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: --

"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, be seen by the motion of a body rising or falling through water. A bubble rising rapidly in water describes a spiral closely resembling a corkscrew, and a body of moderate specific gravity dropped into water may be seen to fall in a curved direction, the spiral tendency of which may be distinctly observed. * * * In this prevailing spiral form of organic bodies, therefore, it appears to me, that there is presented a strong prima facie case for the view I have maintained. * * * The spiral form of the branches of many trees is very apparent, and the universally spiral arrangement of the leaves around the stem of plants needs only to be referred to. * * * The heart commences as a spiral turn, and in its perfect form a manifest spiral may be traced through the left ventricle, right ventricle, right auricle, left auricle, and appendix. And what is the spiral turn in which the heart commences but a necessary result of the lengthening, under a limit, of the cellular mass of which it then consists? * * *

"Every one must have noticed the peculiar curling up of the young leaves of the common fern. The appearance is as if the leaf were rolled up, but in truth this form is merely a phenomenon of growth. The curvature results from the increase of the leaf, it is only another form of the wrinkling up, or turning at right angles by extension under limit.

"The rolling up or imbrication of the petals in many flower-buds is a similar thing; at an early period the small petals may be seen lying side by side; afterwards growing within the capsule, they become folded round one another. * * *

"If a flower-bud be opened at a sufficiently early period, the stamens will be found as if moulded in the cavity between the pistil and the corolla, which cavity the anthers 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, 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.(*)
<fn* 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 reasons given in the preface to that work.>

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.*
<*For details see a paper on "The Physiology of Laughter," published in Macmillan's Magazine for March, 1860, and reprinted in Essays, vol. II.>

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.

Chapter 10   The Rhythm of Motion

§82. When the pennant of a vessel lying becalmed shows the coming breeze, it does so by gentle undulations which 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 whistle of the wind proves 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 movements. 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 t 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. If we study the action and reaction 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. Kindred phenomena may be observed when 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 [of the primitive type], which instead of a smooth rotation falls into a rapid rhythm that sends a tremor through the whole vessel. The sound produced when a bow is drawn over a violin-string, shows us vibrations accompanying the movement of 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 acquires oscillations, both lateral and vertical. Even where a moving mass 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, placed on a table, to be convinced that each pulsation of the heart gives a jar to surrounding things. Motions of another order -- those namely of the ethereal medium -- teach us the same thing. Every fresh discovery confirms the hypothesis that light consists of undulations, and that the rays of heat have a like fundamental nature: their undulations differing from those of light only in their comparative lengths. Nor do the movements of electricity fail to furnish us with illustrations; though 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 by its stratified appearance that the current is not uniform, but comes in gushes of greater and lesser intensity. Should it be said that 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 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 eccentric movement round 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.* <* After having for some years supposed myself alone in the belief that all motion is rhythmical, I discovered that my friend Professor Tyndall also held this doctrine.>

Rhythm is very generally not simple but compound. There are usually at work various forces, causing undulations differing in rapidity; and hence besides the primary rhythms there arise secondary rhythms, produced by the periodic coincidence and opposition 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 phenomena due to what is called interference of light, result from the periodic agreement and disagreement of ethereal 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 rhythms. 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 side, 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 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, 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.

Rhythm results wherever there is a conflict of forces not in equilibrium. If the antagonist forces at any point are balanced, there is rest; and in the absence of motion there can of course be no rhythm. But if instead of a balance there is an excess of force in one direction -- if, as necessarily follows, motion is set up in that direction; then for the motion to continue uniformly in that direction, the moving matter must, notwithstanding its unceasing change of place, present unchanging relations to the sources of force by which its motion is produced and opposed. This however is impossible. Every further transfer through space, by altering the ratio between the forces concerned, must prevent uniformity of movement. And if the movement cannot be uniform, then (save where it is destroyed, or rather transformed, as by the collision of two bodies travelling through space in a straight line towards each other) the only alternative is rhythm.

A secondary conclusion must not be omitted. In the last chapter we saw that motion is never absolutely rectilinear; and here it remains to add that, as a consequence, rhythm is necessarily incomplete. A truly rectilinear rhythm can arise only when the opposing forces are in exactly the same line, and the probabilities against this are infinitely great. To generate a perfectly circular rhythm, the two forces concerned must be exactly at right angles to each other, and must have exactly a certain ratio; and against this the probabilities are likewise infinitely great. All other proportions and directions of the two forces (omitting such as produce parabolas or hyperbolas) will produce an ellipse of greater or less eccentricity. And when, as always happens, above two forces are engaged, the curve described must be more complex, and cannot exactly repeat itself. So that throughout nature, this action and reaction of forces never brings about a complete return to a previous state. Where the movement is that of some aggregate whose units are partially independent, regularity is no longer traceable. And on the completion of any periodic change, the degree in which the state arrived at differs from the state departed from, is marked in proportion as the influences at work are numerous.

