Chapter 7   The Persistence of Relation Among Forces

§63. The first deduction to be drawn from the ultimate universal truth that force persists, is that the relations among forces persist. Supposing a given manifestation of force, under a given form and given conditions, be either preceded by or succeeded by some other manifestation, it must, in all cases where the form and conditions are the same, be preceded by or succeeded by such other manifestation. Every antecedent mode of the Unknowable must have an invariable connexion, quantitative and qualitative, with that mode of the Unknowable which we call its consequent.

For to say otherwise is to deny the persistence of force. If in any two cases there is exact likeness not only between those conspicuous antecedents which we call the causes, but also between those accompanying antecedents which we call the conditions, we cannot affirm that the effects will differ, without affirming either that some force has come into existence or that some force has ceased to exist. If the co-operative forces in the one case are equal to those in the other, each to each, in distribution and amount; then it is impossible to conceive the product of their joint action in the one case as unlike that in the other; without conceiving one or more of the forces to have increased or diminished in quantity; and this is conceiving that force is not persistent.

To impress the truth thus enunciated under its most abstract form, some illustrations will be desirable.

§64. Let two bullets, equal in weights and shapes, be projected with equal energies; then, in equal times, equal distances must be travelled by them. The assertion that one of them will describe an assigned space sooner than the other, though their initial momenta were alike and they have been equally resisted (for if they are unequally resisted the antecedents differ) is an assertion that equal quantities of force have not done equal amounts of work; and this cannot be thought without thinking that some force has disappeared into nothing or arisen out of nothing. Assume, further that during its night one of them has been drawn by the Earth a certain number of inches out of its original line of movement; then the other, which has moved the same distance in the same time, must have fallen just as far towards the Earth. No other result can be imagined without imagining that equal attractions acting for equal times, have produced unequal effects; which involves the inconceivable proposition that some action has been created or annihilated. Again, one of the bullets having penetrated the target to a certain depth, penetration by the other bullet to a smaller depth, unless caused by greater local density in the target, cannot be mentally represented. Such a modification of the consequents without modification of the antecedents, is thinkable only through the impossible thought that something has become nothing or nothing has become something.

It is thus not with sequences only, but also with simultaneous changes and permanent co-existences. Given charges of powder alike in quantity and quality, fired from barrels of the same structure, and propelling bullets of equal weights, sizes, and forms, similarly rammed down;*<* This was written while muzzle-loading was still usual.> and it is a necessary inference that the concomitant actions which make up the explosion, will bear to one another like relations of quantity and quality in the two cases. The proportions among the different products of combustion will be equal. The several amounts of energy taken up in giving momentum to the bullet, heat to the gases, and sound on their escape, will preserve the same ratios. The quantities of light and smoke in the one case will be what they are in the other; and the two recoils will be alike. For no difference, of relation among these concurrent phenomena can be imagined as arising, without imagining it as arising by the creation or annihilation of energy.

That which holds between these two cases must hold among any number of cases; and that which here holds between comparatively simple antecedents and consequents, must hold however involved the antecedents become and however involved the consequents become.

§65. Thus Uniformity of Law, resolvable as we find it into the persistence of relations among forces, is a corollary from the persistence of force. The general conclusion that there exist constant connexions among phenomena, ordinarily regarded as an inductive conclusion only, is really a conclusion deducible from the ultimate datum of consciousness.

More than this may be said. Every apparent inductive proof of the uniformity of law itself takes for granted both the persistence of force and the persistence of relations among forces. For in the exact sciences, in which alone we may seek relations definite enough to prove uniformity, any alleged demonstration must depend on measurement; and as we have already seen, measurement, whether of matter or force, assumes that both are persistent in assuming that the measures have not varied. While at the same time every determination of the relations among them -- in amount, proportion, direction, or what not -- similarly implies measurement, the validity of which as before implies the persistence of force.

That uniformity of law thus follows inevitably from the persistence of force, will become more and more clear as we advance. The next chapter will indirectly supply abundant frustrations of it.

Chapter 8   The Transformation and Equivalence of Forces

§66. When, to the unaided senses, Science began to add supplementary senses in the shape of measuring instruments, men began to perceive various phenomena which eyes and fingers could not distinguish. Of known forms of force, minuter manifestations became appreciable; and forms of force before unknown were rendered cognizable and measurable. Where forces had apparently ended in nothing, and had been carelessly supposed to have actually done so, instrumental observation proved that effects had in every instance been produced: the forces having reappeared in new shapes. Here has at length arisen the inquiry whether the force displayed in each surrounding change, does not in the act of expenditure undergo metamorphosis into an equivalent amount of some other force or forces. And to this inquiry experiment is giving an affirmative answer, which becomes daily more decisive. Séguin, Mayer, Joule, Grove, and Helmholtz, are more than others to be credited with the enunciation of this doctrine. Let us glance at the evidence on which it rests.

