THE DIRECTION OF MOTION.
§ 85. The Absolute Cause of changes, inclusive of those constituting
Evolution, is not less incomprehensible in respect of the unity or
duality of its action, than in all other respects. We cannot decide
between the alternative suppositions, that phenomena are due to the
variously-conditioned workings of a single force, and that they are due
to the conflict of two forces. Whether, as some contend, everything is
explicable on the hypothesis of universal pressure, whence what we call
tension results differentially from inequalities of pressure in opposite
directions; or whether, as might be with equal propriety contended,
things are to be explained on the hypothesis of universal tension, from
which pressure is a differential result; or whether, as most physicists
hold, pressure and tension everywhere co-exist; are questions which it
is impossible to settle. Each of these three suppositions makes the
facts comprehensible, only by postulating an inconceivability. To assume
a universal pressure, confessedly requires us to assume an infinite
plenum—an unlimited space full of something which is everywhere pressed
by something beyond; and this assumption cannot be mentally realized.
That universal tension is the immediate agency to which phenomena are
due, is an idea open to a parallel and equally fatal objection. And
however verbally intelligible may be the proposition that pressure and
tension everywhere co-exist, yet we cannot truly represent to ourselves
one ultimate unit of matter as drawing another while resisting it.
Nevertheless, this last belief is one which we are compelled to
entertain. Matter cannot be conceived except as manifesting forces of
attraction and repulsion. Body is distinguished in our consciousness
from Space, by its opposition to our muscular energies; and this
opposition we feel under the two-fold form of a cohesion that hinders
our efforts to rend, and a resistance that hinders our efforts to
compress. Without resistance there can be merely empty extension.
Without cohesion there can be no resistance. Probably this conception of
antagonistic forces, is originally derived from the antagonism of our
flexor and extensor muscles. But be this as it may, we are obliged to
think of all objects as made up of parts that attract and repel each
other; since this is the form of our experience of all objects.
By a higher abstraction results the conception of attractive and
repulsive forces pervading space. We cannot dissociate force from
occupied extension, or occupied extension from force; because we have
never an immediate consciousness of either in the absence of the other.
Nevertheless, we have abundant proof that force is exercised through
what appears to our senses a vacuity. Mentally to represent this
exercise, we are hence obliged to fill the apparent vacuity with a
species of matter—an etherial medium. The constitution we assign to this
etherial medium, however, like the constitution we assign to solid
substance, is necessarily an abstract of the impressions received from
tangible bodies. The opposition to pressure which a tangible body offers
to us, is not shown in one direction only, but in all directions; and so
likewise is its tenacity. Suppose countless lines radiating from its
centre on every side, and it resists along each of these lines and
coheres along each of these lines. Hence the constitution of those
ultimate units through the instrumentality of which phenomena are
interpreted. Be they atoms of ponderable matter or molecules of ether,
the properties we conceive them to possess are nothing else than these
perceptible properties idealized. Centres of force attracting and
repelling each other in all directions, are simply insensible portions
of matter having the endowments common to sensible portions of
matter—endowments of which we cannot by any mental effort divest them.
In brief, they are the invariable elements of the conception of matter,
abstracted from its variable elements—size, form, quality, &c. And so to
interpret manifestations of force which cannot be tactually experienced,
we use the terms of thought supplied by our tactual experiences; and
this for the sufficient reason that we must use these or none.
After all that has been before shown, and after the hint given above, it
needs scarcely be said that these universally co-existent forces of
attraction and repulsion, must not be taken as realities, but as our
symbols of the reality. They are the forms under which the workings of
the Unknowable are cognizable by us—modes of the Unconditioned as
presented under the conditions of our consciousness. But while knowing
that the ideas thus generated in us are not absolutely true, we may
unreservedly surrender ourselves to them as relatively true; and may
proceed to evolve a series of deductions having a like relative truth.
* * * * *
§ 86. From universally co-existent forces of attraction and repulsion,
there result certain laws of direction of all movement. Where attractive
forces alone are concerned, or rather are alone appreciable, movement
takes place in the direction of their resultant; which may, in a sense,
be called the line of greatest traction. Where repulsive forces alone
are concerned, or rather are alone appreciable, movement takes place
along their resultant; which is usually known as the line of least
resistance. And where both attractive and repulsive forces are
concerned, or are appreciable, movement takes place along the resultant
of all the tractions and resistances. Strictly speaking, this last is
the sole law; since, by the hypothesis, both forces are everywhere in
action. But very frequently the one kind of force is so immensely in
excess that the effect of the other kind may be left out of
consideration. Practically we may say that a body falling to the Earth,
follows the line of greatest traction; since, though the resistance of
the air must, if the body be irregular, cause some divergence from this
line, (quite perceptible with feathers and leaves,) yet ordinarily the
divergence is so slight that we may omit it. In the same manner, though
the course taken by the steam from an exploding boiler, differs somewhat
from that which it would take were gravitation out of the question; yet,
as gravitation affects its course infinitesimally, we are justified in
asserting that the escaping steam follows the line of least resistance.
Motion then, we may say, always follows the line of greatest traction,
or the line of least resistance, or the resultant of the two: bearing in
mind that though the last is alone strictly true, the others are in many
cases sufficiently near the truth for practical purposes.
