The Online Library of Liberty

A project of Liberty Fund, Inc.

• Part I.: The Unknowable.
• Chapter I.: Religion and Science.
• Chapter II.: Ultimate Religious Ideas.
• Chapter III.: Ultimate Scientific Ideas.
• Chapter IV.: The Relativity of All Knowledge.
• Chapter V.: The Reconciliation.
• Part II.: The Knowable.
• Chapter I.: Philosophy Defined.
• Chapter II.: The Data of Philosophy.
• Chapter III.: Space, Time, Matter, Motion, and Force.
• Chapter IV.: The Indestructibility of Matter.
• Chapter V.: The Continuity of Motion.
• Chapter VI.: The Persistence of Force. ∗
• Chapter VII.: The Persistence of Relations Among Forces.
• Chapter VIII.: The Transformation and Equivalence of Forces.
• Chapter IX.: The Direction of Motion.
• Chapter X.: The Rhythm of Motion.
• Chapter XI.: Recapitulation, Criticism, and Recommencement.
• Chapter XII.: Evolution and Dissolution.
• Chapter XIII.: Simple and Compound Evolution.
• Chapter XIV.: The Law of Evolution.
• Chapter XV.: The Law of Evolution Continued.
• Chapter XVI.: The Law of Evolution Continued.
• Chapter XVII.: The Law of Evolution Concluded.
• Chapter XVIII.: The Interpretation of Evolution.
• Chapter XIX.: The Instability of the Homogeneous. ∗
• Chapter XX.: The Multiplication of Effects.
• Chapter XXI.: Segregation.
• Chapter XXII.: Equilibration.
• Chapter XXIII.: Dissolution.
• Chapter XXIV.: Summary and Conclusion.

CHAPTER XXII.

EQUILIBRATION.

§ 170. And now 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 that 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 that 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 the 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 finally die away in generating thermal undulations that radiate into space. Equally in the cinder that falls out of the fire, and in the vast masses of molten lava ejected by a volcano, we see that the molecular agitation known to us as heat, disperses itself by radiation; so that however great its amount, it inevitably sinks at last to the same degree as that existing in surrounding bodies. And if the actions observed be electrical or chemical, we still find that they work themselves out in producing sensible or insensible movements, that are dissipated as before; until quiescence is eventually reached. 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 radiating movements. The heat produced by pressure in a given direction, diffuses itself by undulations in all directions; and so do the light and electricity similarly generated. That is to say, these motions undergo division and subdivision; and by continuance of this process without limit, they are, though never lost, gradually reduced to insensible motions.

In all cases then, there is a progress toward equilibration. 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 illustrated 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 the smooth stream on whose surface have died away the undulations caused by the rising fish, moves as fast as before onward to 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 which 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 the 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 equilibration. 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 temporarily established a condition which the French mathematicians have termed equilibrium mobile. It is true that when the axial velocity 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, all the phenomena described would be displayed, and the moving equilibrium having been once arrived at, would continue until the top became motionless, without any further change of position. 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 an equilibrium mobile. 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 the various kinds of vibration or oscillation as usually witnessed, the motion 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, that is, however, soon lost in invisible rhythms. The third order of equilibration, not hitherto noticed, obtains in those aggregates which continually receive as much motion as they expend. The steam engine (and especially that kind which feeds its own furnace and boiler) supplies an example. Here the force 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 specially noted; since it is one that we shall commonly meet with throughout various phases of Evolution. The equilibration 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.