Motion, wherever we can directly trace its genesis, we find had pre-existed as some other mode of force. Our own voluntary acts have always certain sensations of muscular tension as their antecedents. When, as in letting fall a relaxed limb we are conscious of a bodily movement requiring no effort, the explanation is that the effort was exerted in raising the limb to the position whence it fell. In this case, as in the case of an inanimate body descending to the Earth, the force accumulated by the downward motion is equal to the force previously expended in the act of elevation. Conversely, Motion that is arrested produces, under different circumstances, heat, electricity, magnetism, light. From the warming of the hands by rubbing them together, up to the ignition of a railway-brake by intense friction -- from the lighting of detonating powder by percussion, up to the setting on fire a block of wood by a few blows from a steam-hammer; we have abundant instances in which heat arises as Motion ceases. It is uniformly found that the heat generated is great in proportion as the Motion lost is great; and that to diminish the arrest of motion by diminishing the friction, is to diminish the quantity of heat evolved. The production of electricity by Motion is illustrated equally in the boy's experiment with rubbed sealing-wax, in the common electrical machine, and in the apparatus for exciting electricity by the escape of steam. Wherever there is friction between heterogeneous bodies electrical disturbance is one of the consequences. Magnetism may result from Motion either immediately, as through percussion on steel, or mediately as through electric currents previously generated by Motion. And similarly, Motion may create light; either directly, as in the minute incandescent fragments struck off by violent collisions, or indirectly, as through the electric spark. "Lastly, Motion may be again reproduced by the forces which have emanated from Motion; thus, the divergence of the electrometer, the revolution of the electrical wheel, the deflection of the magnetic needle, are, when resulting from frictional electricity palpable movements reproduced by the intermediate modes of force, which have themselves been originated by motion."

That mode of force which we distinguished as Heat, is now regarded as molecular motion -- not motion as displayed in the changed relations of sensible masses to one another, but as assessed by the units of which such sensible masses consist. Omitting cases in which there is structural rearrangement of the molecules, heated bodies expand; and expansion is interpreted as due to movements of the molecules in relation to one another: wider oscillations. That radiation through which anything of higher temperature than things around it, communicates Heat to them, is clearly a species of motion. Moreover, the evidence afforded by the thermometer that Heat thus diffuses itself, is simply a movement caused in the mercurial column. And that the molecular motion which we call Heat, may be transformed into visible motion, familiar proof is given by the steam-engine; in which "the piston and all its concomitant masses of matter are moved by the molecular dilatation of the vapour of water." Where Heat is absorbed without apparent result, modern inquiries have detected unobtrusive modifications: as in glass, the molecular state of which is so far changed, that a Alarized ray of light passing through it becomes visible, which it does not when the glass is cold; or as on polished metallic surfaces, which are altered in molecular structure by radiations from objects very close to them. The transformation of Heat into electricity occurs when dissimilar metals touching each other are heated at the point of contact: electric currents being so produced. Solid, incombustible matter put into heated gas, as lime into the Oxyhydrogen flame, becomes incandescent; and so exhibits the conversion of Heat into light. The production of magnetism by Heat, if it cannot be proved to take place directly, may be proved to take place indirectly through the agency of electricity. And through the same agency may be established the correlation of Heat and chemical affinity -- a correlation which is directly shown by the marked influence Heat exercises on chemical composition and decomposition.

The transformations of Electricity into other modes of force are clearly demonstrable. Produced by the motion of heterogeneous bodies in contact, Electricity, through attractions and repulsions, will immediately reproduce motion in neighbouring bodies. In this case a current of Electricity magnetizes a bar of soft iron; and in that case the rotation of an equipped magnet generates currents of Electricity. Here is the cell of a battery in which, from the play of chemical affinities, an electric current results; and there, in the adjacent cell, is an electric current effecting chemical decomposition. In the conducting wire we witness the transformation of Electricity into heat; while in electric sparks and in the voltaic arc we see light produced. Molecular arrangement, too, is changed by Electricity: as instance the transfer of matter from pole to pole of a battery; the fractures caused by the disruptive discharge; the formation of crystals under the influence of electric currents. And then that, conversely, Electricity is directly generated by rearrangement of the molecules of matter, is shown when a storage-battery or accumulator is used.

How from Magnetism the other physical forces result, must be next briefly noted -- briefly, because in each successive case the illustrations become in great part the obverse forms of those before given. That Magnetism produces motion is the ordinary evidence we have of its existence. In the magneto-electric machine a rotating magnet evolves electricity. and the electricity so evolved may immediately after exhibit itself as heat, light, or chemical affinity. Faraday' s discovery of the effect of Magnetism on polarized light, as well as the discovery that change of magnetic state is accompanied by heat, point to further like connexions. Lastly, experiments show that the magnetization of a body alters its internal structure; and that, conversely, the alteration of its internal structure, as by mechanical strain, alters its magnetic condition.

Improbable as it seemed, it is now proved that from Light also may proceed the like variety of agencies. Rays of light change the atomic arrangements of particular crystals. Certain mixed gases, which do not otherwise combine, combine in the sunshine. In some compounds light produces decomposition. Since the inquiries of photographers have drawn attention to the subject, it has been shown that "a vast number of substances, both elementary and compound, are notably affected by this agent, even those apparently the most unalterable in character, such as metals." And when a daguerreotype plate is connected with a proper apparatus "we get chemical action on the plate, electricity circulating through the wires, magnetism in the coil, heat in the helix, and motion in the needles."

The genesis of all other modes of force from Chemical Action, scarcely needs pointing out. The ordinary accompaniment of chemical combination is heat; and when the affinities are intense, light also is produced. Chemical changes involving alteration of bulk, cause motion, both in the combining elements and in adjacent masses of matter: witness the propulsion of a bullet by the explosion of gunpowder. In the galvanic battery we see electricity resulting from chemical composition and decomposition. While through the medium of this electricity, Chemical Action produces magnetism.

