Popular Science Monthly/Volume 3/October 1873/The Primary Concepts of Modern Physical Science I
"Natural science," says Du Bois-Reymond, "is a reduction of the changes in the material world to motions of atoms caused by central forces independent of time, or a resolution of the phenomena of Nature into atomic mechanics. . . . The resolution of all changes in the material world into motions of atoms caused by their constant central forces would be the completion of natural science."
Obviously, the proposition thus enounced assigns to physical science limits so narrow that all attempts to bring the characteristic phenomena of organic life (not to speak of mental action) within them are utterly hopeless. Nevertheless, it is asserted that organic phenomena are the product of ordinary physical forces alone, and that the assumption of vital agencies, as distinct from the forces of inorganic Nature, is wholly inadmissible. In view of this, it seems strange that the validity of the proposition above referred to has never, so far as I know, been questioned, except in the interest of some metaphysical or theological system. It is my purpose in the following essays to offer a few suggestions in this behalf, in order to ascertain, if possible, whether the prevailing primary notions of physical science can stand, or are in need of revision.
One of the prime postulates of the mechanical theory is the atomic constitution of matter. A discussion of this theory, therefore, at once leads to an examination of the grounds upon which the assumption of atoms, as the ultimate constituents of the physical world, rests.
The doctrine that an exhaustive analysis of a material body into its real elements, if it could be practically effected, would yield an aggregate of indivisible and indestructible particles, is almost coeval with human speculation, and has held its ground more persistently than any other tenet of science or philosophy. It is true that the atomic theory, since its first promulgation by the early Greek philosophers, and its elaborate statement by Lucretius, has been modified and refined. There is probably no one, at this day, who invests the atoms with hooks and loops, or (Lucretius, De Rerum Natura, ii., 398, et seq.) accounts for the bitter taste of wormwood by the raggedness, and for the sweetness of honey by the smooth roundness of the constituent atoms. But the "atom" of modern science is still of determinate weight, if not of determinate figure, and stands for something more than an abstract unit, even in the view of those who, like Boscovich, Faraday, Ampère, or Fechner, profess to regard it as a mere centre of force. And there is no difficulty in stating the atomic doctrine in terms applicable alike to all the acceptations in which it is now held by scientific men. Whatever diversity of opinion may prevail as to the form, size, etc., of the atoms, all who advance the atomic hypothesis, in any of its varieties, as a physical theory, agree in three propositions, which may be stated as follows:
1. Atoms are absolutely simple, unchangeable, indestructible; they are physically, if not mathematically, indivisible.
2. Matter consists of discrete parts, the constituent atoms being separated by void interstitial spaces. In contrast to the continuity of space stands the discontinuity of matter. The expansion of a body is simply an increase, its contraction a lessening of the spatial intervals between the atoms.
3. The atoms composing the different chemical elements are of determinate specific weights, corresponding to their equivalents of combination?
Confessedly the atomic theory is but an hypothesis. This in itself is not decisive against its value; all physical theories properly so called are hypotheses whose eventual recognition as truths depends upon their consistency with themselves, upon their agreement with the canons of logic, upon their congruence with the facts which they serve to connect and explain, upon their conformity with the ascertained order of Nature, upon the extent to which they approve themselves as reliable anticipations or previsions of facts verified by subsequent observation or experiment, and finally upon their simplicity, or rather their reducing power. The merits of the atomic theory, too, are to be determined by seeing whether or not it satisfactorily and simply accounts for the phenomena as the explanation of which it is propounded, and whether or not it is in harmony with itself and with the known laws of Reason and of Nature.
For what facts, then, is the atomic hypothesis meant to account, and to what degree is the account it offers satisfactory?
It is claimed that the first of the three propositions above enumerated (the proposition which asserts the persistent integrity of atoms, or their unchangeability both in weight and volume) accounts for the indestructibility and impenetrability of matter; that the second of these propositions (relating to the discontinuity of matter) is an indispensable postulate for the explanation of certain physical phenomena, such as the dispersion and polarization of light; and that the third proposition (according to which the atoms composing the chemical elements are of determinate specific gravities) is the necessary general expression of the laws of definite constitution, equivalent proportion, and multiple combination, in chemistry.
