Mathematical Recreations and Essays · W. W. Rouse Ball
Matter, like space and time, cannot be defined, but either the statement that matter is whatever occupies space or the statement that it is anything which can be seen, touched, or weighed, suggests its more important characteristics to anyone already familiar with it.
The means of measuring matter and some of its properties are treated in most text-books on mechanics, and I do not propose to discuss them. I confine the chapter to an account of some of the hypotheses by physicists as to the ultimate constitution of matter, but I exclude metaphysical conjectures, which from their nature are mere assertions incapable of proof and are not subject to mathematical analysis. The question is intimately associated with the explanation of the phenomena of attraction, light, chemistry, electricity, and other branches of physics.
I commence with a list of some of the more plausible of the hypotheses formerly proposed which accounted for the obvious properties of matter, and shall then discuss how far they explain or are consistent with other facts (I have based my account mainly on Recent Advances in Physical Science, by P.G. Tait, Edinburgh, 1876 (chaps, xii, xiii); and on the article Atom by J. Clerk Maxwell in the Encyclopaedia Britannica or his Collected Works, vol. ii, pp. 445--484: see also W.M. Hicks's address, Report of the British Association (Ipswich meeting), 1895, vol. lxv, pp. 595--606. For the more recent speculations see J.J. Thomson, Electricity and Matter, Westminster, 1904, and J. Larmor, Aether and Matter, Cambridge, 1900.). The interest
of the list is largely historical, for within the last few years new views as to the constitution of matter have been propounded, but the details of these more recent hypotheses are so complicated and technical that only professional mathematicians can understand them. Accordingly I allude to them only briefly.
[Hypothesis of Continuous Matter][Matter and Ether Theories] Hypothesis of Continuous Matter It may be
supposed that matter is homogeneous and continuous, in which case there is no limit to the infinite divisibility of bodies. This view was held by Descartes (Descartes, Principia, vol. ii, pp. 18, 23.).
This conjecture is consistent with the facts deducible by untrained observation, but there are many other phenomena for which it does not account; moreover there seems to be no way of reconciling such a structure of matter either with the facts of chemical changes or with the results of spectrum analysis. At any rate the theory must be regarded as extremely improbable.
[Atomic Theories][Matter and Ether Theories]Atomic Theories If matter is not continuous we must suppose that every body is composed of aggregates of molecules. If so, it seems probable that each such molecule is built up by the association of two or more atoms, that the number of kinds of atoms is finite, and that the atoms of any particular kind are alike. As to the nature of the atoms the following hypotheses have been made.
[Popular Atomic Hypothesis][Matter and Ether Theories] Popular Atomic Hypothesis The popular view is that every atom of any particular kind is a minute indivisible article possessing definite qualities, everlasting in its form and properties, and infinitely hard.
This statement is plausible, but the difficulties to which it leads appear to be insuperable. In fact we have reason to think that the atoms which form a molecule are composite systems in incessant vibration at a rate characteristic of the molecule, and it is most probable that they are elastic.
Newton seems to have hazarded a conjecture of this kind when he suggested (Newton, Principia, bk. ii, prop. 50.) that the difficulties, connected with the fact that the velocity of sound was one-ninth greater than that required by theory, might be overcome if the particles of air were little rigid spheres whose distance from one another under normal conditions was nine times the diameter of any one of them. This was ingenious, but obviously the view is untenable, because, if such a structure of air existed, the air could not be compressed beyond a certain limit, namely, about 1/1021 st part of its original volume, which has been often exceeded. The true explanation of the difficulty noticed by Newton was given by Laplace.
[Boscovich's Hypothesis][Matter and Ether Theories] Boscovich's Hypothesis In 1759 Boscovich suggested (Philosophiae naturalis Theoria redacta ad unicam Legem Virium, Vienna, 1759.) that the facts might be explained by supposing that an atom was an infinitely small indivisible mass which was a centre of force--the law of force being attractive for sensible distances, alternately attractive and repulsive for minute distances, and repulsive for infinitely small distances. In this theory all action between bodies is action at a distance.
He explained the apparent extension of bodies by saying that two parts are consecutive (or similarly that two bodies are in contact) when the nearest pair of atoms in them are so close to one another that the repulsion at any point between them is sufficiently great to prevent any other atom coming between them. It is essential to the theory that the atom shall have a mass but shall not have dimensions.