§83. That spiral arrangement common among the more structured nebulae, shows us the progressive establishment of revolution, and therefore of rhythm, in those remote spaces which the nebulae occupy. Double stars, moving in more or less eccentric orbits round common centres of gravity in periods some of which are now ascertained, exhibit settled rhythmical actions in distant parts of our Sidereal System.

The periodicities of the planets, satellites, and comets, familiar though they are, must be named as so many grand illustrations of this general law of movement. But besides the revolutions of these bodies in their orbits (all more or less eccentric), the Solar System presents us with rhythms of a less manifest and more complex kind. In each planet and satellite there is the revolution of the nodes -- a slow change in the position of the orbit-plane, which after completing itself commences afresh. There is the gradual alteration in the length of the axis major of the orbit, and also of its eccentricity: both of which are rhythmical alike in the sense that they alternate between maxima and minima, and in the sense that the progress from one extreme to the other is not uniform, but is made with fluctuating velocity. Then, too, there is the revolution of the line of apsides round the heavens -- not regularly, but through complex oscillations. And, further, we have changes in the directions of the planetary axes -- that known as nutation, and that larger gyration which, in the case of the Earth, causes the precession of the equinoxes. These rhythms, already more or less compound, are compounded with one another. One of the simplest re-compoundings is seen in the secular acceleration and retardation of the moon, consequent on the varying eccentricity of the Earth's orbit. Another, having more important consequences, results from the changing direction of the axis of rotation in a planet having a decidedly eccentric orbit. The Earth furnishes the best example. During a certain long period it presents more of its northern than of its southern hemisphere to the Sun at the time of nearest approach to him; and then again, during a like period, presents more of its southern hemisphere than of its northern: a recurring coincidence which involves an epoch of 21,000 years, during which each hemisphere goes through a cycle of temperate seasons and seasons that are extreme in their heat and cold. Nor is this all. There is even a variation of this variation. For the summers and winters of the whole Earth become more or less strongly contrasted, as the eccentricity of its orbit increases or decreases. Hence during the increase of the eccentricity, the epochs of moderately contrasted seasons and epochs of strongly contrasted seasons, through which alternately each hemisphere passes, must grow more and more different in the degrees of their contrasts; and contrariwise during decrease of the eccentricity. So that in those movements of the Earth which determine the varying quantities of light and heat which any portion of it receives from the Sun, there goes on a quadruple rhythm: that causing day and night; that causing summer and winter; that causing the changing position of the axis at perihelion and aphelion, taking 21,000 years to complete; and that causing the variation of the orbit's eccentricity, gone through in millions of years.

