* * * * * § 91. As in individual animals, inclusive of man, motion follows lines of least resistance, it is to be inferred that among aggregations of men, the like will hold good. The changes in a society, being due to the joint actions of its members, the courses of such changes will be determined as are those of all other changes wrought by composition of forces.
Thus when we contemplate a society as an organism, and observe the direction of its growth, we find this direction to be that in which the average of opposing forces is the least. Its units have energies to be expended in self-maintenance and reproduction. These energies are met by various environing energies that are antagonistic to them—those of geological origin, those of climate, of wild animals, of other human races with whom they are at enmity or in competition. And the tracts the society spreads over, are those in which there is the smallest total antagonism. Or, reducing the matter to its ultimate terms, we may say that these social units have jointly and severally to preserve themselves and their offspring from those inorganic and organic forces which are ever tending to destroy them (either indirectly by oxidation and by undue abstraction of heat, or directly by bodily mutilation); that these forces are either counteracted by others which are available in the shape of food, clothing, habitations, and appliances of defence, or are, as far as may be, eluded; and that population spreads in whichever directions there is the readiest escape from these forces, or the least exertion in obtaining the materials for resisting them, or both. For these reasons it happens that fertile valleys where water and vegetal produce abound, are early peopled. Sea-shores, too, supplying a large amount of easily-gathered food, are lines along which mankind have commonly spread. The general fact that, so far as we can judge from the traces left by them, large societies first appeared in those tropical regions where the fruits of the earth are obtainable with comparatively little exertion, and where the cost of maintaining bodily heat is but slight, is a fact of like meaning. And to these instances may be added the allied one daily furnished by emigration; which we see going on towards countries presenting the fewest obstacles to the self-preservation of individuals, and therefore to national growth. Similarly with that resistance to the movements of a society which neighbouring societies offer. Each of the tribes or nations inhabiting any region, increases in numbers until it outgrows its means of subsistence. In each there is thus a force ever pressing outwards on to adjacent areas—a force antagonized by like forces in the tribes or nations occupying those areas. And the ever-recurring wars that result—the conquests of weaker tribes or nations, and the over-running of their territories by the victors, are instances of social movements taking place in the directions of least resistance. Nor do the conquered peoples, when they escape extermination or enslavement, fail to show us movements that are similarly determined. For migrating as they do to less fertile regions—taking refuge in deserts or among mountains—moving in a direction where the resistance to social growth is comparatively great; they still do this only under an excess of pressure in all other directions: the physical obstacles to self-preservation they encounter, being really less than the obstacles offered by the enemies from whom they fly.
Internal social movements may also be thus interpreted. Localities naturally fitted for producing particular commodities—that is, localities in which such commodities are got at the least cost of force—that is, localities in which the desires for these commodities meet with the least resistance; become localities especially devoted to the obtainment of these commodities. Where soil and climate render wheat a profitable crop, or a crop from which the greatest amount of life-sustaining power is gained by a given quantity of effort, the growth of wheat becomes the dominant industry. Where wheat cannot be economically produced, oats, or rye, or maize, or rice, or potatoes, is the agricultural staple. Along sea-shores men support themselves with least effort by catching fish; and hence choose fishing as an occupation. And in places that are rich in coal or metallic ores, the population, finding that labour devoted to the raising of these materials brings a larger return of food and clothing than when otherwise directed, becomes a population of miners. This last instance introduces us to the phenomena of exchange; which equally illustrate the general law. For the practice of barter begins as soon as it facilitates the fulfilment of men’s desires, by diminishing the exertion needed to reach the objects of those desires. When instead of growing his own corn, weaving his own cloth, sewing his own shoes, each man began to confine himself to farming, or weaving, or shoemaking; it was because each found it more laborious to make everything he wanted, than to make a great quantity of one thing and barter the surplus for the rest: by exchange, each procured the necessaries of life without encountering so much resistance. Moreover, in deciding what commodity to produce, each citizen was, as he is at the present day, guided in the same manner. For besides those local conditions which determine whole sections of a society towards the industries easiest for them, there are also individual conditions and individual aptitudes which to each citizen render certain occupations preferable; and in choosing those forms of activity which their special circumstances and faculties dictate, these social units are severally moving towards the objects of their desires in the directions which present to them the fewest obstacles. The process of transfer which commerce pre-supposes, supplies another series of examples. So long as the forces to be overcome in procuring any necessary of life in the district where it is consumed, are less than the forces to be overcome in procuring it from an adjacent district, exchange does