Both in ancient and in modern times two divergent conceptions of the constitution of matter have been employed in scientific theories. In the first of these matter is regarded as consisting of groups of discrete entities separated from one another by empty spaces; these are the atomic or corpuscular theories of matter. In the rival view matter is regarded as continuous and indefinitely divisible. So long as either of these types of theory of the constitution of matter is regarded realistically as a constituent part of an ultimate philosophical view of the world they are of course mutually exclusive. However in accordance with the view of the true character of all scientific theories which 1 am endeavouring to explain and illustrate in these lectures any theory of the constitution of matter will be taken solely as a conceptual representation of some assigned domain of natural phenomena; thus an atomic theory may legitimately be employed for some purposes and a continuous theory of matter for other purposes. Frequently a theory of mixed type in which both atoms and continuous substances occur as conceptual elements has been made the basis of an attempt to represent classes of phenomena. The employment of different types of theory for different purposes has been a common procedure in modern times. For example an atomic theory has been long prevalent for the purpose of representing facts relating to chemical combinations; and the kinetic theory of gases affords another example of such a corpuscular theory. On the other hand a continuous theory of matter is employed in the theory of Elasticity and in the theory of the motions of fluids; the treatment of these subjects being thus made capable of the application to them of continuous Mathematical Analysis. Various attempts were made especially in the first half of the nineteenth century to represent these latter phenomena by means of corpuscular theories; but all such efforts were based upon complicated hypotheses as to the nature of interactions between corpuscles and they can only be regarded as having attained a moderate degree of success. In any such case the simpler continuous theory is to be preferred so far as it can be shown to have as large a range of applicability for the purposes of representing the phenomena as has a corpuscular theory. It is of course always possible to regard a continuous theory as containing an idealization by a process of averaging of the particles of substances that are taken to be only sensibly continuous; and it has in fact been maintained that a continuous theory must necessarily be regarded in this way if it is to be considered as valid. The advantage of such idealization then consists in the fact that the theory becomes capable of expression in the form in which differential equations are used. In theories of the mixed type imponderable substances have played a large part; we have for instance an example of such a substance in the modern ether of the electromagnetic theory.
Corpuscular Theories of Matter
The parentage of all atomic theories is to be found in Leucippus and Democritus or even earlier; Democritus erected a Cosmology on the basis of the idea that the only existing objects are atoms in empty space; that these atoms are indestructible and eternal; and that all change consists in the aggregation and separation of these atoms. It may be observed that Aristotle as an opponent of the atomistic theory refused to admit the validity either of the conception of empty space or of that of an indivisible atom. The Cosmology of Democritus leaves no room for contingency or for teleology since all change being due to the motion of the atoms is subject to an unconditional necessity. The atoms have an endless variety of form and are infinite in number; in their eternal fall through infinite space the greater atoms strike against the smaller ones and since the former have a greater velocity the impacts give rise to lateral movements and vortices. These form the commencement of the growth of worlds an innumerable series of which come into existence and perish. The atoms act on each other only by collision or pressure and the variety in gross bodies is due to the variety in the number size shape and arrangement in space of the atoms of which they are composed. Democritus regarded such sensations as those of sweetness bitterness warmth and colour only as deceptive opinions; nothing but atoms and empty space were regarded by him as real. The phenomena of life are produced by fine smooth round atoms like those of fire which permeate the whole body and constitute the soul which is thus recognized as distinct from the body. The Physics of Epicurus was founded upon the conceptions of Democritus and was employed by him to remove that dualism of mind and matter which is involved in the Philosophy of Plato and of Aristotle. He regarded space as infinite and containing an infinite number of indestructible and indivisible atoms in perpetual motion. These atoms differ from one another only in size shape and weight and they move with equal velocities. As they move they give rise to new worlds which perpetually tend to dissolution and then to the production of fresh series of worlds. The soul is a fine substance like warm air distributed through the whole body. From the surfaces of external objects there is a constant stream of fine particles; and thus actual material copies of external objects enter the living body which conducts these images to the soul thus giving rise to sense-impressions.
