All impressions from moment to moment made on our organs of sense, stand in direct correlation with physical forces existing externally. The modes of consciousness called pressure, motion, sound, light, heat, are effects produced in us by agencies which, as otherwise expended, crush or fracture pieces of matter, generate vibrations in surrounding objects, cause chemical combinations, and reduce substances from a solid to a liquid form. Hence if we regard the changes of relative position, of aggregation, or of chemical state, thus arising, as being transformed manifestations of the agencies from which they arise; so must we regard the sensations which such agencies produce in us, as new forms of the forces producing them. Any hesitation to admit that, between the physical forces and the sensations there exists a correlation like that between the physical forces themselves, must disappear on remembering how the one correlation, like the other, is not qualitative only but quantitative. Masses of matter which, by scales or dynamometer, are shown to differ greatly in weight, differ as greatly in the feelings of pressure they produce on our bodies. In arresting moving objects, the strains we are conscious of are proportionate to the momenta of such objects as otherwise measured. Under like conditions the impressions of sounds given to us by vibrating strings, bells, or columns of air, are found to vary in strength with the amount of force applied. Fluids or solids proved to be markedly contrasted in temperature by the different degrees of expansion they produce in the mercurial column, produce in us correspondingly different degrees of the sensation of heat. And similarly unlike intensities in our impressions of light, answer to unlike effects as measured by photometers.
Besides the correlation and equivalence between external physical forces, and the mental forces generated by them in us under the form of sensations, there is a correlation andequivalence between sensations and those physical forces which, in the shape of bodily actions, result from them. The feelings we distinguish as light, heat, sound, odour, taste, pressure, &.c, do not die away without immediate results; but are invariably followed by other manifestations of force. In addition to the excitements of secreting organs, that are in some cases traceable, there arises a contraction of the involuntary muscles, or of the voluntary muscles, or of both. Sensations increase the action of the heart—slightly when they are slight; markedly when they are marked; and recent physiological inquiries imply not only that contraction of the heart is excited by every sensation, but also that the muscular fibres throughout the whole, vascular system, are at the same time more or less contracted. The respiratory muscles, too, are stimulated into greater activity by sensations. The rate of breathing is visibly and audibly augmented both by pleasurable and painful impressions on the nerves, when these reach any intensity. It has even of late been shown that inspiration becomes more frequent on transition from darkness into sunshine,—a result probably due to the increased amount of direct and indirect nervous stimulation involved. When the quantity of sensation is great, it generates contractions of the voluntary muscles, as well as of the involuntary ones. Unusual excitement of the nerves of touch, as by tickling, is followed by almost incontrollable movements of the limbs. Violent pains cause violent struggles. The start that succeeds a loud sound, the wry face produced by the taste of anything extremely disagreeable, the jerk with which the hand or foot is snatched out of water that is very hot, are instances of the transformation of feeling: into motion; and in these cases, as in all others, it is manifest that the quantity of bodily action is proportionate to the quantity of sensation. Even where from pride there is a suppression of the screams and groans expressive of great pain (also indirect results of muscular contraction), we may still see in the clenching of the hands, the knitting of thebrows, and the setting of the teeth, that the bodily actions developed are as great, though less obtrusive in their results. If we take emotions instead of sensations, we find the correlation and equivalence equally manifest. Not only are the modes of consciousness directly produced in us by physical forces, re-transformable into physical forces under the form of muscular motions and the changes they initiate; but the like is true of those modes of consciousness which are not directly produced in us by the physical forces. Emotions of moderate intensity, like sensations of moderate intensity, generate little beyond excitement of the heart and vascular system, joined sometimes with increased action of glandular organs. But as the emotions rise in strength, the muscles of the face, body, and limbs, begin to move. Of examples may be mentioned the frowns, dilated nostrils, and stampings of anger; the contracted brows, and wrung hands, of grief; the smiles and leaps of joy; and the frantic struggles of terror or despair. Passing over certain apparent, but only apparent, exceptions, we see that whatever be the kind of emotion, there is a manifest relation between its amount, and the amount of muscular action induced: alike from the erect carriage and elastic step of exhilaration, up to the dancings of immense delight, and from the fidgetiness of impatience up to the almost convulsive movements accompanying great mental agony. To these several orders of evidence must be joined the further one, that between our feelings and those voluntary motions into which they are transformed, there comes the sensation of muscular tension, standing in manifest correlation with both—a correlation that is distinctly quantitative: the sense of strain varying, other things equal, directly as the quantity of momentum generated.
