Chapter XLVIII: Part IV: She Sang (9)

Hence what physicists call “force of inertia” is not a passive resistance proceeding from the inertia of matter, but an active exertion of the molecular powers, and has been so called only because, all other things being equal, its intensity is proportional to the mass of the inert body.(160) Evidently, inertia itself cannot resist or check the advance of an impinging body. Nothing but a positive action can do it; for nothing but a positive action can communicate to the advancing body that impetus in the opposite direction which alone is competent to neutralize the impetus of the advance. Physicists know this very well, though many of them, owing to the difficulty of analyzing and expressing certain things with philosophical accuracy, do not always use, in this particular, a very correct language—a thing which, after all, must not surprise us, as one can be well read in physics without necessarily being a profound philosopher.

The third objection is aimed at our argument against Boscovich’s theory, in which we have said that attraction and repulsion are actions of opposite kinds. Boscovich, on the contrary, maintains that attraction and repulsion differ only as the greater from the less, and therefore cannot be considered as actions of a different kind. He says: “Both actions are of the same kind; for the one, as compared with the other, is negative; and negative things do not differ in kind from positive ones. That the one, as compared with the other, is negative, is evident from this: that they differ only in direction. That the negative and the positive belong to the same kind is evident from the principle, _More and less do not differ in kind_. In fact, from the positive, by a continued subtraction or diminution, we obtain first some smaller positive quantities, then zero, and lastly, if we still go on in our subtraction, negative quantities.”(161)

This argument, notwithstanding its speciousness, is not difficult to upset. It is not true, in the first place, that attraction and repulsion differ only in direction; on the contrary, they differ in everything except in direction. Two points _A_ and _B_ being given, there is only one direction from _A_ to *B*, whether _A_ be attractive or repulsive. If _A_ is attractive, its attraction is directed from _A_ to _B_; and if _A_ is repulsive, its repulsion is no less directed from _A_ to _B_. This is quite evident, as the action must in all cases proceed from the agent to the patient. It is evident, therefore, that the two actions must have the same direction. The movements of _B_ will indeed have opposite directions, according as _B_ is attracted or repelled; but this does not show that the actions themselves have opposite directions; it shows, on the contrary, that those actions, though directed in the same manner from _A_ to _B_, are of a different nature, and proceed from opposite principles. And this conclusion may be confirmed by remarking that the direction is always from a point to a point, or from matter to matter; and consequently it is not the active power or the action, but only the position of the material centres, that can determine any direction. Accordingly, so long as such a position is not inverted, it is impossible to conceive two opposite directions from _A_ to _B_. It is therefore evidently false that attraction and repulsion differ in direction.

It is not true, in the second place, that attraction and repulsion differ only as the positive differs from the negative, or the greater from the less. In the mathematical expression of mechanical relations, if we consider a movement as positive, the movement which points to an opposite direction must, of course, be affected by the negative sign. The same we must do with regard to forces and actions; for we estimate the actions by the movements which they produce, and we express them only in terms of movement—that is, by their effects. But this does not mean that there is either any movement or any action _absolutely_ negative; for a negative movement would be no movement, and a negative action no action. It is in a relative and conventional sense only that movements are considered as positive or negative; and, moreover, either of the two opposite movements can be assumed as positive or as negative, at will; which shows very clearly that the negative and the positive do not differ in this case as the greater differs from the less, as Boscovich assumes; for either of the two can, at pleasure, be taken as positive, whereas it would be absurd to pretend that either of the two can, at pleasure, be pronounced to be the greater. Thus, when a stone is thrown up vertically, and abandoned to itself, if its ascent is taken as positive, its descent will be considered as negative. Now, according to Boscovich’s reasoning, we should infer that _the ascent is greater than the descent_, though they are evidently equal. And in the same manner, if the ascent is taken as negative (which nothing forbids), the descent must be taken as positive; whence, according to Boscovich, we ought to infer also that _the descent is greater than the ascent_. Any argument which leads to such glaring contradictions must be radically false. And therefore it is false that attraction and repulsion differ from one another as the greater from the less.