These materialistic views of the world which were taken up at a later time by Lucretius whatever may be thought of their general tendencies had the effect of eradicating from the minds of their adherents those animistic and magical conceptions which together with the habit of constantly appealing to final causes had done much to hinder the development of scientific methods of investigation. In the middle ages the current view of matter in accordance with the Aristotelian tradition was that it consisted of underlying substantial forms which possessed accidental properties; our perceptions relating only to these latter. For a long period the attention of investigators was devoted to the occult properties of substances but no interest was taken in their quantitative aspect. Atomism as taught by the ancients had been completely submerged by Aristotelianism and it was not until the fifteenth century that atomistic conceptions again arose in connection with the metaphysical speculations of Nicolas de Cusa (1401–1464) and other writers who took part in the growing criticism of the dominant Aristotelianism. The most important influence upon later developments of Atomism was exercised by the speculations of Giordano Bruno although their metaphysical character was such that their immediate effect on Physics was negligible.
The Cosmology of Giordano Bruno (1548–1600) which amounted to a metaphysical Monadology was a scheme in which Being and Thought were coincident so that the structure of time space and matter can be discerned by the operations of Thought alone. In accordance with his Philosophy it is necessary to conceive time space and matter as composed of indivisible minima that is instants points and atoms. That there must exist in each domain a fundamental indivisible whole with which our conception begins he regarded as a necessary postulate of Thought. This notion of the atom Bruno regarded as having a certain relativity; the magnitude of this indivisible or minimum is fixed according to circumstances. In Astronomy for example the heavenly bodies are the irreducible minima and are thus to be regarded as atoms.
It has been the mechanistic view of the world of physical phenomena conceived by Descartes that has exercised the greatest influence on later conceptions of matter. It is difficult to reconcile Descartes' view of mind and matter as the two fundamental substances with his idealism; his theory of the physical world is however practically of a purely materialistic type. In extension and motion he recognized the source of all physical percepts and thus all the occult properties with which medieval thought endowed substance were removed the external world forming a purely mechanical system. He was not an atomist in the same sense as Democritus or Lucretius for he regarded all space as one fundamental substance infinitely divisible; thus for him spatial extension and substance were identical. The only differentiation of substance is due to the motion of its parts; thus a body or portion of matter is what can be moved as a whole relatively to the surrounding substance. Since space is a plenum and since on account of the identity of extension and substance there can take place no diminution of the volume of substance in a portion of space it follows that a circular streaming must form the basis of all motion. Descartes assumed that originally the substance of which the physical world consists was broken up into particles which were in rapid motions of rotation and also in circular translational motion. By means of this motion particles which were originally of irregular shape have become rounded splinters having been broken off from them in the course of the gradual grinding. This process he regards as having given rise to three kinds of corpuscles. The first of these form elementary fire and consist of splinters of various and varying size and form in motion with enormous velocities. The sun and the stars are composed of this kind of elementary matter. The matter of the second kind elementary air consists of imperceptibly small spherical atoms which move with great velocities in vortices; they fill all interplanetary space. The matter of the third kind the elementary earth consists of larger corpuscles of various forms and in less rapid motion; the ordinary material bodies and the earth and planets consist of atoms of this species. The conception of ordinary matter which is in accordance with this scheme is that it consists of atoms which are in fact but not in thought indivisible. The interstices between these atoms are filled with atoms of the other two kinds so that although the amount of ordinary matter in a fixed space may vary the total amount of matter of all three kinds in that space is invariable. Plants and animals like inorganic bodies are machines; their vital spirits consisting of fine material in motion as with Democritus. Descartes described the separate stages of a mechanism involving pressure and collision as forming an uninterrupted chain of effects produced by external objects through the senses upon the brain and back from the brain through nerves and muscular filaments. This view of a materially conceived world subject to a rigorously determined sequence of causes and effects would appear to be irreconcilable with Descartes' idealistic Metaphysics.
