Chapter 4   The Indestructibility of Matter

§52. Not because the truth is unfamiliar, is it needful here to assert the indestructibility of Matter; but partly because the symmetry of our argument demands enunciation of this truth, and partly because the evidence on which it is accepted must be examined. Could it be shown, or could it with reason be supposed, that Matter, either in its aggregates or in its units, ever becomes nonexistent, it would be needful either to ascertain under what conditions it becomes non-existent, or else to confess that Science and Philosophy are impossible. For if, instead of having to deal with fixed quantities and weights, we had to deal with quantities and weights which are apt, wholly or in part, to be annihilated, there would be introduced an incalculable element, fatal to all positive conclusions. Clearly, therefore, the proposition that matter is indestructible must be deliberately considered.

So far from being admitted as a self-evident truth, this would, in primitive times, have been rejected as a self-evident error. There was once universally current, a notion that things could vanish into nothing, or arise out of nothing. If men did not believe this in the strict sense of the word (which would imply that the process of creation or annihilation was clearly represented in consciousness), they still believed that they believed it; and how nearly, in their confused thoughts, the one was equivalent to the other, is shown by their conduct. Nor, indeed, have dark ages and inferior minds alone betrayed this belief. In its dogmas respecting the beginning and end of the world, the current theology clearly implies it; and it may be questioned whether Shakespeare, in his poetical anticipation of a time when all things shall disappear and "leave not a wrack behind," was not under its influence. The accumulation of experiences, however, and still more the organization of experiences, has slowly reversed this conviction. All apparent proofs that something can come out of nothing, a wider knowledge has one by one cancelled. The comet which is suddenly discovered and nightly waxes larger, is proved not to be a newly-created body but a body which was until lately beyond the range of vision. The cloud formed a few minutes ago in the sky, consists not of substance that has just begun to be, but of substance that previously existed in a transparent form. And similarly with a crystal or a precipitate in relation to the fluid depositing it. Conversely, the seeming annihilations of matter turn out to be only changes of state. It is found that the evaporated water, though it has become invisible, may be brought by condensation to its original shape. Though from a discharged fowling-piece the gunpowder has disappeared, there have appeared in place of it certain gases which, in assuming a larger volume, have caused the explosion. Not, however, until the rise of quantitative chemistry, could the conclusion suggested by such experiences be harmonized with all the facts. When, having ascertained not only the combinations formed by various substances, but also the proportions in which they combine, chemists were enabled to account for the matter that had made its appearance or become invisible, scepticism was dissipated. And of the general conclusion thus reached, the exact analysis daily made, by which the same portion of matter is pursued through numerous disguises and finally separated, furnish never-ceasing confirmations.

Such has become the effect of this specific evidence, joined to that general evidence which the continued existence of familiar objects gives us, that the Indestructibility of Matter is now held by many to be a truth of which the negation is inconceivable.

§53. This last fact rises the question whether we have any higher warrant for this fundamental belief than the warrant of conscious induction. Before showing that we have a higher warrant, some explanations are needful.

The consciousness of logical necessity, is the consciousness that a certain conclusion is implicitly contained in certain premises explicitly stated. If, contrasting a young child and an adult, we see that this consciousness of logical necessity, absent from the one is present in the other, we are taught that there is a growing up to the recognition of certain necessary truths, merely by the unfolding of the inherited intellectual forms and facilities.

To state the case more specifically: -- Before a truth can be known as necessary, two conditions must be fulfilled. There must be a mental structure capable of grasping the terms of the proposition and the relation alleged between them; and there must be such definite and deliberate mental representation of these terms, as makes possible a clear consciousness of this relation. Non-fulfilment of either condition may cause non-recognition of the necessity of the truth. Let us take cases.

The savage who cannot count the fingers on one hand, can frame no definite thought answering to the statement that 7 and 5 are 12; still less can he frame the consciousness that no other total is possible.

The boy adding up figures inattentively says to himself that 7 and 5 are 11; and may repeatedly bring out a wrong result by repeatedly making this error.

Neither the non-recognition of the truth that 7 and 5 are 12, which in the savage results from undeveloped mental structure, nor the assertion, due to the boy's careless mental action, that they make 11, leads us to doubt the necessity of the relation between these two separately-existing numbers and the sum they make when existing together. Nor does failure from either cause to apprehend the necessity of this relation, make us hesitate to say that when its terms are distinctly represented in thought, its necessity will be seen; and that, apart from multiplied experiences, this necessity becomes cognizable when structures and functions are so far developed that groups of 7 and 5 and 12 can be mentally grasped.