These facts, the larger part of which are culled from Grove's work on The Correlation of Physical Forces, show that each force is transformable, directly or indirectly, into the others. In every change Force (or Energy, as in these cases it is called) undergoes metamorphosis; and from the new form or forms it assumes, may subsequently result either the previous one or any of the rest, in endless variety of order and combination. It is further now manifest that the physical forces stand not simply in qualitative correlations with one another, but also in quantitative correlations. Besides proving that one mode of force may be transformed into another mode, experiments show that from a definite amount of one, the amounts of others that arise are definite. Ordinarily it is difficult to show this; since it mostly happens that the transformation of any force is not into some one of the rest but into several of them: the proportions being determined by ever-varying conditions. But in certain cases positive results have been reached. Mr. Joule has ascertained that the fall of 772 lb. through one foot, will raise the temperature of a pound of water one degree of Fahrenheit. Dulong, Petit, and Neumann, have proved a relation in amount between the affinities of combining bodies and the heat evolved during their combination. Between chemical action and voltaic electricity a quantitative connexion has been established by Faraday. The well-determined relations between the amounts of heat generated and of water turned to steam, or still better the known expansion produced in steam by each additional degree of heat, may be cited in further evidence. Hence it is no longer doubted that among the several forms which force assumes, the quantitative relations are fixed.

§67. Throughout the Cosmos this truth must invariably hold. Every change, or group of changes, going on in it, must be due to forces affiliable on the like or unlike forces previously existing; while from the forces exhibited in such change or changes must be derived others more or less transformed. And besides recognizing this necessary linking of the forces at any time manifested with those preceding and succeeding them, we must recognize the amounts of these forces as necessarily producing such and such quantities of results, and as necessarily limited to those quantities.

That unification of knowledge which is the business of Philosophy, is but little furthered by the establishment of this truth under its general form. We must trace it out under its leading special forms. Changes, and the accompanying transformations of forces, are everywhere in progress, from the movements of stars to the currents of commodities; and to comprehend the great fact that forces, unceasingly metamorphosed, are nowhere increased or decreased, it is requisite to contemplate the changes of all kinds going on that we may learn whence arise the forces they and what becomes of these forces. Of course if answerable at all, these questions can be answered only in the establish rudest way. The most we can hope is to establish a qualitative correlation that is indefinitely quantitative -- quantitative to the extent of implying something like a due proportion between causes and effects.

Let us, then, consider the several classes of phenomena which the several concrete sciences deal with.

§68. The antecedents of those forces which our Solar System displays, belong to a past of which we can never have anything but inferential knowledge. Many and strong as are the reasons for believing the Nebular Hypothesis, we cannot yet regard it as more than an hypothesis. If, however, we assume that the matter of our Solar System was once diffused and had irregularities of shape and density such as existing nebulae display, or resulted from the coalescences of moving nebulous masses, we have, in the momenta of its parts, original and acquired forces adequate to produce the motions now going on.

Various stages in the formation of spiral nebulae imply that rotation in many cases results from concentration: whether always, there is no proof; for large nebulae are too diffused, small ones too dense, and others are seen too much edgeways, to yield evidence. But in the absence of adverse pre-arrangement some rotation may safely be inferred. So far as the evidence carries us, we perceive some quantitative relation between the motions generated and the gravitative forces expended in generating them. In the Solar System the outermost planets, formed from that matter which has travelled the shortest distance towards the common centre of gravity, have the smallest velocities. Doubtless this is explicable on the teleological hypothesis, since it is a condition to equilibrium. But without insisting that this is beside the question, it will suffice to point out that the like cannot be said of the planetary rotations. No such final cause can be assigned for the rapid axial movement of Jupiter and Saturn, or the slow axial movement of Mars. If, however, we look for the natural antecedents of these gyrations which all planets exhibit, the nebular hypothesis furnishes them; and they bear manifest quantitative relations to the rates of motions. For the planets that turn on their axes with extreme rapidity are those having large orbits -- those of which the once-diffused components, probably formed into broad rings, moved to their centres of aggregation in immense spaces, and so acquired high velocities. While conversely; the planets which rotate with relatively small velocities, are those formed out of small nebulous rings.

"But what," it may be asked, "has in such case become of all that motion which ended in the aggregation of this diffused matter into solid bodies?" The answer is that it has been radiated in the form of heat and light; and this answer the evidence, so far as it goes, confirms. Geologists and physicists agree in concluding that the heat of the Earth's interior is but a remnant of the heat which once made molten the whole mass. The mountainous surfaces of the Moon and of Venus, indicating, as they do, crusts which have, like our own, been corrugated by contraction, imply that these bodies, too, have undergone refrigeration. Lastly we have in the Sun a still-continued production of the heat and light which result from the arrest of diffused matter moving towards a common centre of gravity . Here also, as before, a quantitative relation is traceable. Mars, the Earth, Venus, and Mercury, which severally contain comparatively small amounts of matter whose centripetal motion has been destroyed, have already lost nearly all the produced heat; while the great planets, Jupiter and Saturn, imply by their low specific gravity, as well as by the perturbations of their surfaces, that they still retain much heat. And then the Sun, a thousand times as great in mass as the largest planet, and having to give off an enormously greater quantity of heat and light due to that loss of molar motion which concentration entails, is still radiating with great intensity.

§69. Those forces which have wrought the surface of our planet into its present shape, are traceable to the primordial source just assigned. Geologic changes are either direct or indirect results of the unexpended heat caused by nebular condensation. They are commonly divided into igneous and aqueous -- heads under which we may most conveniently consider them.