The difficulties relating to the possibility of the motion of atoms and bodies in a plenum filled with impenetrable substance were so great that a return was inevitable to the simpler conception of the ancient atomists that atoms are surrounded by empty space. The writings of Pierre Gassendi (1592–1655) had an important effect in hastening the disintegration of the Aristotelian conceptions of matter the authority of which had been already to a considerable extent underlined. Gassendi regarded empty space and atoms as the only principles in nature. All atoms he regarded as consisting of one and the same substance; they are only distinguished by differences of magnitude shape and weight. A limited number of different kinds of atoms suffices to explain the variation of bodies by their different groupings. In this view he was in agreement with that of Epicurus but not with that of Democritus who had regarded the number of different forms of atoms as infinite. The weight of the atoms he regarded as due to an inherent capability of self-determined motion; it is in the motion of the atoms that the explanation of all physical properties of bodies is to be sought. The main importance of Gassendi's work depends upon the fact that he was the first definitely to return to the ancient atomism and thus to complete the breach with the medieval views of matter.
The Philosopher Thomas Hobbes (1588–1679) occupies an important position in the history of Materialism. Under the influence of Galileo in regard to the theory of motion he regarded the motion of bodies in space as the original phenomenon upon which all others depend if they are to be subjected to scientific treatment. He was not an orthodox atomist because he recognized the existence not only of corpuscles but also of a continuous fluid which fills all the inter spaces between corpuscles and in which motion is propagated. This conception of vibratory motion or Conatus is an attempt to objectify pressure or stress and may thus be regarded as a step in the direction of the introduction of forces acting at a distance.
The breach with the Aristotelian conception of substantial forms involved in the schemes of Descartes and Gassendi was consolidated by the great practical experimenter Robert Boyle (1626–1691). Although his chief interest was in the ascertainment of facts by experiment Boyle did not fail to recognize the necessity for a theory which would bind together the results of his experimental investigations in Chemistry and in relation to the weight pressure and elasticity of air. In his general philosophy Boyle was not a Materialist but held a theory formed out of Descartes' Physics and Gassendi's Metaphysics which was designed not only to do justice to his scientific views as a Chemist and Physicist but also to be compatible with his orthodox religious opinions. He distinguished between two orders of corpuscles those of the second order which form the constituents of matter being formed by the aggregation of corpuscles of the first order. Between the corpuscles there are pores containing various effluvia. The primary constituents of matter which we should now call molecules are not absolutely indivisible but the primary corpuscles of which they are composed are so firmly fitted together that they are only with difficulty separated from one another. Boyle set up various hypotheses relating to the corpuscles for the purposes of explaining the constitution of air and other substances and also of chemical combinations. Of these hypotheses varying considerably according to the purposes for which they were designed he appears to have recognized the tentative character. He attempted to explain all chemical changes mechanically and laid considerable stress upon the quantitative determination of weights. He prepared the way for the modern chemical theory of elements recognizing specific weight and chemical reaction as the distinguishing marks of a particular substance. On the theoretical side he recognized the identity in character of the molecules which form the mass of the substance. The physical phenomena of heat electricity magnetism and the transformations into one another of solid liquid and gaseous conditions of matter he regarded as all capable of mechanical explanations.
The great discovery by Newton of the law of universal gravitation led ultimately to the great change in the nature of corpuscular and atomic theories which was produced when what is called action at a distance became an essential element in dynamical theories of matter. Prima facie Newton's discovery involves the discarding of the ancient notion that all action must be due to contact; a prejudice of which the origin is closely connected with the conception of efficient causation. The idea that the gravitation between two bodies is the resultant effect of the attractions upon one another of their individual corpuscular parts is inconsistent with the older atomic theories in which all interaction was regarded as due to impacts. For Newton and his contemporaries under the influence of the notion that impact or contact of some kind is the only species of admissible explanation of physical action the law of gravitation as it stood was incomplete without an indication of some mechanism by which the gravitational attraction can be deemed to be produced. A cause of gravitation must be sought for and discovered before the law could be regarded as in the true sense embodying a physical theory of the phenomenon. Newton himself declared “The reason of these properties of gravity I have not as yet been able to deduce”; and again in a letter to Bentley he writes1:
It is inconceivable that inanimate brute matter should without the mediation of something else which is not material operate upon and affect other matter without mutual contact as it must do if gravitation in the sense of Epicurus be essential and inherent in it. And this is the reason why I desired you would not ascribe innate gravity to me. That gravity should be innate inherent and essential to matter so that one body may act upon another at a distance through a vacuum without the mediation of anything else by and through which their action may be conveyed from one to another is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial I have left to the consideration of my readers.