not take place. But when the adjacent district produces it with an economy that is not out-balanced by cost of transit—when the distance is so small and the route so easy that the labour of conveyance plus the labour of production is less than the labour of production in the consuming district, transfer commences. Movement in the direction of least resistance is also seen in the establishment of the channels along which intercourse takes place. At the outset, when goods are carried on the backs of men and horses, the paths chosen are those which combine shortness with levelness and freedom from obstacles—those which are achieved with the smallest exertion. And in the subsequent formation of each highway, the course taken is that which deviates horizontally from a straight line so far only as is needful to avoid vertical deviations entailing greater labour in draught. The smallest total of obstructive forces determines the route, even in seemingly exceptional cases; as where a detour is made to avoid the opposition of a landowner. All subsequent improvements, ending in macadamized roads, canals, and railways, which reduce the antagonism of friction and gravity to a minimum, exemplify the same truth. After there comes to be a choice of roads between one point and another, we still see that the road chosen is that along which the cost of transit is the least: cost being the measure of resistance. Even where, time being a consideration, the more expensive route is followed, it is so because the loss of time involves loss of force. When, division of labour having been carried to a considerable extent and means of communication made easy, there arises a marked localization of industries, the relative growths of the populations devoted to them may be interpreted on the same principle. The influx of people to each industrial centre, as well as the rate of multiplication of those already inhabiting it, is determined by the payment for labour; that is—by the quantity of commodities which a given amount of effort will obtain. To say that artisans flock to places where, in consequence of facilities for production, an extra proportion of produce can be given in the shape of wages; is to say that they flock to places where there are the smallest obstacles to the support of themselves and families.
Hence, the rapid increase of number which occurs in such places, is really a social growth at points where the opposing forces are the least.
Nor is the law less clearly to be traced in those functional changes daily going on. The flow of capital into businesses yielding the largest returns; the buying in the cheapest market and selling in the dearest; the introduction of more economical modes of manufacture; the development of better agencies for distribution; and all those variations in the currents of trade that are noted in our newspapers and telegrams from hour to hour; exhibit movement taking place in directions where it is met by the smallest total of opposing forces. For if we analyze each of these changes—if instead of interest on capital we read surplus of products which remains after maintenance of labourers; if we so interpret large interest or large surplus to imply labour expended with the greatest results; and if labour expended with the greatest results means muscular action so directed as to evade obstacles as far as possible; we see that all these commercial phenomena are complicated motions set up along lines of least resistance.
Objections of two opposite kinds will perhaps be made to these sociological applications of the law. By some it may be said that the term force as here used, is used metaphorically—that to speak of men as _impelled_ in certain directions by certain desires, is a figure of speech and not the statement of a physical fact. The reply is, that the foregoing illustrations are to be interpreted literally, and that the processes described _are_ physical ones. The pressure of hunger is an actual force—a sensation implying some state of nervous tension; and the muscular action which the sensation prompts is really a discharge of it in the shape of bodily motion—a discharge which, on analyzing the mental acts involved, will be found to follow lines of least resistance. Hence the motions of a society whose members are impelled by this or any other desire, are actually, and not metaphorically, to be understood in the manner shown. An opposite objection may possibly be, that the several illustrations given are elaborated truisms; and that the law of direction of motion being once recognized, the fact that social movements, in common with all others, must conform to it, follows inevitably. To this it may be rejoined, that a mere abstract assertion that social movements must do this, would carry no conviction to the majority; and that it is needful to show _how_ they do it. For social evolution to be interpreted after the method proposed, it is requisite that such generalisations as those of political economy shall be reduced to equivalent propositions expressed in terms of force and motion.
Social movements of these various orders severally conform to the two derivative principles named at the outset. In the first place we may observe how, once set up in given directions, such movements, like all others, tend to continue in these directions. A commercial mania or panic, a current of commodities, a social custom, a political agitation, or a popular delusion, maintains its course for a long time after its original source has ceased; and requires antagonistic forces to arrest it. In the second place it is to be noted that in proportion to the complexity of social forces is the tortuousness of social movements. The involved series of muscular contractions gone through by the artizan, that he may get the wherewithal to buy a loaf lying at the baker’s next door, show us how extreme becomes the indirectness of motion when the agencies at work become very numerous—a truth still better illustrated by the more public social actions; as those which end in bringing a successful man of business, towards the close of his life, into parliament.