Manifestly, then, there are recognitions of necessary truths, as such, which accompany mental evolution. And there are ascending gradations in these recognitions. A boy who has intelligence enough to see that things which are equal to the same thing are equal to one another, may be unable to see that ratios which are severally equal to certain other ratios that are unequal to each other, are themselves unequal; though to a more-developed mind this last axiom is no less obviously necessary than the first.

All this which holds of logical and mathematical truths, holds, with change of terms, of physical truths. There are necessary truths in Physics for the apprehension of which, also, a developed and disciplined intelligence is required; and before such intelligence arises, not only may there be failure to apprehend the necessity of them, but there may be vague beliefs in their contraries. Up to comparatively-recent times, all mankind were in this state of incapacity respecting physical axioms; and the mass of mankind are so still. Effects are expected without causes of fit kinds; or effects extremely disproportionate to causes are looked for; or causes are supposed to end without effects.(*) <* I knew a lady who contended that a dress folded up tightly, weighed more than when loosely folded up; and who under this belief, had her trunks made large that she might diminish the charge for freight! Another whom I know, ascribes the feeling of lightness which accompanies vigour. to actual decrease of weight; believes that by. stepping gently, she can press less upon the ground; and, when cross-questioned. asserts that. If placed in scales, she can make herself lighter by an act of will!> But though many are unable to grasp physical axioms, it no more follows that physical axioms are not knowable a priori by a developed intellect, than it follows that logical relations are not necessary, because undeveloped intellects cannot perceive their necessity.

It is thus with the notions which have been current respecting the creation and annihilation of Matter. In the first place, there has been a confounding of two radically-different things -- disappearance of Matter from a visible form, say by evaporation, and passage of Matter from existence into non-existence. Until this confusion is avoided, the belief that Matter can be annihilated readily obtains currency. In the second place, the currency of it continues so long as there is not power of introspection enough to make manifest what results from the attempt to annihilate Matter in thought. But when the vague ideas arising in a nervous structure imperfectly organized, are replaced by the clear ideas arising in a definite nervous structure; this definite structure, moulded by experience into correspondence with external things, makes necessary in thought the relations answering to uniformities in things. Hence, among others, the conception of the Indestructibility of Matter.

For self-analysis shows this to be a datum of consciousness. Conceive space to be cleared of all bodies save one. Now imagine the remaining one not to be removed from its place, but to lapse into nothing while standing in that place. You fail. The space which was solid you cannot conceive becoming empty, save by transfer of that which made it solid. What is termed the ultimate incompressibility of Matter, is an admitted law of thought. However small the bulk to which we conceive a piece of matter reduced, it is impossible to conceive it reduced into nothing. While we can represent to ourselves its parts as approximated, we cannot represent to ourselves the quantity of matter as made less. To do this would be to imagine some of the parts compressed into nothing, which is no more possible than to imagine compression of the whole into nothing. Our inability to conceive Matter becoming non-existent, is consequent on the nature of thought. Thought consists in the establishment of relations. There can be no relation established, and therefore no thought framed, when one of the related terms is absent from consciousness. Hence it is impossible to think of something becoming nothing, for the same reason that it is impossible to think of nothing becoming something -- the reason, namely, that nothing cannot become an object of consciousness. The annihilation of Matter is unthinkable for the same reason that the creation of Matter is unthinkable.

It must be added that no experimental verification of the truth. that Matter is indestructible, is possible without a tacit assumption of it. For all such verification implies weighing, and weighing assumes that the matter forming the weight remains the same.

§54. And here we are introduced to that which it most concerns us to observe -- the nature of the perceptions by which the permanence of Matter is perpetually illustrated. These perceptions under all their forms simply reveal this -- that the force which a given quantity of matter embodies remains always the same under the same conditions. A toy which long unseen produces in us a set of visual and tactual feelings like those produced in childhood is recognized as the same because it has the power of affecting us in the same ways. The downward strain of some sovereigns which the bank-clerk weighs to save himself the trouble of counting, proves the special amount of a special kind of Matter; and the goldsmith uses the same test when the shape of the Matter has been changed by a workman. So, too, with special properties. Whether a certain crystal is or is not diamond, is decided by its resistance to abrasion and the degree to which it bends light out of its course. And so the chemist when a piece of substance lately visible and tangible has been reduced to an invisible, intangible gas, but has the same weight, or when the quantity of a certain element is inferred from its ability to neutralize a given quantity of some other element, he refers to the amount of action which the Matter exercises as his measure of the amount of Matter.