Newton's contemporaries for the most part shared his view fearing the reintroduction of occult causes into Physics. Thus Huygens declared that “Newton's principle of attraction appeared to him absurd.” John Bernoulli who attempted to explain the motions of the planets by means of a modified form of the Cartesian theory of vortices proclaimed “the two suppositions of an attractive faculty and a perfect void” to be “revolting to minds accustomed to receiving no principle in Physics save those which are incontestable and evident.” Euler insisted on the necessity of supposing that gravitation is due to some subtle material medium; and D'Alembert regarded the real cause of gravitation as unknown in contradistinction to action by impact of which we have a clear mechanical conception. Until far into the nineteenth century this rejection of the notion of action at a distance held sway. Thus for example1 E. Du Bois-Reymond writes:
Forces acting through void space are in themselves inconceivable nay absurd and have become familiar concepts amongst physicists since Newton's time from a misapprehension of his doctrine and against his express warning.
Again Balfour Stewart and Tait2 write:
Of course the assumption of action at a distance may be made to account for anything; but it is impossible (as Newton long ago pointed out in his celebrated letter to Bentley) for anyone who has in philosophical matters a competent faculty of thinking for a moment to admit the possibility of such action.
Since Newton's time very numerous attempts have been made to account for the phenomena of gravitation by propagation through a fluid or an elastic medium or by means of impacts. All these theories must be pronounced to have failed in the purpose for which they were designed; in some cases such as in the impact theory of Le Sage on account of the nature of the assumptions made in them and in other cases on account of their inability to represent the known facts relating to gravitation. In the first place gravitation is propagated instantaneously or at least with a velocity which has been estimated by Laplace to be at least fifty million times that of light. Moreover all bodies appear to be absolutely transparent to gravitational action; and it is not subject to any kind of reflection or refraction. It appears also to be independent of the structure or physical and chemical conditions of the bodies between which it acts; its energy is unchangeable and inexhaustible.
Of all the attempts to account for gravitation on a corpuscular theory that of Le Sage is the most ingenious and is perhaps the only one which has been so far developed that its inherent weakness can be fully exposed. This theory is that the gravitation of bodies towards each other is due to the impact upon them of corpuscles or atoms moving in all directions through space. Each of these so-called ultramundane corpuscles is so small that collisions between pairs of them are of rare occurrence. If a body is not in any way screened from the bombardment of these corpuscles it would not acquire any motion since the effects of the bombardment on all parts of its surface would neutralize one another. If there are two bodies in space each acts to a certain extent as a screen against the bombardment of the other; thus for each body a smaller number of corpuscles will strike it on the side which is towards the other body than on the further side. Each body will appear to be attracted towards the other body owing to the effect of the excess of the impacts it receives on the side furthest from the other body. Leaving out of account those corpuscles that have already struck some mundane body and taking account only of those that come from infinite space it can be shown that the force of attraction between two bodies whose dimensions are small compared with the distance between them will vary as the product of the sections of the bodies taken normal to the distance and inversely as the square of that distance. In order that this may coincide with the attraction as given by the law of gravitation it is necessary that the effective areas of the bodies be proportional to their masses. Le Sage shows that in order that this may be the case whether the body be large or small it must be assumed that the size of the solid atoms of the body is very small compared with the distances between them so that a very small proportion of the corpuscles are stopped by even very dense and large bodies. Maxwell has shown that the energy of the corpuscles that is spent in maintaining the gravitation of a single pound of matter towards the earth must be millions of millions of foot-pounds per second. It can be shown that on the assumption of perfect elasticity of the corpuscles so that they rebound from the body with the same velocity with which they struck it there will be no excess of the impacts on any other body on one side over the other side. On the other hand if the velocity after impact is less than that of approach although the attraction between the bodies will be accounted for the excess of the energy which the corpuscles brought with them over that which they carry away remains to be accounted for. If any appreciable part of this excess appears in the form of heat in the body it will as is stated by Maxwell in a few seconds raise it and in like manner the whole universe to a white heat.