* * * * * * * * * * § 92. And now of the general truth set forth in this chapter, as of that dealt with in the last, let us ask—what is our ultimate evidence? Must we accept it simply as an empirical generalization? or is it to be established as a corollary from a still deeper truth? The reader will anticipate the answer. We shall find it deducible from that datum of consciousness which underlies all science.
Suppose several tractive forces, variously directed, to be acting on a given body. By what is known among mathematicians as the composition of forces, there may be found for any two of these, a single force of such amount and direction as to produce on the body an exactly equal effect. If in the direction of each of them there be drawn a straight line, and if the lengths of these two straight lines be made proportionate to the amounts of the forces; and if from the end of each line there be drawn a line parallel to the other, so as to complete a parallelogram; then the diagonal of this parallelogram represents the amount and direction of a force that is equivalent to the two. Such a resultant force, as it is called, may be found for any pair of forces throughout the group. Similarly, for any pair of such resultants a single resultant may be found. And by repeating this course, all of them may be reduced to two. If these two are equal and opposite—that is, if there is no line of greatest traction, motion does not take place. If they are opposite but not equal, motion takes place in the direction of the greater. And if they are neither equal nor opposite, motion takes place in the direction of their resultant. For in either of these cases there is an unantagonized force in one direction. And this residuary force that is not neutralized by an opposing one, must move the body in the direction in which it is acting. To assert the contrary is to assert that a force can be expended without effect—without generating an equivalent force; and by so implying that force can cease to exist, this involves a denial of the persistence of force. It needs scarcely be added that if in place of tractions we take resistances, the argument equally holds; and that it holds also where both tractions and resistances are concerned. Thus the law that motion follows the line of greatest traction, or the line of least resistance, or the resultant of the two, is a necessary deduction from that primordial truth which transcends proof.
Reduce the proposition to its simplest form, and it becomes still more obviously consequent on the persistence of force. Suppose two weights suspended over a pulley or from the ends of an equal-armed lever; or better still—suppose two men pulling against each other. In such cases we say that the heavier weight will descend, and that the stronger man will draw the weaker towards him. But now, if we are asked how we know which is the heavier weight or the stronger man; we can only reply that it is the one producing motion in the direction of its pull. Our only evidence of excess of force is the movement it produces. But if of two opposing tractions we can know one as greater than the other only by the motion it generates in its own direction, then the assertion that motion occurs in the direction of greatest traction is a truism. When, going a step further back, we seek a warrant for the assumption that of the two conflicting forces, that is the greater which produces motion in its own direction, we find no other than the consciousness that such part of the greater force as is unneutralized by the lesser, must produce its effect—the consciousness that this residuary force cannot disappear, but must manifest itself in some equivalent change—the consciousness that force is persistent. Here too, as before, it may be remarked that no amount of varied illustrations, like those of which this chapter mainly consists, can give greater certainty to the conclusion thus immediately drawn from the ultimate datum of consciousness. For in all cases, as in the simple ones just given, we can identify the greatest force only by the resulting motion. It is impossible for us ever to get evidence of the occurrence of motion in any other direction than that of the greatest force; since our measure of relative greatness among forces is their relative power of generating motion. And clearly, while the comparative greatness of forces is thus determined, no multiplication of instances can add certainty to a law of direction of movement which follows immediately from the persistence of force.