In discussing these claims, it is important, first, to verify the facts and to reduce the statements of these facts to exact expression, and then to see how far they are fused by the theory:
1. The indestructibility of matter is an unquestionable truth. But in what sense, and upon what grounds, is this indestructibility predicated of matter? The unanimous answer of the atomists is: Experience teaches that all the changes to which matter is subject are but variations of form, and that amid these variations there is an unvarying constant—the mass or quantity of matter. The constancy of the mass is attested by the balance, which shows that neither fusion nor sublimation, neither generation nor corruption, can add to or detract from the weight of a body subjected to experiment. When a pound of carbon is burned, the balance demonstrates the continuing existence of this pound in the carbonic acid, which is the product of combustion, and from which the original weight of carbon may be recovered. The quantity of matter is measured by its weight, and this weight is unchangeable.
Such is the fact, familiar to every one, and its interpretation, equally familiar. To test the correctness of this interpretation, we may be permitted slightly to vary the method of verifying it. Instead of burning the pound of carbon, let us simply carry it to the summit of a mountain, or remove it to a lower latitude; is its weight still the same? Relatively it is; it will still balance the original counterpoise. But the absolute weight is no longer the same. This appears at once, if we give to the balance another form, taking a pendulum instead of a pair of scales. The pendulum on the mountain or near the equator vibrates more slowly than at the foot of the mountain or near the pole, for the reason that it has become specifically lighter by being farther removed from the centre of the earth's attraction, in conformity to the law that the attractions of bodies vary inversely as the squares of their distances.
It is thus evident that the constancy, upon the observation of which the assertion of the indestructibility of matter is based, is simply the constancy of a relation, and that the ordinary statement of the fact is crude and inadequate. Indeed, while it is true that the weight of a body is a measure of its mass, this is but a single case of the more general fact that the masses of bodies are inversely as the velocities imparted to them by the action of the same force, or, more generally still, inversely as the accelerations produced in them by the same force. In the case of gravity, the forces of attraction are directly proportional to the masses, so that the action of the forces (weight) is the simplest measure of the relation between any two masses as such; but, in any inquiry relating to the validity of the atomic theory, it is necessary to bear in mind that this weight is not the equivalent, or rather presentation, of an absolute substantive entity in one of the bodies (the body weighed), but the mere expression of a relation between two bodies mutually attracting each other. And it is further necessary to remember that this weight may be indefinitely reduced, without any diminution in the mass of the body weighed, by a mere change of its position in reference to the body between which and the body weighed the relation subsists.
Masses find their true and only measure in the action of forces, and the quantitative persistence of the effect of this action is the simple and accurate expression of the fact which is ordinarily described as the indestructibility of matter. It is obvious that this persistence is in no sense explained or accounted for by the atomic hypothesis. It may be that such persistence is an attribute of the minute, insensible particles which are supposed to constitute matter, as well as of sensible masses; but, surely, the hypothetical recurrence of a fact in the atom is no explanation of the actual occurrence of the same fact in the conglomerate mass. Whatever mystery is involved in the phenomenon is as great in the case of the atom as in that of a solar or planetary sphere. Breaking a magnet into fragments, and showing that each fragment is endowed with the magnetic polarity of the integer magnet, is no explanation of the phenomenon of magnetism. A phenomenon is not explained by being dwarfed. A fact is not transformed into a theory by being looked at through an inverted telescope. The hypothesis of ultimate indestructible atoms is not a necessary implication of the persistence of weight, and can at best account for the indestructibility of matter if it can be shown that there is an absolute limit to the compressibility of matter—in other words, that there is an absolutely least volume for every determinate mass. This brings us to the consideration of that general property of matter which probably, in the minds of most men, most urgently requires the assumption of atoms—its impenetrability.
"Two bodies cannot occupy the same space"—such is the familiar statement of the fact in question. Like the indestructibility of matter, it is claimed to be a datum of experience. "Corpora omnia impenetrabilia esse" says Sir Isaac Newton (Phil. Nat. Princ. Math., lib. iii., reg. 3), "non ratione sed sensu colligimus." Let us see in what sense and to what extent this claim is legitimate.