All these kinds of equilibration may, however, from the highest point of view, be regarded as different modes of one kind. For in every case the balance arrived at is relative, and not absolute—is a cessation of the motion of some particular body in relation to a certain point or points, involving neither the disappearance of the relative motion lost, which is simply transformed into other motions, nor a diminution of the body’s motions with respect to other points. Thus understanding equilibration, it manifestly includes that equilibrium mobile, which at first sight seems of another nature. For any system of bodies exhibiting, like those of the Solar System, a combination of balanced rhythms, has this peculiarity;—that though the constituents of the system have relative movements, the system as a whole has no movement. The centre of gravity of the entire group remains fixed. Whatever quantity of motion any member of it has in any direction, is from moment to moment counter-balanced by an equivalent motion in some other part of the group in an opposite direction; and so the aggregate matter of the group is in a state of rest. Whence it follows that the arrival at a state of moving equilibrium, is the disappearance of some movement which the aggregate had in relation to external things, and a continuance of those movements only which the different parts of the aggregate have in relation to each other. Thus generalizing the process, it becomes clear that all forms of equilibration are intrinsically the same; since in every aggregate, it is the centre of gravity only that loses its motion: the constituents always retaining some motion with respect to each other—the motion of molecules if none else. Every equilibrium commonly regarded as absolute, is in one sense a moving equilibrium; because along with a motionless state of the whole there is always some relative movement of its insensible parts. And, conversely, every moving equilibrium may be in one sense regarded as absolute; because the relative movements of its sensible parts are accompanied by a motionless state of the whole.

Something has still to be added before closing these somewhat too elaborate preliminaries. The reader must now especially 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, as we have seen, 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 the constituent parts are continually so counter-balanced by opposite motions, that the mean state of the whole 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 particularly to observe, is, that as a corollary from the general law of equilibration above set forth, the evolution of every aggregate must go on until this equilibrium mobile 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 each other, 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 permanent kinds on the way towards complete equilibration. 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 slowly 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 ending in the establishment of a complete moving equilibrium. For the genesis of each such ring, implies a perfect balancing of that aggregative 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 connected by forces with external wholes, has reached a state of moving equilibrium; its parts are not balanced with respect to each other. As we before saw (§ 150) the probabilities against the maintenance of an annular form by nebulous matter, are immense: from the instability of the homogeneous, it is inferrable that nebulous matter so distributed must break up into portions; and eventually concentrate into a single mass. That is to say, the ring must 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, severally having residuary relative motions that are no longer resisted by sensible media; and there is thus constituted an equilibrium mobile that is all but absolutely perfect.∗

Hypothesis aside, the principle of equilibration is still perpetually illustrated in those minor changes of state which the: Solar System is undergoing. Each planet, satellite, and comet, exhibits to us at its aphelion a momentary equilibrium between that force which urges it further away from its primary, and that force which retards its retreat; since the retreat goes on until the last of these forces exactly counterpoises the first. In like manner at perihelion a converse equilibrium is momentarily established. The variation of each orbit in size, 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 eventually integration of all the separate masses composing the Solar System, is a belief suggested by certain observed cometary retardations, and entertained by some of high authority. The received opinion that the appreciable diminution in the period of Encke’s comet, implies a loss of momentum caused by resistance of 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 stillcontinued 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 we are more nearly concerned—the equilibration of that molecular motion known as heat. The tacit assumption hitherto current, that the Sun can continue to give off an undiminished amount of light and heat through all future time, is fast being 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 that misleads perpetual-motion schemers. The spreading recognition of the truth that force is persistent, and that consequently whatever force is manifested under one shape must previously have existed under another shape, is carrying with it a 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 gradual dissipation of these radiations into space, this other force is being slowly exhausted. The aggregative force by which the Sun’s substance is drawn to his centre of gravity, is the only one which established physical laws warrant us in suspecting to be the correlate of the forces thus emanating from him: the only source of a known kind that can be assigned for the insensible motions constituting solar light and heat, is the sensible motion which disappears during the progressing concentration of the Sun’s substance. We before saw it to be a corollary from the nebular hypothesis, that there is such a progressing concentration of the Sun’s substance. And here remains to be added the further corollary, that just as in the case of the smaller members of the Solar System, the heat generated by concentration, long ago in great part radiated into space, has left only a central residue that now 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 only an inappreciable internal remnant. With or without the accompaniment of that hypothesis of nebular condensation, whence, as we see, it naturally follows, the doctrine that the Sun is gradually losing his heat, has now gained considerable currency; 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 is likely to 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 a diminution 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 amount of 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 not to be considered as more than 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 (probable, I believe,) 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 of force, militates against the general proposition that this reserve of force is being expended; and must in time be exhausted. Though the residue of undiffused motion in the Sun, may be much greater than is above concluded; though the rate of radiation cannot, as assumed, continue at a uniform rate, but must eventually go on with slowly-decreasing rapidity; and though the period at which the Sun will cease to afford us adequate light and heat, is very possibly far more distant than above implied; yet such a period must some time be reached, and this is all which it here concerns us to observe.