It might be urged, as a fourth objection, that if an attractive and a repulsive power differ in kind, then a repulsive element and an attractive element will be two kinds of material substance; which is inadmissible. For we cannot admit two kinds of primitive material beings essentially different, as the essence of matter must be the same in all the elements.

To this we answer that although there are two kinds of elements, there are not two kinds of matter. In other terms, an attractive element differs from a repulsive one as to the principle of action, but not as to the matter itself. In fact, the essence of a material being _as such_ requires nothing more than a form giving existence to matter; hence, wherever there is a form giving existence to matter, there also is the essence of matter. Now, matter is as much and as completely actuated by a form or act which is a principle of attraction as by a form or act which is a principle of repulsion. For the actuation of the matter by its form is not _efficient_, but _formal_; and its result is not _to approach_ by attraction or _to recede_ by repulsion, but _to be_ simply and absolutely; so that neither attractivity nor repulsivity has any bearing on the essential constitution of a material element as such—that is, inasmuch as it is material. Accordingly, two elements of opposite natures differ in kind as agents, but not as _material_ beings; and thus the essence of matter _as such_ remains one and the same in all the elements. Matter, as we have already shown, is the centre of a sphere of activity; and it is evident that, by this activity of an attractive or of a repulsive nature, the centre remains a centre, and the sphere a sphere, without the least alteration. Gold and ivory differ in kind; but a sphere of ivory and a sphere of gold do not differ in kind _as spheres_, and their centres do not differ in kind _as centres_. In a like manner the sphere of activity of an attractive element does not differ from the sphere of activity of a repulsive element, nor the centre of the one from the centre of the other. And therefore two elements, however different in their nature as agents, do not cease to be of the same kind as material. Their form is different, but informs equally, and their matter is exactly the same.

We have stated that Boscovich was led to admit two opposite powers in the same element, because he thought this to be the only means of accounting for the impenetrability of bodies. We observe that, although the impenetrability of bodies peremptorily proves the existence of repulsive powers, it by no means proves that the repulsive power coexists with the attractive _in the same primitive element_. Hence Boscovich’s inference is not legitimate. Molecules, as we have already remarked, may possess both powers, as their composition involves a great number of elements, which can be of different natures. And this suffices to explain the impenetrability of bodies, and all other properties dependent on molecular actions, without need of arbitrary hypotheses.

A last objection against the doctrine we have established might be drawn from the difficulty of reconciling the existence of repulsive elements with universal attraction; for if we admit that repulsion can be exercised at astronomical distances, it will be difficult to see how the celestial bodies can attract one another in the direct ratio of their masses, as the law of attraction requires.

The answer is obvious. If all matter were repulsive, universal repulsion would be the consequence. But if bodies are made up partly of attractive and partly of repulsive elements, then will either universal repulsion or universal attraction prevail, according as the number and power of the repulsive elements is greater or smaller than that of the attractive ones. Hence, from the fact that in the solar system and elsewhere attraction prevails, it follows, indeed, that the attractive powers are the stronger, but it does not follow that they are the whole stuff of which bodies are compounded.

As to the law of attraction _in the direct ratio of the masses_, a distinction is to be made. The law is certainly true if by masses we mean the masses _acted on_; not so, however, if for the masses acted on we substitute the masses of the attracting bodies. The fact of universal attraction shows that two planets, all other things being equal, must be attracted by the sun in the direct ratio of their masses. This is an established truth. But to say that, all other things being equal, the sun and the earth would attract the moon in the direct ratio of their _absolute_ masses, is to assume what no fact whatever gives us the right to assert. Physicists very commonly admit this second assumption, and consider it a part of the law of attraction; but they would be not a little embarrassed were they required to undertake its demonstration. They take for granted that all the particles of matter are equally and uniformly attractive. Now, this assumption has never been established by facts; it simply arises from an unlawful generalization—that is, from the extension of the law of kinetic forces to dynamical actions. The momenta of two bodies animated by equal velocities are proportional to the masses of the same bodies; but nothing justifies the inference that therefore the attractive powers must be proportional to the masses. Indeed, it is scarcely possible to believe that equal masses of lead, iron, and zinc possess equal powers. Their properties are, in fact, so different that we cannot assume their constitution to be the result of an assemblage of equal powers. Hence we maintain that, unless two bodies have the same molecular constitution, their attractions cannot be proportional to their masses.(162)