All those disturbances known as earthquakes, all those elevations and subsidences which they severally produce, all those accumulated effects of many such elevations and subsidences exhibited in ocean-basins, islands, continents, table-lands, mountain-chains, and all those formations which are distinguished as volcanic, geologists now regard as modifications of the Earth's crust caused by the actions and reactions of its interior. Even supposing that volcanic eruptions, extrusions of igneous rock, and upheaved mountain-chains, could be otherwise satisfactorily accounted for, it would be impossible otherwise to account for those wide-spread elevations and depressions whence continents and oceans result. Such phenomena as the fusion or agglutination of sedimentary deposits, the warming of springs, the sublimation of metals into the fissures where we find them as ores, may be regarded as positive results of the residuary heat of the Earth's interior; while fractures of strata and alterations of level are its negative results, since they ensue on its escape. The original cause of all these effects is still, however, as it has been from the first, the gravitating movement of the Earth's matter towards the Earth's centre; seeing that to this is due both the eternal heat itself and the collapse which takes place as it is radiated into space.

To the question -- Under what forms previously existed the force which works out the geological changes classed as aqueous, the answer is less obvious. The effects of rain, of rivers, of winds, of waves, of marine currents, do not manifestly proceed from one general source. Analysis, nevertheless, proves that they have a common genesis. If we ask, -- Whence comes the power of the river-current, bearing sediment down to the sea? the reply is, -- The gravitation of water throughout the tract which this river drains. If we ask, -- How came the water to be dispersed over this tract? the reply is, -- It fell in the shape of rain. If we ask, -- How came the rain to be in that position whence it fell? the reply is, -- The vapour from which it was condensed was drifted there by the winds. If we ask, -- How came this vapour to be at that height? the reply is, -- It was raised by evaporation. And if we ask, -- What force thus raised it? the reply is, -- The Sun's heat. Just that amount of gravitative force which the Sun's heat overcame in raising the molecules of water, is given out again in the fall of those molecules to the same level. Hence the denudations effected by rain and rivers, during the descent of this condensed vapour to the level of the sea, are indirectly due to the radiated energy of the Sun. Similarly with the winds that transport the vapours hither and thither. Consequent as atmospheric currents are on differences of temperature (either general, as between the equatorial and polar regions, or special as between tracts of the Earth's surface having unlike physical characters) all such currents are due to that source from which the irregularly distributed heat proceeds. And if the winds thus originate, so too do the waves raised by them on the sea's surface. Whence it follows that whatever changes waves produce -- the wearing away of cliffs, the breaking down of rocks into shingle, sand, and mud -- are also traceable to the solar rays as their primary cause. The same may be said of ocean-currents. Generated as the larger ones are by the excess of heat which the ocean in tropical climates acquires from the Sun; and determined as the smaller ones are in part by local shapes of land; it follows that the distribution of sediment and other geological processes which these marine currents effect, are affiliable upon the energy the Sun radiates. The only aqueous agency otherwise originating is that of the tides -- an agency which, equally with the others, is traceable to unexpended celestial motion. But making allowance for the changes this works, we conclude that the slow wearing down of continents and gradual filling up of seas, effected by rain, rivers, winds, waves, and ocean-streams, are the indirect effects of solar heat.

Thus we see that while the geological changes classed as igneous, arise from the still-progressing motion of the Earth's substance to its centre of gravity; the antagonistic changes classed as aqueous, arise from the still-progressing motion of the Sun's substance towards its centre of gravity.

§70. That the forces exhibited in vital actions, vegetal and animal, are similarly derived, is an obvious deduction from the facts of organic chemistry. Let us note first the physiological generalizations; and then the generalizations which they necessitate.

Plant-life is all directly or indirectly dependent on the heat and light of the Sun-directly dependent in the immense majority of plants, and indirectly dependent in plants which, as the fungi, flourish in the dark: since these, growing at the expense of decaying organic matter, mediately draw their forces from the same original source. Each plant owes the carbon and hydrogen of which it mainly consists, to the carbon dioxide and water contained in the surrounding air and earth. These must, however, be decomposed before their carbon and hydrogen can be assimilated. To overcome the affinities which hold their elements together requires the expenditure of energy; and this energy is supplied by the Sun. When, under fit conditions, plants are exposed to the solar rays, they give off oxygen and accumulate carbon and hydrogen. In darkness this process ceases. It ceases, too, when the quantities of light and heat received are greatly reduced, as in winter. Conversely, it is active when the light and heat are great, as in summer. And the like relation is seen in the fact that while plant-life is luxuriant in the tropics, it diminishes in temperate regions, and disappears as we approach the poles. Thus the irresistible inference is that the forces by which plants grow and carry on their functions, are forces which previously existed as solar radiations.

That in the main, the processes of animal life are opposite to those of vegetal life is a truth long current among men of science. Chemically considered, vegetal life is chiefly a process of de-oxidation, and animal life chiefly a process of oxidation; chiefly we must say, because in so far as plants are expenders of force for the purposes of organization, they are oxidizers; and animals, in some of their minor processes, are probably de-oxidizers. But with this qualification, the general truth is that while the plant, decomposing carbon dioxide and water and liberating oxygen, builds up the detained carbon and hydrogen (along with a little nitrogen and small quantities of other elements) into stem, branches, leaves, and seeds; the animal, consuming these branches, leaves, and seeds, and absorbing oxygen, re-composes carbon dioxide and water, forming also certain nitrogenous compounds in minor amounts. And while the decomposition effected by the plant is at the expense of energies emanating from the Sun, the re-composition effected by the animal is at the profit of these energies, which are liberated during the combination of such elements. Thus the movements, internal and external, of the animal, are re-appearances in new forms of a power absorbed by the plant under the shape of light and heat. Just as the solar forces expended in raising vapour from the sea's surface, are given out again in the fall of rain and rivers to the same level, and in the accompanying transfer of solid matters; so, the solar forces that in the plant raised certain chemical elements to a condition of unstable equilibrium, are given out again t the actions of the animal during the fall of these elements to a condition of stable equilibrium.