Thus while the Solar System, if evolved from diffused matter, has illustrated the law of equilibration in the establishment of a complete moving equilibrium; and while, as at present constituted, it illustrates the law of equilibration in the balancing of all its movements; it also illustrates this law in the processes which astronomers and physicists infer are still going on. That motion of masses produced during Evolution, is being slowly re-diffused 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 motions of masses shall be transformed into molecular motion, and all the molecular motion equilibrated; 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 atoms. If the aggregate of such atoms has a rotatory motion, 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 a complete equilibrium of those forces which affect its general outline. The only other process of equilibration which the Earth as a whole can exhibit, is the loss of its axial motion; and that any such loss is going on, we have no direct evidence. It has been contended, however, by Prof. Helmholtz, that inappreciable as may be its effect within known periods of time, the friction of the tidal wave must be slowly diminishing the Earth’s rotatory motion, and must eventually destroy it. Now though it seems an oversight to say that the Earth’s rotation can thus be destroyed, since the extreme effect, to be reached only infinite time by such a process, would be an extension of the Earth’s day to the length of a 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 it as exemplifying, under another form, the universal progress towards equilibrium.

It is needless to point out, 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, perpetually 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, as we have seen, divided and subdivided into motions less and less sensible; until it is finally reduced to insensible motions, and radiated from the Earth in the shape of thermal undulations. In their totality, these complex movements of aerial, liquid, and solid matter on the Earth’s crust, 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 power from moment to moment in course of dissipation, is from moment to moment renewed from without: the rises and falls in the supply, being balanced by rises and falls in the expenditure; as witness the correspondence between the magnetic variations and the cycle of the solar spots. But the fact it chiefly concerns us to observe, 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 temporarily 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 from the highest point of view, 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 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 equilibration; 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 condition; and finally in the complete arrest of vital movements at death. Let us consider the facts under these heads.

The sensible motion constituting each visible action of an organism, is soon brought to a close by some adverse force within or without the organism. When the arm is raised, the motion given to it is antagonized partly by gravity and partly by the internal resistances consequent of 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 requires to be immediately followed by another, because the rapid dissipation of its momentum would otherwise soon bring the mass of circulating fluid to a stand. As much in the actions and re-actions 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. Food is a store of force which 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, as we have seen, 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 motion through muscular activity, there arises a re-active demand on those stores of latent motion which are laid up in the form of consumable matter throughout the tissues: increased respiration and increased rapidity of circulation, are instrumental to an extra genesis of force, that counter-balances 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 in proportion as there has been a prolonged draft upon the spare capital of the system, is there a tendency to a prolonged rest, during which that spare 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 overturn the balance of the functions, and destroy life (in which case a 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 in those extreme cases where some 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. Thus, among the involved rhythmical changes constituting organic life, any disturbing force that works an excess of change in some direction, is gradually diminished and finally neutralized by antagonistic forces; which thereupon work a compensating change in the opposite direction, and so, after more or less of oscillation, restore the medium condition. And this process it is, which constitutes what physicians call the vis medicatrix natures. The third form of equilibration displayed by organic bodies, is a necessary 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. As temporary divergences of the organic rhythms are counteracted by temporary divergences of a reverse kind; so there is an equilibration of their permanent divergences by the genesis of opposing divergences that are equally permanent. 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 daily expenditure of force, and the amount of latent force daily added. The like must manifestly be the case with all organic modifications consequent on change of climate or food. This is a conclusion which we may safely draw without knowing the special re-arrangements that effect the equilibration. If we see that a different mode of life is followed, after a period of functional 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 which we call 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 potential motion balances the day’s expenditure of actual motion. That is to say, during adult life, there is continuously exhibited an equilibration of the third order. Eventually, the daily loss, beginning to out-balance the daily gain, 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 results that complete equilibration which we call death.