Universal attraction being also proportional to the inverse squares of the distances, as we are going to show, we may add that the existence of repulsive elements in the sun and in the planets by no means interferes with this law. In fact, the total action of one celestial body on another, on account of the great distance at which the law of universal attraction is applied, equals the algebraic sum of all the actions by which one body makes an impression upon the other. Hence, if all the elements of which the body consists, whether they be attractive or repulsive, act proportionally to the inverse square of the distance, it is evident that the resultant of all such actions will also be proportional to the inverse square of the distance, whenever the form of the body is spherical, or nearly so, as is the case with the celestial bodies. And thus it is plain that no valid objection can be drawn from universal attraction against the existence of repulsive elements.

Law of elementary actions.

We have now to establish the general law of elementary attraction and repulsion. We hold that _the actions of every primitive element are always inversely proportional to the squares of the distances, no matter whether such distances be great or small, astronomical or molecular_.

This proposition can be briefly proved in the following manner: Astronomy teaches us that the Newtonian law, according to which the actions are inversely proportional to the squares of the distances, is true for all the celestial bodies. Now, the total action of one celestial body upon another is a resultant of elementary actions, and arises from the algebraic sum of them all. Hence it follows that every element of matter, when acting from certain distances, obeys the Newtonian law; for it is evident, from the theory of the composition of forces, that the sum of the elementary actions cannot follow the Newtonian law unless these actions themselves follow it. But if the law is true in the case of astronomical distances, it must be true also in the case of microscopical and molecular distances. For as a primitive element cannot have two laws of action, so neither can it follow at molecular distances any other law than that which it follows at all other distances.

That a primitive element cannot have two different laws of action will be manifest by considering that the law which an element obeys in its actions results from the intrinsic determination of its nature—that is, from its formal constitution—inasmuch as the principle of action is, in every primitive substance, the formal principle of its very being: _Principium essendi est principium operandi_. Now, a primitive element has but one formal principle of being; for it is entitatively one, and therefore it has but one formal determination to act, which, as resulting from its essential constitution, is unchangeable and inviolable. But it is evident that from _one_ formal determination to act only _one_ law of action can possibly result. Two laws would be two formal results, and would require two formal principles giving two different determinations. Accordingly, since each primitive element has but one formal principle, it cannot have two laws of action. And therefore the Newtonian law, which primitive elements follow at astronomical distances, must prevail also at all other distances.

Let the reader observe that this conclusion regards the action of primitive _elements_, not the action of _molecules_. That molecular actions at molecular distances are not inversely proportional to the square of the distance is a known fact. Molecular cohesion, for instance, is immensely greater than it could possibly be by the Newtonian law; so also molecular repulsion. This is what prevented physicists from recognizing the applicability of the Newtonian law at molecular distances. As long as the primitive elements were confounded, under the name of atoms, with the molecules of the so‐called primitive bodies, hydrogen, oxygen, carbon, etc., it was impossible to recognize in the molecular actions any trace of the Newtonian law; hence came the division of attraction into _universal_ and _molecular_, the first following a known law, the second following some other law or laws which physicists could never discover. Their embarrassment was a necessary consequence of an incomplete analysis of the material compound. The molecule of a given substance, though often called an atom, is a system of primitive elements; and elements acting according to the Newtonian law can give rise to molecular systems which, at very small distances, will act according to any other law that may be indicated by molecular phenomena. This other law depends entirely on the number, kind, strength, and geometrical arrangement of the primitive elements which enter into the constitution of the molecule; and since molecules of different primitive substances are very differently constituted, every kind of molecule must have its own peculiar law of acting at molecular distances—a fact on which the scientific explanation of the different physical and chemical properties of different substances entirely depends. Hence it is clear that all the attempts at finding a general law of molecular attraction were, from the very nature of the case, destined to fail. The only general law of action which all matter obeys is the Newtonian law; and what was once considered to form an exception to it is now acknowledged to be the result of its application to a complex system of attractive and repulsive elements.