§84. Those terrestrial processes directly depending on the solar heat, of course exhibit a rhythm that corresponds to the periodically changing amount of heat which each part of the Earth receives. The simplest, though the least obtrusive, instance is supplied by the magnetic variations. In these there is a diurnal increase and decrease, an annual increase and decrease, and a decennial increase and decrease: the latter answering to a period during which the solar spots become alternately abundant and scarce. And besides known variations there are probably others corresponding to the astronomical cycles just described. More obvious examples are furnished by the movements of the ocean and the atmosphere. Marine currents from the equator to the poles above, and from the poles to the equator beneath, show us an unceasing backward and forward motion throughout this vast mass of water -- a motion varying in amount according to the seasons, and compounded with smaller like motions of local origin. The similarly-caused general currents in the air, have similar annual variations similarly modified. Irregular as they are in detail, we still see in the monsoons and other tropical atmospheric disturbances, or even in our autumn equinoctial gales and spring east winds, a periodicity sufficiently decided. Again, we have an alternation of times during which evaporation predominates with times during which condensation predominates; shown in the tropics by strongly marked rainy seasons and seasons of drought, and in the temperate zones by changes of which the periodicity is less definite. The diffusion and precipitation of water furnish us with examples of rhythm of a more rapid kind. During wet weather lasting over some weeks, the tendency to condense, though greater than the tendency to evaporate, does not show itself in continuous rain; but the period is made up of rainy days and days which are wholly or partially fair. Nor is it in this rude alteration only that the law is manifested. During any day throughout this wet weather a minor rhythm is often traceable; and especially so when the tendencies to evaporate and to condense are nearly balanced. Among mountains this minor rhythm and its causes may be studied to advantage. Moist winds, which do not precipitate their contained water in passing over the comparatively warm lowlands, lose so much heat when they reach the cold mountain peaks, that condensation rapidly takes place. Water, however, in passing from the gaseous to the liquid state, gives out heat; and therefore the resulting clouds are warmer than the air that precipitates them, and much warmer than the high rocky surfaces round which they fold themselves. Hence in the course of the storm, these high rocky surfaces are raised in temperature, partly by radiation from the enwrapping cloud, partly by contact of the falling rain-drops. Consequently they no longer lower so much the temperature of the air passing over them, and cease to precipitate its contained water. The clouds break; the sky begins to clear; and a gleam of sunshine promises that the day is going to be fine. But the small supply of heat which the cold mountains' tops have received, is soon lost: especially when partial dispersion of the clouds permits radiation into space. Very soon, therefore, these elevated surfaces, becoming as cold as at first, begin again to condense the vapour in the air above, and there comes another storm, followed by the same effects as before. In lower lands this action and reaction is less conspicuous, because the contrast of temperatures is less marked. Even here, however, it may be traced, not only on showery days, but on days of continuous rain; for in these we do not see uniformity: always there are fits of harder and gentler rain.

Of course these meteorologic rhythms involve corresponding rhythms in the changes wrought by wind and water on the Earth's surface. Variations in the quantities of sediment brought down by rivers that rise and fall with the seasons, must cause variations in the resulting strata -- alternations of colour or quality in the successive laminae. Beds formed from the detritus of shores worn down and carried away by the waves, must similarly show periodic differences answering to the periodic winds of the locality. In so far as frost influences the rate of denudation, its recurrence is a factor in the rhythm of sedimentary deposits. And the geological changes produced by glaciers must similarly have their alternating periods of greater and less intensity.

There is some evidence that modifications in the Earth's crust due to igneous action have an indefinite periodicity. Volcanic eruptions are not continuous but intermittent, and as far as the data enable us to judge, have something like an average rate of recurrence, as witness the case of Kilauea; which rate is complicated by rising into epochs of greater activity and falling into epochs of comparative quiescence. So too, according to Mallet, is it with earthquakes and the elevations or depressions caused by them. Sedimentary formations yield indirect evidence. At the mouth of the Mississippi the alternation of strata gives decisive proof of successive sinkings of the surface, that have taken place at tolerably equal intervals. Everywhere in the extensive groups of conformable strata that imply small subsidences recurring with a certain average frequency, we see a rhythm in the action and reaction between the Earth's crust and its contents -- a rhythm compounded with those slower ones shown in the termination of groups of strata, and the commencement of other groups not conformable to them.

§85. Perhaps nowhere are illustrations of rhythm so numerous and so manifest as among the phenomena of life. Plants do not, indeed, usually show us any decided periodicities, save those determined by day and night and by the seasons. But in animals we have a great variety of movements in which the alternation of opposite extremes goes on with all degrees of rapidity. The swallowing of food is effected by a wave of constriction passing along the oesophagus; its digestion is largely aided by a muscular action of the stomach that is also undulatory; and the peristaltic motion of the intestines is of like nature. The blood obtained from this food is propelled in pulses, and is aerated by lungs that alternately contract and expand. All locomotion results from oscillating movements. Even where it is apparently continuous, as in many minute forms, the microscope proves the vibration of cilia to be the agency by which the creature is moved smoothly forwards.

Primary rhythms of the organic actions are compounded with secondary ones of longer duration. We see this in the periodic need for food, and in the periodic need for repose. Each meal induces a more rapid rhythmic action of the digestive organs; the pulsation of the heart is accelerated; the inspirations become more frequent. During sleep, on the contrary, these several movements slacken. So that in the course of the twenty-four hours, those small undulations of which the different kinds of organic action are constituted, undergo one long wave of increase and decrease, complicated with several minor waves. Experiments have shown that there are still slower rises and falls of functional activity. Waste and assimilation are not balanced by every meal, but one or other maintains for some time a slight excess; so that a person in ordinary health undergoes an increase and decrease of weight during recurring intervals of tolerable equality. There are oscillations of vigour too. Even men in training cannot be kept stationary at their highest power, but when they have reached it begin to retrograde. Further evidence of rhythm in the vital movements is furnished by invalids. Sundry disorders are named from the intermittent character of their symptoms. Even where the periodicity is not very marked, it is mostly traceable. Patients rarely if ever become uniformly worse; and convalescents have usually their days of partial relapse or of less decided advance.

