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 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.
* * * * *
§ 132. 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 in 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,[20] 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, (§ 80) 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.
* * * * *
§ 133. 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 on
structure; and its motion, thus suffering continual deduction, ends when
the arm has reached a position at which the forces are equilibrated. The
limits of each systole and diastole of the heart, severally show us a
momentary equilibrium between muscular strains that produce opposite
movements; and each gush of blood 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
(§ 96); 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 naturæ_. 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 § 96, 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.
* * * * *
§ 134. 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 § 97 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 everywhere meets. If we
contemplate mental actions us 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 ease with which nervous impressions follow one another,
is, other things equal, great in proportion to the number of times they
have been repeated together in experience. Hence, corresponding to such
an invariable relation as that between the resistance of an object and
some extension possessed by it, there arises an indissoluble 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 (§
82), 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.
* * * * *
§ 135. 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 overcome 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.
* * * * *
§ 136. 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—if equilibration, passing through the gradually-perfected
forms of moving equilibrium, must end in complete rest; what is the fate
towards which all things tend? If the bodies constituting our Solar
System are slowly dissipating the forces they possess—if the Sun is
losing his heat at a rate which, though insignificant as stated in terms
of our chronology, will tell in millions of years—if geologic and
meteorologic processes cannot but diminish in activity as the Sun’s
radiations diminish—if with the diminution of these radiations there
must also go on a diminution in the quantity of vegetal and animal
existence—if Man and Society, however high the degree of evolution at
which they arrive, are similarly dependent on this supply of force that
is gradually coming to an end—if thus the highest, equally with the
lowest, terrestrial life, must eventually dwindle and disappear; are we
not manifestly progressing towards omnipresent death? And have we thus
to contemplate, as the out-come of things, a universe of extinct suns
round which circle planets devoid of life?”
That such a state must be the proximate end of the processes everywhere
going on, seems beyond doubt. But the further question tacitly involved,
whether this state will continue eternally, is quite a different one. To
give a positive answer to this further question would be quite
illegitimate; since to affirm any proposition into which unlimited time
enters as one of the terms, is to affirm a proposition of which one term
cannot be represented in consciousness—is to affirm an unthinkable
proposition. At a first glance it may appear that the reverse conclusion
must be equally illegitimate; and that so the question is altogether
insoluble. But further consideration will show that this is not true. So
long as the terms to which we confine our reasonings are finite, the
finite conclusions reached are not necessarily illegitimate. Though, if
the general argument, when carried out, left no apparent escape from the
inference that the state of rest to which Evolution is carrying things,
must, when arrived at, last for ever, this inference would be invalid,
as transcending the scope of human intelligence; yet if, on pushing
further the general argument, we bring out the inference that such a
state will not last for ever, this inference is not necessarily invalid:
since, by the hypothesis, it contains no terms necessarily transcending
the scope of human intelligence. It is permissible therefore, to
inquire, what are the probable ulterior results of this process which
must bring Evolution to a close in Universal Death. Without being so
rash as to form anything like a positive conclusion on a matter so vast
and so far beyond the boundaries of exact science; we may still inquire
what _seems_ to be the remote future towards which the facts point.
It has been already shown that all equilibration, so far as we can trace
it, is relative. The dissipation of a body’s motion by communication of
it to surrounding matter, solid, liquid, gaseous, and ethereal, tends to
bring the body to a fixed position in relation to the matter that
abstracts its motion. But all its other motions continue as before. The
arrest of a cannon-shot does not diminish its movement towards the East
at a thousand miles an hour, along with the wall it has struck; and a
gradual dispersion of the Earth’s rotatory motion, would abstract
nothing from the million and a half miles per day through which the
Earth speeds in its orbit. Further, we have to bear in mind that this
motion, the disappearance of which causes relative equilibration, is not
lost but simply transferred; and by continual division and subdivision
finally reduced to ethereal undulations and radiated through space.
