First Principles

Thus these general truths being necessary implications of the persistence of force, all the re-distributions above traced out as characterizing Evolution in its various phases, are also implications of the persistence of force. Such portions of the permanently effective forces acting on any aggregate, as produce sensible motions in its parts, cannot but work the segregations which we see take place. If of the mixed units making up such aggregate, those of the same kind have like motions impressed on them by a uniform force, while units of another kind are moved by this uniform force in ways more or less unlike the ways in which those of the first kind are moved, the two kinds must separate and integrate. If the units are alike and the forces unlike, a division of the differently affected units is equally necessitated. Thus there inevitably arises the demarcated grouping which we everywhere see. By virtue of this segregation that grows ever more decided while there remains any possibility of increasing it, the change from uniformity to multiformity is accompanied by a change from indistinctness in the relations of parts to distinctness in the relations of parts. As we before saw that the transformation of the homogeneous into the heterogeneous is inferrable from that ultimate truth which transcends proof; so we here see, that from this same truth is inferrable the transformation of an indefinite homogeneity into a definite heterogeneity.

CHAPTER XVI.

EQUILIBRATION

§ 130. 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 replaced 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.

Those readers who happen to bear in mind a proposition concerning the functional characteristics of Evolution, which was set forth in Chapter XII, will probably regard it as wholly at variance with that set forth in this Chapter. It was there alleged that throughout Evolution, integration of matter is accompanied by integration of such motion as the matter previously had; and that thus there is a transformation of diffused motion into aggregated motion, parallel to the transformation of diffused matter into aggregated matter. Here however, it is asserted that every aggregate motion is constantly undergoing diffusion – every integrated motion undergoing perpetual disintegration. And so the motion of masses, which before was said gradually to arise out of molecular motion, is here said to be gradually lost in molecular motion. Doubtless these statements, if severally accepted without qualification, are contradictory. Neither of them, however, expresses the whole truth. Each needs the other as its indispensable complement. It is quite true, as before alleged, that there goes on an integration of motion corresponding to the integration of matter; and that this essential characteristic of Evolution, functionally considered, is clearly displayed in proportion as the Evolution is active. But the disintegration of motion, which, as we before saw, constitutes Dissolution, functionally considered, is all along going on; and though at first it forms but a small deduction from the change constituting Evolution, it gradually becomes equal to it, and eventually exceeding it, entails reverse changes. The aggregation of matter never being complete, but leaving behind less aggregated or unaggregated matter, in the shape of liquid, aeriform, or ethereal media; it results that from the beginning, the integrated motion of integrated masses, is ever being obstructed by these less integrated or unintegrated media. So that though while the integration of matter is rapidly going on, there is an increase of integrated motion, spite of the deductions thus continually made from it, there comes a time when the integration of matter and consequently of motion, ceases to increase, or increases so slowly that the deductions counterbalance it; and thenceforth these begin to decrease it, and, by its perpetual diffusion, to bring about a relative equilibration. From the beginning, the process of Evolution is antagonized by a process of Dissolution; and while the first for a long time predominates, the last finally arrests and reverses it.

Returning from this parenthetical explanation, we 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.

§ 131. 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 (§ 110) 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.18

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 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 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 1454th is being diffused: showing that a diminution of the Sun’s diameter to the extent of 110,000, would produce heat, at the present rate, for more than 2000 years; or in other words, that a contraction of 120,000,000 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 120 in the lapse of the next million years.19 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.