Aggregates of living creatures illustrate the general truth in other ways. If each species of organism be regarded as a whole, it displays two kinds of rhythm. Life as it exists in every member of such species, is an extremely complex kind of movement, more or less distinct from the kinds of movement which constitute life in other species. This extremely complex kind of movement begins, rises to its climax, declines, and ceases in death. And every individual in each generation thus exhibits a wave of that peculiar activity characterizing the species as a whole. The other form of rhythm is seen in that variation of number which each tribe of animals and plants undergoes. Throughout the unceasing conflict between the tendency of a species to increase and the antagonistic tendencies, there is never an equilibrium: one always predominates. In the case even of a cultivated plant or domesticated animal, where artificial means are used to maintain the supply at a uniform level, oscillations of abundance and scarcity cannot be avoided. And among creatures uncared for by man, such oscillations are usually more marked. After a race of organisms has been greatly thinned by enemies or innutrition, its surviving members become more favourably circumstanced than usual. During the decline in their numbers their food has grown relatively abundant, while their enemies have somewhat diminished from want of prey. The conditions thus remain for some time favourable to their increase, and they multiply rapidly. By-and-by their food is rendered relatively scarce, at the same time that their enemies have become more numerous; and the destroying influences being thus in excess, their number begins to diminish again. Yet one more rhythm, extremely slow, may be traced in the phenomena of Life under their most general aspect. The researches of palaeontologists show that there have been going on, during the vast period of which our sedimentary rocks bear record, successive changes of organic forms. Species have appeared, become abundant, and then disappeared. Genera, at first constituted of but few species, have for a time gone on growing more multiform, and then have declined in the number of their subdivisions: leaving at last but one or two, or none at all. During longer epochs whole orders have thus arisen, culminated, and dwindled away. And even those wider divisions containing many orders have similarly undergone a gradual rise, a high tide, and a long-continued ebb. The stalked Crinoidea, for example, which during the carboniferous epoch became abundant, have almost disappeared: only a single species being extant. Once a large family, the Brachiopoda have now become rare. The shelled Cephalopods, at one time dominant among the inhabitants of the ocean, both in number of forms and of individuals, are in our day nearly extinct. And after an "age of reptiles" has come an age in which reptiles have been in great measure supplanted by mammals. Thus Life on the Earth has not progressed uniformly, but in immense undulations.

§86. It is not manifest that changes of consciousness are in any sense rhythmical. Yet here, too, analysis proves both that the mental state existing at any moment is not uniform, but is decomposable into rapid oscillations, and also that mental states pass through longer intervals of increasing and decreasing intensity.

Though while attending to any single sensation, or any group of related sensations constituting the consciousness of an object, we seem to remain in a persistent and homogeneous condition of mind, self-examination shows that this apparently unbroken mental state is traversed by many minor states, in which various other sensations and preceptions are rapidly presented and disappear. As thinking consists in the establishment of relations, it follows that continuance of it in any one state to the entire exclusion of other states, would be a cessation of thought, that is, of consciousness. So that any seemingly uniform feeling, say of pressure, really consists of portions of that feeling perpetually recurring after momentary intrusions of other feelings and ideas -- quick thoughts concerning the place where it is felt, the external object producing it, its consequences, etc. Much more conspicuous rhythms, having longer waves, are seen during the outflow of emotion into dancing, poetry and music. The current of mental energy expended in one of these modes of bodily action, is not continuous but falls into successive pulses. The measure of a dance is produced by the alternation of strong muscular contractions with weaker ones; and, save in measures of the simplest order, such as are found among barbarians and children, this alternation is compounded with longer rises and falls in the degree of muscular excitement. Poetry is a form of speech in which the emphasis is regularly recurrent, that is,in which the muscular effort of pronunciation has definite periods of greater and less intensity: periods that are complicated with others answering to the successive verses. Music more variously exemplifies the law. There are the recurring bars, in each of which there is a primary and a secondary beat. There is the alternate increase and decrease of muscular strain implied by the ascents and descents to the higher and lower notes -- ascents and descents composed of smaller waves, breaking the rises and falls of the larger ones, in a mode peculiar to each melody. And then we have, further, the alternations of piano and forte passages. That these several kinds of rhythm, characterizing aesthetic expression, are not, in the common sense of the word, artificial, but are intenser forms of an undulatory movement habitually generated by feeling in its bodily discharge, is shown by the fact that they are all traceable in ordinary speech, which in every sentence has its primary and secondary emphases, and its cadence containing a chief rise and fall complicated with subordinate rises and falls. Still longer undulations may be observed by every one in himself and in others, on occasions of extreme pleasure or extreme pain. During hours in which bodily pain never actually ceases, it has its variations of intensity -- fits or paroxysms; and then after these intervals of suffering there usually come intervals of comparative ease. Moral pain has the like smaller and larger waves. One possessed by intense grief does not utter continuous moans, or shed tears with an equable rapidity; but these signs of passion come in recurring bursts. Then after a time during which such stronger and weaker waves of emotion alternate, there comes a calm -- a time of comparative deadness; after which dull sorrow rises afresh into acute anguish, with its series of paroxysms. Similarly great delight, as shown by children who display it without control, undergoes variations in intensity: there are fits of laughter and dancing about, separated by pauses in which smiles, and other slight manifestations of pleasure, suffice to discharge the lessened excitement. Nor are there wanting evidences of mental undulations greater in length than any of these. We continually hear of moods which recur at intervals. Many persons have their days of vivacity and days of depression. Others have periods of industry following periods of idleness; and times at which particular subjects or tastes are cultivated with zeal, alterating with times at which they are neglected. Respecting which slow oscillations the only qualification to be made is, that being affected by numerous influences they are irregular.