“But how,” it may be asked, “can we interpret by the law of correlation the genesis of those thoughts and feelings which, instead of following external stimuli, arise spontaneously? Between the indignation caused by an insult, and theloud sounds or violent acts that follow, the alleged connexion may hold; but whence come the crowd of ideas and the mass of feelings that expend themselves in these demonstrations? They are clearly not equivalents of the sensations produced by the words on the ears; for the same words otherwise arranged, would not have caused them. The thing said bears to the mental action it excites, much the same relation that the pulling of a trigger bears to the subsequent explosion—does not produce the power, but merely liberates it. Whence then arises this immense amount of nervous energy which a whisper or a glance may call forth?” The reply is, that the immediate correlates of these and other such modes of consciousness, are not to be found in the agencies acting on us externally, but in certain internal agencies. The forces called vital, which we have seen to be correlates of the forces called physical, are the immediate sources of these thoughts and feelings; and are expended in producing them. The proofs of this are various. Here are some of them. It is a conspicuous fact that mental action is contingent on the presence of a certain nervous apparatus; and that, greatly obscured as it is by numerous and involved conditions, a general relation may be traced between the size of this apparatus and the quantity of mental action as measured by its results. Further, this apparatus has a particular chemical constitution on which its activity depends; and there is one element in it between the amount of which and the amount of function performed, there is an ascertained connexion: the proportion of phosphorus present in the brain being the smallest in infancy, old age and idiotcy, and the greatest during the prime of life. Note next, that the evolution of thought and emotion varies, other things equal, with the supply of blood to the brain. On the one hand, a cessation of the cerebral circulation, from arrest of the heart’s action, immediately entails unconsciousness. On the other hand, excess of cerebral circulation (unless it is such as to cause undue pressure) results in an excitementrising finally to delirium. Not the quantity only, but also the condition of the blood passing through the nervous system, influences the mental manifestations. The arterial currents must be duly aerated, to produce the normal amount of cerebration. At the one extreme, we find that if the blood is not allowed to exchange its carbonic acid for oxygen, there results asphyxia, with its accompanying stoppage of ideas and feelings. While at the other extreme, we find that by the inspiration of nitrous oxide, there is produced an excessive, and indeed irrepressible, nervous activity. Besides the connexion between the development of the mental forces and the presence of sufficient oxygen in the cerebral arteries, there is a kindred connexion between the development of the mental forces and the presence in the cerebral arteries of certain other elements. There must be supplied special materials for the nutrition of the nervous centres, as well as for their oxidation. And how what we may call the quantity of consciousness, is, other things equal, determined by the constituents of the blood, is unmistakably seen in the exaltation that follows when certain chemical compounds, as alcohol and the vegeto-alkalies, are added to it. The gentle exhilaration which tea and coffee create, is familiar to all; and though the gorgeous imaginations and intense feelings of happiness produced by opium and hashish, have been experienced by few, (in this country at least,) the testimony of those who have experienced them is sufficiently conclusive. Yet another proof that the genesis of the mental energies is immediately dependent on chemical change, is afforded by the fact, that the effete products separated from the blood by the kidneys, vary in character with the amount of cerebral action. Excessive activity of mind is habitually accompanied by the excretion of an unusual quantity of the alkaline phosphates. Conditions of abnormal nervous excitement bring on analogous effects. And the “peculiar odour of the insane,” implying as it does morbid products in the perspiration, shows a connexion betweeninsanity and a special composition of the circulating fluids—a composition which, whether regarded as cause or consequence, equally implies correlation of the mental and the physical forces. Lastly we have to note that this correlation too, is, so far as we can trace it, quantitative. Provided the conditions to nervous action are not infringed on, and the concomitants are the same, there is a tolerably constant ratio between the amounts of the antecedents and consequents. Within the implied limits, nervous stimulants and anæsthetics produce effects on the thoughts and feelings, proportionate to the quantities administered. And conversely, where the thoughts and feelings form the initial term of the relation, the degree of reaction on the bodily energies is great, in proportion as they are great: reaching in extreme cases a total prostration of physique.
