University of Virginia Library

Chapter 22
Equilibration

§170. towards what do these changes tend? Will they go on for ever? or will there be an end to them? Can things increase in heterogeneity through all future time? or must there be a degree which the differentiation and integration of Matter and Motion cannot pass? Is it possible for this universal metamorphosis to proceed in the same general course indefinitely? or does it work towards some ultimate state admitting no further modification of like kind? The last of these alternative conclusions is that to which we are inevitably driven. Whether we watch concrete processes, or whether we consider the question in the abstract, we are alike taught that Evolution has an impassable limit.

The re-distributions of matter which go on around us, are ever being brought to conclusions by the dissipation of the motions which effect them. The rolling stone parts with portions of its momentum to the things it strikes, and finally comes to rest; as do also, in like manner, the various things it has struck. Descending from the clouds and trickling over the Earth's surface till it gathers into brooks and rivers, water, still running towards a lower level, is at last arrested by the resistance of other water that has reached the lowest level. In the lake or sea thus formed, every agitation raised by a wind or the immersion of a solid body, propagates itself around in waves which diminish as they widen, and gradually become lost to observation in motions communicated to the atmosphere and the matter on the shores. The impulse given by a player to a harp-string is transformed through its vibrations into aerial pulses; and these, spreading on all sides, and weakening as they spread, soon cease to be perceptible, and are gradually expended in generating thermal undulations that radiate into space: each aerial pulse causing compression and evolution of heat. Equally in the cinder which falls out of the fire, and in the vast mass of molten lava ejected by a volcano, we see that the molecular agitation disperses itself by radiation; so that the temperature inevitably sinks at last to the same degree as that of surrounding bodies. The proximate rationale of the process exhibited under these several forms, lies in the fact dwelt on when treating of the Multiplication of Effects, that motions are ever being decomposed into divergent motions, and these into re-divergent motions. The rolling stone sends off the stones it hits in directions differing more or less from its own, and they do the like with the things they hit. Move water or air, and the movement is quickly resolved into dispersed movements. The heat produced by pressure in a given direction diffuses itself by undulations in all directions. That is to say, these motions undergo division and subdivision, and by continuance of this process without limit they are, though never lost, gradually dissipated.

In all cases, then, there is a progress toward equilibrium. That universal co-existence of antagonist forces which, as we before saw, necessitates the universality of rhythm, and which, as we before saw, necessitates the decomposition of every force into divergent forces, at the same time necessitates the ultimate establishment of a balance. Every motion, being motion under resistance, is continually suffering deductions; and these unceasing deductions finally result in the cessation of the motion.

The general truth thus frustrated under its simplest aspect, we must now look at under those more complex aspects it usually presents throughout Nature. In nearly all cases, the motion of an aggregate is compound; and the equilibration of each of its components, being carried on independently, does not affect the rest. The ship's bell that has ceased to vibrate, still continues those vertical and lateral oscillations caused by the ocean-swell. The water of a smooth stream on whose surface have died away the undulations caused by a rising fish, moves as fast as before towards the sea. The arrested bullet travels with undiminished speed round the Earth's axis. And were the rotation of the Earth destroyed, there would not be implied any diminution of the Earth's movement with respect to the Sun and other external bodies. So that in every case, what we regard as equilibration is a disappearance of some one or more of the many movements a body possesses, while its other movements continue as before. That this process may be duly realized and the state of things towards which it tends fully understood, it will be well here to cite a case in which we may watch this successive equilibration of combined movements more completely than we can do in those above instanced. Our end will best be served not by the most imposing but by the most familiar example. Let us take that of a spinning top. When the string which has been wrapped round a top's axis is violently drawn off, and the top falls on to the table, it usually happens that besides the rapid rotation two other movements are given to it. A slight horizontal momentum, unavoidably impressed on it when leaving the handle, carries it. away bodily from the place on which it drops; and in consequence of its axis being more or less inclined, it falls into a certain oscillation, described by the expressive though inelegant word "wabbling." These two subordinate motions, variable in their proportions to each other and to the chief motion, are commonly soon brought to a close by separate processes of equilibrium. The momentum which carries the top bodily along the table, resisted somewhat by the air but mainly by the irregularities of the surface, shortly disappears; and the top thereafter continues to spin on one spot. Meanwhile, in consequence of that opposition which the axial momentum of a rotating body makes to any change in the plane of rotation, (so beautifully exhibited by the gyroscope,) the "wabbling" diminishes, and like the other is quickly ended. These minor motions having been dissipated, the rotatory motion, interfered with only by atmospheric resistance and the friction of the pivot, continues some time with such uniformity that the top appears stationary: there being thus temporary established a condition which the French mathematicians have termed equilibrium mobile. It is true that when the velocity of rotation sinks below a certain point, new motions commence and increase till the top falls; but these are merely incidental to a case in which the centre of gravity is above the point of support. Were the top, having an axis of steel, to be suspended from a surface adequately magnetized, the moving equilibrium would continue until the top became motionless, without any further change of attitude. Now the facts which it behoves us here to observe are these. First, that the various motions which an aggregate possesses are separately equilibrated: those which are smallest, or which meet with the greatest resistance, or both, disappearing first; and leaving at last that which is greatest, or meets with least resistance, or both. Second, that when the aggregate has a movement of its parts with respect to each other which encounters but little external resistance, there is apt to be established a moving equilibrium. Third, that this moving equilibrium eventually lapses into complete equilibrium.