Whether the sensible motion dissipated during relative equilibration, is
directly transformed into insensible motion, as happens in the case of
the Sun; or whether, as in the sensible motions going on around us, it
is directly transformed into smaller sensible motions, and these into
still smaller, until they become insensible, matters not. In every
instance the ultimate result is, that whatever motion of masses is lost,
re-appears as molecular motion pervading space. Thus the questions we
have to consider, are—Whether after the completion of all the relative
equilibrations above contemplated as bringing Evolution to a close,
there remain any further equilibrations to be effected?—Whether there
are any other motions of masses that must eventually be transformed into
molecular motion?—And if there are such other motions, what must be the
consequence when the molecular motion generated by their transformation,
is added to that which already exists?
To the first of these questions the answer is, that there _do_ remain
motions which are undiminished by all the relative equilibrations thus
far considered; namely, the motions of translation possessed by those
vast masses of incandescent matter called stars—masses now known to be
suns that are in all probability, like our own, surrounded by circling
groups of planets. The belief that the stars are literally fixed, has
long since been exploded: observation has proved many of them to have
sensible proper motions. Moreover, it has been ascertained by
measurement, that in relation to the stars nearest to us, our own star
is moving at the rate of about half a million miles per day; and if, as
is admitted to be not improbable by sundry astronomers, our own star is
traversing space in the same direction with adjacent stars, its absolute
velocity may be, and most likely is, immensely greater than this. Now no
such changes as those taking place within the Solar System, even when
carried to the extent of integrating the whole of its matter into one
mass, and diffusing all its relative movements in an insensible form
through space, can affect these sidereal movements. Hence, there appears
no alternative but to infer, that these sidereal movements must remain
to be equilibrated by some subsequent process.
The next question that arises, if we venture to inquire the probable
nature of this process, is—To what law do sidereal motions conform? And
to this question Astronomy replies—the law of gravitation. The relative
motions of binary stars have proved this. When it was discovered that
certain of the double stars are not optically double but physically
double, and move round each other, it was at once suspected that their
revolutions might be regulated by a mutual attraction like that which
regulates the revolutions of planets and satellites. The requisite
measurements having been from time to time made, the periodic times of
sundry binary stars were calculated on this assumption; and the
subsequent performances of their revolutions in the predicted periods,
have completely verified the assumption. If, then, it is demonstrated
that these remote bodies are centres of gravitation—if we infer that all
other stars are centres of gravitation, as we may fairly do—and if we
draw the unavoidable corollary, that this gravitative force which so
conspicuously affects stars that are comparatively near each other, must
affect remote stars; we find ourselves led to the conclusion that all
the members of our Sidereal System gravitate, individually and as an
aggregate.
But if these widely-dispersed moving masses mutually gravitate, what
must happen? There appears but one tenable answer. Even supposing they
were all absolutely equal in weight, and arranged into an annulus with
absolute regularity, and endowed with exactly the amounts of centrifugal
force required to prevent nearer approach to their common centre of
gravity; the condition would still be one which the slightest disturbing
force would destroy. Much more then are we driven to the inference, that
our actual Sidereal System cannot preserve its present arrangement: the
irregularities of its distribution being such as to render even a
temporary moving equilibrium impossible. If the stars are so many
centres of an attractive force that varies inversely as the square of
the distance, there appears to be no escape from the conclusion, that
the structure of our galaxy must be undergoing change; and must continue
to undergo change.
Thus, in the absence of tenable alternatives, we are brought to the
positions:—1, that the stars are in motion;—2, that they move in
conformity with the law of gravitation;—3, that, distributed as they
are, they cannot move in conformity with the law of gravitation, without
undergoing change of arrangement. If now we permit ourselves to take a
further step, and ask the nature of this change of arrangement, we find
ourselves obliged to infer a progressive concentration. Whether we do or
do not suppose the clustering which is now visible, to have been caused
by mutual gravitation acting throughout past eras, as the hypothesis of
Evolution implies, we are equally compelled to conclude that this
clustering must increase throughout future eras. Stars at present
dispersed, must become locally aggregated; existing aggregations, at the
same time that they are enlarged by the drawing in of adjacent stars,
must grow more dense; and aggregations must coalesce with each other:
each greater degree of concentration augmenting the force by which
further concentration is produced.