The ultimate structural state accompanying that ultimate functional state towards which an organism tends, both individually and as a species, 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 arrived at whenever the equilibration of any aggregate becomes complete—that the re-distribution of matter can continue so long only as there continues any motion unbalanced. Whence we found it to follow that the final structural arrangements, must be such as will meet all the forces acting on the aggregate, by equivalent antagonist forces. What is the implication in the case of organic aggregates; the equilibrium of which is a moving one? We have seen that the maintenance of such a moving equilibrium, 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 connections of organs. Hence the structural complexity accompanying functional equilibration, 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 and absence of enemies rising above its average; and then by a consequent scarcity of food and 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. Since 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 what we know as 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 nervous force from moment to moment generated, (and it was shown in § 86 that nervous currents are not continuous but rhythmical) is met by counteracting forces; in overcoming which it is dispersed and equilibrated. When tracing out the correlation and equivalence of forces, we saw that each sensation and emotion, or rather such part of it as remains after the excitation of associated ideas and feelings, is expended in working bodily changes—contractions of the involuntary muscles, the voluntary muscles, or both; as also in a certain stimulation of secreting organs. That the movements thus initiated are ever being brought to a close by the opposing forces they evoke, was pointed out above; and here it is to be observed that the like holds with the nervous changes thus initiated. Various facts prove that the arousing of a thought or feeling, always 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 habitual rapidity; instance the converse fact that at times of unusual energy, natural or artificial, the friction of thought becomes relatively small, and more numerous, more remote, or more difficult connections 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 conditions at the instant render lines of least resistance; and spreading widely in proportion to its amount, ends only when it is equilibrated by the resistances it every-where 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. In the one case as in the other, there are rhythms which exhibit a balancing of opposing forces at each extreme, and the maintenance of a certain general balance. 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 force 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 of passion, expressing itself in vehement bodily actions, presently reaches an extreme whence the counteracting forces produce a 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 partially differing from it in its medium state. But the species of mental equilibration to be more especially noted, is that shown in the establishment of a correspondence between relations among our states of consciousness and relations in the external world. Each outer connection of phenomena which we are capable of perceiving, generates, through accumulated experiences, an inner connection of mental states; and the result towards which this process tends, is the formation of a mental connection having a relative strength that answers to the relative constancy of the physical connection 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 that will be more readily pursued by future motion; we have seen that the case 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 connection in consciousness; and this connection, 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 hence happens that to such uncertain relations of phenomena as that between clouds and rain, there arise relations of ideas of a like uncertainty; and if, under given aspects of the sky, the tendencies to infer fair or foul weather, correspond to the frequencies with which fair or foul weather follow 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 connections having different degrees of constancy, and that during the evolution of intelligence there arise answering internal 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. This equilibration can end only when each relation of things has generated in us a relation of thought, such that on the occurrence of the conditions, the relation in thought arises as certainly as the relation in things. Supposing this state to be reached (which however it can be only in infinite time) experience will cease to produce any further mental evolution—there will have been reached a perfect correspondence between ideas and facts; and the intellectual adaptation of man to his circumstances will be complete. The like general truths are exhibited in the process moral of adaptation; which is a continual approach to equilibrium between the emotions and the kinds of conduct necessitated by surrounding conditions. The connections of feelings and actions, are determined in the same way as the connections of ideas: 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. Hence 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 the pressure of the painful feelings which these conditions entail when disregarded, impels him to perform this action to a greater extent—if by every more frequent or more lengthened performance of it under such pressure, the resistance is somewhat diminished; then, clearly, 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 eventually bring about a state in which this mode of directing the energies will be no more repugnant than the various other modes previously natural to the race. Hence the limit towards which emotional modification perpetually tends, and to which it must approach indefinitely near (though it can absolutely reach it only in infinite time) is a combination of desires that correspond to all the different orders of activity which the circumstances of life call for—desires severally proportionate in strength to the needs for these orders of activity; and severally satisfied by these orders of activity. In what we distinguish as acquired habits, and in the moral differences of races and nations produced by habits that are maintained through successive generations, we have countless illustrations of this progressive adaptation; which can cease only with the establishment of a complete equilibrium between constitution and conditions.