I have emphasized the extreme reluctance which from Newton's time onwards men of Science have shown to regard the law of gravitation as anything but a mere stepping-stone on the way to the construction of a genuine scientific theory of gravitation because for us Newton's law has all the characteristics of a genuine theory to represent a certain class of phenomena. In the hands of Newton himself the law of gravitation together with his scheme of Dynamics proved a sufficient basis for the mathematical deduction of Kepler's laws of planetary motion and for a deductive treatment of the principal inequalities in the motion of the moon. By the labours of a large number of Mathematical Astronomers lasting into our own time it has been shown that Dynamical Astronomy with the Newtonian law as its base is sufficient to afford an accurate representation of very nearly all the observed motions of the bodies of the solar system and that the condition of predictability of such motions for a considerable time is satisfied. The law itself could hardly be surpassed in point of simplicity and of comprehensiveness of statement. It will not lose its importance as the foundation of a valid conceptual scheme if as seems at present not unlikely the new law of gravitation given by Einstein supersedes Newton's law as a more accurate law of the phenomenon. The detailed consequences of the two laws are indistinguishable from one another in the motions they assign to the bodies of the solar system except apparently in the single instance of the motion of the Perihelion of Mercury's orbit. The idea that matter cannot act where it is not has no relevant meaning for us; since the notion of efficient action is no longer part of the stock of notions which Natural Science employs. The acceptance of Newton's law as a genuine scientific law depends upon the ascertained fact that it resumes in a formula with sufficient degree of approximation for nearly all purposes a whole class of observed facts relating to the motions of actual bodies.
In the first half of the eighteenth century owing to the influence of Newton's theory the conception that atoms exert an attractive force on one another rapidly modified the older atomic theories. The attractions between atoms made it unnecessary to conceive of them as having rough surfaces provided with hooks since impacts no longer played the all-important part which they did in the older theories. There also arose the conception of imponderable atoms exercising repulsive forces on one another filling the interstices between the gravitating atoms. These imponderable atoms were regarded as very much smaller than the ponderable atoms. Gradually these imponderable atoms came to be replaced by a continuous atmosphere of light and heat surrounding the ponderable atoms.
The views which were accepted in England late in the eighteenth century when Dalton was developing his conceptions of chemical actions were stated1 by him as follows:
These observations have tacitly led to the conclusion which seems universally adopted that all bodies of sensible magnitude whether liquid or solid are constituted of a vast number of extremely small particles or atoms of matter bound together by a force of attraction which is more or less powerful according to circumstances and which as it endeavours to prevent their separation is very properly called in that view attraction of cohesion; but as it collects them from a dispersed state (as from steam into water) it is called attraction of aggregation or more simply affinity. Whatever names it may go by they still signify one and the same power... Besides the force of attraction which in one character or another belongs universally to ponderable bodies we find another force that is likewise universal or acts upon all matter which comes under our cognisance namely a force of repulsion. This is now generally and I think properly ascribed to the agency of heat. An atmosphere of this subtile fluid constantly surrounds the atoms of all bodies and prevents them from being drawn into actual contact.
Dalton was led to the fundamentally important conception of atomic weight by an interpretation in terms of the atomic theory of the observed fact that chemical combinations take place in definite and simple numerical proportions. He regarded all the atoms of a single substance as identical in size and weight; and thus the weight of a body is the product of the weight of an atom by the number of atoms in the body. If one atom of the one substance always unites with one two etc. atoms of the other then the regularity in the combining weights is made intelligible.
An important modification of Dalton's atomic theory was made early in the nineteenth century by the molecular theory initiated by Avogadro. This theory did not at first attain to general acceptance on account of the rise of the electrochemical theory in accordance with which the cause of affinities is to be found in the electrical relations of the atoms. Gay-Lussac had discovered that the various gases under equal pressures and temperatures combine in simple volumetric proportions. Avogadro explained this by the assumption that the numbers of smallest particles in equal volumes of different gases are the same when they are under equal pressures and temperatures. He supposed that in compound gases and at least partially in simple gases there exist combinations of two or more atoms; thus the smallest particle of a chemical body is not the atom but the molecule a group of atoms. Chemical change by combination or separation he regarded as due to a change of place of atoms which grouped themselves into molecules of altered atomic composition.
