University of Virginia Library

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.

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.

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