This hypothesis is not inconsistent with any known facts, but it has been described, perhaps not unjustly, as a mere mathematical fiction, and certainly it is opposed to the apparent indications of our senses. At any rate it is artificial, though it may be a prejudice to regard that as an argument against its adoption. To some extent this view was accepted by Faraday.
Lord Kelvin, better known as Sir William Thomson, has shown (Proceedings of the Royal Society of Edinburgh, April 21, 1862, vol. iv, pp. 604--606.) that, if we assume the existence of gravitation, then each of the above hypotheses will account for cohesion.
[Hypothesis of an Elastic Solid Ether. Labile Ether] [Matter and Ether Theories]Hypothesis of an Elastic Solid Ether Some physicists have tried to explain the known phenomena by properties of the medium through which our impressions are derived. By postulating that all space is filled with a medium possessed of many of the characteristics of an elastic solid, it has been shown by Fresnel, Green, Cauchy, Neumann, MacCullagh, and others that a large number of the properties of light and electricity may be explained. In spite of the difficulties to which this hypothesis necessarily leads, and of its inherent improbability, it has been discussed by Stokes, Lamé, Boussinesq, Sarrau, Lorenz, Lord Rayleigh, and Kirchhoff.
This hypothesis has been modified and rendered somewhat more plausible by von Helmholtz, Lommel, Ketteler (Theoretische Optik, Braunschweig, 1885.), and Voigt, who based their researches on the assumption of a mutual reaction between the ether and the material molecules located in it: on this view the problems connected with refraction and dispersion have been simplified. Finally, Sir William Thomson, in his Baltimore Lectures, 1885, suggested a mechanical analogue to represent the relations between matter and this ether, by which a possible constitution of the ether can be realized. He also suggested later a form of labile ether, from whose properties most of the more familiar physical phenomena can be deduced, provided the arrangement can be considered stable; a labile ether is an elastic solid, and its properties in two dimensions may be compared with those of a soap-bubble film, in three dimensions.
It is, however, difficult to criticise any of these hypotheses as a theory of the constitution of matter until the arrangement of the atoms or their nature is more definitely expressed.
[Dynamical Theories][Matter and Ether Theories]Dynamical Theories In recent years the suggestion has been made that the so-called atoms may be forms of motion ( permanent eddies) in one elementary material known as the ether; on this view all the atoms are constituted of the same matter, but the physical conditions are different for the different kinds of atoms. It has been said that there is an initial difficulty in any such hypothesis, since the all-pervading elementary fluid must possess inertia, so that to explain matter we assume the existence of a fluid possessing one of the chief characteristics of matter. This is true as far as it goes, but it is not more unreasonable than to attribute all the fundamental properties of matter to the atoms themselves, as is done by many writers. The next paragraph contains a statement of one of the earliest attempts to formulate a dynamical atomic hypothesis.
[The Vortex Ring Hypothesis][Matter and Ether Theories] The Vortex Ring Hypothesis This hypothesis assumes that each atom is a vortex ring in an incompressible frictionless homogeneous fluid.
Vortex rings--though, since friction is brought into play, of an imperfect character--can be produced in air by many smokers. Better specimens can be formed by taking a cardboard box in one side of which a circular hole is cut, filling it with smoke, and hitting the opposite side sharply. The tendency of the particles forming a ring to maintain their annular connection may be illustrated by placing such a box on one side of a room in a direct line with the flame of a lighted candle on the other side. If properly aimed, the ring will travel across the room and put out the flame. If the box is filled only with air, so that the ring is not visible, the experiment is more effective.
In 1858 von Helmholtz (Crelle's Journal, 1858, vol. lv, pp. 25--55; translated by Tait in the Philosophical Magazine, June, 1867, supplement, series 4, vol. xxxiii, pp. 485--512.) showed that a closed vortex filament in a perfect fluid is indestructible and retains certain
characteristics always unaltered. In 1867 Sir William Thomson propounded (Proceedings of the Royal Society of Edinburgh, Feb. 18, 1867, vol. vi, pp. 94--105.) the idea that matter consists of vortex rings in a fluid which fills space. If the fluid is perfect we could neither create new vortex rings nor destroy those already created, and thus the permanence of the atoms is explained. Moreover the atoms would be flexible, compressible, and in incessant vibration at a definite fundamental rate. This rate is very rapid, and Sir William Thomson gave the number of vibrations per second of a sodium ring as probably being greater than 10^14.