§87. In nomadic societies the changes of place, determined by exhaustion or failure of the supply of food, are periodic; and in many cases recur with the seasons. Each tribe that has become partially fixed in its locality, goes on increasing until, under pressure of hunger, there results migration of some part of it -- a process repeated at intervals. From such excesses of population, and such waves of migration, come conflicts with other tribes; which are also increasing and tending to diffuse themselves. Their antagonisms result not in a uniform motion, but in an intermittent one. War, exhaustion, recoil-peace, prosperity, and renewed aggression: -- see here the alteration as occurring among both savage and civilized peoples. And irregular as is this rhythm, it is not more so than the different sizes of the societies, and the involved causes of variation in their strengths, would lead us to anticipate.

Passing from external to internal social changes, we meet this backward and forward movement under many forms. In commercial currents it is especially conspicuous. Exchange during early times is carried on mainly at fairs, held at long intervals. The flux and reflux of people and commodities which each of these exhibits, becomes more frequent as national development brings greater social activity. The rapid rhythm of weekly markets begins to supersede the slow rhythm of fairs. And eventually exchange becomes at some places so active, as to bring about daily meetings of buyers and sellers -- a daily wave of accumulation and distribution of cotton, or corn, or capital. In production and consumption there are undulations almost equally obvious. Supply and demand are never completely adjusted, but each, from time to time in excess, leads presently to excess of the other. Farmers whO have one season grown wheat abundantly, are disgusted with the consequent low price, and next season, sowing a much smaller quantity, bring to market a deficient crop; whence follows a converse effect. Consumption undergoes parallel undulations that need not be specified. The balancing of supplies between different districts, too, entails oscillations. A place at which some necessary of life is scarce, becomes a place to which currents of it are set up from other places where it is relatively abundant; and these currents lead to a wave of accumulation where they meet -- a glut: whence follows a recoil -- a partial return of the currents. But the undulatory character of these actions is best seen in the rises and falls of prices. These, when tabulated and reduced to diagrams, show us in the clearest manner how commercial movements are compounded of oscillations of various magnitudes. The price of consols or the price of wheat, as thus represented, is seen to undergo vast ascents and descents having highest and lowest points that are reached only in the course of years. These largest waves of variation are broken by lesser ones extending over periods of months. On these come others severally having a week or two's duration. And were the changes marked in greater detail, we should see the smaller undulations that take place each day and the still smaller ones which brokers telegraph from hour to hour. The whole outline would show a complication like that of a vast ocean-swell, having on its surface large billows, which themselves bear waves of moderate size, covered by wavelets, that are roughened by a minute ripple. Similar diagrammatic representations of births, marriages, and deaths, of disease, of crime, of pauperism, exhibit involved conflicts of rhythmical motions throughout society under these several aspects.