Fully to comprehend the process of equilibration, is not easy; since we have simultaneously to contemplate various phases of it. The best course will be to glance separately at what we may conveniently regard as its four different orders. The first order includes the comparatively simple motions, as those of projectiles, which are not prolonged enough to exhibit their rhythmical character, but which, being quickly divided and subdivided into motions communicated to other portions of matter, are presently dissipated in the rhythm of ethereal undulations. In the second order, comprehending various kinds of ordinary vibration or oscillation, the implied energy is used up in generating a tension which, having become equal to it or momentarily equilibrated with it, thereupon produces a motion in the opposite direction, that is subsequently equilibrated in like manner: thus causing a visible rhythm which is presently lost in invisible rhythms. The third order of equilibration, not hitherto noticed, obtains in those aggregates which continually receive as much energy as they expend. The steam-engine (and especially that kind which feeds its own furnace and boiler) supplies an example. Here the energy from moment to moment dissipated in overcoming the resistance of the machinery driven, is from moment to moment re-placed from the fuel; and the balance of the two is maintained by a raising or lowering of the expenditure according to the variation of the supply: each increase or decrease in the quantity of steam, resulting in a rise or fall of the engine's movement, such as brings it to a balance with the increased or decreased resistance. This, which we may fitly call the dependent moving equilibrium, should be specify noted; since it is one that we shall commonly meet with throughout various phases of Evolution. The equilibrium to be distinguished as of the fourth order, is the independent or perfect moving equilibrium. This we see illustrated in the rhythmical motions of the Solar System, which, being resisted only by a medium of inappreciable density, undergo no sensible diminution in such periods of time as we can measure.

Something has still to be added. The reader must note two leading truths brought out by the foregoing exposition: the one concerning the ultimate, or rather the penultimate, state of motion which the processes described tend to bring about; the other concerning the concomitant distribution of matter. This penultimate state of motion is the moving equilibrium, which tends to arise in an aggregate having compound motions, as a transitional state on the way towards complete equilibrium. Throughout Evolution of all kinds there is a continual approximation to, and more or less complete maintenance of, this moving equilibrium. As in the Solar System there has been established an independent moving equilibrium — an equilibrium such that the relative motions of its members are continually so counterbalanced by opposite motions, that the mean state of the aggregate never varies; so is it, though in a less distinct manner, with each form of dependent moving equilibrium. The state of things exhibited in the cycles of terrestrial changes, in the balanced functions of organic bodies that have reached their adult forms, and in the acting and re-acting processes of fully-developed societies, is similarly one characterized by compensating oscillations. The involved combination of rhythms seen in each of these cases, has an average condition which remains practically constant during the deviations ever taking place on opposite sides of it. And the fact which we have here to observe is that, as a corollary from the general law of equilibrium, every evolving aggregate must go on changing until a moving equilibrium is established; since, as we have seen, an excess of force which the aggregate possesses in any direction, must eventually be expended in overcoming resistances to change in that direction: leaving behind only those movements which compensate one another, and so form a moving equilibrium. Respecting the structural state simultaneously reached, it must obviously be one presenting an arrangement of forces that counterbalance all the forces to which the aggregate is subject. So long as there remains a residual force in any direction — be it excess of a force exercised by the aggregate on its environment, or of a force exercised by its environment on the aggregate, equilibrium does not exist; and therefore the re-distribution of matter must continue. Whence it follows that the limit of heterogeneity towards which every aggregate progresses, is the formation of as many specializations and combinations of parts, as there are specialized and combined forces to be met.

§171. Those successively changed forms which, if the nebular hypothesis be granted, must have arisen during the evolution of the Solar System, were so many transitional kinds of moving equilibrium, severally giving place to more enduring kinds. Thus the assumption of an oblate spheroidal figure by condensing nebulous matter, was the assumption of a temporary and partial moving equilibrium among the component parts — a moving equilibrium that must have grown more settled as local conflicting movements were dissipated. In the formation and detachment of the nebulous rings which, according to this hypothesis, from time to time took place, we have instances of progressive equilibration severally ending in the establishment of a complete moving equilibrium. For the genesis of each such ring implies a balancing of that attractive force which the whole spheroid exercises on its equatorial portion, by that centrifugal force which the equatorial portion has acquired during previous concentration. So long as these two forces are not equal, the equatorial portion follows the contracting mass; but as soon as the second force has increased up to an equality with the first, the equatorial portion can follow no further and remains behind. While, however, the resulting ring, regarded as a whole, has reached a state of moving equilibrium, its parts are not balanced with respect to one another. As we before saw (§150) the probabilities against the maintenance of an annular form by nebulous matter are great: from the instability of the homogeneous, it is inferable that nebulous matter so distributed will break up into portions, and eventually concentrate into a single mass. That is to say, the ring will progress towards a moving equilibrium of a more complete kind, during the dissipation of that motion which maintained its particles in a diffused form; leaving at length a planetary body attended perhaps by a group of minor bodies similarly produced, constituting a moving equilibrium that is all but perfect.