Various classes of facts thus unite to prove that the law of metamorphosis, which holds among the physical forces, holds equally between them and the mental forces. Those modes of the Unknowable which we call motion, heat, light, chemical affinity, &c., are alike transformable into each other, and into those modes of the Unknowable which we distinguish as sensation, emotion, thought: these, in their turns, being directly or indirectly re-transformable into the original shapes. That no idea or feeling arises, save as a result of some physical force expended in producing it, is fast becoming a common place of science; and whoever duly weighs the evidence will see, that nothing but an overwhelming bias in favour of a pre-conceived theory, can explain its non-acceptance. How this metamorphosis takes place—how a force existing as motion, heat, or light, can become a mode of consciousness—how it is possible for aerial vibrations to generate the sensation we call sound, or for the forces liberated by chemical changes in the brain to give rise to emotion—these are mysteries which it is impossible to fathom. But they are not profounder mysteries than the transformations of the physical forces into each other.They are not more completely beyond our comprehension than the natures of Mind and Matter. They have simply the same insolubility as all other ultimate questions. We can learn nothing more than that here is one of the uniformities in the order of phenomena.
§ 83. Of course if the law of correlation and equivalence holds of the forces we class as vital and mental, it must hold also of those which we class as social. Whatever takes place in a society is due to organic or inorganic agencies, or to a combination of the two—results either from the undirected physical forces around, from these physical forces as directed by men, or from the forces of the men themselves. No change can occur in its organization, its modes of activity, or the effects it produces on the face of the Earth, but what proceeds, mediately or immediately, from these. Let us consider first the correlation between the phenomena which societies display, and the vital phenomena.
Social power and life varies, other things equal, with the population. Though different races, differing widely in their fitness for combination, show us that the forces manifested in a society are not necessarily proportionate to the number of people; yet we see that under given conditions, the forces manifested are confined within the limits which the number of people imposes. A small society, no matter how superior the character of its members, cannot exhibit the same quantity of social action as a large one. The production and distribution of commodities must be on a comparatively small scale. A multitudinous press, a prolific literature, or a massive political agitation, is not possible. And there can be but a small total of results in the shape of art-products and scientific discoveries. The correlation of the social with the physical forces through the intermediation of the vital ones, is, however, most clearly shown in the different amounts of activity displayed by the same society according as its members are supplied with different amounts of forcefrom the external world. In the effects of good and bad harvests, we yearly see this relation illustrated. A greatly deficient yield of wheat is soon followed by a diminution of business. Factories are worked half-time, or close entirely; railway traffic falls; retailers find their sales much lessened; house-building is almost suspended; and if the scarcity rises to famine, a thinning of the population still more diminishes the industrial vivacity. Conversely, an unusually abundant harvest, occurring under conditions not otherwise unfavourable, both excites the old producing and distributing agencies and sets up new ones. The surplus social energy finds vent in speculative enterprises. Capital seeking investment carries out inventions that have been lying unutilized. Labour is expended in opening new channels of communication. There is increased encouragement to those who furnish the luxuries of life and minister to the æsthetic faculties. There are more marriages, and a greater rate of increase in population. Thus the social organism grows larger, more complex, and more active. When, as happens with most civilized nations, the whole of the materials for subsistence are not drawn from the area inhabited, but are partly imported, the people are still supported by certain harvests elsewhere grown at the expense of certain physical forces. Our own cotton-spinners and weavers supply the most conspicuous instance of a section in one nation living, in great part, on imported commodities, purchased by the labour they expend on other imported commodities. But though the social activities of Lancashire are due chiefly to materials not drawn from our own soil, they are none the less evolved from physical forces elsewhere stored up in fit forms and then brought here.
If we ask whence come these physical forces from which, through the intermediation of the vital forces, the social forces arise, the reply is of course as heretofore—the solar radiations. Based as the life of a society is on animal and vegetal products; and dependent as these animal and vegetalproducts are on the light and heat of the sun; it follows that the changes going on in societies are effects of forces having a common origin with those which produce all the other orders of changes that have been analyzed. Not only is the force expended by the horse harnessed to the plough, and by the labourer guiding it, derived from the same reservoir as is the force of the falling cataract and the roaring hurricane; but to this same reservoir are eventually traceable those subtler and more complex manifestations of force which humanity, as socially embodied, evolves. The assertion is a startling one, and by many will be thought ludicrous; but it is an unavoidable deduction which cannot here be passed over.
