University of Virginia Library

Chapter 9
The Direction of Motion

§74. The Absolute Cause of changes, no matter what may be their special natures, is not less incomprehensible in respect of the unity or duality of its action, than in all other respects. Are phenomena due to the variously-conditioned workings of a single force, or are they due to the conflict of two forces? Whether everything is explicable on the hypothesis of universal pressure, whence so-called tension results differentially from inequalities of pressure; or whether 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 agency, is an idea open to a parallel and equally fatal objection. And verbally intelligible as is the proposition that pressure and tension everywhere co-exist, yet we cannot truly represent to ourselves one ultimate unit of matter as drawing another while resisting it.

Nevertheless, this last belief we are compelled to entertain. Matter cannot be conceived except as manifesting forces of attraction and repulsion. In our consciousness, Body is distinguished from Space by its opposition to our muscular energies; and this opposition we feel under the twofold form of a cohesion which hinders our efforts to rend, and a resistance which hinders our efforts to compress. Without resistance there can be nothing but empty extension. Without cohesion there can be no resistance. Probably this conception of antagonistic forces originates 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 one another, 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 ethereal medium. The constitution we assign to this ethereal medium, however, 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, 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 molecules 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 one another 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, etc. 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.

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. How these ideas st and related to the absolute truth we cannot know, but we may unreservedly surrender ourselves to them as relatively true, and may proceed to evolve a series of deductions having a like relative truth.

§75. Universally co-existent forces of attraction and repulsion, imply 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, and are appreciable, movement takes place along the resultant of 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 disregard it. In the same manner though the courses taken by steam from an exploding boiler, differ somewhat from those which it would take were gravitation out of the question; yet, as gravitation affects its courses only infinitesimally, we are justified in saying that the escaping steam goes along lines of least resistance. Motion, then, always follows the line of greatest traction, or the line of least resistance, or the resultant of the two; and though the last is alone strictly true, the others are in many cases sufficiently near the truth for practical purposes.

Motion set up in any direction is itself a cause of further motion in that direction, since it is the manifestation 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 which all the calculations of physical astronomy assume. 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 most readily 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 appear to imply 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. It may be added that in proportion as the forces at work are numerous and varied, the line 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.

As a step towards unification of knowledge, we have now to trace these general laws throughout the various orders of changes which the Cosmos exhibits.

§76. In the Solar System the principles thus briefly summarized are every instant exemplified. Each planet aid satellite has a momentum which would, if acting alone, carry it forward in the direction it is at any instant pursuing — a momentum which would make a straight line its line of least resistance. Each planet and satellite, however, is drawn by a force which, if it acted alone, 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 consequent on the unsymmetrical distribution of the forces around. When more closely examined, its path supplies 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 perturbations; that is, slight divergences 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. When with this axial motion is contemplated 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.

§77. We come next to terrestrial changes: present ones as observed, and past ones as inferred by geologists. Let us set out with the unceasing movements in the Earth's atmosphere; descend to the slow 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 ascend: the resistance being less than the resistance to lateral movement. Adjacent atmospheric masses, moving in the directions of the diminished resistance, displace the expanded air. When, again, by the ascent of heated air from great tracts like the torrid zone, there is produced at the upper surface of the atmosphere a protuberance — when the air forming this protuberance overflows laterally towards the poles; it does so because, while the tractive force of the Earth is nearly the same, the lateral resistance is diminished. And throughout the course of each current thus generated, as well as throughout the course of each counter-current flowing into the space vacated, 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 generated, and by collision with prominences on the Earth's crust. The movements of water, in both its gaseous and liquid states, furnish further examples. Evaporation is the escape of particles of water in the direction of least resistance; and as the resistance (which is due to gaseous pressure) diminishes, the evaporation increases. On the other hand 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 raindrops, 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. In the course the rain-drops take while trickling over the 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. So far from a cascade furnishing 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.

The Earth's solid crust undergoes changes which 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.

§78. That organic growth takes place in the direction of least resistance, is a proposition 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 formu1ates 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. Shaking of plants, he says: —

"Throughout almost the whole of organic nature the spiral form is more or less distinctly marked. Now, motion under resistance takes a spiral direction, 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.

Without endorsing all Mr. Hinton's illustrations, his conclusion may be accepted as a large instalment of the truth. But 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 the tractive forces here form so considerable an element that the formula is not complete without them. The shapes of plants are manifestly modified by gravitation. The direction of each branch is not what it would have been in the absence of the pull exercised by the Earth; 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 and ducts along which blood, lymph, bile, and all the secretions, find their ways, are channels of least resistance, is an illustration almost too conspicuous to be named. Less conspicuous, however, is the truth that the currents set ting 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 facts that dropsy in the legs gets greater by day and decreases at night, while, conversely that oedematous fullness under the eyes common in debility, grows worse during the hours of reclining and decreases after getting up, we see how the transudation of liquid 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 just to note the bearing of the principle on the development of species. From a dynamic point of view, "natural selection" implies structural changes 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 which succeed better than their allies in coping with surrounding conditions, is the continuance of vital movements in those directions where the obstacles to them are most eluded.