Movement set up in any direction is itself a cause of further movement
in that direction, since it is the embodiment of a surplus force in that
direction. This holds equally with the transit of matter through space,
the transit of matter through matter, and the transit through matter of
any kind of vibration. In the case of matter moving through space, this
principle is expressed in the law of inertia—a law on which the
calculations of physical astronomy are wholly based. In the case of
matter moving through matter, we trace the same truth under the familiar
experience that any breach made by one solid through another, or any
channel formed by a fluid through a solid, becomes a route along which,
other things equal, subsequent movements of like nature take place. And
in the case of motion passing through matter under the form of an
impulse communicated from part to part, the facts of magnetization go to
show that the establishment of undulations along certain lines,
determines their continuance along those lines.
It further follows from the conditions, that the direction of movement
can rarely if ever be perfectly straight. For matter in motion to pursue
continuously the exact line in which it sets out, the forces of
attraction and repulsion must be symmetrically disposed around its path;
and the chances against this are infinitely great. The impossibility of
making an absolutely true edge to a bar of metal—the fact that all which
can be done by the best mechanical appliances, is to reduce the
irregularities of such an edge to amounts that cannot be perceived
without magnifiers—sufficiently exemplifies how, in consequence of the
unsymmetrical distribution of forces around the line of movement, the
movement is rendered more or less indirect. It may be well to add
that in proportion as the forces at work are numerous and varied, the
curve a moving body describes is necessarily complex: witness the
contrast between the flight of an arrow and the gyrations of a stick
tossed about by breakers.
We have now to trace these laws of direction of movement throughout the
process of Evolution, under its various forms. We have to note how every
change in the arrangement of parts, takes place along the line of
greatest traction, of least resistance, or of their resultant; how the
setting up of motion along a certain line, becomes a cause of its
continuance along that line; how, nevertheless, change of relations to
external forces, always renders this line indirect; and how the degree
of its indirectness increases with every addition to the number of
influences at work.
* * * * *
§ 87. If we assume the first stage in nebular condensation to be the
precipitation into flocculi of denser matter previously diffused through
a rarer medium, (a supposition both physically justified, and in harmony
with certain astronomical observations,) we shall find that nebular
motion is interpretable in pursuance of the above general laws. Each
portion of such vapour-like matter must begin to move towards the common
centre of gravity. The tractive forces which would of themselves carry
it in a straight line to the centre of gravity, are opposed by the
resistant forces of the medium through which it is drawn. The direction
of movement must be the resultant of these—a resultant which, in
consequence of the unsymmetrical form of the flocculus, must be a curve
directed, not to the centre of gravity, but towards one side of it. And
it may be readily shown that in an aggregation of such flocculi,
severally thus moving, there must, by composition of forces, eventually
result a rotation of the whole nebula in one direction.
Merely noting this hypothetical illustration for the purpose of showing
how the law applies to the case of nebular evolution, supposing it to
have taken place, let us pass to the phenomena of the Solar System as
now exhibited. Here the general principles above set forth are every
instant exemplified. Each planet and satellite has a momentum which
would, if acting alone, carry it forward in the direction it is at any
instant pursuing. This momentum hence acts as a resistance to motion in
any other direction. Each planet and satellite, however, is drawn by a
force which, if unopposed, would take it in a straight line towards its
primary. And the resultant of these two forces is that curve which it
describes—a curve manifestly consequent on the unsymmetrical
distribution of the forces around its path. This path, when more closely
examined, supplies us with further illustrations. For it is not an exact
circle or ellipse; which it would be were the tangential and centripetal
forces the only ones concerned. Adjacent members of the Solar System,
ever varying in their relative positions, cause what we call
perturbations; that is, slight divergences in various directions from
that circle or ellipse which the two chief forces would produce. These
perturbations severally show us in minor degrees, how the line of
movement is the resultant of all the forces engaged; and how this line
becomes more complicated in proportion as the forces are multiplied.
If instead of the motions of the planets and satellites as wholes,
we consider the motions of their parts, we meet with comparatively
complex illustrations. Every portion of the Earth’s substance in its
daily rotation, describes a curve which is in the main a resultant of
that resistance which checks its nearer approach to the centre of
gravity, that momentum which would carry it off at a tangent, and those
forces of gravitation and cohesion which keep it from being so carried
off. If this axial motion be compounded with the orbital motion, the
course of each part is seen to be a much more involved one. And we find
it to have a still greater complication on taking into account that
lunar attraction which mainly produces the tides and the precession of
the equinoxes.
* * * * *
§ 88. We come next to terrestrial changes: present ones as observed, and
past ones as inferred by geologists. Let us set out with the
hourly-occurring alterations in the Earth’s atmosphere; descend to the
slower alterations in progress on its surface; and then to the still
slower ones going on beneath.