The proposition, according to which a space occupied by one body cannot be occupied by another, implies the assumption that space is an absolute, self-measuring entity—an assumption which I may have occasion to examine hereafter—and the further assumption that there is a least space which a given body will absolutely fill so as to exclude any other body. A verification of this proposition by experience, therefore, must amount to proof that there is an absolute limit to the compressibility of all matter whatsoever. Now, does experience authorize us to assign such a limit? Assuredly not. It is true that in the case of solids and liquids there are practical limits beyond which compression by the mechanical means at our command is impossible; but even here we are met by the fact that the volumes of fluids, which effectually resist all efforts at further reduction by external pressure, are readily reduced by mere mixture. Thus, sulphuric acid and water at ordinary temperatures do not sensibly yield to pressure; but, when they are mixed, the resulting volume is materially less than the agrregate volumes of the liquids mixed. But, waiving this, as well as the phenomena which emerge in the processes of solution and chemical action, it must be said that experience does not in any manner vouch for the impenetrability of matter as such in all its states of aggregation. When gases are subjected to pressure, the result is simply an increase of the expansive force in proportion to the pressure exerted, according to the law of Boyle and Mariotte (the modifications of and apparent exceptions to which, as exhibited in the experimental results obtained by Regnault and others, need not here be stated, because they do not affect the argument). A definite experimental limit is reached in the case of those gases only in which the pressure produces liquefaction or solidification. The most significant phenomenon, however, which experience contributes to the testimony on this subject is the diffusion of gases. Whenever two or more gases which do not act upon each other chemically are introduced into a given space, each gas diffuses itself in this space as though it were alone present there; or, as Dalton, the reputed father of the modern atomic theory, expresses it, "Gases are mutually passive, and pass into each other as into vacua."
Whatever reality may correspond to the notion of the impenetrability of matter, this impenetrability is not, in the sense of the atomists, a datum of experience.
Upon the whole, it would seem that the validity of the first proposition of the atomic theory is not sustained by the facts. Even if the assumed unchangeability of the supposed ultimate constituent particles of matter presented itself, upon its own showing, as more than a bare reproduction of an observed fact in the form of an hypothesis, and could be dignified with the name of a generalization or of a theory, it would still be obnoxious to the criticism that it is a generalization from facts crudely observed and imperfectly apprehended.
In this connection it may be observed that the atomic theory has become next to valueless as an explanation of the impenetrability of matter, since it has been pressed into the service of the undulatory theory of light, heat, etc., and assumed the form in which it is now held by the majority of physicists, as we shall presently see. According to this form of the theory, the atoms are either mere points, wholly without extension, or their dimensions are infinitely small as compared with the distances between them, whatever be the state of aggregation of the substances into which they enter. In this view the resistance which a body, i. e., a system of atoms, offers to the intrusion of another body is due, not to the rigidity or unchangeability of volume of the individual atoms, but to the relation between the attractive and repulsive forces with which they are supposed to be endowed. There are physicists holding this view who are of opinion that the atomic constitution of matter is consistent with its impenetrability—among them M. Cauchy, who, in his Physique Générale (ed. Moigno, Paris, 1868, p. 38), after defining atoms as "material points without extension," uses this language: "Thus, this property of matter which we call impenetrability is explained, when we consider the atoms as material points exerting on each other attractions and repulsions which vary with the distances that separate them. . . . From this it follows that, if it pleased the author of Nature simply to modify the laws according to which the atoms attract or repel each other, we might instantly see the hardest bodies penetrate each other" (that we might see), "the smallest particles of matter occupy immense spaces, or the largest masses reduce themselves to the smallest volumes, the entire universe concentrating itself, as it were, in a single point."
2. The second fundamental proposition of the modern atomic theory avouches the essential discontinuity of matter. The advocates of the theory affirm that there is a series of physical phenomena which are inexplicable, unless we assume that the constituent particles of matter are separated by void interspaces. The most notable among these phenomena are the dispersion and polarization of light. The grounds upon which the assumption of a discrete molecular structure of matter is deemed indispensable for the explanation of these phenomena may be stated in a few words.