These molecular and atomic theories of chemical combination were inspired by a spirit of physical realism in which sensuous images accessible to the imagination played a preponderating part. Although atoms and molecules are not perceptual objects it is undoubtedly the case that this attitude of mind has been advantageous in facilitating the formation of theories which we may now regard as having a purely conceptual character. This use of the sensuous imagination attained a luxuriant growth after the discoveries of dimorphism and of isomerism when it was found that substances of like chemical constitution appear in very different forms. Elaborate schemes for the localization in the molecule and the transposition and various groupings of atoms arose in this connection. But there was soon a reaction against the idea that anything more than a convenient symbolism was implied in these formulations. Thus for example Liebig1 declared in 1838 that:
we know nothing as to the condition in which the elements of two compound bodies are so soon as they have united in a chemical combination and the way in which we conceive these elements as grouped in the combination rests merely upon a convention which has been consecrated by habit under the prevailing theory.
Again Kekulé in his manual of Organic Chemistry 1861 speaking of the proportional numbers of combining weights as representing fact says2:
If to the symbols in these formulas another meaning is assigned if they are regarded as denoting the atoms and the atomic weights of the elements as is now most common the question arises: what are the sizes or (relative) weights of the atoms? Since the atoms can be neither measured nor weighed it is obvious that we can only be led by reflection and speculation to the hypothetical assumption of determinate atomic weights.
After the time of Dalton who may be regarded both as a Physicist and a Chemist the researches of Chemists and of Physicists led them along very divergent paths. Physics was treated in a manner which involved Mathematical Analysis whereas Chemistry remained for a long time inaccessible to such methods. In our own day the barrier between these two branches of Science is being broken down.
Returning to the purely physical side of the atomic theory we observe that the plausibility which attached to the notion that matter consists of solid hard impenetrable atoms which come into collision with one another loses its cogency when we inquire closely what happens as the result of such collisions. It seems impossible to attribute to such atoms the property which in sensible bodies is called elasticity because that involves relative motions of the parts which cannot take place in a perfectly rigid atom. The atom must be therefore regarded as inelastic. But in that case every collision between a pair of atoms would entail a loss of energy of motion and the kinetic energy of an aggregation of such atoms would in consequence gradually disappear. Efforts of various kinds have been made to surmount this difficulty of the apparent impossibility of attributing elasticity to the atom in the sense in which the term is employed in connection with gross bodies. One method is to regard the smallest particle of matter not as the atom but as the molecule consisting of a group of atoms; in fact to follow the procedure adopted on other grounds by the Chemists. The suggestion is then that in a shock between two molecules the atomic constitution of the molecules may be such as to admit of their behaving like elastic bodies although the constituent atoms are inelastic. The necessity of attributing perfect elasticity to the molecules has been recognized by those physicists who have developed the modern kinetic theory of gases. Both Clausius and Maxwell have emphasized this view. Lord Kelvin1 has asserted that:
we are forbidden by the modern physical theory of the conservation of energy to assume inelasticity or anything short of perfect elasticity in the ultimate molecules whether of ultramundane or of mundane matter.
That the introduction of the molecular scheme for the purpose of getting over this difficulty relating to elasticity is a simple shifting of the difficulty further back to the atoms constituting the molecules and not a solution of it was the opinion that led Secchi to consider a different mode of dealing with the matter. He suggested that the apparent repulsion of the atoms and their reciprocal collisions can be simply referred to an appropriate motion; it being sufficient for this purpose to suppose them to be in rotation. Relying on a theorem of Poinsot relating to the reflection of a rotating body from a resisting obstacle Secchi attempted without success to show that taking into account both the energy of rotational and of translatory motion the total energy of two atoms is unaltered by an impact. Secchi also made unsuccessful attempts to explain the aggregation of atoms so as to form molecules and the phenomenon of gravitation.