Besides thus tracing a qualitative correlation between these two great orders of organic activity, as well as between both of them and inorganic activities, we may rudely trace a quantitative correlation. Where vegetal life is abundant, we usually find abundant animal life; and as we advance from torrid to temperate and frigid climates, the two decrease together. Speaking generally, the animals of each class reach larger sizes in regions where vegetation is luxuriant, than in those where it is sparse.

Certain facts of development in both plants and animals, illustrate still more directly the truth we are considering. In pursuance of a suggestion made by Mr. (afterwards Sir William) Grove, Dr. Carpenter pointed out that a connexion between physical and vital forces is exhibited during incubation. The transformation of the unorganized contents of an egg into the organized chick, is a question of heat: withhold heat and the process does not commence; supply heat and it goes on while the temperature is maintained, but ceases when the egg is allowed to cool. The developmental changes can be completed only by keeping the temperature with tolerable constancy at a definite height for a definite time; that is -- only by supplying a definite quantity of heat. Though the proclivities of the molecules determine the typical structure assumed, yet the energy supplied by the thermal undulations gives them the power of arranging themselves into that structure. In the metamorphoses of insects we may discern parallel facts. The hatching of their eggs is determined by temperature, as is also the evolution of the pupa into the imago; and both are accelerated or retarded according as heat is artificially supplied or withheld. It will suffice just to add, that the germination of plants presents like relations of cause and effect, as every season shows .

Thus then the various changes exhibited by the organic creation, whether considered as a whole, or in its two great divisions, or in its individual members, conform, so far as we can ascertain, to the general principle.

§71. Even after all that has been said in the foregoing part of this work, many will be alarmed by the assertion that the forces which we distinguish as mental, come within the same generalization. Yet there is no alternative but to make this assertion: the facts which justify, or rather which necessitate, it being abundant and conspicuous. At the same time they are extremely involved. The essential correlations occur in organs which are mostly invisible, and between forces or energies quite other than those which are apparent. Let us first take a superficial view of the evidence.

The modes of consciousness called pressure, motion, sound, light, heat, are effects produced in us by agencies which as otherwise expended, crush or fracture pieces of matter, generate vibrations in surrounding objects, cause chemical combinations, and reduce substances from a solid to a liquid form. Hence if we regard the changes of relative position, of aggregation, or of chemical union, thus arising, as being transformed manifestations of certain energies; so, too, must we regard the sensations which such energies produce in us. Any hesitation to admit this must disappear on remembering that the last correlations, like the first, are not qualitative only but quantitative. Masses of matter which, by scales or dynamometer, are shown to differ greatly in weight, differ as greatly in the feelings of pressure they produce on our bodies. In arresting moving objects, the strains we are conscious of are proportionate to the momenta of such objects as otherwise measured. The impressions of sounds given to us by vibrating strings, bells, or columns of air, are found to vary in strength with the amount of force applied. Fluids or solids proved to be markedly contrasted in temperature by the different degrees of expansion they produce in the mercurial column, produce in us correspondingly different degrees of the sensation of heat. And unlike intensities in our impressions of light, answer to unlike effects as measured by photometers.

Besides the correlation and equivalence between external physical forces and the mental forces generated by them under the form of sensations, there appears to be a correlation and equivalence between sensations and those physical forces which, in the shape of bodily actions, result from them. In addition to the excitements of secreting organs, sometimes traceable, there arise contractions of the involuntary muscles. Sensations increase the action of the heart, and recent experiments imply that the muscular fibres of the arteries are at the same time contracted. The respiratory muscles, too are stimulated. The rate of breathing is visibly and audibly augmented both by pleasurable and painful excitements of the nerves, if these reach any intensity. When the quantity of sensation is great, it generates contractions of the voluntary muscles, as well as of the involuntary ones. Violent pains cause violent struggles. The start that follows a loud sound, the wry face produced by an extremely disagreeable taste, the jerk with which the hand or foot is snatched out of very hot water exemplify the genesis of motions by feelings; and in these cases it is manifest that the quantity of bodily. action is proportionate to the quantity of sensation. even where pride causes suppression of the screams and groans expressive of great pain (also indirect results of muscular contraction), we may still see in the clenching of the hands, the knitting of the brows, and the setting of the teeth, that the bodily actions excited are as great, though less obtrusive in their results. If we take emotions instead of sensations, we find the correlation and equivalence similarly suggested. emotions of moderate intensity, like sensations of moderate intensity, generate little beyond excitement of the heart and vascular system, joined sometimes with increased action of glandular organs. But as the emotions rise in strength, the muscles of the face, body, and limbs, begin to move. Of examples may be mentioned the frowns, dilated nostrils, and stampings of anger; the contracted brows, and wrung hands, of grief; the laughs and leaps of joy; the frantic struggles of terror or despair. Passing over cases in which extreme agitation causes fainting, we see that whatever be the kind of emotion, there is a manifest relation between its amount, and the amount of muscular action induced, from the fidgettiness of impatience up to the almost convulsive movements accompanying great mental agony. To these several orders of evidence must be joined the further order, that between feelings and those voluntary motions which result from them, there comes the sensation of muscular tension, standing in manifest correlation with both -- a correlation that is distinctly quantitative: the sense of strain varying, other things equal, directly as the quantity of momentum generated.