According to the undulatory theory, the dispersion of light, or its separation into spectral colors, by means of refraction, is a consequence of the unequal retardation experienced by the different waves, which produce the different colors, in their transmission through the refracting medium. This unequal retardation presupposes differences in the velocities with which the various-colored rays are transmitted through any medium whatever, and a dependence of these velocities upon the lengths of the waves. But, according to a well-established mechanical theorem, the velocities with which undulations are propagated through a continuous medium depend solely upon the elasticity of the medium as compared with its inertia, and are wholly independent of the length and form of the waves. The correctness of this theorem is attested by experience in the case of sound. Sounds of every pitch travel with the same velocity. If it were otherwise, music heard at a distance would evidently become chaotic; differences of velocity in the propagation of sound would entail a distortion of the rhythm, and, in many cases, a reversal of the order of succession. Now, differences of color are analogous to differences of pitch in sound, both reducing themselves to differences of wave-length. The lengths of the waves increase as we descend the scale of sounds from those of a higher to those of a lower pitch; and similarly, the length of a luminar undulation increases as we descend the spectral scale, from violet to red. It follows, then, that the rays of different color, like the sounds of different pitch, should be propagated with equal velocities, and be equally refracted; that, therefore, no dispersion of light should take place.
This theoretical impossibility of dispersion has always been recognized as one of the most formidable difficulties of the undulatory theory. In order to obviate it, Cauchy, at the suggestion of his friend Coriolis, entered upon a series of analytical investigations, in which be succeeded in showing that the velocities with which the various colored rays are propagated may vary according to the wave-lengths, if it be assumed that the ethereal medium of propagation, instead of being continuous, consists of particles separated by sensible distances.
By means of a similar assumption, Fresnel has sought to remove the difficulties presented by the phenomena of polarization. In ordinary light, the different undulations are supposed to take place in different directions, all transverse to the course or line of propagation, while in polarized light the vibrations, though still transverse to the ray, are parallelized, so as to occur in the same plane. Soon after this hypothesis had been expanded into an elaborate theory of polarization, Poisson observed that, at any considerable distance from the source of the light, all transverse vibrations in a continuous elastic medium must become longitudinal. As in the case of dispersion, this objection was met by the hypothesis of the existence of "definite intervals" between the ethereal particles.
These are the considerations, succinctly stated, which theoretical physics are supposed to bring to the support of the atomic theory. In reference to the cogency of the argument founded upon them, it is to be said, generally, that evidence of the discrete molecular arrangement of matter is by no means proof of the alternation of unchangeable and indivisible atoms with absolute spatial voids. But it is to be feared that the argument in question is not only formally, but also materially, fallacious. It is very questionable whether the assumption of definite intervals between the particles of the luminiferous ether is competent to relieve the undulatory theory of light from its embarrassments. This subject, in one of its aspects, has been thoroughly discussed by E. B. Hunt, in an article on the dispersion of light (Silliman's Journal, vol. vii., 2d series, p. 364, et seq.), and the suggestions there made appear to me worthy of serious attention. They are briefly these:
M. Cauchy brings the phenomena of dispersion within the dominion of the undulatory theory, by deducing the differences in the velocities of the several chromatic rays from the differences in the corresponding wave-lengths by means of the hypothesis of definite intervals between the particles of the light-bearing medium. He takes it for granted, therefore, that these chromatic rays are propagated with different velocities. But is this the fact? Astronomy affords the means to answer this question.
We experience the sensation of white light, when all the chromatic rays of which it is composed strike the eye simultaneously. The light proceeding from a luminous body will appear colorless, even if the component rays move with unequal velocities, provided all the colored rays, which together make up white light, concur in their action on the retina at a given moment; in ordinary cases it is immaterial whether these rays have left the luminous body successively or together. But it is otherwise when a luminous body becomes visible suddenly, as in the case of the satellites of Jupiter, or Saturn, after their eclipses. At certain periods, more than 49 minutes are requisite for the transmission of light from Jupiter to the earth. Now, at the moment when one of Jupiter's satellites, which has been eclipsed by that planet, emerges from the shadow, the red rays, if their velocity were the greatest, would evidently reach the eye first, the orange next, and so on through the chromatic scale, until finally the complement of colors would be filled by the arrival of the violet ray, whose velocity is supposed to be the least. The satellite, immediately after its emersion, would appear red, and gradually, in proportion to the arrival of the other rays, pass into white. Conversely, at the beginning of the eclipse, the violet rays would continue to arrive after the red and other intervening rays, and the satellite, up to the moment of its total disappearance, will gradually shade into violet.