From this same primordial truth, too, may be deduced the principle that motion once set up along any line, becomes itself a cause of subsequent motion along that line. The mechanical axiom that, if left to itself, matter moving in any direction will continue in that direction with undiminished velocity, is but an indirect assertion of the persistence of force; since it is an assertion that the force manifested in the transfer of a body along a certain length of a certain line in a certain time, cannot disappear without producing some equal manifestation—a manifestation which, in the absence of conflicting forces, must be a further transfer in the same direction at the same velocity. In the case of matter traversing matter the like inference is necessitated. Here indeed the actions are much more complicated. A liquid that follows a certain channel through or over a solid, as water along the Earth’s surface, loses part of its motion in the shape of heat, through friction and collision with the matters forming its bed. A further amount of its motion may be absorbed in overcoming forces which it liberates; as when it loosens a mass which falls into, and blocks up, its channel. But after these deductions by transformation into other modes of force, any further deduction from the motion of the water is at the expense of a reaction on the channel, which by so much diminishes its obstructive power: such reaction being shown in the motion acquired by the detached portions which are carried away. The cutting out of river-courses is a perpetual illustration of this truth. Still more involved is the case of motion passing through matter by impulse from part to part; as a nervous discharge through animal tissue. Some chemical change may be wrought along the route traversed, which may render it less fit than before for conveying a current. Or the motion may itself be in part metamorphosed into some obstructive form of force; as in metals, the conducting power of which is, for the time, decreased by the heat which the passage of electricity itself generates. The real question is, however, what structural modification, if any, is produced throughout the matter traversed, apart from _incidental_ disturbing forces—apart from everything but the _necessary_ resistance of the matter: that, namely, which results from the inertia of its units. If we confine our attention to that part of the motion which, escaping transformation, continues its course, then it is a corollary from the persistence of force that as much of this remaining motion as is taken up in changing the positions of the units, must leave these by so much less able to obstruct subsequent motion in the same direction.
Thus in all the changes heretofore and at present displayed by the Solar System; in all those that have gone on and are still going on in the Earth’s crust; in all processes of organic development and function; in all mental actions and the effects they work on the body; and in all modifications of structure and activity in societies; the implied movements are of necessity determined in the manner above set forth. Every alteration in the arrangement of parts, constituting Evolution under each of its phases, must conform to this universal principle. Wherever we see motion, its direction must be that of the greatest force. And wherever we see the greatest force to be acting in a given direction, in that direction motion must ensue.
----- Footnote 13: This paragraph is a re-statement, somewhat amplified, of an idea set forth in the _Medico-Chirurgical Review_ for January, 1859 (pp. 189 and 190); and contains the germ of the intended fifth part of the _Principles of Psychology_, which was withheld for the reasons given in the preface to that work.
Footnote 14: For details see a paper on “The Physiology of Laughter,” published in _Macmillan’s Magazine_ for March 1860.
CHAPTER XI. THE RHYTHM OF MOTION.
§ 93. When the pennant of a vessel lying becalmed first shows the coming breeze, it does so by gentle undulations that travel from its fixed to its free end. Presently the sails begin to flap; and their blows against the mast increase in rapidity as the breeze rises. Even when, being fully bellied out, they are in great part steadied by the strain of the yards and cordage, their free edges tremble with each stronger gust. And should there come a gale, the jar that is felt on laying hold of the shrouds shows that the rigging vibrates; while the rush and whistle of the wind prove that in it, also, rapid undulations are generated. Ashore the conflict between the current of air and the things it meets results in a like rhythmical action. The leaves all shiver in the blast; each branch oscillates; and every exposed tree sways to and fro. The blades of grass and dried bents in the meadows, and still better the stalks in the neighbouring corn-fields, exhibit the same rising and falling movement. Nor do the more stable objects fail to do the like, though in a less manifest fashion; as witness the shudder that may be felt throughout a house during the paroxysms of a violent storm. Streams of water produce in opposing objects the same general effects as do streams of air. Submerged weeds growing in the middle of a brook, undulate from end to end. Branches brought down by the last flood, and left entangled at the bottom where the current is rapid, are thrown into a state of up and down movement that is slow or quick in proportion as they are large or small; and where, as in great rivers like the Mississippi, whole trees are thus held, the name “sawyers,” by which they are locally known, sufficiently describes the rhythm produced in them. Note again the effect of the antagonism between the current and its channel. In shallow places, where the action of the bottom on the water flowing over it is visible, we see a ripple produced—a series of undulations. And if we study the action and re-action going on between the moving fluid and its banks, we still find the principle illustrated, though in a different way. For in every rivulet, as in the mapped-out course of every great river, the bends of the stream from side to side throughout its tortuous course constitute a lateral undulation—an undulation so inevitable that even an artificially straightened channel is eventually