§79. Throughout mental phenomena the law enunciated is not readily established. In a large part of them, as those of thought and emotion, there is no perceptible movement. Even in sensation and action, which show us in one part of the body an effect produced by a force applied to another part, the intermediate movement is inferential only. Some suggestions may be made however.

A stimulation 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: implying some tension of molecular state between the two localities. Hence if, in the life of a minute animal, there are circumstances involving that a stimulation in one particular place is habitually followed by a contraction in another particular place — if there is thus a repeated motion through some line of least resistance between these places; what must be the result as respects the line? If this line — 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. Every repetition will further diminish the resistance offered; and thus will gradually be formed a permanent line of communication, differing greatly from the surrounding tissue in respect of the ease with which force traverses it. Hence in small creatures may result rudimentary nervous connexions. Only an adumbration of nervous processes thus hinted as conforming to the general law, is here possible. But the effects of associations between impressions and motions as seen in habits, all yield illustrations. In knitting, in reading aloud, in the performance of the skilled pianist who talks while he plays, we have examples of the way in which channels of nervous communication are eventually made so permeable by perpetual discharges along them as to bring about a state almost automatic or reflex: illustrating at once the fact that molecular motion follows lines of least resistance, and the fact that motion along such lines, by diminishing the resistance, further facilitates the motion. Though qualifications arising in the same manner as those indicated in the last chapter complicate these nervo-motor processes in ways which cannot here be followed, they do not conflict with the law set forth. Moreover they are congruous with the principle that 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. In this way 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.)

The relation between emotions and actions may be similarly construed. Observe what happens with emotions which are undirected by volitions. 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 add that the order in which these muscles are affected conforms to the principle. A pleasurable or painful feeling of but slight intensity does little more than increase the action of the heart. Why? For the reason that the relation between nervous excitement and cardiac contraction, being common to every species of feeling, is the one of most frequent repetition; that hence the nervous connexion offering the least resistance to a discharge, is the one along which a feeble force produces motion. A stronger sentiment 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 nervo-motor forces. By a further increase of emotion the respiratory and vocal muscles become perceptibly excited. Finally, under violent passion, the muscles of the trunk and limbs are strongly contracted. 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; 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 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 voluntary acts. Yet we are not without evidence that the transition from special desires to special muscular motions, conforms to the same principle. The mental antecedents of a voluntary movement, are such as temporarily make the line through which this movement is initiated, the line of least resistance. For a volition, suggested as it is by some previous thought joined with it by associations that determine the transition, is itself a representation of the movements which 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 must be noted; namely that the particular set of movements by which an object of desire is reached, are usually movements implying the smallest total of forces to be overcome. As the motion initiated by each feeling takes the line of least resistance, it is inferable that a group of feelings constituting a more or less complex desire will initiate motions along a series of lines of least resistance; that is, the desired end will be achieved with the smallest effort. Doubtless through want of knowledge or want of skill or want of resolution to make immediate exertion, a man often takes the more laborious of two courses. But it remains true that relatively to his mental state at the time, his course is the easiest to him — the one least resisted by the aggregate of his feelings.

§80. As with individual men so is it with aggregations of men. Social changes take directions that are due to the joint actions of citizens, determined as are those of all other changes wrought by composition of forces.