From the fact that the actions of all elements are proportional to the inverse squares of the distances, it follows that the sphere of activity of material elements extends beyond any assignable limit. The intensity of the action cannot, in fact, become = 0 unless the distance becomes infinite. The objections to which this corollary of the Newtonian law may give rise will be answered in our next article, where all the difficulties concerning the _actio in distans_ will be solved.

Mode of action.

A last question remains here to be examined respecting the action of primitive material elements—viz., whether such an action needs a medium through which it may be transmitted and communicated to distant bodies, or whether, on the contrary, it is exerted upon them directly without dependence on any material medium.

In answering this question we must be careful not to confound action with movement. Movement, though not properly transmitted, is propagated, as we shall explain; and this cannot take place where there is no movable matter. Those who are wont to identify movement with force, and force with action, as is unfortunately the fashion even in scientific treatises, will no doubt imagine that actions must be transmitted or propagated through a material medium, just as sound through air, or as light through luminiferous ether. But action is not movement; and therefore the question how elementary actions—that is, how attractions or repulsions—reach distant bodies has to be resolved on its own merit, as one altogether distinct from the question about the propagation of movement. This premised, we are going to show that _the elementary actions are independent of all material medium of communication_.

In the first place, there is no reason why we should assume that the elementary action (attraction or repulsion) depends on a medium of communication, except inasmuch as we may apprehend that the action itself, or the active power whence it proceeds, is in need of being transmitted to some matter located at a certain distance. But neither the elementary power nor the elementary action can be transmitted to the distant matter. And therefore neither the power nor the action can be dependent on a medium of communication.

In this syllogism the major is evident; and the minor can be proved in two manners: First, because the power and the action are, of their own nature, intransmissible. Secondly, because, prescinding from their intransmissibility, no medium can be assigned which would be capable of transmitting them. And as to the first, we know that nothing can be transmitted to a distant place except by local movement; but neither the active power nor the elementary action is capable of receiving local movement; for there is no other subject capable of local movement than matter alone, on account of its passive potentiality. Hence neither power nor action can be transmitted. And in the second place, even were they transmissible, what medium could be found for their transmission? If any such medium could be found, it would consist of some matter like ether or air, this being the view of those who admit the necessity of such a medium. On the other hand, a material substance is not a suitable medium for transmitting action or power. For whenever an active power is exerted upon matter, the result of the exertion is nothing but a determination to a change of place; as it is well known that matter cannot receive any other determination. And therefore it is not the power that is received in the matter acted on, but only the act produced by its exertion, which act is otherwise called a momentum either statical or dynamical. Strictly speaking, not even the action itself is received in the matter, although we are wont to tolerate such an expression; for the action properly so called is the production of an act, and the matter receives, indeed, the act produced, but not its production. And thus the action, properly speaking, is _terminated_ to the matter, and not _received_ in it. Hence we see that neither the power of the agent nor its exertion is received in the matter acted on; it is merely the produced accidental act, or, in other terms, the momentum, that is received. But evidently matter cannot transmit what it does not receive. And therefore matter cannot be a medium for transmitting either power or action. Whether it can transmit movement we shall examine at the end of the present question.

This argument would suffice to show that elementary actions are quite independent of a material medium. Yet as the prejudice against which we are fighting is ancient, popular, and deeply rooted, we think it will not be superfluous to confirm our proof by a few other considerations.