Thus, then, by the Indestructibility of Matter, we reilly mean the indestructibility of the force with which Matter affects us. And this truth is made manifest not only by analysis of the a posteriori cognition, but equally so by analysis of the a priori one.(*)

<* Lest he should not have observed it, the reader must be warned that the terms "a priori truth" and "necessary truth," as used in this work, are to be interpreted not in the old sense, as implying cognitions wholly independent of experiences, but as implying cognitions that have been rendered organic by immense accumulations of experiences, received partly by the individual, but mainly by all ancestral individuals whose nervous systems he inherits. On referring to the Principles of Psychology (§§426-433), it will be seen that the warrant alleged for one of these irreversible ultimate convictions is that, on the hypothesis of Evolution, it represents an immeasurably-greater accumulation of experiences than can be acquired by any single individual.>

Chapter 5   The Continuity of Motion

§55. Like the Indestructibility of Matter, the Continuity of Motion, or, more strictly, of that something which has Motion for one of its sensible forms, is a truth on which depends the possibility of exact Science, and therefore of a Philosophy which unifies the results of exact Science. Motions, visible and invisible, of masses and of molecules, form the larger half of the phenomena to be interpreted; and if such motions might either proceed from nothing or lapse into nothing, there could be no scientific interpretation of them.

This second fundamental truth, like the first, is not self-evident to primitive men nor to the uncultured among ourselves. Contrariwise, to uninstructed minds the opposite seems self-evident. The facts that a stone thrown up soon loses its ascending motion, and that after the blow its fall gives to the Earth, it remains quiescent, apparently prove that the principle of activity(*)<* Throughout this chapter I use this phrase. not with any metaphysical meaning, but merely to avoid foregone conclusions.> which the stone manifested may disappear absolutely. Accepting the dicta of unaided perception, all men once believed, and most believe still, that motion can pass into nothing, and ordinarily does so pass. But the establishment of certain facts having opposite implications, led to inquiries which have proved these appearances to be illusive. The discovery that the celestial motions do not diminish, raised the suspicion that a moving body, when not interfered with, will go on for ever without change of velocity; and suggested the question whether bodies which lose their motion, do not at the same time communicate as much motion to other bodies. It was a familiar fact that a stone would glide further over a smooth surface, as that of ice, presenting no small objects to which it could part with its motion by collision, than over a surface strewn with such small objects; and that a stick hurled into the air would travel a far greater distance than if hurled into a dense medium like water. Thus the primitive notion that moving bodies have an inherent tendency to stop -- a notion which the Greeks did not get rid of, and which lasted till the time of Galileo -- began to give way. It was further shaken by such experiments as those of Hooke, which proved that a top spins the longer in proportion as it is prevented from communicating motion to surrounding matter.

To explain here all disappearances of visible motions is out of the question. It must suffice to state, generally, that the molar motion which disappears when a bell is struck by its clapper, re-appears in the bell's vibrations and in the waves of air they produce; that when a moving mass is stopped by coming against a mass that is immovable, the motion which does not show itself in sound shows itself in molecular motion; and that when bodies rub against one another, the motion lost by friction is gained in the motion of molecules. But one aspect of this general truth, as it is displayed in the motions of masses, we must carefully contemplate; for, otherwise, the doctrine of the Continuity of Motion will be misapprehended.

§56. As expressed by Newton, the first law of motion is that "every body must persevere in its state of rest, Or of uniform motion in a straight line, unless it be compelled to change that state by forces impressed upon it."

With this truth may be associated the truth that a body describing a circular orbit round a centre which detains it by a tractive force, moves in that orbit with undiminished velocity.

The first of these abstract truths is never realized in the concrete, and the second of them is but approximately realized. Uniform motion in a straight line implies the absence of a resisting medium; and it further implies the absence of forces, gravitative or other exercised by neighbouring masses: conditions never fulfilled. So, too, the maintenance of a circular orbit by any celestial body, implies that there are no perturbing bodies, and that there is an exact adjustment between its velocity and the tractive force of its primary: neither requirement ever being conformed to. In actual orbits, sensibly elliptical as they are, the velocity is sensibly variable. And along with great eccentricity there goes great variation.