Thus when we note the direction of a nation's growth, we find it to be that in which the aggregate of opposing forces is least. Its units have energies to be expended in self-maintenance and reproduction. These energies are met by various antagonistic energies — those of geologic origin, those of climate, of wild animals, of other human races with whom there is enmity or competition. And the tracts the society spreads over, are those in which there is the smallest total of antagonisms while they yield the best supply of food and other materials which further the genesis of energies. For these reasons it happens that fertile valleys where water and vegetal products abound, are early peopled. Sea-shores, too, supplying much 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 warm 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 wars that result — the conquests of weaker tribes or nations, and the overrunning of their territories by the victors, are instances of social movements taking place in the directions of least resistance. Nor do the conquered peoples, when they escape extermination or enslavement, fail to show us movements which are similarly determined. For, migrating as they do to less fertile regions — taking refuge in deserts or among mountains — moving in directions where the resistances to social growth are 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 also may be thus interpreted. Localities naturally fitted for producing particular commodities — that is, localities in which such commodities are got at the least cost of energy — that is, localities in which the desires for these commodities meet with the least resistance; become localities 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 a dominant industry. Where wheat cannot be economically produced, oats, or rye, or maize, or potatoes, or rice, is the agricultural staple. Along sea-shores men support themselves with least effort by catching fish, and hence fishing becomes the occupation. And in places which are rich in coal or metallic ores, the population, finding that labour expended in raising these materials brings a larger return of food and clothing than when otherwise expended, 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 other things. Moreover, in deciding what commodity to produce, each citizen was, as he is at the present day, guided in the same manner. In choosing those forms of activity which their special circumstances and special faculties dictate, the social units severally move towards the objects of their desires in the directions which present to them the fewest obstacles. The process of transfer which commerce presupposes, 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 outbalanced by cost of transit — when the distance is so small and the route so easy that the labour of conveyance plus the labour of production is less than the labour of production in the consuming district, transfer commences. Movement in the direction of least resistance is also seen in the establishment of the channels along which intercourse takes place. At the outset, when goods are carried on the backs of men and horses, the paths chosen are those which combine shortness with levelness and freedom from obstacles — those which are achieved with the smallest exertion. And in the subsequent formation of each highway, the course taken is that which deviates horizontally from a straight line so far only as is needful to avoid vertical deviations entailing greater labour in draught. The smallest total of obstructive forces determines the route, even in seemingly exceptional cases; as where a detour is made to avoid the opposition of a landowner. All subsequent improvements, ending in macadamized roads, canals, and railways, which reduce the antagonism of friction and gravity to a minimum, exemplify the same truth. After there comes to be a choice of roads between one point and another, we still see that the road chosen is that along which the cost of transit is the least: cost being the measure of resistance. When 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 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; and so growth of the social organism takes place where the resistance is 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, exhibit movements taking place in directions where they are met by the smallest totals 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 thus interpret large interest or large surplus to imply labour expended with the greatest results — and if labour expended with the greatest results means muscular action so directed as to evade obstacles as far as possible; we see that all these commercial phenomena imply complicated motions set up along lines of least resistance.

Social movements of these various orders severally conform to the two derivative principles named at the outset. In the first place we see that, once set up in given directions, such movements, like all others, tend to produce continuance in these directions. A commercial mania or panic, a current of commodities, a social custom, a political agitation, or a popular delusion, maintains its course long after its original cause 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 various processes through which a man is returned to Parliament, or through which afterwards, by an Act he finally gets passed, certain doings of his fellow-citizens are changed, show this.

§81. And now of the general truth above set forth what is our ultimate evidence? Must we accept it simply as an empirical generalization? or may it be established as a corollary from a still deeper truth? The reader will anticipate the answer.

Suppose several tractive forces, variously directed, to be acting on a given body. By what is known 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. Such a resultant force, as it is called, may be found for any pair of forces throughout the group. Similarly, for any pair of resultants a single resultant may be found. And by repeating this course, all of them may be reduced to two. If these two are equal and opposite — that is, if there is no line of greatest traction, motion does not arise. If they are opposite but not equal, motion arises in the direction of the greater. If they are neither equal nor opposite, motion arises in the direction of their resultant. For in either of these cases there is an unantagonized force in one direction. And this residuary force 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; and this involves a denial of the persistence of force. If in place of tractions we take resistances, the argument equally holds; and 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 its truth becomes still more obvious. Suppose two weights suspended over a pulley, or suppose two men pulling against each other. The heavier weight will descend, and the stronger man will draw the weaker towards him. If 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. But if of two opposing tractions we can know one as greater than the other only by the motion it generates in its own direction, then the assertion that motion occurs in the direction of greatest traction is a truism. When, going a step further back, we seek a warrant for the assumption that of the two conflicting forces, the one which produces motion in its own direction is the greatest, 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 number 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.

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 that kind of force called energy; since it is an assertion that the energy 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 a like inference is necessitated. Here however the actions are complicated. A liquid that follows a certain channel through or over a solid, as water along the Earth's surface, loses part of its motion in the shape of heat, through friction and collision with the matters forming its bed. A further amount may be absorbed in overcoming the forces it liberates; as when it loosens a mass which falls into its channel. But after these deductions, any further deduction from the energy embodied in the motion of the water, is at the expense of a reaction on the channel which diminishes its obstructive power: such reaction being shown in the motion acquired by the detached portions carried away. The cutting out of river-courses perpetually illustrates 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. There are conceivable anomalies. Some chemical change wrought along the route traversed, may render it less fit than before for conveying a current. Or some obstructive form of force may be generated; as in metals, the conducting power of which is, for the time, decreased by the heat which the electric current produces. The real question is, however, what structural modification, if any, is produced throughout the matter traversed, apart from incidental disturbing forces — apart from everything but the necessary resistance of the matter: that, namely which results from the inertia of its units. If we confine our attention to that part of the motion which, escaping transformation, continues its course, then the persistence of force necessitates that as much of it as is taken up in changing the positions of the units, must leave these by so much less able to obstruct subsequent motion in the same direction.

Thus in all the changes displayed by the Solar System, in all those which are going on in the Earth's crust, in all processes of organic development and function, in all mental actions and the effects they work on the body, and in all modifications of structure and activity in societies, the implied movements are of necessity determined in the manner above set forth. The truth set forth holds not only of one class, or of some classes, of phenomena, but it is among those universal truths by which our knowledge of phenomena in general is unified.

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