated is obviously consequent on the fact, that the several parts of any homogeneous aggregation are necessarily exposed to different forces – forces that differ either in kind or amount; and being exposed to different forces they are of necessity differently modified. The relations of outside and inside, and of comparative nearness to neighbouring sources of influence, imply the reception of influences that are unlike in quantity or quality, or both; and it follows that unlike changes will be produced in the parts thus dissimilarly acted upon.

For like reasons it is manifest that the process must repeat itself in each of the subordinate groups of units that are differentiated by the modifying forces. Each of these subordinate groups, like the original group, must gradually, in obedience to the influences acting upon it, lose its balance of parts – must pass from a uniform into a multiform state. And so on continuously. Whence indeed it is clear that not only must the homogeneous lapse into the non-homogeneous, but that the more homogeneous must tend ever to become less homogeneous. If any given whole, instead of being absolutely uniform throughout, consist of parts distinguishable from each other – if each of these parts, while somewhat unlike other parts, is uniform within itself; then, each of them being in unstable equilibrium, it follows that while the changes set up within it must render it multiform, they must at the same time render the whole more multiform than before. The general principle, now to be followed out in its applications, is thus somewhat more comprehensive than the title of the chapter implies. No demurrer to the conclusions drawn, can be based on the ground that perfect homogeneity nowhere exists; since, whether that state with which we commence be or be not one of perfect homogeneity, the process must equally be towards a relative heterogeneity.

§ 110. The stars are distributed with a three-fold irregularity. There is first the marked contrast between the plane of the milky way and other parts of the heavens, in respect of the quantities of stars within given visual areas. There are secondary contrasts of like kind in the milky way itself, which has its thick and thin places; as well as throughout the celestial spaces in general, which are much more closely strewn in some regions than in others. And there is a third order of contrasts produced by the aggregation of stars into small clusters. Besides this heterogeneity of distribution of the stars in general, considered without distinction of kinds, a further such heterogeneity is disclosed when they are classified by their differences of colour, which doubtless answer to differences of physical constitution. While the yellow stars are found in all parts of the heavens, the red and blue stars are not so: there are wide regions in which both red and blue stars are rare; there are regions in which the blue occur in considerable numbers, and there are other regions in which the red are comparatively abundant. Yet one more irregularity of like significance is presented by the nebulæ, – aggregations of matter which, whatever be their nature, most certainly belong to our sidereal system. For the nebulæ are not dispersed with anything like uniformity; but are abundant around the poles of the galactic circle and rare in the neighbourhood of its plane. No one will expect that anything like a definite interpretation of this structure can be given on the hypothesis of Evolution, or any other hypothesis. The most that can be looked for is some reason for thinking that irregularities, not improbably of these kinds, would occur in the course of Evolution, supposing it to have taken place. Any one called on to assign such reason might argue, that if the matter of which stars and all other celestial bodies consist, be assumed to have originally existed in a diffused form throughout a space far more vast even than that which our sidereal system now occupies, the instability of the homogeneous would negative its continuance in that state. In default of an absolute balance among the forces with which the dispersed particles acted on each other (which could not exist in any aggregation having limits) he might show that motion and consequent changes of distribution would necessarily result. The next step in the argument would be that in matter of such extreme tenuity and feeble cohesion there would be motion towards local centres of gravity, as well as towards the general centre of gravity; just as, to use a humble illustration, the particles of a precipitate aggregate into flocculi at the same time that they sink towards the earth. He might urge that in the one case as in the other, these smallest and earliest local aggregations must gradually divide into groups, each concentrating to its own centre of gravity, – a process which must repeat itself on a larger and larger scale. In conformity with the law that motion once set up in any direction becomes itself a cause of subsequent motion in that direction, he might further infer that the heterogeneities thus set up would tend ever to become more pronounced. Established mechanical principles would justify him in the conclusion that the motions of these irregular masses of slightly aggregated nebular matter towards their common centre of gravity must be severally rendered curvelinear, by the resistance of the medium from which they were precipitated; and that in consequence of the irregularities of distribution already set up, such conflicting curvelinear motions must, by composition of forces, end in a rotation of the incipient sidereal system. He might without difficulty show that the resulting centrifugal force must so far modify the process of general aggregation, as to prevent anything like uniform distribution of the stars eventually formed – that there must arise a contrast such as we see between the galactic circle and the rest of the heavens. He might draw the further not unwarrantable inference, that differences in the process of local concentration would probably result from the unlikeness between the physical conditions existing around the general axis of rotation and those existing elsewhere. To which he might add, that after the formation of distinct stars, the ever-increasing irregularities of distribution due to continuance of the same causes would produce that patchiness which distinguishes the heavens in both its larger and smaller areas. We need not here however commit ourselves to such far-reaching speculations. For the purposes of the general argument it is needful only to show, that any finite mass of diffused matter, even though vast enough to form our whole sidereal system, could not be in stable equilibrium; that in default of absolute sphericity, absolute uniformity of composition, and absolute symmetry of relation to all forces external to it; its concentration must go on with an ever-increasing irregularity; and that thus the present aspect of the heavens is not, so far as we can judge, incongruous with the hypothesis of a general evolution consequent on the instability of the homogeneous.