§71a. But now, reverting to the caution which preceded these two paragraphs, we have to note, first, that the facts do not prove transformation of feeling into motion but only a certain constant ratio between feeling and motion; and then we have further to note that what seems a direct quantitative correlation is illusory. For example, tickling is followed by almost uncontrollable movements of the limbs; but obviously there is no proportion between the amount of force applied to the surface and the amount of feeling or the amount of motion: rather there is an inverse proportion, for while a rough touch does not produce the effect a gentle one does. Even when it is recognized that the feeling is not the correlate of the external touching action but of a disturbance in certain terminal tactile structures, it still remains demonstrable that there is no necessary relation between the amount of such disturbance and the amount of feeling produced; for under some conditions muscular motion results without the intercalation of any feeling. When the spinal cord has been so injured as to cut off all nervous communication between the lower part of the body and the brain, tickling the sole of the foot produces convulsion of the leg more violent than it would do were it accompanied by sensation: there is a reflex transmission of the stimulus and genesis of motion without passage through consciousness. Cases of another class show that between central feelings or emotions and the muscular movements they initiate there are no fixed ratios: instance the sense of effort felt in making a small movement by one who is exhausted, or the inability of an patient to raise a limb from the bed however strong the desire to do it. So that neither the feelings peripherally initiated nor those centrally initiated, though they are correlated with motions, are quantitatively correlated. Even still more manifest becomes the lack of direct relation, either qualitative or quantitative, between outer stimuli and inner feelings, or between such inner feelings and muscular motions, when we contemplate the complex kinds of mental processes. The emotions and actions of a man who has been insulted are clearly not equivalents of the sensations produced by the words in his ears for the same words otherwise arranged, would not have caused them. The thing said bears to the mental action it excites, much the same relation that the pulling of a trigger bears to the subsequent explosion -- does not produce the power but merely liberates it. Whence, then, arises this immense amount of nervous energy which a whisper or a glance may call forth?

Evidently we shall go utterly wrong if the problem of the transformation and equivalence of forces is dealt with as though an organism were simple and passive instead of being complex and active. In the living body there are already going on multitudinous transformations of energy very various in their natures, and between any physical action filling on it and any motion which follows, there are intercalated numerous changes of kind and quantity. The fact of chief significance for us here, is that organization is, under one of its aspects, a set of appliances for the multiplication of energies -- appliances which, by their successive actions, make the energy eventually given out enormous as compared with the energy which liberated it. A physical stimulus affecting an organ of sense, is in some cases multiplied by local nervous agents; the augmented energy is again multiplied in some part of the spinal cord or in some higher ganglion; and this usually again multiplied in the cerebrum and discharged to the muscles, is there enormously multiplied in the contracting fibres. Of these transformations Only some carried on centrally have accompanying states of consciousness; so that, manifestly, there can be no quantitative equivalence either between the sensation and the original stimulus, or between it and the eventual motion. All we can say is that, other things equal, the three vary together; so that if in one case successive stages of increase are 1, 9, 27, 270 they in another case be 2, 18, 54, 540. This kind of correlation is all which the foregoing facts imply. But now let us glance at the indirect evidences which confirm the view that mental and physical forces are connected, though in an indirect way.

Nowadays no one doubts that mental processes and the resulting actions are contingent on the presence of a nervous system; and that, greatly obscured as it is by numerous and involved conditions, a general relation may be traced between the size of this system and the quantity of mental action as measured by its results. Further, this nervous apparatus has a chemical constitution on which its activity, depends; and there is one element in it between the amount of which and the amount of function performed, there is an ascertained connexion: the proportion of phosphorus present in the brain being the smallest in infancy, old age, and idiotcy, and the greatest during the prime of life. Note, next, that the evolution of thought and emotion varies, other things equal, with the supply of blood to the brain. On the one hand, an arrest of the cerebral circulation from stoppage of the heart, immediately entails unconsciousness. On the other hand, excess of cerebral circulation (unless it is such as to cause undue pressure) results in unusual excitement. Not the quantity only but also the condition, of the blood passing through the brain, influences the mental manifestations. The arterial currents must be duly aerated, to produce the normal amount of cerebration. If the blood is not allowed to exchange its carbon dioxide for oxygen, there results asphyxia, with its accompanying stoppage of ideas and feelings. That the quantity of consciousness is, other things equal, determined by the constituents of the blood, is unmistakably seen in the exaltation which certain vegeto-alkalies commonly produce when taken into it. The gentle exhilaration which tea and coffee create, is familiar to all; and though the gorgeous imaginations and intense feelings produced by opium and hashish, have been experienced by few (in this country at least), the testimony of those who have experienced them is sufficiently conclusive. Yet another proof that the genesis of the mental energies depends on chemical change, is afforded by the fact that the effete products separated from the blood by the kidneys, vary in character with the amount of cerebral action. Excessive activity of mind is accompanied by excretion of an unusual quantity of the alkaline phosphates.

§71b. But now after recognizing the classes of facts which unite to prove that the law of metamorphosis, and in a partial way the law of equivalence, holds between physical energies and nervous energies, let us enter upon the ultimate question -- What is the nature of the relation between nervous energies and mental states? how are we to conceive molecular changes in the brain as producing feelings, or feelings as producing molecular changes which end in motion?