Possibly some will fail to see how the equilibrations described in this section, can be classed with those preceding them; and will be inclined to say that what are here set down as facts, are but analogies. Nevertheless such equilibrations are as truly physical as the rest. To show this fully, would require a more detailed analysis than can now be entered on. For the present it must suffice to point out, as before (§ 71), that what we know subjectively as states of consciousness, are, objectively, modes of force; that so much feeling is the correlate of so much motion; that the performance of any bodily action is the transformation of a certain amount of feeling into its equivalent amount of motion; that this bodily action is met by forces which it is expended in overcoming; and that the necessity for the frequent repetition of this action, implies the frequent recurrence of forces to be so overcome. Hence the existence in any individual of an emotional stimulus that is in equilibrium with certain external requirements, is literally the habitual production of a certain specialized portion of nervous energy, equivalent in amount to a certain order of external resistances that are habitually met. And thus the ultimate state, forming the limit towards which Evolution carries us, is one in which the kinds and quantities of mental energy daily generated and transformed into motions, are equivalent to, or in equilibrium with, the various orders and degrees of surrounding forces which antagonize such motions.

§ 175. Each society taken as a whole, 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 about that average number which the locality can support. Though by artificial production, and by successive improvements in artificial production, 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 so 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, is the expression of 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 by the labourer who purchases it, in other kinds and amounts of motion. And the variations of price represent a rhythmical balancing of these forces. Every rise or fall in the rate of interest, or change 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 increase of 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, there is given to them an amount of other commodities larger than was before habitual—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 again, that the total resistance over come in obtaining a given amount of produce, 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, or advantageous business, must multiply till there arises an approximate balance between this locality or business and others accessible to the same citizens. In determining the career of every youth, we see an estimation by parents of the respective advantages offered by all that are available, and a choice of the one which promises best; and through the consequent influx into trades that are at the time most profitable, and the withholding of recruits from over-stocked trades, there is insured a general equipoise between the power of each social organ and the function it has to perform.

The various industrial actions and re-actions thus continually alternating, constitute a dependent moving equilibrium like that which is maintained among the functions of an individual organism. And this dependent moving equilibrium parallels those already contemplated, in its tendency to become more complete. During early stages of social evolution, while yet 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, under the form of acceleration or retardation of growth. 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, it is observable that 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 extremely imperfect: great over-production of each commodity followed by great under-production, constitute a rhythm having extremes that depart very 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 lapse into weekly markets, and these into daily markets; there is gradually produced a better balance of production and consumption. Extra demand is much more quickly followed by augmented supply; and 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 of 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. This limit, however, though we are inevitably advancing towards it, is indefinitely remote; and can never indeed be absolutely reached. The peopling of the Earth up to the point supposed, cannot take place by simple spreading. In the future, as in the past, the process will be carried on rhythmically, by waves of emigration from new and higher centres of civilization successively arising; and by the supplanting of inferior races by the superior races they beget; and the process so carried on must be extremely slow. Nor does it seem to me that such an equilibration will, as Mr. Mill suggests, leave scope for further mental culture and moral progress; but rather that the approximation to it must be simultaneous with the approximation to complete equilibrium between man’s nature and the conditions of his existence.