Hypothesis aside, the principle of equilibration is still perpetually illustrated in those minor changes of state which the Solar System undergoes. Each planet, satellite, and comet, exhibits at its aphelion a momentary equilibrium between that force which urges it further away from its primary, and that force which retards its retreat. In like manner at perihelion a converse equilibrium is momentarily established. The variation of each orbit in eccentricity, and in the position of its plane, has similarly a limit at which the forces producing change in the one direction, are equalled by those antagonizing it; and an opposite limit at which an opposite arrest takes place. Meanwhile, each of these simple perturbations, as well as each of the complex ones resulting from their combination, exhibits, besides the temporary equilibration at each of its extremes, a certain general equilibration of compensating deviations on either side of a mean state. That the moving equilibrium thus constituted tends, in the course of indefinite time, to lapse into a complete equilibrium, by the gradual decrease of planetary motions and eventual integration of all the separate masses composing the Solar System, is a belief suggested by certain observed cometary retardations — a belief entertained by some of high authority. The received option that the appreciable diminution in the period of Encke's comet, implies a loss of momentum caused by resistance to the ethereal medium, commits astronomers who hold it, to the conclusion that this same resistance must cause a loss of planetary motions — a loss which, infinitesimal though it may be in such periods as we can measure, will, if indefinitely continued, bring these motions to a close. Even should there be, as Sir John Herschel suggests, a rotation of the ethereal medium in the same direction with the planets, this arrest, though immensely postponed, would not be absolutely prevented. Such an eventuality, however, must in any case be so inconceivably remote as to have no other than a speculative interest for us. It is referred to here, simply as illustrating the still-continued tendency towards complete equilibrium, through the still-continued dissipation of sensible motion, or transformation of it into insensible motion.

But there is another species of equilibration going on in the Solar System, with which the human race is less remotely concerned. The tacit assumption that the Sun can continue to give off an undiminished amount of light and heat through all future time, is now abandoned. Involving as it does, under a disguise, the conception of power produced out of nothing, it is of the same order as the belief which misleads perpetual-motion schemers. The spreading recognition of the truth that whatever force is manifested under one shape must previously have existed under another shape, implies recognition of the truth that the force known to us in solar radiations, is the changed form of some other force of which the Sun is the seat; and that, by the emission of these radiations, this other force is being slowly exhausted. The force by which the Sun's substance is drawn to his centre of gravity, is the only one which physical laws warrant us in concluding to be the correlate of the forces emanating from him: the only assignable source for the insensible motions constituting solar light and heat, is the sensible motion which disappears during the concentration of the Sun's mass. We before saw it to be a corollary from the nebular hypothesis, that there is such a progressing concentration of the Sun's mass. And here remains to be added the further corollary, that just as in the case of the small members of the Solar System, the heat generated by concentration, once escaping rapidly, has in each left a central residue which escapes but slowly; so in the case of that immensely larger mass forming the Sun, the immensely greater quantity of heat generated and still in process of rapid diffusion, must, as the concentration approaches its limit, diminish in amount, and eventually leave but a relatively small internal remnant. With or without the accompaniment of that hypothesis of nebular condensation whence it naturally follows, the doctrine that the Sun is gradually losing his heat, has now gained general acceptance; and calculations have been made, both respecting the amount of heat and light already radiated, as compared with the amount that remains, and respecting the period during which active radiation will continue. Prof. Helmholtz estimates that since the time when, according to the nebular hypothesis, the matter composing the Solar System extended to the Orbit of Neptune, there has been evolved by the arrest of sensible motion, an amount of heat 454 times as great as that which the Sun still has to give out. He also makes an approximate estimate of the rate at which this remaining 1/454th is being diffused: showing that decrease of the Sun's diameter to the extent of 1/10,000 would produce heat, at the present rate, for more than 2000 years; or in other words, that a contraction of 1/20,000,000 of his diameter, suffices to generate the light and heat annually emitted; and that thus at the present rate of expenditure, the Sun's diameter will diminish by something like 1/20 in the lapse of the next million years. Of course these conclusions are but rude approximations to the truth. Until quite recently, we have been totally ignorant of the Sun's chemical composition, and even now have obtained but a superficial knowledge of it. We know nothing of his internal structure; and it is quite possible that the assumptions respecting central density, made in the foregoing estimates, are wrong.

But no uncertainty in the data on which these calculations proceed, and no consequent error in the inferred rate at which the Sun is expending his reserve energy, militates against the general proposition that this reserve of energy is being expended, and must in time be exhausted.