Masses of air, absorbing heat from surfaces warmed by the sun, expand,
and so lessen the weight of the atmospheric columns of which they are
parts. Hence they offer to adjacent atmospheric columns, diminished
lateral resistance; and these, moving in the directions of the
diminished resistance, displace the expanded air; while this, pursuing
an upward course, displays a motion along that line in which there is
least pressure. When again, by the ascent of such heated masses from
extended areas like the torrid zone, there is produced at the upper
surface of the atmosphere, a protuberance beyond the limits of
equilibrium—when the air forming this protuberance begins to overflow
laterally towards the poles; it does so because, while the tractive
force of the Earth is nearly the same, the lateral resistance is greatly
diminished. And throughout the course of each current thus generated, as
well as throughout the course of each counter-current flowing: into the
vacuum that is left, the direction is always the resultant of the
Earth’s tractive force and the resistance offered by the surrounding
masses of air: modified only by conflict with other currents similarly
determined, and by collision with prominences on the Earth’s crust.
The movements of water, in both its gaseous and liquid states,
furnish further examples. In conformity with the mechanical theory of
heat, it may be shown that evaporation is the escape of particles of
water in the direction of least resistance; and that as the resistance
(which is due to the pressure of the water diffused in a gaseous state)
diminishes, the evaporation increases. Conversely, that rushing together
of particles called condensation, which takes place when any portion of
atmospheric vapour has its temperature much lowered, may be interpreted
as a diminution of the mutual pressure among the condensing particles,
while the pressure of surrounding particles remains the same; and so is
a motion taking place in the direction of lessened resistance. In the
course followed by the resulting rain-drops, we have one of the simplest
instances of the joint effect of the two antagonist forces. The Earth’s
attraction, and the resistance of atmospheric currents ever varying in
direction and intensity, give as their resultants, lines which incline
to the horizon in countless different degrees and undergo perpetual
variations. More clearly still is the law exemplified by these same
rain-drops when they reach the ground. In the course they take while
trickling over its surface, in every rill, in every larger stream, and
in every river, we see them descending as straight as the antagonism of
surrounding objects permits. From moment to moment, the motion of water
towards the Earth’s centre is opposed by the solid matter around and
under it; and from moment to moment its route is the resultant of the
lines of greatest traction and least resistance. So far from a cascade
furnishing, as it seems to do, an exception, it furnishes but another
illustration. For though all solid obstacles to a vertical fall of the
water are removed, yet the water’s horizontal momentum is an obstacle;
and the parabola in which the stream leaps from the projecting ledge, is
generated by the combined gravitation and momentum. It may be well
just to draw attention to the degree of complexity here produced in the
line of movement by the variety of forces at work. In atmospheric
currents, and still more clearly in water-courses (to which might be
added ocean-streams), the route followed is too complex to be defined,
save as a curve of three dimensions with an ever varying equation.
The Earth’s solid crust undergoes changes that supply another group of
illustrations. The denudation of lands and the depositing of the removed
sediment in new strata at the bottoms of seas and lakes, is a process
throughout which motion is obviously determined in the same way as is
that of the water effecting the transport. Again, though we have no
direct inductive proof that the forces classed as igneous, expend
themselves along lines of least resistance; yet what little we know of
them is in harmony with the belief that they do so. Earthquakes
continually revisit the same localities, and special tracts undergo for
long periods together successive elevations or subsidences,—facts which
imply that already-fractured portions of the Earth’s crust are those
most prone to yield under the pressure caused by further contractions.
The distribution of volcanoes along certain lines, as well as the
frequent recurrence of eruptions from the same vents, are facts of like
meaning.
* * * * *
§ 89. That organic growth takes place in the direction of least
resistance, is a proposition that has been set forth and illustrated by
Mr. James Hinton, in the _Medico-Chirurgical Review_ for October, 1858.
After detailing a few of the early observations which led him to this
generalization, he formulates it thus:—
“Organic form is the result of motion.”
“Motion takes the direction of least resistance.”
“Therefore organic form is the result of motion in the direction of
least resistance.”
After an elucidation and defence of this position, Mr. Hinton proceeds
to interpret, in conformity with it, sundry phenomena of development.
Speaking of plants he says:—
“The formation of the root furnishes a beautiful illustration of the law
of least resistance, for it grows by insinuating itself, cell by cell,
through the interstices of the soil; it is by such minute additions that
it increases, winding and twisting whithersoever the obstacles it meets
in its path determine, and growing there most, where the nutritive
materials are added to it most abundantly. As we look on the roots of a
mighty tree, it appears to us as if they had forced themselves with
giant violence into the solid earth. But it is not so; they were led on
gently, cell added to cell, softly as the dews descended, and the
loosened earth made way. Once formed, indeed, they expand with an
enormous power, but the spongy condition of the growing radicles utterly
forbids the supposition that they are forced into the earth. Is it not
probable, indeed, that the enlargement of the roots already formed may
crack the surrounding soil, and help to make the interstices into which
the new rootlets grow?” * * *
“Throughout almost the whole of organic nature the spiral form is more
or less distinctly marked. Now, motion under resistance takes a spiral
direction, as may be seen by the motion of a body rising or falling
through water. A bubble rising rapidly in water describes a spiral
closely resembling a corkscrew, and a body of moderate specific gravity
dropped into water may be seen to fall in a curved direction, the spiral
tendency of which may be distinctly observed. * * * In this prevailing
spiral form of organic bodies, therefore, it appears to me, that there
is presented a strong _prima facie_ case for the view I have maintained.