And now what must be the limit of this concentration? The mutual
attraction of two individual stars, when it so far predominates over
other attractions as to cause approximation, almost certainly ends in
the formation of a binary star; since the motions generated by other
attractions, prevent the two stars from moving in straight lines to
their common centre of gravity. Between small clusters, too, having also
certain proper motions as clusters, mutual attraction may lead, not to
complete union, but to the formation of binary clusters. As the process
continues however, and the clusters become larger, it seems clear that
they must move more directly towards each other, thus forming clusters
of increasing density; and that eventually all clusters must unite into
one comparatively close aggregation. While, therefore, during the
earlier stages of concentration, the probabilities are immense against
the actual contact of these mutually-gravitating masses; it is tolerably
manifest, that as the concentration increases, collision must become
probable, and ultimately certain. This is an inference not lacking the
support of high authority. Sir John Herschel, treating of those numerous
and variously-aggregated clusters of stars revealed by the telescope,
and citing with apparent approval his father’s opinion, that the more
diffused and irregular of these, are “globular clusters in a less
advanced state of condensation;” subsequently remarks, that “among a
crowd of solid bodies of whatever size, animated by independent and
partially opposing impulses, motions opposite to each other _must_
produce collision, destruction of velocity, and subsidence or near
approach towards the centre of preponderant attraction; while those
which conspire, or which remain outstanding after such conflicts, _must_
ultimately give rise to circulation of a permanent character.” Now what
is here alleged of these minor sidereal aggregations, cannot be denied
of the large aggregations; and thus the above-described process of
concentration, appears certain to bring about an increasingly-frequent
integration of masses.
We have next to consider the consequences of the accompanying loss of
velocity. The sensible motion which disappears, cannot be destroyed; but
must be transformed into insensible motion. What will be the effect of
this insensible motion? Some approach to a conception of it, will be
made by considering what would happen were the comparatively
insignificant motion of our planet thus transformed. In his essay on
“The Inter-action of Natural Forces,” Prof. Helmholtz states the thermal
equivalent of the Earth’s movement through space; as calculated on the
now received datum of Mr. Joule. “If our Earth,” he says, “were by a
sudden shock brought to rest in her orbit,—which is not to be feared in
the existing arrangement of our system—by such a shock a quantity of
heat would be generated equal to that produced by the combustion of
fourteen such Earths of solid coal. Making the most unfavourable
assumption as to its capacity for heat, that is, placing it equal to
that of water, the mass of the Earth would thereby be heated 11,200
degrees; it would therefore be quite fused, and for the most part
reduced to vapour. If then the Earth, after having been thus brought to
rest, should fall into the Sun, which of course would be the case, the
quantity of heat developed by the shock would be 400 times greater.” Now
so relatively small a momentum as that acquired by the Earth in falling
through 95,000,000 of miles to the Sun, being equivalent to a molecular
motion such as would reduce the Earth to gases of extreme rarity; what
must be the molecular motion generated by the mutually-arrested momenta
of two stars, that have moved to their common centre of gravity through
spaces immeasurably greater? There seems no alternative but to conclude,
that this molecular motion must be so great, as to reduce the matter of
the stars to an almost inconceivable tenuity—a tenuity like that which
we ascribe to nebular matter. Such being the immediate effect of
the integration of any two stars in a concentrating aggregate, what must
be the ulterior effect on the aggregate as a whole? Sir John Herschel,
in the passage above quoted, describing the collisions that must arise
in a mutually-gravitating group of stars, adds that those stars “which
remain outstanding after such conflicts, _must_ ultimately give rise to
circulation of a permanent character.” The problem, however, is here
dealt with purely as a mechanical one: the assumption being, that the
mutually-arrested masses will continue as masses—an assumption to which
no objection was apparent at the time when Sir John Herschel wrote this
passage; since the doctrine of the correlation of forces was not then