Thus while the Solar System, if evolved from diffused matter, has illustrated the law of equilibration in the establishment of a moving equilibrium; and while, as at present constituted, it illustrates the law of equilibration in the perpetual balancing of all its movements; it also illustrates this law in these processes which astronomers and physicists infer are still going on. That motion of masses produced during Evolution, is being slowly rediffused in molecular motion of the ethereal medium; both through the progressive integration of each mass, and the resistance to its motion through space. Infinitely remote as may be the state when all the relative motions of its masses shall be transformed into molecular motion, and all the molecular motion dissipated; yet such a state of complete integration and complete equilibration, is that towards which the changes now going on throughout the Solar System inevitably tend.

§172. A spherical figure is the one which can alone equilibrate the forces of mutually-gravitating molecules. If an aggregate of such molecules rotates, the form of equilibrium becomes a spheroid of greater or less oblateness, according to the rate of rotation; and it has been ascertained that the Earth is an oblate spheroid, diverging just as much from sphericity as is requisite to counterbalance the centrifugal force consequent on its velocity round its axis. That is to say, during the evolution of the Earth, there has been reached an equilibrium of those forces which affect its general outline. The only other equilibration which the Earth as a whole can exhibit, is the loss of its rotation; and that any such loss is going on we have no direct evidence. It has been contended, however, by Prof. Helmholtz and others, that inappreciable as may be its effect within known periods of time, the friction of the tidal wave must be diminishing the Earth's motion round its axis, and must eventually destroy it. Now though it seems an oversight to say that the axial motion can thus be destroyed, since the extreme effect, to be reached only in infinite time, would be an extension of the Earth's day to the length of lunation; yet it seems clear that this friction of the tidal wave is a real cause of decreasing rotation. Slow as its action is, we must recognize its retarding effect as exemplifying, under another form, the universal progress towards equilibrium.

It is needless to show in detail how those movements which the Sun's rays generate in the air and water on the Earth's surface, and through them in the Earth's solid substance, † one and all teach the same general truth. Evidently the winds and waves and streams, as well as the denudations and depositions they effect, illustrate on a grand scale, and in endless modes, that gradual dissipation of motions described in the first section, and the consequent tendency towards a balanced distribution of forces. Each of these sensible motions, produced directly or indirectly by integration of those insensible motions communicated from the Sun, becomes divided and subdivided into motions less and less sensible; until by gradual or sudden arrest of each, and production of its equivalent in molecular motion, there is an escape of it into space in the shape of thermal undulations. In their totality, these complex motions constitute a dependent moving equilibrium. As we before saw there is traceable throughout them an involved combination of rhythms. The unceasing circulation of water from the ocean to the land and from the land back to the ocean, is a type of these various compensating actions which, in the midst of all the irregularities produced by their mutual interferences, maintain an average. And in this, as in other equilibrations of the third order, we see that the energy ever in course of dissipation, is ever renewed from without: the rises and falls in the supply being balanced by rises and falls in the expenditure; as witness the variations of meteorologic activity in northern zones caused by changes of the seasons. But the fact it chiefly concerts us to note is that this process must go on bringing things ever nearer to complete rest. These mechanical movements, meteorologic and geologic, which are continually being equilibrated, both temporary by counter-movements and permanently by the dissipation of such movements and counter-movements, will slowly diminish as the quantity of force received from the Sun diminishes. As the insensible motions propagated to us from the centre of our system become feebler, the sensible motions here produced by them must decrease; and at that remote period when the solar heat has ceased to be appreciable, there will no longer be any appreciable re-distributions of matter on the surface of our planet.

Thus, all terrestrial changes are incidents in the course of cosmical equilibration. It was before pointed out (§69), that of the incessant alterations which the Earth's crust and atmosphere undergo, those which are not due to the action of the moon and to the still-progressing motion of the Earth's substance towards its centre of gravity, are due to the still-progressing motion of the Sun's substance towards its centre of gravity. Here it is to be remarked that this continuance of integration in the Earth and in the Sun, is a continuance of that transformation of sensible motion into insensible motion which we have seen ends in equilibrium; and that the arrival in each case at the extreme of integration, is the arrival at a state in which no more sensible motion remains to be transformed into insensible motion — a state in which the forces producing integration and the forces opposing integration have become equal.

§173. Every living body exhibits, in a four-fold form, the process we are tracing out — exhibits it from moment to moment in the balancing of mechanical forces; from hour to hour in the balancing of functions; from year to year in the changes of state that compensate changes of conditions; and finally in the arrest of vital movements at death. Let us consider the facts under these heads.