With the case of these celestial bodies which, moving in eccentric orbits, display at one time little motion and at another much motion, may be associated as partially analogous the case of the pendulum. With speed now increasing and now decreasing, the pendulum alternates between extremes at which motion ceases.

How shall we so conceive these allied phenomena as to express rightly the truth common to them? The first law of motion, nowhere literally fulfilled, is yet, in a sense, implied by these facts which seem at variance with it. Though in a circular orbit the direction of the motion is continually being changed, yet the velocity remains unchanged. Though in an elliptical orbit there is now acceleration and now retardation, yet the average speed is constant through successive revolutions. Though the pendulum comes to a momentary rest at the end of each swing, and then begins a reverse motion, yet the oscillation, considered as a whole, is continuous: friction and atmospheric resistance being absent, this alternation of states would go on for ever.

What, then, do these cases show us in common? That which vision familiarizes us with in Motion, and that which has thus been made the dominant element in our conception of Motion, is not the element of which we can allege continuity. If we regard Motion simply as change of place, then the pendulum shows us both that the rate of this change may vary from instant to instant, and that, ceasing at intervals, it may be afresh initiated.

But if what we may call the translation-element in Motion is not continuous, what is continuous? If, like Galileo, we watch a swinging chandelier, and observe, not the isochronism of its oscillations but the recurring reversal of direction, we are impressed with the fact that though, at the end of each swing, the translation through space ceases, yet there is something which does not cease; for the translation recommences in the opposite direction. And on remembering that when a violent push was given to the chandelier it described a larger arc, and was a longer time before the resistance of the air brought it to rest, we are shown that what continues to exist during its alternating movements is some correlative of the muscular effort which put it in motion. The truth forced on our attention is that translation through space is not itself an existence; and that hence the cessation of Motion, considered simply as translation, is not the cessation of an existence, but is the cessation of a certain sign of an existence.

Still there remains a difficulty If that element in the chandelier's motion of which alone we can allege continuity is the correlative of the muscular effort which moved, the chandelier, what becomes of this element at either extreme of the oscillation? Arrest the chandelier in the middle of its swing, and it gives a blow to the hand-exhibits some principle of activity such as muscular effort can give. But touch it at either turning point and it displays no such principle of activity. This has disappeared just as much as the translation through space has disappeared. How then, can it be alleged that though the Motion through space is not continuous, the principle of activity implied by the Motion is continuous?

Unquestionably the facts show that the principle of activity continues to exist under some form. When not perceptible it must be latent. How is it latent? A clue to the answer is gained on observing that though the chandelier when seized at the turning point of its swing, gives no impact in the direction of its late movement, it forthwith begins to pull in the opposite direction; and on observing, further, that its pull is great when the swing has been made extensive by a violent push. Hence the loss of visible activity at the highest point of the upward motion, is accompanied by the production of an invisible activity which generates the subsequent motion downwards. To conceive this latent activity gained, as an existence equal to the perceptible activity lost, is not easy; but we may help ourselves so to conceive it by considering cases of another class.

§57. When one who pushes against a door that has stuck fast, produces by great effort no motion, but eventually by a little greater effort bursts the door open, swinging it back and tumbling headlong into the room, he has evidence that the first muscular strain which did not produce transfer of matter through space, was yet equivalent to a certain amount of such transfer. Again, when a railway-porter gradually stops a detached carriage by pulling at the buffer, he shows us that (supposing friction, etc., absent) the slowly-diminished motion of the carriage over a certain space, is the equivalent of the constant backward strain put upon the carriage while it is traveling through that space. Carrying with us the conception thus reached, we will now consider a case which makes it more definite.

When used as a plaything, a ball fastened to the end of an india-rubber string yields a clear idea of the correlation between perceptible activity and latent activity. If, retaining one end of the string, a boy throws the ball from him horizontally, its motion is resisted by the increasing strain on the string; and the string, stretched more and more as the ball recedes, presently brings it to rest. Where now exists the principle of activity which the moving ball displayed? It exists in the strained thread of india-rubber. Under what form of changed molecular state it exists we need not ask. It suffices that the string is the seat of a tension generated by the motion of the ball, and equivalent to it. When the ball has been arrested the stretched string begins to generate in it an opposite motion, and continues to accelerate that motion until the ball comes back to the point at which the stretching of the string commenced -- a point at which, but for loss by atmospheric resistance and molecular redistribution, its velocity would be equal to the original velocity. Here the truth that the principle of velocity, alternating between visible and invisible modes, does not cease to exist when the translation through space ceases to exist, is readily comprehensible; and it becomes easy to understand the corollary that at each point in the path of the ball, the quantity of its perceptible activity, plus the quantity which is latent in the stretched string, yields a constant sum.