In his lecture on Animal Automatism, Prof. Huxley set forth the proofs that alike in animals and in Man, the great mass of those complex actions which we associate with purpose and intelligence may be performed automatically: and contended that the consciousness which ordinarily accompanies them is outside the series of changes constituting the nervous coordination -- does not form a link in the chain but is simply a "concomitant" or a "collateral product." In so far as it correlates the nervous actions by which our bodily and mental activities are carried on, with physical forces in general, Prof. Huxley's conclusion accords with the conclusions above set forth; but in so far as it regards the accompanying states of consciousness as collateral products only, and not as factors in any degree, it differs from them. Here I cannot do more than indicate the set of evidences by which I think my own conclusion is supported if not justified.

One of them we have in the facts of habit, which prove that states of consciousness which were at first accompaniments of sensory impressions and resulting motions, gradually cease to be concomitants. The little boy who is being taught to read has definite perceptions and thoughts about the form and sound of each letter, but in maturity all these have lapsed, so that only the words are consciously recognized: each letter produces its effect automatically. So, too, the girl learning to knit is absorbed in thinking of each movement made under the direction of her eyes, but eventually the movements come to be performed almost like those of a machine while her mind is otherwise occupied. Such cases seem at variance with the belief that consciousness is outside the lines of nervous communication, and suggest, rather that it exists in any line of communication in course of establishment and disappears when the communication becomes perfect. If it is not a link in the line, it is not easy to see how these changes can arise.

Sundry facts appear to imply that consciousness is needful as an initiator in cases where there are no external stimuli to set up the co-ordinated nervous changes: the nervous structures, though capable of doing everything required if set going, are not set going unless there a rises an idea. Now this implies that an idea, or co-ordinated set of feelings, has the power of working changes in the nervous centres and setting up motions: the state of consciousness is a factor.

Then what we may call passive emotions -- emotions which do not initiate actions -- apparently imply that between feelings and nervous changes there is not merely a concomitance but a physical nexus. Intense grief or anxiety in one who remains motionless, is shown to be directly dependent on nervous changes by the fact that there is an unusual excretion of phosphates by the kidneys. Now unless we suppose that in such cases there is great activity of certain nervous plexuses ending in nothing, we must say that the feeling is a product of the molecular changes in them.

Once more there is the question -- if feeling is not a factor how is its existence to be accounted for? To any one who holds in full the Cartesian doctrine that animals are automata, and that a howl no more implies feeling than does the bark of a toy dog, I have nothing to say. But whoever does not hold this, is obliged to hold that as we ascribed anger and affection to our fellow-men, though we literally know no such feelings save in ourselves, so must we ascribe them to animals under like conditions, if so, however -- if feelings are not factors and the appropriate actions might be automatically performed without them -- then, on the supernatural hypothesis it must be assumed that feelings were given to animals for no purpose, and on the natural hypothesis it must be assumed that they have arisen to do nothing.

§71c. But whether feeling is only a concomitant of certain nervous actions, or whether it is, as concluded above, a factor in such actions, the connexion between the two is inscrutable. If we suppose that in which consciousness inheres to be an immaterial something, not implicated in these nervous actions but nevertheless affected by them in such way as to produce feeling, then we are obliged to conceive of certain material changes -- molecular motions -- as producing changes in something in which there is nothing to be moved; and this we cannot conceive. If, on the other hand, we regard this something capable of consciousness, as so related to certain nervous changes that the feelings arising in it jot them in producing muscular motions, then we meet the same difficulty under its converse aspect. We have to think of an immaterial something -- a something which is not molecular motion -- which is capable of affecting molecular motions: we have to endow it with the power to work effects which, so far as our knowledge goes, can be worked only by material forces. So that this alternative, too, is in the last resort inconceivable.

The only supposition having consistency is that that in which consciousness inheres is the all-pervading ether. This we know can be affected by molecules of matter in motion and conversely can affect the motions of molecules; as witness the action of light on the retina. In pursuance of this supposition we may assume that the ether which pervades not only all space but all matter, is, under special conditions in certain parts of the nervous system, capable of being affected by the nervous changes in such way as to result in feeling, and is reciprocally capable under these conditions of affecting the nervous changes. But if we accept this explanation we must assume that the potentiality of feeling is universal, and that the evolution of feeling in the ether takes place only under the extremely complex conditions occurring in certain nervous centres. This, however, is but a semblance of an explanation, since we know not what the ether is, and since, by the confession of those most capable of judging, no hypothesis that has been framed accounts for all its powers. Such an explanation may be said to do no more than symbolize the phenomena by symbols of unknown natures.

Thus though the facts oblige us to say that physical and psychical actions are correlated, and in a certain indirect way quantitatively correlated, so as to suggest transformation, yet how the material affects the mental and how the mental affects the material, are mysteries which it is impossible to fathom. But they are not profounder mysteries than the transformations of the physical forces into one another. They are not more completely beyond our comprehension than the natures of Mind and Matter. They have simply the same insolubility as all other ultimate questions. We can learn nothing more than that here is one of the uniformities in the order of phenomena.

§72. If the general law of transformation and equivalence holds of the forces we class as vital and mental, it must hold also of those which we class as social. Whatever takes place in a society results either from the undirected physical energies around, from these energies as directed by men, or from the energies of the men themselves.