The sensible motion constituting each visible action of an animal, is soon brought to a close by some opposing force within or without the animal. When a man's arm is raised, the motion given to it is antagonized partly by gravity and partly by the internal resistances consequent on structure; and its motion, thus suffering continual deduction, ends when the arm has reached a position at which the forces are equilibrated. The limits of each systole and diastole of the heart, severally show us a momentary equilibrium between muscular strains that produce opposite movements; and each gush of blood has to be immediately followed by another because the rapid dissipation of its momentum would otherwise soon bring the circulating mass to a stand. As much in the actions and reactions going on among the internal organs, as in the mechanical balancing of the whole body there is at every instant a progressive equilibration of the motions at every instant produced. Viewed in their aggregate, and as forming a series, the organic functions constitute a dependent moving equilibrium, a moving equilibrium of which the motive power is ever being dissipated through the special equilibrations just exemplified, and is ever being renewed by the taking in of additional motive power. The force stored up in food continually adds to the momentum of the vital actions, as much as is continually deducted from them by the forces overcome. All the functional movements thus maintained are rhythmical (§85); by their union compound rhythms of various lengths and complexities are produced; and in these simple and compound rhythms, the process of equilibration, besides being exemplified at each extreme of every rhythm, is seen in the habitual preservation of a constant mean, and in the re-establishment of that mean when accidental causes have produced divergence. from it. When, for instance, there is a great expenditure of muscular energy, there arises a reactive demand on those stores of energy which are laid up in the form of consumable matter throughout the tissues: increased respiration and increased circulation aid an extra genesis of force, that counterbalances the extra dissipation of force. This unusual transformation of molecular motion into sensible motion, is presently followed by an unusual absorption of food — the source of molecular motion; and the prolonged draft on the spare capital in the tissues, is followed by a prolonged rest, during which the abstracted capital is replaced. If the deviation from the ordinary course of the functions has been so great as to derange them, as when violent exertion produces loss of appetite and loss of sleep, an equilibration is still eventually effected. Providing the disturbance is not such as to destroy life (in which case complete equilibration is suddenly effected), the ordinary balance is by-and-by re-established: the returning appetite is keen in proportion as the waste has been large; while sleep, sound and prolonged, makes up for previous wakefulness. Not even when some extreme excess has wrought a derangement that is never wholly rectified, is there an exception to the general law; for in such cases the cycle of the functions is, after a time, equilibrated about a new mean state, which thenceforth becomes the normal state of the individual. And this process exemplifies in a large way what physicians call the vis medicatrix naturae. The third form of equilibration displayed by organic bodies, is a sequence of that just illustrated. When, through a change of habit or circumstance, an organism is permanently subject to some new influence, or different amount of an old influence, there arises, after more or less disturbance of the organic rhythms, a balancing of them around the new average condition produced by this additional influence. if the quantity of motion to be habitually generated by a muscle becomes greater than before, its nutrition becomes greater than before. if the expenditure of the muscle bears to its nutrition, a greater ratio than expenditure bears to nutrition in other parts of the system, the excess of nutrition becomes such that the muscle grows. And the cessation of its growth is the establishment of a balance between the daily waste and the daily repair. The like is manifestly the case with all organic modifications consequent on changes of climate or food. If we see that a different mode of life is followed, after a period of derangement, by some altered condition of the system — if we see that this altered condition, becoming by-and-by established, continues without further change; we have no alternative but to say that the new forces brought to bear on the system, have been compensated by the opposing forces they have evoked. And this is the interpretation of the process called adaptation. Finally, each organism illustrates the law in the ensemble of its life. At the outset it daily absorbs under the form of food, an amount of force greater than it daily expends; and the surplus is daily equilibrated by growth. As maturity is approached this surplus diminishes; and in the perfect organism the day's absorption of latent energy balances the day's expenditure of actual energy. That is to say, during adult life there is continuously exhibited an equilibrium of the third order. Eventually, the daily loss begins to outbalance the daily gain, and there results a diminishing amount of functional action; the organic rhythms extend less and less widely on each side of the medium state; and there finally comes that complete equilibrium we call death.

The ultimate structural state accompanying that ultimate functional state towards which an organism tends, may be deduced from one of the propositions set down in the opening section of this chapter. We saw that the limit of heterogeneity is reached when the equilibration of any aggregate becomes complete — that the re-distribution of matter can continue so long only as there continues some motion unbalanced. What is the implication in the case of organic aggregates? We have seen that to maintain the moving equilibrium of one, requires the habitual genesis of internal forces corresponding in number, directions, and amounts to the external incident forces — as many inner functions, single or combined, as there are single or combined outer actions to be met. But functions are the correlatives of organs; amounts of functions are, other things equal, the correlatives of sizes of organs; and combinations of functions the correlatives of connexions of organs. Hence the structural complexity accompanying functional equilibrium, is definable as one in which there are as many specialized parts as are capable, separately and jointly, of counteracting the separate and joint forces amid which the organism exists. And this is the limit of organic heterogeneity. to which Man has approached more nearly than any other creature.