recognized. But obliged as we now are to conclude, that stars moving at
the high velocities acquired during concentration, will, by mutual
arrest, be dissipated into gases of great tenuity, the problem becomes
different; and a different inference appears unavoidable. For the
diffused matter produced by such conflicts, must form a resisting
medium, occupying that central region of the aggregate through which its
members from time to time pass in describing their orbits—a resisting
medium which they cannot move through without having their velocities
diminished. Every further such collision, by augmenting this resisting
medium, and making the losses of velocity greater, must further aid in
preventing the establishment of that equilibrium which would else arise;
and so must conspire to produce more frequent collisions. And the
nebulous matter thus formed, presently enveloping and extending beyond
the whole aggregate, must, by continuing to shorten their gyrations,
entail an increasingly-active integration and re-active disintegration
of the moving masses; until they are all finally dissipated. This,
indeed, is the conclusion which, leaving out all consideration of the
process gone through, presents itself as a simple deduction from the
persistence of force. If the stars have been, and still are,
concentrating however indirectly on their common centre of gravity, and
must eventually reach it; it is a corollary from the persistence of
force, that the quantities of motion they have severally acquired, must
suffice to carry them away from the common centre of gravity to those
remote regions whence they originally began to move towards it. And
since, by the conditions of the case, they cannot return to these remote
regions in the shape of concrete masses, they must return in the shape
of diffused masses. Action and reaction being equal and opposite, the
momentum producing dispersion, must be as great as the momentum acquired
by aggregation; and being spread over the same quantity of matter, must
cause an equivalent distribution through space, whatever be the form of
the matter. One condition, however, essential to the literal
fulfilment of this result, must be specified; namely, that the quantity
of molecular motion produced and radiated into space by each star in the
course of its formation from diffused matter, shall be compensated by an
equal quantity of molecular motion radiated from other parts of space
into the space which our Sidereal System occupies. In other words, if we
set out with that amount of molecular motion implied by the existence of
the matter of our Sidereal System in a nebulous form; then it follows
from the persistence of force, that if this matter undergoes the
re-distribution constituting Evolution, the quantity of molecular motion
given out during the integration of each mass, plus the quantity of
molecular motion given out during the integration of all the masses,
must suffice again to reduce it to the same nebulous form. Here
indeed we arrive at an impassable limit to our reasonings; since we
cannot know whether this condition is or is not fulfilled. On the
hypothesis of an unlimited space, containing, at certain intervals,
Sidereal Systems like our own, it may be that the quantity of molecular
motion radiated into the region occupied by our Sidereal System, is
equal to that which our Sidereal System radiates; in which case the
quantity of motion possessed by it, remaining undiminished, our Sidereal
System may continue during unlimited time, to repeat this alternate
concentration and diffusion. But if, on the other hand, throughout
boundless space there exist no other Sidereal Systems subject to like
changes, or if such other Sidereal Systems exist at more than a certain
average distance from each other; then it seems an unavoidable
conclusion that the quantity of motion possessed, must diminish by
radiation into unoccupied space; and that so, on each successive
resumption of the nebulous form, the matter of our Sidereal System will
occupy a less space; until at the end of an infinite time it reaches
either a state in which its concentrations and diffusions are relatively
small, or a state of complete aggregation and rest. Since, however, we
have no evidence showing the existence or non-existence of Sidereal
Systems throughout remote space; and since, even had we such evidence, a
legitimate conclusion could not be drawn from premises of which one
element (unlimited space) is inconceivable; we must be for ever without
answer to this transcendent question. All we can say is, that so far as
the data enable us to judge, the integration of our Sidereal System will
be followed by disintegration; that such integration and disintegration
will be repeated; and that, for anything we know to the contrary, the
alternation of them may continue without limit.