Descending to that more limited form of the nebular hypothesis which regards the solar system as having resulted by gradual concentration; and assuming this concentration to have advanced so far as to produce a rotating spheroid of nebulous matter; let us consider what further consequence the instability of the homogeneous necessitates. Having become oblate in figure, unlike in the densities of its centre and surface, unlike in their temperatures, and unlike in the velocities with which its parts move round their common axis, such a mass can no longer be called homogeneous; and therefore any further changes exhibited by it as a whole, can illustrate the general law, only as being changes from a more homogeneous to a less homogeneous state. Changes of this kind are to be found in the transformations of such of its parts as are still homogeneous within themselves. If we accept the conclusion of Laplace, that the equatorial portion of this rotating and contracting spheroid will at successive stages acquire a centrifugal force great enough to prevent any nearer approach to the centre round which it rotates, and will so be left behind by the inner parts of the spheroid in its still-continued contraction; we shall find, in the fate of the detached ring, a fresh exemplification of the principle we are following out. Consisting of gaseous matter, such a ring, even if absolutely uniform at the time of its detachment, cannot continue so. To maintain its equilibrium there must be an almost perfect uniformity in the action of all external forces upon it (almost, we must say, because the cohesion, even of extremely attenuated matter, might suffice to neutralize very minute disturbances); and against this the probabilities are immense. In the absence of equality among the forces, internal and external, acting on such a ring, there must be a point or points at which the cohesion of its parts is less than elsewhere – a point or points at which rupture will therefore take place. Laplace assumed that the ring would rupture at one place only; and would then collapse on itself. But this is a more than questionable assumption – such at least I know to be the opinion of an authority second to none among those now living. So vast a ring, consisting of matter having such feeble cohesion, must break up into many parts. Nevertheless, it is still inferrable from the instability of the homogeneous, that the ultimate result which Laplace predicted would take place. For even supposing the masses of nebulous matter into which such a ring separated, were so equal in their sizes and distances as to attract each other with exactly equal forces (which is infinitely improbable); yet the unequal action of external disturbing forces would inevitably destroy their equilibrium – there would be one or more points at which adjacent masses would begin to part company. Separation once commenced, would with ever-accelerating speed lead to a grouping of the masses. And obviously a like result would eventually take place with the groups thus formed; until they at length aggregated into a single mass.

Leaving the region of speculative astronomy, let us consider the Solar System as it at present exists. And here it will be well, in the first place, to note a fact which may be thought at variance with the foregoing argument – namely, the still-continued existence of Saturn’s rings; and especially of the internal nebulous ring lately discovered. To the objection that the outer rings maintain their equilibrium, the reply is that the comparatively great cohesion of liquid or solid substance would suffice to prevent any slight tendency to rupture from taking effect. And that a nebulous ring here still preserves its continuity, does not really negative the foregoing conclusion; since it happens under the quite exceptional influence of those symmetrically disposed forces which the external rings exercise on it. Here indeed it deserves to be noted, that though at first sight the Saturnian system appears at variance with the doctrine that a state of homogeneity is one of unstable equilibrium, it does in reality furnish a curious confirmation of this doctrine. For Saturn is not quite concentric with his rings; and it has been proved mathematically that were he and his rings concentrically situated, they could not remain so: the homogeneous relation being unstable, would gravitate into a heterogeneous one. And this fact serves to remind us of the allied one presented throughout the whole Solar System. All orbits, whether of planets or satellites, are more or less excentric – none of them are perfect circles; and were they perfect circles they would soon become ellipses. Mutual perturbations would inevitably generate excentricities. That is to say, the homogeneous relations would lapse into heterogeneous ones.