Unfortunately for Cauchy's hypothesis, the most careful observation of the eclipses in question has failed to reveal any such variations of color, either before immersion, or after emersion, the transition between light and darkness taking place instantaneously, and without chromatic gradations.
If it be said that these chromatic gradations escape our vision by reason of the inappreciability of the differences under discussion, astronomy points to other phenomena no less subversive of the doctrine of unequal velocities in the movements of the chromatic undulations. Fixed stars beyond the parallactic limit, whose light must travel more than three years before it reaches us, are subject to great periodical variations of splendor; and yet these variations are unaccompanied by variations of color. Again, the assumption of different velocities for the different chromatic rays is discountenanced by the theory of aberration. Aberration is due to the fact that, in all cases where the orbit of the planet, on which the observer is stationed, forms an angle with the direction of the luminar ray, a composition takes place between the motion of the light and the motion of the planet, so that the direction in which the light meets the eye is a resultant of the two component directions—the direction of the ray and that of the observer's motion. If the several rays of color moved with different velocities there would evidently be several resultants, and each star would appear as a colored spectrum longitudinally parallel to the direction of the earth's motion.
The alleged dependence of the velocity of the undulatory movements, which correspond to, or produce, the different colors, upon the length of the waves, is thus at variance with observed fact. The hypothesis of definite intervals is unavailable as a supplement to the undulatory theory; other methods will have to be resorted to in order to free this theory from its difficulties.
3. The third proposition of the atomic hypothesis assigns to the atoms, which are said to compose the different chemical elements, determinate weights corresponding to their equivalents of combination, and is supposed to be necessary to account for the facts whose enumeration and theory constitute the science of chemistry. The proper verification of these facts is of great difficulty, because they have generally been observed through the lenses of the atomic theory, and stated in its doctrinal terms. Thus the differentiation and integration of bodies are invariably described as decomposition and composition; the equivalents of combination are designated as atomic weights or volumes, and the greater part of chemical nomenclature is a systematic reproduction of the assumptions of atomism. Nearly all the facts to be verified are in need of preparatory enucleation from the envelops of this theory.
The phenomena usually described as chemical composition and decomposition present themselves to observation thus: A number of heterogeneous bodies concur in definite proportions of weight or volume; they interact; they disappear, and give rise to a new body possessing properties which are neither the sum nor the mean of the properties of the bodies concurring and interacting (excepting the weight which is the aggregate of the weights of the interacting bodies), and this conversion of several bodies into one is accompanied, in most cases, by changes of volume, and in all cases by the evolution or involution of heat, or light, or of both. Conversely, a single homogeneous body gives rise to heterogeneous bodies, between which and the body out of which they originate the persistence of weight is the only relation of identity.
For the sake of convenience, these phenomena may be distributed into three classes, of which the first embraces the persistence of weight and the combination in definite proportions; the second, the changes of volume and the evolution of light and heat; and the third, the emergence of a wholly new complement of chemical properties.
Obviously, the atomic hypothesis is in no sense an explanation of the phenomena of the second class. It is clearly and confessedly incompetent to account for changes of volume or of temperature. And, with the phenomena of the third class, it is apparently incompatible. For, in the light of the atomic hypothesis, chemical compositions and decompositions are in their nature nothing more than aggregations and segregations of masses whose integrity remains inviolate. But the radical change of chemical properties, which is the result of all true chemical action, and serves to distinguish it from mere mechanical mixture or separation, evinces a thorough destruction of that integrity. It may be that the appearance of this incompatibility can be obliterated by the device of ancillary hypotheses; but that leads to an abandonment of the simplicity of the atomic hypothesis itself, and thus to a surrender of its claims to merit as a theory.