One of the most important attempts to evade the difficulty of defining precisely the character of the interaction between atoms which impinge upon one another or come into contact consisted of the radical step of depriving the atoms of all extension and supposing them to be mere centres of attractive or repulsive force. In the middle of the eighteenth century an atomic theory of this kind was propounded by Boscovich. According to his theory matter consists of a swarm of atoms each of which occupies a geometrical point of space is capable of motion and possesses a certain mass so that a certain force is required in order to give such an atom a given acceleration. Two atoms at a distance from one another exceeding a certain small length attract one another with a force varying as the inverse square of the distance. For smaller distances the force is attractive for some distances and repulsive for others. In order to obviate the possibility of two atoms ever being in the same position Boscovich supposes that for all distances below a certain minimum the force is repulsive and increases indefinitely as the distance is diminished. The system of atoms which constitutes a material body occupies a certain region of space by reason of the forces between the component atoms of the system and any other atoms which may be brought near them. No second body can come to occupy the same region of space because before it could do so the mutual actions of the atoms of the two systems would produce a repulsion between the two bodies too great to be overcome by any force which we can apply. In this scheme all action between bodies is action at a distance and there is no such thing as actual contact between two bodies although they may be so close to one another that the atoms of the two which are nearest exercise a great force of repulsion. When atoms were no longer regarded in accordance with the view of the earlier atomists as acting immediately on one another by contact but by forces of attraction and repulsion acting at a distance through empty space there seemed no longer any sufficient reason to attribute the property of extension to the atom. Even if it was retained it was merely in deference to a desire to satisfy the sensuous imagination by making the atom resemble the bodies perceptible by our senses. Ampére Cauchy and Faraday all regarded the atoms as unextended or as simple centres of force.
Another interesting and remarkable theory of the nature of the atom of quite a different character from those to which I have referred is Lord Kelvin's theory of vortex atoms. He imagines all space to be filled by an absolutely homogeneous incompressible frictionless fluid. It had been shown by Helmholtz that in such a fluid vortex tubes or filaments can exist in which the fluid is in permanent rotational motion and that such a filament can form a closed ring which may be called a vortex ring. Such a ring at all times consists of the same portions of the fluid and is consequently of invariable volume. It is indestructible and could not be formed in any portion of the fluid that is in irrotational motion. Two such rings could never amalgamate or come into contact with one another. As such rings might be knotted and two or more of them might be linked together by the passage of one ring through another without contact of their cores the possibility occurred to Lord Kelvin that a new atomic theory might be founded on the existence of such rings; their convolutions and linkings admitting of an endless variety of forms. If such a convoluted or linked ring be regarded as an atom such an atom would have permanence in magnitude and strength capability of internal vibrations and indestructibility. Thus not the original fluid although it possesses inertia but only the vortex rings in it are regarded as having the character of matter. Such a vortex ring would seem to have more of the properties requisite to the atom than any of the earlier kinds of atoms. The difficulty of explaining the inertia of what is only a mode of motion of a substance and not a substance itself was pointed out by Maxwell. No substantial progress has been made in the direction of showing that the phenomenon of gravitation or the thermal and optical properties of matter are explained by this theory of vortex atoms.
The only theory of the constitution of matter which really comes to close quarters with the thermal and mechanical properties of the substance and that can be regarded as an atomic theory although the elementary parts of matter with which it deals consist of molecules assumed to behave on impact with one another like perfectly elastic spheres is the dynamical theory dealing with gases known as the kinetic theory of gases. It is impossible here to enter into the complicated details of this theory any adequate description of which would involve mathematical formulae. It has had very considerable success although it would seem not complete success in coordinating a large number of known facts relating to the mechanical and thermal properties of gases and it may consequently be regarded as being the most comprehensive theory of the atomic type that has been proposed for coordinating the physical properties of matter in at least one of its forms. The theory has even been pushed so far as to assign rough estimates for the size and mass of a molecule of a gas such as hydrogen. As early as 1738 Daniel Bernoulli conceived the idea that a gaseous mass consists of a large number of perfectly elastic molecules in rapid motion of translation. On this hypothesis the pressure on the walls of the containing vessel is due to the impact against them of the molecules of the gas. This leads very simply to an explanation of the law of Boyle and Mariotte that the pressure in the gas varies inversely as its volume the temperature being unchanged. The further working out of the theory entails the use of calculation by probabilities or in other words the statistical method. This method was introduced by Maxwell and further developed by Willard Gibbs and Boltzmann. The molecules are divided into groups in each of which the molecules are in the same state of motion. It is shown that in every gas every molecule has on the average for a given temperature the same kinetic energy and that this is a fixed multiple of the absolute temperature of the gas. The theory has been applied to explain the diffusion of gases and to the theory of their spectra.