Those who maintain the transmission of forces admit a material medium, in which, by successive contact of particles with particles, the transmission of the force to a distant body is supposed to be carried on. By the word “force” they understand action as well as movement. Now, let us ask them whether the particles of their material medium come into mathematical contact or not. If they do not come into mathematical contact, then the action is not transmitted by the medium from one particle to another, for there will be a vacuum between them; and vacuum is not a material medium. If, on the contrary, the particles come into mathematical contact with their own matter, then, as we have already shown in our past article, they cannot by such a contact communicate any movement to each other; and since the transmission in question should be carried on by successive communications of movement, it is plain that no such transmission will be possible. And accordingly the theory of the transmission of actions through a medium must be rejected.

Moreover, elementary actions are either attractive or repulsive, and neither of them can be conceived without intensity and direction. Now, no direction is possible unless there be two points distinctly ubicated in space. And therefore the action, no matter whether attractive or repulsive, cannot reach any material point which is not distant from the matter of the agent. But if so, the action is independent of a medium of communication; for the material medium, if it were needed, should lie between the agent and the patient in such a manner as to link them together, and fill by its material continuity the gap by which they are separated; and if this were the case, the medium could not be set in motion, as its contact with the agent would exclude distance, and consequently the possibility of any direction from the agent to the medium itself.

Some will say that this argument proves nothing, as the direction of the action can be sufficiently accounted for by the direction of the impulse. But this conclusion is evidently wrong. For what impulse can they imagine to proceed from the sun to the moon? Uncultivated minds are easily deluded by unlawful generalizations. They apply to all actions what they imagine to agree with some special phenomenon; and because they see that in the case of impact there is an impulse in a certain direction, they hastily conclude that the direction of every action depends on the direction of some impulse. We may remark that, even in the case of impact, it is not safe to conclude that the direction of the movement will follow the direction of the impulse, unless the impulse be central, and the body impinged upon homogeneous. But leaving aside the theory of impact, which has nothing to do with the present question, what impulse can explain the continuous resistance of a body to statical forces? What impulse can account for the expansive tendency of gases, and for their continuous pressure against the recipients in which they are contained? What impulse, above all, can account for universal attraction?

We have mentioned this objection, not because it needed any scientific or philosophical discussion, but simply because it is one of those notions to which the prejudices of our infancy give easy admittance into our minds when we allow ourselves to be guided, as is often the case, by our senses and imagination, in matters pertaining in great part to the intellectual order. Our mistakes in the appreciation of the character and conditions of natural facts most ordinarily originate in the unwarranted assumption that, since the facts are sensible, our knowledge of them must wholly depend on our senses; whilst the truth is that our senses perceive the movements, but not the actions which cause them, and therefore do not see the entirety of the natural facts, but that portion only which is most superficial. “A fundamental fact, like an elementary principle, never fails us,” says M. Faraday, speaking of natural philosophy; “its evidence is always true; but, on the other hand, we frequently have to ask, What is the fact? often fail in distinguishing it—often fail in the very statement of it—and mostly overpass or come short of its true recognition. If we are subject to mistake in the interpretation of our mere sense impressions, we are much more liable to error when we proceed to deduce from these impressions (as supplied to us by our ordinary experience) the relation of cause and effect; and the accuracy of our judgment, consequently, is more endangered.”(163)

And now, let no one imagine that we have any intention of denying the existence of a material medium between the celestial bodies. We only deny that there is a medium _for transmitting actions_. Again, we do not deny that when the earth, for instance, acts upon the moon, the elements of matter lying between the earth and the moon exert their activity on one another. But we maintain that their actions are _their own_, and proceed from their own intrinsic and permanent power, and not from any extrinsic agent, and that such actions are not travelling from element to element till they reach the moon. Neither do we deny that the elements located between the earth and the moon are also acted on, for it is clear that gravity must tend to alter their position in space; but we hold that the whole possible effect of gravity on all such elements is movement, and that movement is a mere change of place, and not a transmission of the action by which it is produced. How the movements themselves are communicated from element to element we shall explain presently.