There are like traits in social changes of more complex kinds. Both in England and on the Continent the actions and reactions of political progress are now generally recognized. Religion has its periods of exaltation and depression -- generations of belief and self-mortification, following generations of indifference and laxity. There are poetical epochs, and epochs in which the sense of the beautiful seems almost dormant. Philosophy, after having been awhile dominant, lapses for a long season into neglect, and then again slowly revives. Each concrete science has its eras of deductive reasoning, and its eras in which attention is chiefly directed to collecting and colligating facts. And that in such minor phenomena as those of fashion, there are oscillations from one extreme to the other, is a trite observation.

As may be foreseen, social rhythms well illustrate the irregularity that results from combination of many causes. Where the variations are those of one simple element in national life, as the supply of a particular commodity, we do indeed witness a return, after many involved movements, to a previous state -- the price becomes what it was before: implying a like relative abundance. But where the action is one into which many factors enter, there is never a complete recurrence. A political reactIon never brings round just the old form of things. The rationalism of the present day differs widely from the rationalism of the last century. And though fashion from time to time revives extinct types of dress, these always reappear with decided modifications.

§88. Rhythm being thus manifested in all forms of movement, we have reason to suspect that it is determined by some primordial condition to action in general. The tacit implication is that it is deducible from the persistence of force. This we shall find to be the fact.

When the prong of a tuning-fork is pulled on one side by the finger, some extra tension is produced among its cohering particles, which resist any force that draws them out of their state of equilibrium. As much force as the finger exerts, so much opposing force arises among the cohering particles. Hence, when the prong is liberated, it is urged back by a force equal to that used in detecting it. When, therefore, the prong reaches its original position, the force impressed during its recoil, has generated in it a corresponding amount of momentum -- an amount nearly equivalent to the force originally impressed (nearly, we must say, because a certain portion has gone in giving motion to the air, and a certain other portion has been transformed into heat). This momentum carries the prong beyond the position of rest, nearly as far as it was originally drawn in the reverse direction; until at length, being gradually used up in producing an opposing tension among the particles, it is all lost. This opposing tension then generates a second recoil, and so on continually: the vibration eventually ceasing only because at each movement a certain amount of force goes in creating atmospheric and ethereal undulations. Now evidently this repeated action and reaction is a consequence of the persistence of force. The force exerted by the finger in bending the prong cannot disappear. Under what form then does it exist? It exists under the form of that cohesive tension which it has generated among the particles. This cohesive tension cannot cease without an equivalent result. What is its equivalent result? The momentum generated in the prong while being carried back to its position of rest. This momentum too -- what becomes of it? It must either continue as momentum, or produce some correlative force of equal amount. It cannot continue as momentum, since change of place is resisted by the cohesion of the parts; and thus it gradually disappears by being transformed into tension among these parts. This is retransformed into the equivalent momentum; and so on continuously. If, instead of motion that is directly antagonized by the cohesion of matter, we consider motion through space, as of a comet, the same truth presents itself under another form. Though while it is approaching the Sun no opposing force seems at work, and therefore no cause of rhythm, yet its own accumulated momentum must eventually carry the moving body beyond the attracting body; and so must become a force in conflict with that which generated it. This force cannot be destroyed, but it can have its direction changed by the still continued attraction: the result being that a passage round the attracting body is followed by a retreat during which this embodied force, gradually becoming non-apparent, is transformed into gravitative strain, until all of it having been thus transformed there begins a return from aphelion.

Before ending, two qualifications must be made. As the rhythm of motion itself postulates continuity of motion, it cannot be looked for when motion has suddenly become invisible. A hint tacitly given in §82 implies that what we may call a fragmentary motion -- a motion which under its perceptible form is suddenly brought to an end -- cannot under that form exhibit rhythm: instance the stoppage of a hammer by an anvil. In such cases, however, we observe that this non-continuous motion is transformed into motions that are continuous and rhythmical -- the sound-waves, the ether-waves of the heat generated, and the waves of vibration sent through the mass struck: the rhythms of these motions continuing as long as the motions themselves do.

The other qualification is that the motions shall be those occurring within a closed system, such as is constituted by our own Sun, planets, satellites, and periodic comets. If a body approaching a centre of attraction from remote space, has any considerable proper motion not towards that centre, this body, passing round it, may take a course which negatives return -- an hyperbola. I say an hyperbola because the chances against a parabolic course are infinity to one.

But bearing in mind these two qualifications, of which the last may be considered almost nominal, we may conclude that under the conditions existing within our Solar System and among terrestrial phenomena, rhythm, everywhere arising from the play of antagonist forces, is a corollary from the persistence of force.