If we take a general survey of the ideas which have inspired atomists both in ancient and in modern times we see that the leading motive has been to reduce the complexities of the various forms of matter and of the phenomena connected with them by assuming that all matter is made up of parts each of which has only the simplest of the perceptual properties of matter in bulk those of indestructibility and of motion through space. The assumption that the world consists of atoms and of empty space has in appearance the supreme merit of simplicity and it satisfies the instinctive craving for unification of heterogeneous and complex elements in our actual perceptions. The idea that all interaction requires contact has the merit of apparent accordance with our own experience and thus by habit it has acquired the great advantage of picturability to the imagination. The roughnesses and hooks which atoms were often supposed to possess served to increase the feeling of atomists that they possessed a picture which appealed to what was familiar in actual experience. In fact all the assumptions as to the nature and properties of atoms were inspired by the desire to explain the complex forms and properties in the material world by reducing everything in the smallest parts of matter to simple processes of the most familiar type. The extreme reluctance that was exhibited to assign to the atoms any properties which were not familiar features of matter in bulk is characteristic of the thoroughgoing realistic spirit which has dominated the minds of nearly all atomists through the centuries. The supposed necessity that atoms or corpuscles should satisfy this condition of picturability has naturally exercised a considerable restrictive influence upon the possibility of developing atomic theories which should really be adequate for describing the more complex phenomena connected with matter; and this may account for many failures. Those of us who do not feel bound by such requirements are entitled to regard a purely conceptual atomic theory as admissible whatever properties are assigned to the atoms provided the requirements of a self-consistent scheme are satisfied whether these properties are directly copied or not from perceptual properties of gross bodies. Subject to this condition of applicability the success of the scheme in representing actual properties of matter as the result of a synthetic process of combining the effects of the conceptual atoms or molecules in an aggregation is the only criterion which an atomic scheme need satisfy; a reasonable degree of simplicity being presupposed. This view of atomic theories or one closely approaching it is certainly held by those Chemists who regard the number and arrangement of atoms in molecules as having a symbolic meaning only.
When Chemists found it necessary to regard the molecule and not the atom as the smallest part of a particular substance the question whether the atom could be regarded as the ultimate constituent of all matter became insistent. It seemed that it would be necessary to assume the existence of as many different kinds of atoms as there are chemical elements. If we stop there the notion that all matter is reducible to atoms consisting of one primitive substance has to be given up. The knowledge obtained of the relations between the atomic weights of different elements made it difficult to stop short at the recognition of the existence of some seventy elements. The idea then suggested itself that the atom must be regarded as consisting of a group of smaller atoms of the second order. It seems difficult to stop at any particular stage of the indefinite regress into which we are launched when an atom of any order is regarded as composed of smaller atoms of the next higher order. If at any stage we substitute extensionless centres of force the whole scheme loses that character of picturability which was one of its chief recommendations.
As soon as the conception of forces acting at a distance came to be accepted in consequence of the Newtonian doctrine of gravitation Atomism in the primitive meaning of the term underwent a profound modification. The theory of matter became a dynamical scheme in which the notion of central forces is introduced as a necessary conception on a parity with the older conceptions of atoms or corpuscles and empty space. Of this Dynamical scheme of relations I shall speak in a later lecture. I must also postpone any consideration of the modern electron theory of matter as also of the still more revolutionary theory associated with the name of Einstein in accordance with which matter and its relations are represented by a purely geometrical conceptual scheme.
The reluctance with which the notion of force as an independent conception was accepted is accounted for by the inveterate materialistic prejudice in accordance with which matter is regarded as the only ultimately real object. That this view of the unique reality of matter is no longer tenable has been concisely expressed by Helmholtz who wrote1:
It is just as inaccurate to try and explain matter as something real and force as a mere notion to which nothing real corresponds; both are rather abstractions from the real formed in exactly the same way. We can perceive matter only through its forces never in itself.
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