By a development of this hypothesis Prof. J.J. Thomson (A Treatise on the Motion of Vortex Rings, Cambridge, 1883.) showed, some years ago, that chemical combination may be explained. He supposed that a molecule of a compound is formed by the linking together of vortex filaments representing atoms of different elements: this arrangement may be compared with that of helices on an anchor ring. For stability not more than six filaments may be combined together, and their strengths must be equal. Another way of explaining chemical combination on the vortex atom hypothesis has been suggested by W.M. Hicks. It is known (See a memoir by M.J.M. Hill in the Philosophical Transactions of the Royal Society, London, 1894, part i, pp. 213--246.) that a spherical mass of fluid, whose interior possesses vortex motion, can move through liquid like a rigid sphere, and he has shown that one of these spherical vortices can swallow up another, thus forming a compound element.
[The Vortex Sponge Hypothesis][Matter and Ether Theories] The Vortex Sponge Hypothesis Any vortex atom hypothesis labours under the difficulty of requiring that the density of the fluid ether shall be comparable with that of ordinary matter. In order to obviate this and at the same time to enable it to transmit transversal radiations Sir William Thomson suggested what has been
termed, not perhaps very happily, the vortex sponge hypothesis (Philosophical Magazine, London, October, 1887, series 5, vol. xxiv, pp. 342--353.): this rests on the assumption that laminar motion can be propagated through a turbulently moving inviscid liquid. The mathematical difficulties connected with such motion have prevented an adequate discussion of this hypothesis, and I therefore confine myself to merely mentioning it.
These hypotheses, of vortex motion in a fluid, account for the indestructibility of matter and for many of its properties. But in order to explain statical electrical attraction it would seem necessary to suppose that the ether is elastic; in other words, that an electric field must be a field of strain. If so, complete fluidity in the ether would be impossible, and hence the above theories are now regarded as untenable.
[The Ether-Squirts Hypothesis][Matter and Ether Theories] The Ether-Squirts Hypothesis Prof. Karl Pearson (American Journal of Mathematics, 1891, vol. xiii, pp. 309--362.) has suggested another dynamical theory in which an atom is conceived as a point at which ether is pouring into our space from space of four dimensions.
If an observer lived in two dimensional space filled with ether and confined by two parallel and adjacent surfaces, and if through a hole in one of these surfaces fresh ether were squirted into this space, the variations of pressure thereby produced might give the impression of a hard impenetrable body. Similarly an ether-squirt from space of four dimensions into our space might give us the impression of matter.
It seems necessary on this hypothesis to suppose that there are also ether-sinks, or atoms of negative mass; but as ether-squirts and ether-sinks would repel one another we may suppose that the latter have moved out of the universe known to our senses.
By defining the mass of an atom as the mean rate at which
ether is squirting into our space at that point, we can deduce the Newtonian law of gravitation, and by assuming certain periodic variations in the rate of squirting we can deduce some of the phenomena of cohesion, of chemical action, and of electromagnetism and light. But of course the hypothesis rests on the assumption of the existence of a world beyond our senses.
[The Electron Hypothesis][Matter and Ether Theories] The Electron Hypothesis MacCullagh, in 1837 and 1839, proposed to account for optical phenomena on the assumption of an elastic ether possessing elasticity of the type required to enable it to resist rotation. This suggestion has been recently modified and extended by Dr J. Larmor (Philosophical Transactions of the Royal Society, London, 1894, pp. 719--822; 1895, pp. 695--743.), and, as now enunciated, it accounts for many of the electrical and magnetic (as well as the optical) properties of matter.