Aided by this illustration, we can vaguely conceive what happens between bodies connected, not by a stretched string, but by a traction exercised by an invisible agency. It matters not to our general conception that the intensity of this traction varies in a different manner: decreasing as the square of the distance increases, but being practically constant for terrestrial distances. Notwithstanding these differences there is a truth common to the two cases. The weight of something held in the hand shows that between one body in space and another there exists a strain. This downward pull affects the hand as it might be affected by a stretched elastic string. Hence, when a body projected upwards and gradually retarded by gravity, finally stops, we must regard the principle of activity manifested as having become latent in the strain between it and the Earth -- a strain of which the quantity is to be conceived as the product of its intensity and the distance through which it acts. Carrying a step further our illustration of the stretched string, will elucidate this. To simulate the action of gravity at terrestrial distances, let us imagine that when the attached moving body has stretched the elastic string to its limit, say at the distance of ten feet (from which point it is prevented from contracting back), a second like string could instantly be tied to the end of the first and to the body, which continuing its course stretched this second string, and so on with a succession of such strings, till the body was arrested. Then, obviously, the quantity of the principle of activity which the moving body possessed, but which has now become latent in the stretched strings, is measured by the number of such strings over which the strain extends. Now though the tractive force of the Earth is not exercised in a like way -- though gravity, utterly unknown in its nature, is probably a resultant of actions pervading the ethereal medium; yet the above analogy suggests the belief that the principle of activity exhibited by a stone thrown up and presently arrested, has not ceased to exist, but has become so much imperceptible or latent activity in the medium occupying space; and that when the stone falls, this is re-transformed into its equivalent of perceptible activity. If we conceive the process at all, we must conceive it thus: otherwise, we have to conceive that a power has been changed into a space-relation, and this is inconceivable.

Here, then, is the solution of the difficulty The space-element of Motion is not in itself a thing. Change of position is not an existence, but the manifestation of an existence. This existence (supposing it not transferred by collision or friction) may cease to display itself as translation; but it can do so only by displaying itself as strain. And this principle of activity now shown by translation, now by strain, and often by the two together, is alone that which in Motion we can call continuous.

§58. What is this principle of activity? Vision gives us no idea of it. If by a mirror we cast the image of an illuminated object on to a dark wall, and then suddenly changing the attitude of the mirror make the reflected image pass from side to side, no thought arises that there is present in the image a principle of activity. Before we can conceive the presence of this, we must regard the visual impression as symbolizing something tangible. Sight of a moving body suggests a principle of activity which would be appreciable by skin and muscles were the body laid hold of. This principle of activity which Motion shows us, is the objective sense of effort. By pushing and pulling we get feelings which, generalized and abstracted, yield our ideas of resistance and tension. Now displayed by changing position and now by unchanging strain, this principle of activity is ultimately conceived by us under the single form of its equivalent muscular effort. So that the continuity of Motion, as well as the indestructibility of Matter, is really known to us in terms of Force. Here, however, the Force is of the kind known as Energy -- a word applied to the force, molar or molecular, possessed by matter in action, as distinguished from the passive force by which matter maintains its shape and occupies space: a force which physicists appear to think needs no name.

§59. And now we reach the truth to be here especially noted. All proofs of the Continuity of Motion involve the postulate that the quantity of Energy is constant. Observe what results when we analyze the reasonings by which the Continuity of Motion is shown.

A particular planet is identified by its constant power to affect our eyes in a special way. Further, such planet has not been seen to move by the astronomer; but its motion is inferred from a comparison of its present position with the position it before occupied. This comparison proves to be a comparison between the different impressions produced on him by the different adjustments of his observing instruments. And the validity of the inferences. drawn depends on the truth of the assumption that these masses of matter, celestial and terrestrial, continue to affect his senses in the same ways under the same conditions. On going a step further back, it turns out that difference in the adjustment of his observing instrument, and by implication in the planet's position, is meaningless until shown to correspond with a certain calculated position which the planet must occupy, supposing that no motion has been lost. And if, finally, we examine the implied calculation, we find that it takes into account those accelerations and retardations which ellipticity of the orbit involves, as well as those variations of motion caused by adjacent planets -- we find, that is, that the motion is concluded to be indestructible not from the uniform velocity of the planet, but from the constant quantity of motion exhibited after allowances have been made for the motions communicated to, or received from, other celestial bodies. And when we ask how this is estimated, we discover that the estimate assumes certain laws of force or energy; which laws, one and all, embody the postulate that energy cannot be destroyed.