Groups of organisms display this universal tendency towards a balance very obviously. in §85, every species of plant and animal was shown to be perpetually undergoing a rhythmical variation in number — now from abundance of food or absence of enemies rising above its average; and then, by a consequent scarcity of food or abundance of enemies, being depressed below its average. And here we have to observe that there is thus maintained an equilibrium between the sum of those forces which result in the increase of each race, and the sum of those forces which result in its decrease. Either limit of variation is a point at which the one set of forces, before in excess of the other, is counterbalanced by it. And amid these oscillations produced by their conflict, lies that average number of the species at which its expansive tendency is in equilibrium with surrounding repressive tendencies. Nor can it be questioned that this balancing of the preservative and destructive forces which we see going on in every race, must necessarily go on. Increase of number cannot but continue until increase of mortality stops it; and decrease of number cannot but continue until it is either arrested by fertility or extinguishes the race entirely.

§174. The equilibrations of those nervous actions which constitute the obverse face of mental life, may be classified in like manner with those which constitute what we distinguish as bodily life. We may deal with them in the same order.

Each pulse of nerve force from moment to moment generated, (and it was explained in §86 that nerve currents are not continuous but rhythmical,) is met by counteracting forces, in overcoming which it is dispersed and equilibrated. Such part of it as does not work mental changes works bodily changes — contractions of the involuntary muscles, the voluntary muscles, or both; as also some stimulation of secreting organs. That the movements thus initiated are ever being brought to a close by the opposing forces they evoke, we have just seen; and here it is to be observed that the like holds with the cerebral changes thus initiated. The arousing of a thought or feeling, involves the overcoming of a certain resistance: instance the fact that where the association of mental states has not been frequent, a sensible effort is needed to call up the one after the other; instance the fact that during nervous prostration there is a comparative inability to think — the ideas will not follow one another with the ordinary rapidity; instance the converse fact that at times of unusual energy, natural or artificial, thinking is easy, and more numerous, more remote, or more difficult connexions of ideas are formed. That is to say, the wave of nervous energy each instant generated, propagates itself throughout body and brain, along those channels which the passing conditions render lines of least resistance; and spreading widely in proportion to its amount, ends only when it is equilibrated by the resistances it everywhere meets. If we contemplate mental actions as extending over hours and days, we discover equilibrations analogous to those hourly and daily established among the bodily functions. This is seen in the daily alternation of mental activity and mental rest — the forces expended during the one being compensated by the forces acquired during the other. It is also seen in the recurring rise and fall of each desire. Each desire reaching a certain intensity, is equilibrated either by expenditure of the energy it embodies in the desired actions, or, less completely, in the imagination of such actions: the process ending in that satiety or that comparative quiescence, forming the opposite limit of the rhythm. And it is further manifest under a two-fold form on occasions of intense joy or grief. Each paroxysm, expressing itself in violent actions and loud sounds, presently reaches an extreme whence the counteracting forces produce return to a condition of moderate excitement; and the successive paroxysms, finally diminishing in intensity, end in a mental equilibrium either like that before existing, or having a partially different medium state. But the kind of mental equilibration to be especially noted, is that shown in the establishment of a correspondence between relations among our ideas and relations in the external world. Each outer connexion of phenomena which we are capable of perceiving, generates, through accumulated experiences, an inner connexion of mental states; and the result towards which this process tends, is the formation of a mental connexion having a relative strength that answers to the relative constancy of the physical connexion represented. In conformity with the general law that motion pursues the line of least resistance, and that, other things equal, a line once taken by motion is made a line which will be more readily taken by future motion, we have seen that the ease with which nervous impressions follow one another is, other things equal, great in proportion to the number of times they have been repeated together in experience. Hence, corresponding to such an invariable relation as that between the resistance of an object and some extension possessed by it, there arises an indissoluble connexion in consciousness; and this connexion, being as absolute internally as the answering one is externally, undergoes no further change — the inner relation is in perfect equilibrium with the outer relation. Conversely, it happens that, answering to such uncertain relations of phenomena as that between clouds and rain, there arise relations of ideas of like uncertainty; and if, under given aspects of the sky, the tendencies to infer fair or foul weather, corresponds to the frequencies with which fair or foul weather follows such aspects, the accumulation of experiences has balanced the mental sequences and the physical sequences. When it is remembered that between these extremes there are countless orders of external associations having different degrees of constancy, and that during the evolution of intelligence there arise answering eternal associations having different degrees of cohesion; it will be seen that there is a progress towards equilibrium between the relations of thought and the relations of things. The like general truths are exhibited in the process of moral adaptation, which is a continual approach to equilibrium between the emotions and the kinds of conduct required by surrounding conditions. Just as repeating the association of two ideas facilitates the excitement of the one by the other, so does each discharge of feeling into action render the subsequent discharge of such feeling into such action more easy. Thus it happens that if an individual is placed permanently in conditions which demand more action of a special kind than has before been requisite, or than is natural to him — if by every more frequent or more lengthened performance of it under such pressure, the resistance is somewhat diminished; then, dearly, there is an advance towards a balance between the demand for this kind of action and the supply of it. Either in himself, or in his descendants continuing to live under these conditions, enforced repetition must at length bring about a state in which this mode of directing the energies will be no more repugnant than the other modes previously natural to the race. Hence the limit towards which emotional modification perpetually tends, is a combination of desire that correspond to the various orders of activity which the circumstances of life call for. In acquired habits, and in the moral differences of races and nations that are produced by habits maintained through successive generations, we have illustrations of this progressive adaptation, which can cease only with the establishment of equilibrium between constitution and conditions.