The hypothesis is however very artificial. The assumed ether is a rotationally elastic incompressible fluid. In this fluid Larmor introduces monad electric elements or electrons, which are nuclei of radial rotational strain. He supposes that these electrons constitute the basis of matter. He further supposes that an electrical current consists of a procession of these electrons, and that a magnetic particle is one in which these entities are revolving in minute orbits. Dynamical considerations applied to such a system lead to an explanation of nearly all the more obvious phenomena. By further postulating that the orbital motion of electrons in the atom constitute it a fluid vortex it is possible to apply the hydrodynamical pulsatory theory of Bjerknes or Hicks and obtain an explanation of gravitation.
Thus on this view mass is explained as an electrical manifestation. Electricity in its turn is explained by the existence of electrons, that is, of nuclei of strain in the ether, which are supposed to be in incessant and rapid motion. Whilst, to render this possible, properties are attributed to the ether which are apparently inconsistent with our experience of the space it fills. Put thus, the hypothesis seems very artificial.
Perhaps the utmost we can say for it is that, from some points of view, it may, so far as analysis goes, be an approximation to the true theory; in any case much work will have to be done before it can be considered established even as a working hypothesis.
tocsubsectionSpeculations due to investigations on Radio-activity Most of the above was written in 1891. Since then investigations on radio-activity have opened up new avenues of conjecture which tend to strengthen the electron theory as a working hypothesis. More than thirty years ago Clerk Maxwell had shown that light and electricity were closely connected phenomena. It was then believed that both were due to waves in the hypothetical ether, but it was supposed that the phenomena of matter on the one side and of light and electricity on the other were sharply distinguished one from the other. The differences, however, between matter and light tend to disappear as investigations proceed. In 1895 Röntgen established the existence of rays which could produce light, which had the same velocity as light, which were not affected by a magnet, and which could traverse wood and certain other opaque substances like glass. A year later Becquerel showed that uranium was constantly emitting rays which, though not affecting the eye as light, were capable of producing an image on a photographic plate. Like Röntgen rays they can go through thin sheets of metal; like heat rays they burn the skin; like electricity they generate ozone from oxygen. Passed into the air they enable it to conduct the electric current. Their speed has been measured and found to be rather more than half that of light and electricity. It was soon found that thorium possessed a similar property, but in 1903 Prof. Curie showed that radium possessed radio-activity to an extent previously unsuspected in any body, and in fact the rays were so powerful as to make the substance directly visible. Further experiments showed that numerous bodies are radio-active, but the effects are so much more marked in radium that it is convenient to use that substance for most experimental purposes.
Radium gives off no less than three kinds of rays besides a radio-active emanation. In these discharges there appears to be a gradual change from what had been supposed to be an elementary form of matter to another. This leads to the belief that of the known forms of matter some, perhaps even all, are not absolutely stable. On the other hand, it may be that only radio-active bodies are unstable, and that in their disintegration we are watching the final stage in the evolution of stable and constant forms of matter. It may, however, in any case turn out that some, or perhaps all, of the so-called elements may be capable of resolution into different combinations of electrons or electricity.
At an earlier date J.J. Thomson had concluded that the glow, seen when an electric current passes through a high vacuum tube, is due to a rush of minute particles across the tube. He calculated their weight, their velocity, and the charge of electricity transported by or represented by them, and found these to be constant. They were deflected like Becquerel rays. All space seems to contain them, and electricity, if not identical with them, is at least carried by them. This suggested that these minute particles might be electrons. If so, they might thus give the ultimate explanation of electricity as well as matter, and the atom of the chemist would be not an irreducible unit of matter, but a system comprising numerous such minute particles. These conclusions are consistent with those subsequently deduced from experiments with radium. In 1904 the hypothesis was carried one stage further. In that year J.J. Thomson investigated the conditions of stability of certain systems of revolving particles; and on the hypothesis that an atom of matter consists of a number of particles carrying negative charges of electricity revolving in orbits within a sphere of positive electrification he deduced many of the properties of the different chemical atoms corresponding to different possible stable systems of this kind. His scheme led to results agreeing closely with the results of Mendeléeff's periodic hypothesis. An interesting
consequence of this view is that Franklin's description of electricity as subtle particles pervading all bodies, may turn out to be substantially correct. It is also remarkable that corpuscles somewhat analogous to those whose existence was suggested in Newton's corpuscular theory of light should be now supposed to exist in cathode and Becquerel rays.