Similarly with the a priori conclusion that Motion is continuous. That which defies suppression in thought (disciplined thought, of course), is the force which the motion indicates. We can imagine retardation to result from the actions of other bodies. But to imagine this we must imagine loss of some of the energy implied by the motion. We are obliged to conceive this energy as impressed in the shape of reaction on the bodies causing the retardation. And the motion communicated to them, we are compelled to regard as a product of the communicated energy. We can mentally diminish the velocity or space-element of motion, by diffusing the momentum or force-element over a larger mass of matter; but the quantity of this force-element is unchangeable in thought.*

<* This exposition differs in its point of view from the expositions ordinarily given; and some of the words employed, such as strain, have somewhat larger implications. Unable to learn anything about the nature of Force, physicists have, of late years, formulated ultimate physical truths in such ways as often tacitly to exclude the consciousness of Force: conceiving cause, as Hume proposed, in terms of antecedence and sequence only. "Potential energy," for example, is defined as constituted by such relations in space as permit masses to generate in one another certain motions, but as being in itself nothing. While this mode of conceiving the phenomena suffices for physical inquiries. It does not suffice for the purposes of philosophy. In the Principles of Psychology, §§ 347-350, I have shown that our ideas of Body, Space, Motion, are derived from our ideas of muscular tension, which are the ultimate symbols into which all our other mental symbols are interpretable. Hence to formulate phenomena in the proximate terms of Body, Space, Motion, while discharging from the concepts the consciousness of Force, is to acknowledge the superstructure while ignoring the foundation.

When, in 1875, I recast the foregoing chapter, and set forth more fully the doctrine contained in the answering chapters of preceding editions, I supposed myself to be alone in dissenting from the prevailing doctrine. But a year after, in the Philosophical Magazine for October, 1876, I was glad to see the same view enunciated and defended by Dr. Croll, in an essay "On the Transformation of Gravity." I commend his arguments to those who are not convinced by the arguments used above.

Let me add a remark concerning the nature of the question at issue. It is assumed that, as a matter of course, it is a question falling within the sphere of the mathematicians and physicists. I demur to the assumption. It is a question falling within the sphere of the psychologists -- a question concerning the right interpretation of our ideas.>

Chapter 6   The Persistence of Force (*)

<* Some explanation of this title is needful. In the text itself are given the reasons for using the word "force" instead of the word "energy" and here I must say why I think "persistence" preferable to "conservation." Some two years ago (this was written in 1861) I expressed to my friend Prof. Huxley, my dissatisfaction with the (then) current expression -- "Conservation of Force," assigning as reasons, first, that the word "conservation" implies a conserver and an act of conserving; and, second, that it does not imply the existence of the force before the particular manifestation of it which is contemplated. And I may now add, as a further fault, the tacit assumption that, without some act of conservation, force would disappear. All these implications are at variance with the conception to be conveyed. In place of "conservation" Prof. Huxley suggested persistence. This meets most of the objections; and though it may be urged that it does not directly imply pre-existence of the force at any time manifested, yet no word less faulty in this respect can be found. In the absence of a word coined for the Purpose, it seems the best; and as such I adopt it.>

§60. In the foregoing two chapters, manifestations of force of two fundamentally-different classes have been dealt with -- the force by which matter demonstrates itself to us as existing, and the force by which it demonstrates itself to us as acting.

Body is distinguishable from space by its power of affecting our senses, and, in the last resort, by its opposition to our efforts. We can conceive of body only by joining in thought extension and resistance: take away resistance, and there remains only space. In what way this force which produces space-occupancy is conditioned we do not know. The mode of force which is revealed to us only by opposition to our own powers, may have for one of its factors the mode of force which reveals itself by the changes initiated in our consciousness. That the space a body occupies is in part determined by the degree of that activity of its molecules known as heat, is a familiar truth. Moreover, such molecular rearrangement as occurs when water is changed into ice, is shown to be accompanied by an evolution of force which may burst the containing vessel and give motion to the fragments. Nevertheless, the forms of our experience oblige us to distinguish between two modes of force; the one not a worker of change and the other a worker of change, actual or potential. The first of these -- the space-occupying kind of force -- has no specific name.