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. There is a demand and supply in political affairs as in industrial affairs; and in the one case as in the other, the antagonist forces produce a rhythm which, at first extreme in its oscillations, slowly settles down into a moving equilibrium of comparative regularity. 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 eventual separation of citizens. Contrariwise, those desires whose ends can be achieved only by union, as well as those sentiments which find satisfaction through intercourse with fellow-men, and 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 citizen, more or less of resistance against all restraints imposed on his actions by other citizens: a resistance which, tending continually to widen each individual’s sphere of action, and reciprocally to limit the spheres of action of other individuals, 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 sundry 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 their separation. Like all other opposing forces, those exerted by citizens on each other, are ever producing alternating movements, which, at first extreme, undergo a gradual diminution on the way to ultimate equilibrium. In small, undeveloped societies, marked rhythms result from these conflicting tendencies. A tribe whose members have held together for a generation or two, reaches a size at which it will not hold together; and on the occurrence of some event causing unusual antagonism among its members, divides. Each primitive nation, depending largely for its continued union on the character of its chief, exhibits wide oscillations between an extreme in which the subjects are under rigid restraint, and an extreme in which the restraint is not enough to prevent disorder. 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 all bonds. In this familiar fact, that a period of tyranny is followed by a period of license and vice versâ, we see how these opposing forces are ever equilibrating each other; and we also see, in the tendency of such movements and counter-movements to become more moderate, how the equilibration progresses towards completeness. 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. This process, now so far advanced among ourselves that the oscillations are comparatively unobtrusive, must go on till the balance between the antagonist forces approaches indefinitely near perfection. For, as we have already seen, the adaptation of man’s nature to the conditions of his existence, cannot cease until the internal forces which we know as feelings are in equilibrium with the external forces they encounter. And the establishment of this equilibrium, is the arrival at a state of human nature and social organization, such that the individual has no desires but those which may be satisfied without exceeding his proper sphere of action, while society maintains no restraints but those which the individual voluntarily respects. The progressive extension of the liberty of citizens, and the reciprocal removal of political restrictions, are the steps by which we advance towards this state. And the ultimate abolition of all limits to the freedom of each, save those imposed by the like freedom of all, must result from the complete equilibration between man’s desires and the conduct necessitated by surrounding conditions.

Of course in this case, as in the preceding ones, there is thus involved a limit to the increase of heterogeneity. A few pages back, we reached the conclusion that each advance in mental evolution, is the establishment of some further internal action, corresponding to some further external action—some additional connection of ideas or feelings, answering to some before unknown or unantagonized connection of phenomena. 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. Whence we saw it to follow that increase of heterogeneity can come to an end only as equilibration is completed. Evidently the like must simultaneously take place with society. Each increment of heterogeneity in the individual, must directly or indirectly involve, as cause or consequence, some increment of heterogeneity in the arrangements of the aggregate of individuals. And the limit to social complexity can be arrived at, 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 a more or less distinct 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 forces—if the Sun is losing his heat at a rate which will tell in millions of years—if with diminution of the Sun’s radiations there must go on a diminution in the activity of geologic and meteorologic processes as well as in the quantity of vegetal and animal existence—if Man and Society are similarly dependent on this supply of force that is gradually coming to an end; are we not manifestly progressing towards omnipresent death?”

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

We have seen (§ 74) that phenomena are interpretable only as the results of universally-coexistent forces of attraction and repulsion. These universally-coexistent forces of attraction and repulsion, are, indeed, the complementary aspects of that absolutely persistent force which is the ultimate datum of consciousness. Just in the same way that the equality of action and re-action is a corollary from the persistence of force, since their inequality would imply the disappearance of the differential force into nothing, or its appearance out of nothing; so, we cannot become conscious of an attractive force without becoming simultaneously conscious of an equal and opposite repulsive force. For every experience of a muscular tension, (under which form alone we can immediately know an attractive force,) presupposes an equivalent resistance—a resistance shown in the counter-balancing pressure of the body against neighbouring objects, or in that absorption of force which gives motion to the body, or in both—a resistance which we cannot conceive as other than equal to the tension, without conceiving force to have either appeared or disappeared, and so denying the persistence of force. And from this necessary correlation, results our inability, before pointed out, of interpreting any phenomena save in terms of these correlatives—an inability shown alike in the compulsion we are under to think of the statical forces which tangible matter displays, as due to the attraction and repulsion of its atoms, and in the compulsion we are under to think of dynamical forces exercised through space, by regarding space as filled with atoms similarly endowed. Thus from the existence of a force that is for ever unchangeable in quantity, there follows, as a necessary corollary, the co-extensive existence of these opposite forms of force—forms under which the conditions of our consciousness oblige us to represent that absolute force which transcends our knowledge.