While, as among primitive tribes, men's actions are mainly independent of one another, social forces can scarcely be said to exist: they come into existence along with co-operation. The effects which can be achieved only by the joint actions of many, we may distinguish as social. At first these are obviously due to accumulated individual efforts, but as fast as societies become large and highly organized, they acquire such separateness from individual efforts as to give them a character of their own. The network of roads and railways and telegraph wires -- agencies in the formation of which individual labours were so merged as to be practically lost -- serve to carry on a social life that is no longer thought of as caused by the independent doings of citizens. The prices of stocks, the rates of discount, the reported demand for this or that commodity, and the currents of men and things setting to and from various localities, show us large movements and changes scarcely at all affected by the lives and deaths and deeds of persons. But these and multitudinous social activities displayed in the growth of towns, the streams of traffic in their streets, the daily issue and distribution of newspapers, the delivery of food at people's doors, etc., are unquestionably transformed individual energies, and have the same source as these energies -- the food which the population consumes. The correlation of the social with the physical forces through the intermediation of the vital ones, is, however, best shown in the different amounts of activity displayed by the same society according as its members are supplied with different amounts of force from the external world. A very bad harvest is followed by a diminution of business. Factories are worked half-time railway traffic falls; retailers find their sales lessened; and if the scarcity rises to famine, a thinning of the population still more diminishes the industrial vivacity . Conversely, an unusually abundant supply of food, occurring under conditions not otherwise unfavourable, both excites the old producing and distributing agencies and sets up new ones. The surplus social energy finds vent in speculative enterprises. Labour is expended in opening new channels of communication. There is increased encouragement to those who furnish the luxuries of life and minister to the aesthetic faculties. There are more marriages, and a greater rate of increase in population. Thus the society grows larger, more complex, and more active. When the whole of the materials for subsistence are not drawn from the area inhabited, but are partly imported, the people are still supported by certain harvests elsewhere grown at the expense of certain physical forces, and the energies they expend originate from them.

If we ask whence come these physical forces, the reply is of course as heretofore -- the Sun's rays. Based as the life of a society is on animal and vegetal products, and dependent as these are on the light and heat of the Sun, it follows that the changes wrought by men as socially organized, are effects of forces having a common origin with those which produce all the other orders of changes we have analyzed. Not only is the energy extended by the horse harnessed to the plough, and by the labourer guiding it, derived from the same reservoir as is the energy of the cataract and the hurricane; but to this same reservoir are traceable those subtler and more complex manifestations of energy which humanity, as socially embodied, evolves. The assertion is startling but it is an unavoidable deduction.

Of the physical forces that are directly transformed into social ones, the like is to be said. Currents of air and water, which before the use of steam were the only agents brought in aid of muscular effort for performing industrial processes, are, as we have seen, generated by solar heat. And the inanimate power that now, to so vast an extent, supplements human labour, is similarly derived. Sir John Herschel was the first to recognize the truth that the force impelling a locomotive, originally emanated from the Sun. Step by step we go back -- from the motion of the piston to the evaporation of the water; thence to the heat evolved during the burning of coal; thence to the assimilation of carbon by the plants of whose imbedded products coal consists; thence to the carbon di-oxide from which their carbon was obtained; and thence to the rays of light which effected the de-oxidation. Solar forces millions of years ago expended on the Earth's vegetation, and since locked up in deep-seated strata, now smelt the metals required for our machines, turn the lathes by which the machines are shaped, work them when put together, and distribute the fabrics they produce. And since economy of labour makes possible a larger population, gives a surplus of human power that would else be absorbed in manual occupations, and thus facilitates the development of higher kinds of activity; these social forces which are directly correlated with Physical forces anciently derived from the Sun, are only less important than those of which the correlates are the vital forces recently derived from it.

§73. Many who admit that among physical phenomena at large, transformation of forces is now established, will probably say that inquiry has not yet gone far enough to enable us to assert equivalence. And in respect of the forces classed as vital, mental, and social, the evidence assigned they will consider by no means conclusive even of transformation, much less of equivalence.

But the universal truth above followed out under its various aspects, is a corollary from the persistence of force. From the proposition that force can neither come into existence nor cease to exist, the several foregoing conclusions inevitably follow. Each manifestation of force can be interpreted only as the effect of some antecedent force; no matter whether it be an inorganic action, an animal movement, a thought, or a feeling. Either bodily and mental energies, as well as inorganic ones, are quantitatively correlated to certain energies expended in their production, and to certain other energies which they initiate; or else nothing must become something and something must become nothing. The alternatives are, to deny the persistence of force, or to admit that from given amounts of antecedent energies neither more nor less than certain physical and psychical changes can result. This corollary cannot indeed be made more certain by accumulating illustrations. Whatever proof of correlation and equivalence is reached by experimental inquiry, is based on measurement of the forces expended and the forces produced. But, as was shown in the last chapter, any such process implies the use of some unit of force which is assumed to remain constant; and its constancy can be assumed only as being a corollary from the persistence of force. How then can any reasoning based on this corollary, prove the equally direct corollary that when a given quantity of force ceases to exist under one form, an equal quantity must come into existence under some other form or forms?

"What, then," it may be asked, "is the use of investigations by which transformations and equivalence of forces is sought to be inductively established? If the correlation cannot be made more certain by them than it is already does not their uselessness necessarily follow?" No. They are of value as disclosing the many particular implications which the general truth does not specify. They are of value as teaching us how much of one mode of force is the equivalent of so much of another mode. They are of value as detecting under what conditions each metamorphosis occurs. And they are of value as leading us to inquire in what shape the remnant of force has escaped, when the apparent results are not equivalent to the cause.