§ 111. Already so many references have been made to the gradual formation of a crust over the originally incandescent Earth, that it may be thought superfluous again to name it. It has not, however, been before considered in connexion with the general principle under discussion. Here then it must be noted as a necessary consequence of the instability of the homogeneous. In this cooling down and solidification of the Earth’s surface, we have one of the simplest, as well as one of the most important, instances, of that change from a uniform to a multiform state which occurs in any mass through exposure of its different parts to different conditions. To the differentiation of the Earth’s exterior from its interior thus brought about, we must add one of the most conspicuous differentiations which the exterior itself afterwards undergoes, as being similarly brought about. Were the conditions to which the surface of the Earth is exposed, alike in all directions, there would be no obvious reason why certain of its parts should become permanently unlike the rest. But being unequally exposed to the chief external centre of force – the Sun – its main divisions become unequally modified: as the crust thickens and cools, there arises that contrast, now so decided, between the polar and equatorial regions.

Along with these most marked physical differentiations of the Earth, which are manifestly consequent on the instability of the homogeneous, there have been going on numerous chemical differentiations, admitting of similar interpretation. Without raising the question whether, as some think, the so-called simple substances are themselves compounded of unknown elements (elements which we cannot separate by artificial heat, but which existed separately when the heat of the Earth was greater than any which we can produce), – without raising this question, it will suffice the present purpose to show how, in place of that comparative homogeneity of the Earth’s crust, chemically considered, which must have existed when its temperature was high, there has arisen, during its cooling, an increasing chemical heterogeneity: each element or compound, being unable to maintain its homogeneity in presence of various surrounding affinities, having fallen into heterogeneous combinations. Let us contemplate this change somewhat in detail. There is every reason to believe that at an extreme heat, the bodies we call elements cannot combine. Even under such heat as can be generated artificially, some very strong affinities yield; and the great majority of chemical compounds are decomposed at much lower temperatures. Whence it seems not improbable that, when the Earth was in its first state of incandescence, there were no chemical combinations at all. But without drawing this inference, let us set out with the unquestionable fact that the compounds which can exist at the highest temperatures, and which must therefore have been the first formed as the Earth cooled, are those of the simplest constitutions. The protoxides – including under that head the alkalies, earths, &c. – are, as a class, the most fixed compounds known: the majority of them resisting decomposition by any heat we can generate. These, consisting severally of one atom of each component element, are combinations of the simplest order – are but one degree less homogeneous than the elements themselves. More heterogeneous than these, more decomposable by heat, and therefore later in the Earth’s history, are the deutoxides, tritoxides, peroxides, &c.; in which two, three, four, or more atoms of oxygen are united with one atom of metal or other base. Still less able to resist heat, are the salts; which present us with compound atoms each made up of five, six, seven, eight, ten, twelve, or more atoms, of three, if not more, kinds. Then there are the hydrated salts, of a yet greater heterogeneity, which undergo partial decomposition at much lower temperatures. After them come the further-complicated supersalts and double salts, having a stability again decreased; and so throughout. After making a few unimportant qualifications demanded by peculiar affinities, I believe no chemist will deny it to be a general law of these inorganic combinations that, other things equal, the stability decreases as the complexity increases. And then when we pass to the compounds that make up organic bodies, we find this general law still further exemplified: we find much greater complexity and much less stability. An atom of albumen, for instance, consists of 482 ultimate atoms of five different kinds. Fibrine, still more intricate in constitution, contains in each atom, 298 atoms of carbon, 49 of nitrogen, 2 of sulphur, 228 of hydrogen, and 92 of oxygen – in all, 660 atoms; or, more strictly speaking – equivalents. And these two substances are so unstable as to decompose at quite moderate temperatures; as that to which the outside of a joint of roast meat is exposed. Possibly it will be objected that some inorganic compounds, as phosphuretted hydrogen and chloride of nitrogen, are more decomposable than most organic compounds. This is true. But the admission may be made without damage to the argument. The proposition is not that all simple combinations are more fixed than all complex ones. To establish our inference it is necessary only to show that, as an average fact, the simple combinations can exist at a higher temperature than the complex ones. And this is wholly beyond question. Thus it is manifest that the present chemical heterogeneity of the Earth’s surface has arisen by degrees as the decrease of heat has permitted; and that it has shown itself in three forms – first, in the multiplication of chemical compounds; second, in the greater number of different elements contained in the more modern of these compounds; and third, in the higher and more varied multiples in which these more numerous elements combine.

Without specifying them, it will suffice just to name the meteorologic processes eventually set up in the Earth’s atmosphere, as further illustrating the alleged law. They equally display that destruction of a homogeneous state which results from unequal exposure to incident forces.