For the second kind of force, the specific name now accepted is "Energy." That which in the last chapter was spoken of as perceptible activity, is called by physicists, "actual energy;" and that which was there spoken of as latent activity, they call "potential energy." While including the mode of activity shown in molar motion, Energy includes also the several modes of activity into which molar motion is transformable -- heat, light, etc. It is the common name for the power shown alike in the movements of masses and in the movements of molecules. To our perceptions this second kind of force differs from the first kind as being not intrinsic but extrinsic.

In aggregated matter as presented to sight and touch, this antithesis is, as above implied, much obscured. Especially in a compound substance, both the latent energy locked up in the chemically-combined molecules and the actual energy made perceptible to us as heat, complicate the manifestations of intrinsic force by the manifestations of extrinsic force. But the antithesis, here partially hidden, is clearly seen on reducing the data to their lowest terms -- a unit of matter, or atom, and its motion. The force by which it exists is passive but independent; while the force by which it moves is active but dependent on its past and present relations to other atoms. These two cannot be identified in our thoughts. For as it is impossible to think of motion without something that moves, so it is impossible to think of energy without something possessing the energy.

While recognizing this fundamental distinction between that intrinsic force by which body manifests itself as occupying space, and that extrinsic force distinguished as energy, I here treat of them together as being alike persistent. And I thus treat of them together partly because, in our consciousness of them, there is the same essential element. The sense of effort is our subjective symbol for objective force in general, passive and active. Power of resisting that which we know as our own muscular strain, is the ultimate element in our idea of body as distinguished from space; and any motor energy which we give to body, or receive from it, is thought of as equal to a certain amount of muscular strain. The two consciousnesses differ essentially in this, that the feeling of effort common to them is in the last case joined with consciousness of change of position, but in the first case is not.* <* Concerning the fundamental distinction here made between the space-occupying kind of force, and the kind of force shown by various modes of activity I am, as in the last chapter, at issue with some of my scientific friends. They do not admit that the conception of force is involved in the conception of a unit of matter. From the psychological point of view however, Matter, in all its properties, is the unknown cause of the sensations it produces in us; of which the one which remains when all ot hers are absent, is resistance to our efforts -- a resistance we are obliged to symbolize as the equivalent of the muscular force it opposes. In imagining a unit of matter we may not ignore this symbol, by which alone a unit of matter can be figured in thought as an existence. It is not allowable to speak as though there remained a conception of an existence when that conception has been eviscerated -- deprived of the element of thought by which it is distinguished from empty space. Divest the conceived unit of matter of the objective correlate to our subjective sense of effort, and the entire fabric of physical conceptions disappears.>

There is, however, a further and more important reason for here dealing with the proposition that Force under each of these forms persists. We have to examine its warrant.

§61. A little more patience is asked. We must reconsider the reasoning by which the indestructibility of Matter and the continuity of Motion are established, that we may see how impossible it is to arrive by parallel reasoning at the Persistence of Force.