changed into a serpentine one. Analogous phenomena may be observed where the water is stationary and the solid matter moving. A stick drawn laterally through the water with much force, proves by the throb which it communicates to the hand that it is in a state of vibration. Even where the moving body is massive, it only requires that great force should be applied to get a sensible effect of like kind: instance the screw of a screw-steamer, which instead of a smooth rotation falls into a rapid rhythm that sends a tremor through the whole vessel. The sound which results when a bow is drawn over a violin-string, shows us vibrations produced by the movement of a solid over a solid. In lathes and planing machines, the attempt to take off a thick shaving causes a violent jar of the whole apparatus, and the production of a series of waves on the iron or wood that is cut. Every boy in scraping his slate-pencil finds it scarcely possible to help making a ridged surface. If you roll a ball along the ground or over the ice, there is always more or less up and down movement—a movement that is visible while the velocity is considerable, but becomes too small and rapid to be seen by the unaided eye as the velocity diminishes. However smooth the rails, and however perfectly built the carriages, a railway-train inevitably gets into oscillations, both lateral and vertical. Even where moving matter is suddenly arrested by collision, the law is still illustrated; for both the body striking and the body struck are made to tremble; and trembling is rhythmical movement. Little as we habitually observe it, it is yet certain that the impulses our actions impress from moment to moment on surrounding objects, are propagated through them in vibrations. It needs but to look through a telescope of high power, to be convinced that each pulsation of the heart gives a jar to the whole room. If we pass to motions of another order—those namely which take place in the etherial medium—we still find the same thing. Every fresh discovery confirms the hypothesis that light consists of undulations. The rays of heat, too, are now found to have a like fundamental nature; their undulations differing from those of light only in their comparative length. Nor do the movements of electricity fail to furnish us with an illustration; though one of a different order. The northern aurora may often be observed to pulsate with waves of greater brightness; and the electric discharge through a vacuum shows us by its stratified appearance that the current is not uniform, but comes in gushes of greater and lesser intensity.
Should it be said that at any rate there are some motions, as those of projectiles, which are not rhythmical, the reply is, that the exception is apparent only; and that these motions would be rhythmical if they were not interrupted. It is common to assert that the trajectory of a cannon ball is a parabola; and it is true that (omitting atmospheric resistance) the curve described differs so slightly from a parabola that it may practically be regarded as one. But, strictly speaking, it is a portion of an extremely eccentric ellipse, having the Earth’s centre of gravity for its remoter focus; and but for its arrest by the substance of the Earth, the cannon ball would travel round that focus and return to the point whence it started; again to repeat this slow rhythm. Indeed, while seeming at first sight to do the reverse, the discharge of a cannon furnishes one of the best illustrations of the principle enunciated. The explosion produces violent undulations in the surrounding air. The whizz of the shot, as it flies towards its mark, is due to another series of atmospheric undulations. And the movement to and from the Earth’s centre, which the cannon ball is beginning to perform, being checked by solid matter, is transformed into a rhythm of another order; namely, the vibration which the blow sends through neighbouring bodies.[15] Rhythm is very generally not simple but compound. There are usually at work various forces, causing undulations differing in rapidity; and hence it continually happens that besides the primary rhythms there are secondary rhythms, produced by the periodic coincidence and antagonism of the primary ones. Double, triple, and even quadruple rhythms, are thus generated. One of the simplest instances is afforded by what in acoustics are known as “beats:” recurring intervals of sound and silence which are perceived when two notes of nearly the same pitch are struck together; and which are due to the alternate correspondence and antagonism of the atmospheric waves. In like manner the various phenomena due to what is called interference of light, severally result from the periodic agreement and disagreement of etherial undulations—undulations which, by alternately intensifying and neutralizing each other, produce intervals of increased and diminished light. On the sea-shore may be noted sundry instances of compound rhythm. We have that of the tides, in which the daily rise and fall undergoes a fortnightly increase and decrease, due to the alternate coincidence and antagonism of the solar and lunar attractions. We have again that which is perpetually furnished by the surface of the sea: every large wave bearing smaller ones on its sides, and these still smaller ones; with the result that each flake of foam, along with the portion of water bearing it, undergoes minor ascents and descents of several orders while it is being raised and lowered by the greater billows. A quite different and very interesting example of compound rhythm, occurs in the little rills which, at low tide, run over the sand out of the shingle banks above. Where the channel of one of these is narrow, and the stream runs strongly, the sand at the bottom is raised into a series of ridges corresponding to the ripple of the water. On watching for a short time, it will be seen that these ridges are being raised higher and the ripple growing stronger; until at length, the action becoming violent, the whole series of ridges is suddenly swept away, the stream runs smoothly, and the process commences afresh. Instances of still more complex rhythms might be added; but they will come more appropriately in connexion with the several forms of Evolution, hereafter to be dealt with.