* * * The spiral form of the branches of many trees is very apparent,
and the universally spiral arrangement of the leaves around the stem of
plants needs only to be referred to. * * * The heart commences as a
spiral turn, and in its perfect form a manifest spiral may be traced
through the left ventricle, right ventricle, right auricle, left auricle
and appendix. And what is the spiral turn in which the heart commences
but a necessary result of the lengthening, under a limit, of the
cellular mass of which it then consists?” * * *
“Every one must have noticed the peculiar curling up of the young leaves
of the common fern. The appearance is as if the leaf were rolled up, but
in truth this form is merely a phenomenon of growth. The curvature
results from the increase of the leaf, it is only another form of the
wrinkling up, or turning at right angles by extension under limit.”
“The rolling up or imbrication of the petals in many flower-buds is a
similar thing; at an early period the small petals may be seen lying
side by side, afterwards growing within the capsule, they become folded
round one another.” * * *
“If a flower-bud be opened at a sufficiently early period, the stamens
will be found as if moulded in the cavity between the pistil and the
corolla, which cavity the antlers exactly fill; the stalks lengthen at
an after period. I have noticed also in a few instances, that in those
flowers in which the petals are imbricated, or twisted together, the
pistil is tapering as growing up between the petals; in some flowers
which have the petals so arranged in the bud as to form a dome (as the
hawthorn; e. g.), the pistil is flattened at the apex, and in the bud
occupies a space precisely limited by the stamens below, and the
enclosing petals above and at the sides. I have not, however, satisfied
myself that this holds good in all cases.”
Without endorsing all Mr. Hinton’s illustrations, to some of which
exception might be taken, his conclusion may be accepted as a large
instalment of the truth. It is, however, to be remarked, that in the
case of organic growth, as in all other cases, the line of movement is
in strictness the resultant of tractive and resistant forces; and that
the tractive forces here form so considerable an element that the
formula is scarcely complete without them. The shapes of plants are
manifestly modified by gravitation: the direction of each branch is not
what it would have been were the tractive force of the Earth absent; and
every flower and leaf is somewhat altered in the course of development
by the weight of its parts. Though in animals such effects are less
conspicuous, yet the instances in which flexible organs have their
directions in great measure determined by gravity, justify the assertion
that throughout the whole organism the forms of parts must be affected
by this force.
The organic movements which constitute growth, are not, however, the
only organic movements to be interpreted. There are also those which
constitute function. And throughout these the same general principles
are discernible. That the vessels along which blood, lymph, bile, and
all the secretions, find their ways, are channels of least resistance,
is a fact almost too conspicuous to be named as an illustration. Less
conspicuous, however, is the truth, that the currents setting along
these vessels are affected by the tractive force of the Earth: witness
varicose veins; witness the relief to an inflamed part obtained by
raising it; witness the congestion of head and face produced by
stooping. And in the fact that dropsy in the legs gets greater by day
and decreases at night, while, conversely, that œdematous fullness under
the eyes common in debility, grows worse during the hours of reclining
and decreases after getting up, shows us how the transudation of fluid
through the walls of the capillaries, varies according as change of
position changes the effect of gravity in different parts of the body.
It may be well in passing just to note the bearing of the principle on
the development of species. From a dynamic point of view, “natural
selection” is the evolution of Life along lines of least resistance. The
multiplication of any kind of plant or animal in localities that are
favourable to it, is a growth where the antagonistic forces are less
than elsewhere. And the preservation of varieties that succeed better
than their allies in coping with surrounding conditions, is the
continuance of vital movement in those directions where the obstacles to
it are most eluded.
* * * * *
§ 90. Throughout the phenomena of mind the law enunciated is not so
readily established. In a large part of them, as those of thought and
emotion, there is no perceptible movement. Even in sensation and
volition, which show us in one part of the body an effect produced by a
force applied to another part, the intermediate movement is inferential
rather than visible. Such indeed are the difficulties that it is not
possible here to do more than briefly indicate the proofs which might be
given did space permit.
Supposing the various forces throughout an organism to be previously in
equilibrium, then any part which becomes the seat of a further force,
added or liberated, must be one from which the force, being resisted by
smaller forces around, will initiate motion towards some other part of
the organism. If elsewhere in the organism there is a point at which
force is being expended, and which so is becoming minus a force which it
before had, instead of plus a force which it before had not, and thus is
made a point at which the re-action against surrounding forces is
diminished; then, manifestly, a motion taking place between the first
and the last of these points is a motion along the line of least
resistance. Now a sensation implies a force added to, or evolved in,
that part of the organism which is its seat; while a mechanical movement
implies an expenditure or loss of force in that part of the organism
which is its seat. Hence if, as we find to be the fact, motion is
habitually propagated from those parts of an organism to which the
external world adds forces in the shape of nervous impressions, to those
parts of an organism which react on the external world through muscular
contractions, it is simply a fulfilment of the law above enunciated.
From this general conclusion we may pass to a more special one.