§175. Each society displays the process of equilibration in the continuous adjustment of its population to its means of subsistence. A tribe of men living on wild animals and fruits, is manifestly, like every tribe of inferior creatures, always oscillating from side to side of that average number which the locality can support. Though, by artificial production unceasingly improved, a superior race continually alters the limit which external conditions put to population; yet there is ever a checking of population at the temporary limit reached. It is true that where the limit is being rapidly changed, as among ourselves, there is no actual stoppage: there is only a rhythmical variation in the rate of increase. But in noting the causes of this rhythmical variation — in watching how, during periods of abundance, the proportion of marriages increases, and how it decreases during periods of scarcity, it will be seen that the expansive force produces unusual advance whenever the repressive force diminishes, and vice versâ; and thus there is as near a balancing of the two as the changing conditions permit.

The internal actions constituting social functions, exemplify the general principle no less clearly. Supply and demand are continually being adjusted throughout all industrial processes; and this equilibration is interpretable in the same way as preceding ones. The production and distribution of a commodity imply a certain aggregate of forces causing special kinds and amounts of motion. The price of this commodity, is the measure of a certain other aggregate of forces expended in other kinds and amounts of motion by the labourer who purchases it. And the variations of price represent a rhythmical balancing of these forces. Every rise or fall in the value of a particular security, implies a conflict of forces in which some, becoming temporarily predominant, cause a movement that is. presently arrested, or equilibrated, by the increased opposing forces; and amid these daily and hourly oscillations lies a more slowly-varying medium, into which the value ever tends to settle, and would settle but for the constant addition of new influences. As in the individual organism so in the social organism, functional equilibrations generate structural equilibrations. When on the workers in any trade there comes an increased demand, and when in return for the increased supply they receive an amount of other commodities larger than before — when, consequently, the resistances overcome by them in sustaining life are less than the resistances overcome by other workers; there results a flow of other workers into this trade. This flow continues until the extra demand is met, and the wages so far fall that the total resistance overcome in obtaining a livelihood, is as great in this newly-adopted occupation as in the occupations whence it drew recruits. The occurrence of motion along lines of least resistance, was before shown to necessitate the growth of population in those places where the labour required for self-maintenance is the smallest; and here we further see that those engaged in any such advantageous locality, must multiply till there arises an approximate balance between its population and that of others available by the same citizens.

These various industrial actions and reactions constitute a dependent moving equilibrium like that maintained among the functions of an individual organism, and like it tends ever to become more complete. During early stages of social evolution, while the resources of the locality inhabited are unexplored and the arts of production undeveloped, there is never anything more than a temporary and partial balancing of such actions. But when a society approaches the maturity of that type on which it is organized, the various industrial activities settle down into a comparatively constant state. Moreover, advance in organization, as well as advance in growth, is conducive to a better equilibrium of industrial functions. While the diffusion of mercantile information is slow and the means of transport deficient, the adjustment of supply to demand is very imperfect. Great over-production of a commodity is followed by great under-production, and there results a rhythm having extremes that depart widely from the mean state in which demand and supply are equilibrated. But when good roads are made and there is a rapid diffusion of printed or written intelligence, and still more when railways and telegraphs come into existence — when the periodical fairs of early days grow into weekly markets, and these into daily markets, there is gradually produced a better balance of production and consumption: the rapid oscillations of price within narrow limits on either side of a comparatively uniform mean, indicate a near approach to equilibrium. Evidently this industrial progress has for its limit, that which Mr. Mill has called "the stationary state." When population shall have become dense over all habitable parts of the globe; when the resources of every region have been fully explored; and when the productive arts admit of no further improvements; there must result an almost complete balance, both between the fertility and mortality in each society, and between its producing and consuming activities. Each society will exhibit only minor deviations from its average number, and the rhythm of its industrial functions will go on from day to day and year to year with comparatively insignificant perturbations.