Of the physical forces that are directly transformed into social ones, the like is to be said. Currents of air and water, which before the use of steam were the only agencies brought in aid of muscular effort for the performance of industrial processes, are, as we have seen, generated by the heat of the sun. And the inanimate power that now, to so vast an extent, supplements human labour, is similarly derived. The late George Stephenson was one of the first to recognize the fact that the force impelling his locomotive, originally emanated from the sun. Step by step we go back—from the motion of the piston to the evaporation of the water; thence to the heat evolved during the oxidation of coal; thence to the assimilation of carbon by the plants of whose imbedded remains coal consists; thence to the carbonic acid from which their carbon was obtained; and thence to the rays of light that de-oxidized this carbonic acid. Solar forces millions of years ago expended on the Earth’s vegetation, and since locked up beneath its surface, now smelt the metals required for our machines, turn the lathes by which the machines are shaped, work them when put together, and distribute the fabrics they produce. And in so far as economy of labour makes possible the support of a larger population; gives a surplus of human power that would else be absorbed in manual occupations; and so facilitates the development ofhigher kinds of activity; it is clear that these social forces which are directly correlated with physical forces anciently derived from the sun, are only less important than those whose correlates are the vital forces recently derived from it.
§ 84. Regarded as an induction, the doctrine set forth in this chapter will most likely be met by a demurrer. Many who admit that among physical phenomena at least, the correlation of forces is now established, will probably say that inquiry has not yet gone far enough to enable us to predicate equivalence. And in respect of the forces classed as vital, mental, and social, the evidence assigned, however little to be explained away, they will consider by no means conclusive even of correlation, much less of equivalence.
To those who think thus, it must now however be pointed out, that the universal truth above illustrated under its various aspects, is a necessary corollary from the persistence of force. Setting out with the proposition that force can neither come into existence, nor cease to exist, the several foregoing general conclusions inevitably follow. Each manifestation of force can be interpreted only as the effect of some antecedent force: no matter whether it be an inorganic action, an animal movement, a thought, or a feeling. Either this must be conceded, or else it must be asserted that our successive states of consciousness are self-created. Either mental energies, as well as bodily ones, are quantitatively correlated to certain energies expended in their production, and to certain other energies which they initiate; or else nothing must become something and something must become nothing. The alternatives are, to deny the persistence of force, or to admit that every physical and psychial change is generated by certain antecedent forces, and that from given amounts of such forces neither more nor less of such physical and psychial changes can result. And since the persistence of force, being a datum of consciousness, cannot be denied, its unavoidable corollary must be accepted. This corollary cannot indeed bemade more certain by accumulating illustrations. The truth as arrived at deductively, cannot be inductively confirmed. For every one of such facts as those above detailed, is established only through the indirect assumption of that persistence of force, from which it really follows as a direct consequence. The most exact proof of correlation and equivalence which it is possible to reach by experimental inquiry, is that based on measurement of the forces expended and the forces produced. But, as was shown in the last chapter, any such process of measurement implies the use of some unit of force which is assumed to remain constant; and for this assumption there can be no warrant but that it is a corollary from the persistence of force. How then can any reasoning based on this corollary, prove the equally direct corollary that when a given quantity of force ceases to exist under one form, an equal quantity must come into existence under some other form or forms? Clearly theà prioritruth expressed in this last corollary, cannot be more firmly established by anyà posterioriproofs which the first corollary helps us to.
“What then,” it may be asked, “is the use of these investigations by which the correlation and equivalence of forces is sought to be established as an inductive truth? Surely it will not be alleged that they are useless. Yet if this correlation cannot be made more certain by them than it is already, does not their uselessness necessarily follow?” No. They are of value as disclosing the many particular implications which the general truth does not specify. They are of value as teaching us how much of one mode of force is the equivalent of so much of another mode. They are of value as determining under what conditions each metamorphosis occurs. And they are of value as leading us to inquire in what shape the remnant of force has escaped, when the apparent results are not equivalent to the cause.
CHAPTER X.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 trulyrepresent 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 weconceive 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 thehypothesis, 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 commoncentre 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 theplanets 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 resultantof 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 projectingledge, 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 theMedico-Chirurgical Reviewfor 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 strongprima faciecase 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 elementthat 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 theirallies 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, involvingthat 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 sequencesthat 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 (atask 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 implyingthe 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, reducingthe 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 usmovements 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, eachprocured 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 antagonismof 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 withthe 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 asimpelledin 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 describedarephysical 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 showhowthey 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 inthese 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 singleresultant 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 warrantfor 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 shapeof 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 fromincidentaldisturbing forces—apart from everything but thenecessaryresistance 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.