When there is anything in the circumstances of an animal’s life,
involving that a sensation in one particular place is habitually
followed by a contraction in another particular place—when there is thus
a frequently-repeated motion through the organism between these places;
what must be the result as respects the line along which the motions
take place? Restoration of equilibrium between the points at which the
forces have been increased and decreased, must take place through some
channel. If this channel is affected by the discharge—if the obstructive
action of the tissues traversed, involves any reaction upon them,
deducting from their obstructive power; then a subsequent motion between
these two points will meet with less resistance along this channel than
the previous motion met with; and will consequently take this channel
still more decidedly. If so, every repetition will still further
diminish the resistance offered by this route; and hence will gradually
be formed between the two a permanent line of communication, differing
greatly from the surrounding tissue in respect of the ease with which
force traverses it. We see, therefore, that if between a particular
impression and a particular motion associated with it, there is
established a connexion producing what is called reflex action, the law
that motion follows the line of least resistance, and that, if the
conditions remain constant, resistance in any direction is diminished by
motion occurring in that direction, supplies an explanation.
Without further details it will be manifest that a like
interpretation may be given to the succession of all other nervous
changes. If in the surrounding world there are objects, attributes, or
actions, that usually occur together, the effects severally produced by
them in the organism will become so connected by those repetitions which
we call experience, that they also will occur together. In proportion to
the frequency with which any external connexion of phenomena is
experienced, will be the strength of the answering internal connexion of
nervous states. Thus there will arise all degrees of cohesion among
nervous states, as there are all degrees of commonness among the
surrounding co-existences and sequences that generate them: whence must
result a general correspondence between associated ideas and associated
actions in the environment.[13]
The relation between emotions and actions may be similarly construed. As
a first illustration let us observe what happens with emotions that are
undirected by volitions. These, like feelings in general, expend
themselves in generating organic changes, and chiefly in muscular
contractions. As was pointed out in the last chapter, there result
movements of the involuntary and voluntary muscles, that are great in
proportion as the emotions are strong. It remains here to be pointed
out, however, that the order in which these muscles are affected is
explicable only on the principle above set forth. Thus, a pleasurable or
painful state of mind of but slight intensity, does little more than
increase the pulsations of the heart. Why? For the reason that the
relation between nervous excitement and vascular contraction, being
common to every genus and species of feeling, is the one of most
frequent repetition; that hence the nervous connexion is, in the way
above shown, the one which offers the least resistance to a discharge;
and is therefore the one along which a feeble force produces motion. A
sentiment or passion that is somewhat stronger, affects not only the
heart but the muscles of the face, and especially those around the
mouth. Here the like explanation applies; since these muscles, being
both comparatively small, and, for purposes of speech, perpetually used,
offer less resistance than other voluntary muscles to the nerve-motor
force. By a further increase of emotion the respiratory and vocal
muscles become perceptibly excited. Finally, under strong passion, the
muscles in general of the trunk and limbs are violently contracted.
Without saying that the facts can be thus interpreted in all their
details (a task requiring data impossible to obtain) it may be safely
said that the order of excitation is from muscles that are small and
frequently acted on, to those which are larger and less frequently acted
on. The single instance of laughter, which is an undirected discharge of
feeling that affects first the muscles round the mouth, then those of
the vocal and respiratory apparatus, then those of the limbs, and then
those of the spine;[14] suffices to show that when no special route is
opened for it, a force evolved in the nervous centres produces motion
along channels which offer the least resistance, and if it is too great
to escape by these, produces motion along channels offering successively
greater resistance.
Probably it will be thought impossible to extend this reasoning so as to
include volitions. Yet we are not without evidence that the transition
from special desires to special muscular acts, conforms to the same
principle. It may be shown that the mental antecedents of a voluntary
movement, are antecedents which temporarily make the line along which
this movement takes place, the line of least resistance. For a volition,
suggested as it necessarily is by some previous thought connected with
it by associations that determine the transition, is itself a
representation of the movements that are willed, and of their sequences.
But to represent in consciousness certain of our own movements, is
partially to arouse the sensations accompanying such movements,
inclusive of those of muscular tension—is partially to excite the
appropriate motor-nerves and all the other nerves implicated. That is to
say, the volition is itself an incipient discharge along a line which
previous experiences have rendered a line of least resistance. And the
passing of volition into action is simply a completion of the discharge.
One corollary from this must be noted before proceeding; namely, that
the particular set of muscular movements by which any object of desire
is reached, are movements implying the smallest total of forces to be
overcome. As each feeling generates motion along the line of least
resistance, it is tolerably clear that a group of feelings, constituting
a more or less complex desire, will generate motion along a series of
lines of least resistance. That is to say, the desired end will be
achieved with the smallest expenditure of effort. Should it be objected
that through want of knowledge or want of skill, a man often pursues the
more laborious of two courses, and so overcomes a larger total of
opposing forces than was necessary; the reply is, that relatively to his
mental state the course he takes is that which presents the fewest
difficulties. Though there is another which in the abstract is easier,
yet his ignorance of it, or inability to adopt it, is, physically
considered, the existence of an insuperable obstacle to the discharge of
his energies in that direction. Experience obtained by himself, or
communicated by others, has not established in him such channels of
nervous communication as are required to make this better course the
course of least resistance to him.
* * * * *
§ 91. As in individual animals, inclusive of man, motion follows lines
of least resistance, it is to be inferred that among aggregations of
men, the like will hold good. The changes in a society, being due to the
joint actions of its members, the courses of such changes will be
determined as are those of all other changes wrought by composition of
forces.