§ 112. Take a mass of unorganized but organizable matter – either the body of one of the lowest living forms, or the germ of one of the higher. Consider its circumstances. Either it is immersed in water or air, or it is contained within a parent organism. Wherever placed, however, its outer and inner parts stand differently related to surrounding agencies – nutriment, oxygen, and the various stimuli. But this is not all. Whether it lies quiescent at the bottom of the water or on the leaf of a plant; whether it moves through the water preserving some definite attitude; or whether it is in the inside of an adult; it equally results that certain parts of its surface are more exposed to surrounding agencies than other parts – in some cases more exposed to light, heat, or oxygen, and in others to the maternal tissues and their contents. Hence must follow the destruction of its original equilibrium. This may take place in one of two ways. Either the disturbing forces may be such as to overbalance the affinities of the organic elements, in which case there result those changes which are known as decomposition; or, as is ordinarily the case, such changes are induced as do not destroy the organic compounds, but only modify them: the parts most exposed to the modifying forces being most modified. To elucidate this, suppose we take a few cases.

Note first what appear to be exceptions. Certain minute animal forms present us either with no appreciable differentiations or with differentiations so obscure as to be made out with great difficulty. In the Rhizopods, the substance of the jelly-like body remains throughout life unorganized, even to the extent of having no limiting membrane; as is proved by the fact that the thread-like processes protruded by the mass, coalesce on touching each other. Whether or not the nearly allied Amœba, of which the less numerous and more bulky processes do not coalesce, has, as lately alleged, something like a cell-wall and a nucleus, it is clear that the distinction of parts is very slight; since particles of food pass bodily into the inside through any part of the periphery, and since when the creature is crushed to pieces, each piece behaves as the whole did. Now these cases, in which there is either no contrast of structure between exterior and interior or very little, though seemingly opposed to the above inference, are really very significant evidences of its truth. For what is the peculiarity of this division of the Protozoa? Its members undergo perpetual and irregular changes of form – they show no persistent relation of parts. What lately formed a portion of the interior is now protruded, and, as a temporary limb, is attached to some object it happens to touch. What is now a part of the surface will presently be drawn, along with the atom of nutriment sticking to it, into the centre of the mass. Either the relations of inner and outer have no permanent existence, or they are very slightly marked. But by the hypothesis, it is only because of their unlike positions with respect to modifying forces, that the originally like units of a living mass become unlike. We must therefore expect no established differentiation of parts in creatures which exhibit no established differences of position in their parts; and we must expect extremely little differentiation of parts where the differences of position are but little determined – which is just what we find. This negative evidence is borne out by positive evidence. When we turn from these proteiform specks of living jelly to organisms having an unchanging distribution of substance, we find differences of tissue corresponding to differences of relative position. In all the higher Protozoa, as also in the Protophyta, we meet with a fundamental differentiation into cell-membrane and cell-contents; answering to that fundamental contrast of conditions implied by the terms outside and inside. On passing from what are roughly classed as unicellular organisms, to the lowest of those which consist of aggregated cells, we equally observe the connection between structural differences and differences of circumstance. Negatively, we see that in the sponge, permeated throughout by currents of sea-water, the indefiniteness of organization corresponds with the absence of definite unlikeness of conditions: the peripheral and central portions are as little contrasted in structure as in exposure to surrounding agencies. While positively, we see that in a form like the Thalassicolla, which, though equally humble, maintains its outer and inner parts in permanently unlike circumstances, there is displayed a rude structure obviously subordinated to the primary relations of centre and surface: in all its many and important varieties, the parts exhibit a more or less concentric arrangement.

After this primary modification, by which the outer tissues are differentiated from the inner, the next in order of constancy and importance is that by which some part of the outer tissues is differentiated from the rest; and this corresponds with the almost universal fact that some part of the outer tissues is more exposed to certain environing influences than the rest. Here, as before, the apparent exceptions are extremely significant. Some of the lowest vegetal organisms, as the Hematococci and Protococci, evenly imbedded in a mass of mucus, or dispersed through the Arctic snow, display no differentiations of surface; the several parts of their surfaces being subjected to no definite contrasts of conditions. Ciliated spheres such as the Volvox have no parts of their periphery unlike other parts; and it is not to be expected that they should have; since, as they revolve in all directions, they do not, in traversing the water, permanently expose any part to special conditions. But when we come to organisms that are either fixed, or while moving preserve definite attitudes, we no longer find uniformity of surface. The most general fact which can be asserted with respect to the structures of plants and animals, is, that however much alike in shape and texture the various parts of the exterior may at first be, they acquire unlikenesses corresponding to the unlikenesses of their relations to surrounding agencies. The ciliated germ of a Zoophyte, which, during its locomotive stage, is distinguishable only into outer and inner tissues, no sooner becomes fixed, than its upper end begins to assume a different structure from its lower. The disc-shaped gemmæ of the Marchantia, originally alike on both surfaces, and falling at random with either side uppermost, immediately begin to develop rootlets on the under side, and stomata on the upper side: a fact proving beyond question, that this primary differentiation is determined by this fundamental contrast of conditions.