But the forces of attraction and repulsion being universally co-existent, it follows, as before shown, that all motion is motion under resistance. Units of matter, solid, liquid, aeriform, or ethereal, filling the space which any moving body traverses, offer to such body the resistance consequent on their cohesion, or their inertia, or both. In other words, the denser or rarer medium which occupies the places from moment to moment passed through by such moving body, having to be expelled from them, as much motion is abstracted from the moving body as is given to the medium in expelling it from these places. This being the condition under which all motion occurs, two corollaries result. The first is, that the deductions perpetually made by the communication of motion to the resisting medium, 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 till equilibration takes place; and equilibration must eventually take place. Both these are manifest deductions from the persistence of force. To say that the whole or part of a body’s motion can disappear, save by transfer to something which resists its motion, is to say that the whole or part of its motion can disappear without effect; which is to deny the persistence of force. Conversely, to say that the medium traversed can be moved out of the body’s path, without deducting from the body’s motion, is to say that motion of the medium can arise out of nothing; which is to deny the persistence of force. Hence this primordial truth is our immediate warrant for the conclusions, that the changes which Evolution presents, cannot end until equilibrium is reached; and that equilibrium must at last be reached.

Equally necessary, because equally deducible from this same truth that transcends proof, are the foregoing propositions respecting the establishment and maintenance of moving equilibria, under their several aspects. It follows from the persistence of force, that the various motions possessed by any aggregate, either as a whole or among its parts, must be severally dissipated by the resistances they severally encounter; and that thus, such of them as are least in amount, or meet with greatest opposition, or both, will be brought to a close while the others continue. Hence in every diversely moving aggregate, there results a comparatively early dissipation of motions which are smaller and much resisted; followed by long-continuance of the larger and less-resisted motions; and so there arise dependent and independent moving equilibria. Hence also may be inferred the tendency to conservation of such moving equilibria. For the new motion given to the parts of a moving equilibrium by a disturbing force, must either be of such kind and amount 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 of such kind and amount 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 that cosmical equilibration which brings Evolution under all its forms to a close; but also those less manifest equilibrations shown in the re-adjustments of moving equilibria that have been disturbed. By this ultimate principle is proveable 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. After finding that from it are deducible the various characteristics of Evolution, we finally draw from it a warrant for the belief, that Evolution can end only in the establishment of the greatest perfection and the most complete happiness.

[∗]Sir David Brewster has recently been citing with approval, a calculation by M. Babinet, to the effect that on the hypothesis of nebular genesis, the matter of the Sun, when it filled the Earth’s orbit, must have taken 3181 years to rotate; and that therefore the hypothesis cannot be true. This calculation of M. Babinet may pair-off with that of M. Comte, who, contrariwise, made the time of this rotation agree very nearly with the Earth’s period of revolution round the Sun: for if M. Comte’s calculation involved a petitio principii, that of M. Babinet is manifestly based on two assumptions, both of which are gratuitous, and one of them totally inconsistent with the doctrine to be tested. He has evidently proceeded on the current supposition respecting the Sun’s internal density, which is not proved, and from which there are reasons for dissenting; and he has evidently taken for granted that all parts of the nebulous spheroid, when it filled the Earth’s orbit, had the same angular velocity; whereas if (as is implied in the nebular hypothesis, rationally understood) this spheroid resulted from the concentration of far more widely-diffused matter, the angular velocity of its equatorial portion would obviously be immensely greater than that of its central portion.

[∗]See paper “On the Inter-action of Natural Forces,” by Prof. Helmholtz, translated by Prof. Tyndall, and published in the Philosophical Magazine, supplement to Vol. XI. fourth series.

[∗]Until recently consulted his “Outlines of Astronomy” on another question, I was not aware that so far back as 1833, Sir John Herschel had enunciated the doctrine that “the sun’s rays are the ultimate source of almost every motion which takes place on the surface of the earth.” He expressly includes all geologic, meteorologic, and vital actions; as also those which we produce by the combustion of coal. The late George Stephenson appears to have been wrongly credited with this last idea