Thus when we contemplate a society as an organism, and observe the
direction of its growth, we find this direction to be that in which the
average of opposing forces is the least. Its units have energies to be
expended in self-maintenance and reproduction. These energies are met by
various environing energies that are antagonistic to them—those of
geological origin, those of climate, of wild animals, of other human
races with whom they are at enmity or in competition. And the tracts the
society spreads over, are those in which there is the smallest total
antagonism. Or, reducing the matter to its ultimate terms, we may say
that these social units have jointly and severally to preserve
themselves and their offspring from those inorganic and organic forces
which are ever tending to destroy them (either indirectly by oxidation
and by undue abstraction of heat, or directly by bodily mutilation);
that these forces are either counteracted by others which are available
in the shape of food, clothing, habitations, and appliances of defence,
or are, as far as may be, eluded; and that population spreads in
whichever directions there is the readiest escape from these forces, or
the least exertion in obtaining the materials for resisting them, or
both. For these reasons it happens that fertile valleys where
water and vegetal produce abound, are early peopled. Sea-shores, too,
supplying a large amount of easily-gathered food, are lines along which
mankind have commonly spread. The general fact that, so far as we can
judge from the traces left by them, large societies first appeared in
those tropical regions where the fruits of the earth are obtainable with
comparatively little exertion, and where the cost of maintaining bodily
heat is but slight, is a fact of like meaning. And to these instances
may be added the allied one daily furnished by emigration; which we see
going on towards countries presenting the fewest obstacles to the
self-preservation of individuals, and therefore to national growth.
Similarly with that resistance to the movements of a society which
neighbouring societies offer. Each of the tribes or nations inhabiting
any region, increases in numbers until it outgrows its means of
subsistence. In each there is thus a force ever pressing outwards on to
adjacent areas—a force antagonized by like forces in the tribes or
nations occupying those areas. And the ever-recurring wars that
result—the conquests of weaker tribes or nations, and the over-running
of their territories by the victors, are instances of social movements
taking place in the directions of least resistance. Nor do the conquered
peoples, when they escape extermination or enslavement, fail to show us
movements that are similarly determined. For migrating as they do to
less fertile regions—taking refuge in deserts or among mountains—moving
in a direction where the resistance to social growth is comparatively
great; they still do this only under an excess of pressure in all other
directions: the physical obstacles to self-preservation they encounter,
being really less than the obstacles offered by the enemies from whom
they fly.
Internal social movements may also be thus interpreted. Localities
naturally fitted for producing particular commodities—that is,
localities in which such commodities are got at the least cost of
force—that is, localities in which the desires for these commodities
meet with the least resistance; become localities especially devoted to
the obtainment of these commodities. Where soil and climate render wheat
a profitable crop, or a crop from which the greatest amount of
life-sustaining power is gained by a given quantity of effort, the
growth of wheat becomes the dominant industry. Where wheat cannot be
economically produced, oats, or rye, or maize, or rice, or potatoes, is
the agricultural staple. Along sea-shores men support themselves with
least effort by catching fish; and hence choose fishing as an
occupation. And in places that are rich in coal or metallic ores, the
population, finding that labour devoted to the raising of these
materials brings a larger return of food and clothing than when
otherwise directed, becomes a population of miners. This last
instance introduces us to the phenomena of exchange; which equally
illustrate the general law. For the practice of barter begins as soon as
it facilitates the fulfilment of men’s desires, by diminishing the
exertion needed to reach the objects of those desires. When instead of
growing his own corn, weaving his own cloth, sewing his own shoes, each
man began to confine himself to farming, or weaving, or shoemaking; it
was because each found it more laborious to make everything he wanted,
than to make a great quantity of one thing and barter the surplus for
the rest: by exchange, each procured the necessaries of life without
encountering so much resistance. Moreover, in deciding what commodity to
produce, each citizen was, as he is at the present day, guided in the
same manner. For besides those local conditions which determine whole
sections of a society towards the industries easiest for them, there are
also individual conditions and individual aptitudes which to each
citizen render certain occupations preferable; and in choosing those
forms of activity which their special circumstances and faculties
dictate, these social units are severally moving towards the objects of
their desires in the directions which present to them the fewest
obstacles. The process of transfer which commerce pre-supposes,
supplies another series of examples. So long as the forces to be
overcome in procuring any necessary of life in the district where it is
consumed, are less than the forces to be overcome in procuring it from
an adjacent district, exchange does not take place. But when the
adjacent district produces it with an economy that is not out-balanced
by cost of transit—when the distance is so small and the route so easy
that the labour of conveyance plus the labour of production is less than
the labour of production in the consuming district, transfer commences.