In all three cases the question is one of quantity. Does the Matter or Motion, or Force, ever diminish in quantity? Quantitative science implies measurement, and measurement implies a unit of measure. The units of measure from which all others of any exactness are derived, are units of linear extension. Our units of linear extension are the lengths of masses of matter or the spaces between marks made on the masses, and we assume these lengths, or these spaces between marks, to remain unchanged while the temperature is unchanged. From the standard-measure preserved at Westminster, are derived the measures for trigonometrical surveys, for geodesy, the measurement of terrestrial arcs, and the calculations of astronomical distances, dimensions, etc., and therefore for Astronomy at large. Were these units of length, original and derived, irregularly variable, there could be no celestial dynamics, nor any of that verification yielded by it of the constancy of the celestial masses and of their energies. Hence, persistence of the space-occupying species of force cannot be proved, for the reason that it is tacitly assumed in every experiment or observation by which it is proposed to prove it. The like holds of the force distinguished as energy. The endeavour to establish this by measurement, takes for granted both the persistence of the intrinsic force by which body manifests itself as existing, and the persistence of the extrinsic force by which body acts. For it is from these equal units of linear extension, through the medium of the equal-armed lever or scales, that we derive our equal units of weight, or gravitative force; and only by means of these can we make those quantitative comparisons by which the truths of exact science are reached. Throughout the investigations leading the chemist to the conclusion that of the carbon which has disappeared during combustion, no portion has been lost, what is his repeatedly-assigned proof? That afforded by the scales. In what terms is the verdict of the scales given? In grammes -- in units of weight -- in units of gravitative force. And what is the total content of the verdict? That as many units of gravitative force as the carbon exhibited at first, it exhibits still. The validity of the inference, then, depends entirely upon the constancy of the units of force. If the force with which the portion of metal called a gramme-weight tends towards the Earth, has varied, the inference that matter is indestructible is vicious. Everything turns on the truth of the assumption that the gravitation of the weights is persistent; and of this no proof is assigned, or can be assigned. In the reasonings of the astronomer there is a like implication, from which we may draw the like conclusion. No problem in celestial dynamics can be solved without the assumption of some unit of force. This unit need not be, like a pound or a ton, one of which we can take direct cognizance. It is requisite only that the mutual attraction which some two of the bodies concerned exercise at a given distance, shall be taken as one; so that the other attractions with which the problem deals, may be expressed in terms of this one. Such unit being assumed, the motions which the respective masses will generate in one another in a given time, are calculated; and compounding these with the motions they already have, their places at the end of that time are predicted. The prediction is verified by observation. From this, either of two inferences may be drawn. Assuming the masses to be unchanged, their energies may be proved undiminished; or assuming their energies undiminished, the masses may be proved unchanged. But the validity of one or other inference depends wholly on the truth of the assumption that the unit of force is unchanged. Let it be supposed that the gravitation of the two bodies towards each other at the given distance has varied, and the conclusions drawn are no longer true. Nor is it only in their concrete data that the reasonings of terrestrial and celestial physics assume the Persistence of Force. The equality of action and reaction is taken for granted from beginning to end of either argument; and to assert that action and reaction are equal and opposite, is to assert that Force persists. The implication is that there cannot be an isolated force, but that any force manifested implies an equal antecedent force from which it is derived, and against which it is a reaction.

We might indeed be certain, even in the absence of any such analysis as the foregoing, that there must exist some principle which, as being the basis of science, cannot be established by science. All reasoned-out conclusions whatever must rest on some postulate. As before shown (§23), we cannot go on merging derivative truths in those wider truths from which they are derived, without reaching at last a widest truth which can be merged in no other, or derived from no other. And the relation in which it stands to the truths of science in general, shows that this truth transcending demonstration is the Persistence of Force. To this an ultimate analysis brings us down, and on this a rational synthesis must build up.

§62. But now what is the force of which we predicate persistence? That which the word ordinarily stands for is the consciousness of muscular tension -- the feeling of effort which we have either when putting something in motion or when resisting a pressure. This feeling, however, is but a symbol.

In §18 it was said that though, since action and reaction are equal and opposite, we are obliged to think of the downward pull of a weight as equal to the upward pull which supports it, and though the thought of equality suggests kinship of nature, yet, as we cannot ascribe feeling to the weight, we are obliged to admit that Force as it exists beyond consciousness has no likeness to force as we conceive it, though there is between them the kind of equivalence implied by simultaneous variation. The effort of one who throws a cricket ball is followed by the motion of the ball through space, and its momentum is re-transformed into muscular strain in one who catches it. What the force was when it existed in the flying cricket ball it is impossible to imagine: we have no terms of thought in which to represent it. And it is thus with all the transformations of energy taking place in the world around. Those illustrations given in §66, showing the changes of form which energy undergoes and the equivalence between so much of it in one form and so much in another, fail to enlighten us respecting the energy itself. It assumes under this or that set of conditions this or that shape, and the quantity of it is not altered during its transformations. For that interpretation of things which is alone possible for us this is all we require to know -- that the force or energy manifested, now in one way now in another, persists or remains unchanged in amount. But when we ask what this energy is, there is no answer save that it is the noumenal cause implied by the phenomenal effect.

Hence the force of which we assert persistence is that Absolute Force we are obliged to postulate as the necessary correlate of the force we are conscious of. By the Persistence of Force, we really mean the persistence of some Cause which transcends our knowledge and conception. In asserting it we assert an Unconditioned Reality, without beginning or end.

Thus, quite unexpectedly, we come down once more to that ultimate truth in which, as we saw, Religion and Science coalesce -- the continued existence of an Unknowable as the necessary correlative of the Knowable.