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 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.[[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.
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.