But leaving this ultimate insoluble problem, and confining ourselves to
the proximate and not necessarily insoluble one, we find reason for
thinking that after the completion of those various equilibrations which
bring to a close all the forms of Evolution we have contemplated, there
must still continue an equilibration of a far wider kind. When that
integration everywhere in progress throughout our Solar System, has
reached its climax, there will remain to be effected the immeasurably
greater integration of our Solar System, with all other such systems. As
in those minor forms now going on around us, this integration with its
concomitant equilibration, involves the change of aggregate motion into
diffused motion; so in those vaster forms hereafter to be carried out,
there must similarly be gained in molecular motion what is lost in the
motion of masses; and the inevitable transformation of this motion of
masses into molecular motion, cannot take place without reducing the
masses to a nebulous form. Thus we seem led to the conclusion that the
entire process of things, as displayed in the aggregate of the visible
Universe, is analogous to the entire process of things as displayed in
the smallest aggregates. Where, as in organic bodies, the whole series
of changes constituting Evolution can be traced, we saw that,
dynamically considered, Evolution is a change from molecular motion to
the motion of masses; and this change, becoming more active during the
ascending phase of Evolution while the masses increase in bulk and
heterogeneity, eventually begins to get less active; until, passing
through stages in which the integration grows greater, and the
equilibrium more definite, it finally ceases; whereupon there arises, by
an ulterior process, an increase of molecular motion, ending in the more
or less complete dissolution of the aggregate. And here we find reason
to believe that, along with each of the thousands of similar ones
dispersed through the heavens, our Solar System, after passing through
stages during which the motion of masses is produced at the expense of
lost molecular motion, and during which there goes on an increasingly
active differentiation and integration, arrives at a climax whence these
changes, beginning to decline in activity, slowly bring about that
complete integration and equilibration which in other cases we call
death; and that there afterwards comes a time, when the still-remaining
motions of masses are transformed into a molecular motion which causes
dissolution of the masses. Motion as well as Matter being fixed in
quantity, it would seem that the change in the distribution of Matter
which Motion effects, coming to a limit in whichever direction it is
carried, the indestructible Motion thereupon necessitates a reverse
distribution. Apparently, the universally-coexistent forces of
attraction and repulsion, which, as we have seen, necessitate rhythm in
all minor changes throughout the Universe, also necessitate rhythm in
the totality of its changes—produce now an immeasurable period during
which the attractive forces predominating, cause universal
concentration, and then an immeasurable period during which the
repulsive forces predominating, cause universal diffusion—alternate eras
of Evolution and Dissolution. And thus there is suggested the conception
of a past during which there have been successive Evolutions similar to
that which is now going on; and a future during which successive other
such Evolutions may go on.
Let none suppose, however, that this is to be taken as anything more
than a speculation. In dealing with times and spaces and forces so
immensely transcending those of which we have definite experience, we
are in danger of passing the limits to human intelligence. Though these
times and spaces and forces cannot literally be classed as infinite; yet
they are so utterly beyond the possibility of definite conception, as to
be almost equally unthinkable with the infinite. What has been above
said, should therefore be regarded simply as a possible answer to a
possible doubt. When, pushing to its extreme the argument that Evolution
must come to a close in complete equilibrium or rest, the reader
suggests that for aught which appears to the contrary, the Universal
Death thus implied will continue indefinitely; it is legitimate to point
out how, on carrying the argument still further, we are led to infer a
subsequent Universal Life. But while this last inference may fitly be
accepted as a demurrer to the first, it would be unwise to accept it in
any more positive sense.
* * * * *
§ 137. Returning from this parenthetical discussion, concerning the
probable or possible state of things that may arise after Evolution has
run its course; and confining ourselves to the changes constituting
Evolution, with which alone we are immediately concerned; we have now to
inquire whether the cessation of these changes, in common with all their
transitional characteristics, admits of _à priori_ proof. It will soon
become apparent that equilibration, not less than the preceding general
principles, is deducible from the persistence of force.
We have seen (§ 85) 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, aëriform, 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; since, whenever the new motion
given to the parts of a moving equilibrium by a disturbing force, is not
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) 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.
-----
Footnote 18:
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.
Footnote 19:
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.
Footnote 20:
Until I 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.