Movement in the direction of least resistance is also seen in the
establishment of the channels along which intercourse takes place. At
the outset, when goods are carried on the backs of men and horses, the
paths chosen are those which combine shortness with levelness and
freedom from obstacles—those which are achieved with the smallest
exertion. And in the subsequent formation of each highway, the course
taken is that which deviates horizontally from a straight line so far
only as is needful to avoid vertical deviations entailing greater labour
in draught. The smallest total of obstructive forces determines the
route, even in seemingly exceptional cases; as where a detour is made to
avoid the opposition of a landowner. All subsequent improvements, ending
in macadamized roads, canals, and railways, which reduce the antagonism
of friction and gravity to a minimum, exemplify the same truth. After
there comes to be a choice of roads between one point and another, we
still see that the road chosen is that along which the cost of transit
is the least: cost being the measure of resistance. Even where, time
being a consideration, the more expensive route is followed, it is so
because the loss of time involves loss of force. When, division of
labour having been carried to a considerable extent and means of
communication made easy, there arises a marked localization of
industries, the relative growths of the populations devoted to them may
be interpreted on the same principle. The influx of people to each
industrial centre, as well as the rate of multiplication of those
already inhabiting it, is determined by the payment for labour; that
is—by the quantity of commodities which a given amount of effort will
obtain. To say that artisans flock to places where, in consequence of
facilities for production, an extra proportion of produce can be given
in the shape of wages; is to say that they flock to places where there
are the smallest obstacles to the support of themselves and families.
Hence, the rapid increase of number which occurs in such places, is
really a social growth at points where the opposing forces are the
least.
Nor is the law less clearly to be traced in those functional changes
daily going on. The flow of capital into businesses yielding the largest
returns; the buying in the cheapest market and selling in the dearest;
the introduction of more economical modes of manufacture; the
development of better agencies for distribution; and all those
variations in the currents of trade that are noted in our newspapers and
telegrams from hour to hour; exhibit movement taking place in directions
where it is met by the smallest total of opposing forces. For if we
analyze each of these changes—if instead of interest on capital we read
surplus of products which remains after maintenance of labourers; if we
so interpret large interest or large surplus to imply labour expended
with the greatest results; and if labour expended with the greatest
results means muscular action so directed as to evade obstacles as far
as possible; we see that all these commercial phenomena are complicated
motions set up along lines of least resistance.
Objections of two opposite kinds will perhaps be made to these
sociological applications of the law. By some it may be said that the
term force as here used, is used metaphorically—that to speak of men as
_impelled_ in certain directions by certain desires, is a figure of
speech and not the statement of a physical fact. The reply is, that the
foregoing illustrations are to be interpreted literally, and that the
processes described _are_ physical ones. The pressure of hunger is an
actual force—a sensation implying some state of nervous tension; and the
muscular action which the sensation prompts is really a discharge of it
in the shape of bodily motion—a discharge which, on analyzing the mental
acts involved, will be found to follow lines of least resistance. Hence
the motions of a society whose members are impelled by this or any other
desire, are actually, and not metaphorically, to be understood in the
manner shown. An opposite objection may possibly be, that the
several illustrations given are elaborated truisms; and that the law of
direction of motion being once recognized, the fact that social
movements, in common with all others, must conform to it, follows
inevitably. To this it may be rejoined, that a mere abstract assertion
that social movements must do this, would carry no conviction to the
majority; and that it is needful to show _how_ they do it. For social
evolution to be interpreted after the method proposed, it is requisite
that such generalisations as those of political economy shall be reduced
to equivalent propositions expressed in terms of force and motion.
Social movements of these various orders severally conform to the two
derivative principles named at the outset. In the first place we may
observe how, once set up in given directions, such movements, like all
others, tend to continue in these directions. A commercial mania or
panic, a current of commodities, a social custom, a political agitation,
or a popular delusion, maintains its course for a long time after its
original source has ceased; and requires antagonistic forces to arrest
it. In the second place it is to be noted that in proportion to the
complexity of social forces is the tortuousness of social movements. The
involved series of muscular contractions gone through by the artizan,
that he may get the wherewithal to buy a loaf lying at the baker’s next
door, show us how extreme becomes the indirectness of motion when the
agencies at work become very numerous—a truth still better illustrated
by the more public social actions; as those which end in bringing a
successful man of business, towards the close of his life, into
parliament.
* * * * *
§ 92. And now of the general truth set forth in this chapter, as of that
dealt with in the last, let us ask—what is our ultimate evidence? Must
we accept it simply as an empirical generalization? or is it to be
established as a corollary from a still deeper truth? The reader will
anticipate the answer. We shall find it deducible from that datum of
consciousness which underlies all science.
Suppose several tractive forces, variously directed, to be acting on a
given body. By what is known among mathematicians as the composition of
forces, there may be found for any two of these, a single force of such
amount and direction as to produce on the body an exactly equal effect.
If in the direction of each of them there be drawn a straight line, and
if the lengths of these two straight lines be made proportionate to the
amounts of the forces; and if from the end of each line there be drawn a
line parallel to the other, so as to complete a parallelogram; then the
diagonal of this parallelogram represents the amount and direction of a
force that is equivalent to the two. Such a resultant force, as it is
called, may be found for any pair of forces throughout the group.
Similarly, for any pair of such resultants a single resultant may be
found. And by repeating this course, all of them may be reduced to two.