At best, then, the hypothesis of atoms of definite and different weights can be offered as an explanation of the phenomena of the first class. Does it explain them in the sense of generalizing them, of reducing many facts to one? Not at all; it accounts for them, as it professed to account for the indestructibility and impenetrability of matter, by simply iterating the observed fact in the form of an hypothesis. It is another case (to borrow a scholastic phrase) of illustrating idem per idem. It says: The large masses combine in definitely-proportionate weights because the small masses, the atoms of which they are multiples, are of definitely-proportionate weight. It pulverizes the fact, and claims thereby to have sublimated it into a theory.
Upon closer examination, moreover, the assumption of atoms of different specific gravities proves to be, not only futile, but absurd. Its manifest theoretical ineptitude is found to mask the most fatal inconsistencies. According to the mechanical conception which underlies the whole atomic hypothesis, differences of weight are differences of density; and differences of density are differences of distance between the particles contained in a given space. Now, in the atom there is no multiplicity of particles, and no void space; hence differences of density or weight are impossible in the case of atoms.
It is to be observed that the attribution of different weights to different atoms is an indispensable feature of the atomic theory in chemistry, especially in view of the combination of gases in simple ratios of volume, so as to give rise to gaseous products bearing a simple ratio to the volumes of its constituents, and in view of the law of Ampère and Clausius, according to which all gases, of whatever nature or weight, contain equal numbers of molecules in equal volumes.
The inadequacy of the atomic hypothesis as a theory of chemical changes has been repeatedly pointed out by men of the highest scientific authority, such as Grove (Correlation of Physical Forces, in Youmans's "Correlation and Conservation of Forces," p. 164, et seq.), and is becoming more apparent from day to day. I shall have occasion to inquire, hereafter, what promise there is, in the present state of chemical science, of a true generalization of the phenomena of combination in definite proportions, both of weight and volume, which is independent of the atomic doctrine, and will serve to connect a number of concomitant facts for which this doctrine is utterly incompetent to account.
It is not infrequently asserted by the advocates of the atomic theory that there is a number of other phenomena, in addition to those of combination in definite proportions, which are strongly indicative of the truth of the atomic theory. Among these phenomena are isomerism, polymerism, and allotropy. But it is very doubtful whether this theory is countenanced by the phenomena in question. The existence of different allotropic states, in an elementary body said to consist of but one kind of atoms, is explicable by the atomic hypothesis in no other way than by deducing these different states from diversities in the grouping of the different atoms. But this explanation applies to solids only, and fails in the cases of liquids and gases. The same remark applies to isomerism and polymerism.
From the foregoing considerations, I take it to be clear that the atomic hypothesis mistakes many of the facts which it seeks to explain; that it accounts imperfectly or not at all for a number of other facts which are correctly apprehended; and that there are cases in which it appears to be in irreconcilable conflict with the data of experience. As a physical theory, it is barren and useless, inasmuch as it lacks the first requisite of a true theory—that of being a generalization, a reduction of several facts to one; it is essentially one of those spurious figments of the brain, based upon an ever-increasing multiplicatio entium praeter necessitatem, which are characteristic of the pre-scientific epochs of human intelligence, and against which the whole spirit of modern science is an emphatic protest. Moreover, in its logical and psychological aspect, as we shall hereafter see more clearly, it is the clumsiest attempt ever made to transcend the sphere of relations in which all objective reality, as well as all thought, has its being, and to grasp the absolute "ens per sese, finitum, reale, totum."
I do not speak here of a number of other difficulties which emerge upon a minute examination of the atomic hypothesis in its two principal varieties, the atoms being regarded by some physicists as extended and figured masses, and by others as mere centres of force. In the former case the assumption of physical indivisibility becomes gratuitous, and that of mathematical indivisibility absurd; while in the latter case the whole basis of the relation between force and mass, or rather force and inertia, without which the conception of either term of the relation is impossible, is destroyed. Some of these difficulties are frankly admitted by leading men of science for instance, by Du Bois-Reymond, in the lecture above cited. Nevertheless, it is asserted that the atomic, or at least molecular, constitution of matter is the only form of material existence which can be realized in thought. In what sense, and to what extent, this assertion is well founded, will be my next subject of examination.