Meanwhile, from the fact that the elementary actions are independent of all material medium of communication, we infer that bodies, in attracting and in repelling, act with equal promptitude, and without loss of time, whether the distance of the body acted on be great or small. Time, in fact, follows movement; for without movement there is no succession. Now, the action of a body does not reach the distant body through movement—that is, through successive transmission; on the contrary, each element is, of its own nature, determined to act _directly_ and _immediately_ on every other element existing in the indefinite sphere of its activity. Hence a body will indeed act with a greater intensity at a less distance, but will not act sooner than at a greater distance. There have been scientists who surmised that the solar attraction may perhaps need time for reaching the earth and the planets, and therefore that the attraction may reach Mercury in a shorter time than Jupiter or Neptune. From what precedes it is manifest that the surmise is wholly without foundation. Light needs time for its propagation, because it consists in a kind of movement; but attraction, as we have just remarked, is not movement, and therefore is not dependent on time.

Propagation of movements.

We have shown that there is no material medium for the transmission of forces, if the word “forces” is taken to mean “actions”; but if the word is intended to express “movements,” then the material medium is quite indispensable. We read very frequently in scientific books that actions are transmitted; but as this is not true of the actions themselves, we must suppose that the phrase is intended to express only the fact of a progressive development of the effects resulting from those actions. In the same way, when we read that actions are conveyed through a material medium, we interpret this expression as meaning that a material medium is strictly required for the progressive development of the series of effects due to such actions. We will explain the fact by an example.

If, a mass of air being at rest, a string is stretched in order to elicit sound, the vibrations of the string will be communicated to the neighboring molecules of air by the action (not by the movement) of the string itself; these first molecules, being thrust out of their position of equilibrium, will, by their action (that is, by the exertion of a power residing in each of their component elements, not of a power coming from the string, nor by their movement, nor by transmitted action), put in movement a following set of molecules, and so on indefinitely; so that, in the whole series of molecular vibrations, each preceding molecule causes the motion of the following one, and causes it by the exertion of its own powers, not of any power transmitted. It is evident that the string cannot give activity to the molecules of air. These molecules, whether the string vibrates or not, have already their own activity and their own mutual action; only their actions balance each other as long as the mass of air is at rest. But when the string begins to vibrate, the equilibrium being broken near it, those molecules of air which first cease to be in equilibrium begin to act on the following molecules with a different intensity, according to the change of the molecular distance. Thus the movement by which the distance is altered is not the cause, but the condition, of the phenomenon.

What we say of air and sound applies to any other medium, as ether with its vibrations, whether luminous or calorific. The molecules of ether have their own powers, and exert them continually, whether there exists a flame determining a series of vibrations or not; but with the flame the first molecules of ether which are displaced from their position of equilibrium will acquire a new local relation with regard to the following, and their actions will be of a new intensity, sufficient to cause the displacement of the next set of molecules, and so on. The flame, then, causes the displacement of the first set of molecules; the first set displaced causes the displacement of the second; the second displaced causes the displacement of the third, etc.; each set producing its own effect by its own inherent powers, not by the exertion of any power communicated to them by the flame, and their displacement being not a cause, but only a condition, on which the intensity of the exertion depends.

Hence it appears that in phenomena of this description it is not the action, and much less the power, that is transmitted, but only the movement, or the formal perturbation of the equilibrium; and even the movement is not properly _transmitted_, but only _propagated_; because the movement of each following molecule is not the identical movement of each preceding one, but is a movement really produced in the very impact of the one on the other, as our reader must have easily gathered from our preceding discussion. And therefore one movement succeeds another indefinitely, the one being a condition for the existence of the other; which constitutes propagation, not properly transmission.

To Be Continued.

Antar And Zara; Or, “The Only True Lovers.” V.

An Eastern Romance Narrated In Songs.

By Aubrey De Vere.