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.
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