If these two are equal and opposite—that is, if there is no line of
greatest traction, motion does not take place. If they are opposite but
not equal, motion takes place in the direction of the greater. And if
they are neither equal nor opposite, motion takes place in the direction
of their resultant. For in either of these cases there is an
unantagonized force in one direction. And this residuary force that is
not neutralized by an opposing one, must move the body in the direction
in which it is acting. To assert the contrary is to assert that a force
can be expended without effect—without generating an equivalent force;
and by so implying that force can cease to exist, this involves a denial
of the persistence of force. It needs scarcely be added that if in
place of tractions we take resistances, the argument equally holds; and
that it holds also where both tractions and resistances are concerned.
Thus the law that motion follows the line of greatest traction, or the
line of least resistance, or the resultant of the two, is a necessary
deduction from that primordial truth which transcends proof.
Reduce the proposition to its simplest form, and it becomes still more
obviously consequent on the persistence of force. Suppose two weights
suspended over a pulley or from the ends of an equal-armed lever; or
better still—suppose two men pulling against each other. In such cases
we say that the heavier weight will descend, and that the stronger man
will draw the weaker towards him. But now, if we are asked how we know
which is the heavier weight or the stronger man; we can only reply that
it is the one producing motion in the direction of its pull. Our only
evidence of excess of force is the movement it produces. But if of two
opposing tractions we can know one as greater than the other only by the
motion it generates in its own direction, then the assertion that motion
occurs in the direction of greatest traction is a truism. When, going a
step further back, we seek a warrant for the assumption that of the two
conflicting forces, that is the greater which produces motion in its own
direction, we find no other than the consciousness that such part of the
greater force as is unneutralized by the lesser, must produce its
effect—the consciousness that this residuary force cannot disappear, but
must manifest itself in some equivalent change—the consciousness that
force is persistent. Here too, as before, it may be remarked that
no amount of varied illustrations, like those of which this chapter
mainly consists, can give greater certainty to the conclusion thus
immediately drawn from the ultimate datum of consciousness. For in all
cases, as in the simple ones just given, we can identify the greatest
force only by the resulting motion. It is impossible for us ever to get
evidence of the occurrence of motion in any other direction than that of
the greatest force; since our measure of relative greatness among forces
is their relative power of generating motion. And clearly, while the
comparative greatness of forces is thus determined, no multiplication of
instances can add certainty to a law of direction of movement which
follows immediately from the persistence of force.
From this same primordial truth, too, may be deduced the principle that
motion once set up along any line, becomes itself a cause of subsequent
motion along that line. The mechanical axiom that, if left to itself,
matter moving in any direction will continue in that direction with
undiminished velocity, is but an indirect assertion of the persistence
of force; since it is an assertion that the force manifested in the
transfer of a body along a certain length of a certain line in a certain
time, cannot disappear without producing some equal manifestation—a
manifestation which, in the absence of conflicting forces, must be a
further transfer in the same direction at the same velocity. In
the case of matter traversing matter the like inference is necessitated.
Here indeed the actions are much more complicated. A liquid that follows
a certain channel through or over a solid, as water along the Earth’s
surface, loses part of its motion in the shape of heat, through friction
and collision with the matters forming its bed. A further amount of its
motion may be absorbed in overcoming forces which it liberates; as when
it loosens a mass which falls into, and blocks up, its channel. But
after these deductions by transformation into other modes of force, any
further deduction from the motion of the water is at the expense of a
reaction on the channel, which by so much diminishes its obstructive
power: such reaction being shown in the motion acquired by the detached
portions which are carried away. The cutting out of river-courses is a
perpetual illustration of this truth. Still more involved is the
case of motion passing through matter by impulse from part to part; as a
nervous discharge through animal tissue. Some chemical change may be
wrought along the route traversed, which may render it less fit than
before for conveying a current. Or the motion may itself be in part
metamorphosed into some obstructive form of force; as in metals, the
conducting power of which is, for the time, decreased by the heat which
the passage of electricity itself generates. The real question is,
however, what structural modification, if any, is produced throughout
the matter traversed, apart from _incidental_ disturbing forces—apart
from everything but the _necessary_ resistance of the matter: that,
namely, which results from the inertia of its units. If we confine our
attention to that part of the motion which, escaping transformation,
continues its course, then it is a corollary from the persistence of
force that as much of this remaining motion as is taken up in changing
the positions of the units, must leave these by so much less able to
obstruct subsequent motion in the same direction.
Thus in all the changes heretofore and at present displayed by the Solar
System; in all those that have gone on and are still going on in the
Earth’s crust; in all processes of organic development and function; in
all mental actions and the effects they work on the body; and in all
modifications of structure and activity in societies; the implied
movements are of necessity determined in the manner above set forth.
Every alteration in the arrangement of parts, constituting Evolution
under each of its phases, must conform to this universal principle.
Wherever we see motion, its direction must be that of the greatest
force. And wherever we see the greatest force to be acting in a given
direction, in that direction motion must ensue.
-----
Footnote 13:
This paragraph is a re-statement, somewhat amplified, of an idea set
forth in the _Medico-Chirurgical Review_ for January, 1859 (pp. 189
and 190); and contains the germ of the intended fifth part of the
_Principles of Psychology_, which was withheld for the reasons given
in the preface to that work.
Footnote 14:
For details see a paper on “The Physiology of Laughter,” published in
_Macmillan’s Magazine_ for March 1860.