One other kind of social equilibration has still to be considered: — that which results in the establishment of governmental institutions, and which becomes complete as these institutions fall into harmony with the desires of the people. Those aggressive impulses inherited from the pre-social state — those tendencies to seek self-satisfaction regardless of injury to other beings, which are essential to a predatory life, constitute an anti-social force tending ever to cause conflict and separation. Contrariwise, those desires which can be fulfilled only by co-operation and those which find satisfaction through intercourse with fellow-men, as well as those resulting in what we call loyalty, are forces tending to keep the units of a society together. On the one hand, there is in each man more or less of resistance against restraints imposed on his actions by other men — a resistance which, tending ever to widen each man's sphere of action, and reciprocally to limit the spheres of action of other men, constitutes a repulsive force mutually exercised by the members of a social aggregate. On the other hand, the general sympathy of man for man and the more special sympathy of each variety of man for others of the same variety, together with allied feelings which the social state gratifies, act as an attractive force, tending ever to keep united those who have a common ancestry. And since the resistances to be overcome in satisfying the totality of their desires when living separately, are greater than the resistances to be overcome in satisfying the totality of their desires when living together, there is a residuary force that prevents separation. Like other opposing forces, those exerted by citizens on one another produce alternating movements which, at first extreme, undergo gradual diminution on the way to ultimate equilibrium. In small, undeveloped societies, marked rhythms result from these conflicting tendencies. A tribe that has maintained its unity for a generation or two, reaches a size at which it will no longer hold together; and, on the occurrence of some event causing unusual antagonism among its members, divides. Each primitive nation exhibits wide oscillations between an extreme in which the subjects are under rigid restraint, and an extreme in which the restraint fails to prevent rebellion and disintegration. In more advanced nations of like type, we always find violent actions and reactions of the same essential nature: "despotism tempered by assassination," characterizing a political state in which unbearable repression from time to time brings about a bursting of bonds. Among ourselves the conflicts between Conservatism (which stands for the restraints of society over the individual) and Reform (which stands for the liberty of the individual against society), fall within slowly approximating limits. so that the temporary predominance of either produces a less marked deviation from the medium state — a smaller disturbance of the moving equilibrium.

Of course in this case, as in preceding cases, there is involved a limit to the increase of heterogeneity. A few pages back, it was shown that an advance in mental evolution is the establishment of some further internal action corresponding to some further external action. We inferred that each such new function, involving some new modification of structure, implies an increase of heterogeneity; and that thus, increase of heterogeneity must go on while there remain any outer relations affecting the organism which are unbalanced by inner relations. Evidently the like must simultaneously take place with society. Each increment of heterogeneity in the individual implies, as cause or consequence, some increment of heterogeneity in the arrangements of the aggregate of individuals. And the limit to social complexity can be reached only with the establishment of the equilibrium, just described, between social and individual forces.

§176. Here presents itself a final question, which has probably been taking shape in the minds of many while reading this chapter. "If Evolution of every kind is an increase in complexity of structure and function that is incidental to the universal process of equilibration, and if equilibration must end in complete rest, what is the fate towards which all things tend? If the Solar System is slowly dissipating its energies — if the Sun is losing his heat at a rate which will tell in millions of years — if with decrease of the Sun's radiations there must go on a decrease in the activity of geologic and meteorologic processes as well as in the quantity of vegetable and animal life — if Man and Society are similarly dependent on this supply of energy which is gradually coming to an end; are we not manifestly processing towards omnipresent death?"

That such a state must be the outcome of the changes everywhere going on, seems beyond doubt. Whether any ulterior process may reverse these processes and initiate a new life, is a question to be considered hereafter. For the present it must suffice that the end of all the transformations we have traced, is quiescence. This admits of a priori proof. The law of equilibration, not less than the preceding general laws, is deducible from the ultimate datum of consciousness.

The forces of attraction and repulsion being, as shown in §74, universally co-existent, it follows that all motion is motion under resistance: either that exercised on the moving body by other bodies, or that exercised by the medium traversed. There are two corollaries. The first is that deductions perpetually made by the communication of motion to that which resists, cannot but bring the motion of the body to an end in a longer or shorter time. The second is that the motion of the body cannot cease until these deductions destroy it. In other words, movement must continue while equilibration is incomplete, and equilibration must eventually become complete. Both these are manifest deductions from the persistence of force. Hence this primordial truth is our warrant for the conclusions that the changes which Evolution presents cannot end until equilibrium is reached, and that equilibrium must at last be reached.

At the same time it follows that in every aggregate having compound motions, there results a comparatively early dissipation of the motions which are smaller and much resisted, followed by long-continuance of the larger and less resisted motions; and that so there arise moving equilibria. Hence, also, may be inferred the tendency to conservation of such moving equilibria. For any new motion given to the parts of a moving equilibrium by a disturbing force, must either be such that it cannot be dissipated before the pre-existing motions, in which case it brings the moving equilibrium to an end. or else it must be such that it can be dissipated before the pre-existing motions, in which case the moving equilibrium is re-established.

Thus from the persistence of force follow, not only the various direct and indirect equilibrations going on around, together with th at cosmical equilibration which brings Evolution under all its forms to a close, but also those less manifest equilibrations shown in the readjustments of moving equilibria that have been disturbed. By this ultimate principle is provable the tendency of every organism, disordered by some unusual influence, to return to a balanced state. To it also may be traced the capacity, possessed in a slight degree by individuals and in a greater degree by species, of becoming adapted to new circumstances. And not less does it afford a basis for the inference that there is a gradual advance towards harmony between man's mental nature and the conditions of his existence.

NOTES