[The Bubble Hypothesis][Matter and Ether Theories] The Bubble Hypothesis (O. Reynolds, Submechanics of the Universe, Cambridge, 1903.) The difficulty of conceiving the motion of matter through a solid elastic medium has been met in another way, namely, by suggesting that what we call matter is a deficiency of the ether, and that this region of deficiency can move through the ether in a manner somewhat analogous to that in which a bubble can move in a liquid. To express this in technical language we may suppose the ether to consist of an arrangement of minute uniform spherical grains piled together so closely that they cannot change their neighbours, although they can move relatively one to another. Places where the number of grains is less or greater than the number necessary to render the piling normal, move through the medium, as a wave moves through water, though the grains do not move with them. Places where the ether is in excess of the normal amount would repel one another and move away out of our ken, but places where it is below the normal amount would attract each other according to the law of gravity, and constitute particles of matter which would be indestructible. It is alleged that the theory accounts for the known phenomena of gravity, electricity, and light, provided the size of its grains is properly chosen. Reynolds has calculated that for this purpose their diameter should be rather more than 5 × 10^(-18) centimetres, and that the pressure in the medium would be about 10^4 tons per square centimetre. This theory is in itself more plausible than the electron hypothesis, but its consequences have not yet been fully worked out.
Conjectures as to the cause of Gravity The cause of Gravity Returning from these novel hypotheses to the classical theories of matter, we may now proceed a step further. Before a hypothesis on the structure of matter can be ranked as a scientific theory we may reasonably expect it to afford some explanation of three facts. These are (a) the Newtonian law of attraction; (b) the fact that there are only a finite number of ultimate kinds of matter--such as oxygen, iron, etc.--which can be arranged in a series such that the properties of the successive members are connected by a regular law; and (c) the main results of spectrum analysis.
In regard to the first point (a), we can say only that none of the above theories are inconsistent with the known laws of attraction; and as far as the ether-squirts, the electron, and the bubble hypotheses are concerned, they have been elaborated into a form from which the gravitational law of attraction can be deduced. But we may still say that as to the cause of gravity--or indeed of force--we know nothing.
Newton, in his Letters to Bentley, while declaring his ignorance of the cause of gravity, refused to admit the possibility of force acting at a finite distance through a vacuum. "You sometimes speak of gravity," said he (Letter dated Jan. 17, 1693. I quote from the original, which is in the Library of Trinity College, Cambridge; it is printed in the Letters to Bentley, London, 1756, p. 20.), "as essential and inherent to matter: pray do not ascribe that notion to me, for the cause of gravity is what I do not pretend to know." And in another place he wrote (Letter dated Feb. 25, 1693; ibid:17 Letters to Bentley, pp. 25, 26.), "'Tis 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 if gravitation in the sense of Epicurus, be essential and inherent in it That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance thro' a vacuum, without the mediation of anything else, by and through which their action and force 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."
I have already alluded to conjectural explanations of gravity dependent on the ether-squirts, the electron, and the bubble hypotheses. Of other conjectures as to the cause of gravity, three, which do not involve the idea of force acting at a distance, may be here mentioned:
(1) The first of these conjectures was propounded by Newton in the Queries at the end of his Opticks, where he suggested as a possible explanation the existence of a stress in the ether surrounding a particle of matter (Quoted by S.P. Rigaud in his Essay on the Principia, Oxford, 1838, appendix, pp. 68--70. On other guesses by Newton see Rigaud, text, pp. 61--62, and references there given.).
This has been elaborated on a statical basis by Maxwell, who showed (Article Attraction, in Encyclopaedia Britannica, or Collected Works, vol. ii, p. 489.) that the stress would have to be at least 3000 times greater than that which the strongest steel would support. Sir William Thomson (Lord Kelvin) has suggested (Proceedings of the Royal Society of Edinburgh, Feb. 7, 1870, vol. vii, pp. 60--63.) a dynamical way of producing the stress by supposing that space is filled with an incompressible fluid, constantly being annihilated by each atom of matter at a rate proportional to its mass, a constant supply being kept up at an infinite distance. It is true that this avoids Maxwell's difficulty, but we have no right to introduce such sinks and sources of fluid unless we have other grounds for believing in their existence. The conclusion is that Newton's conjecture is very improbable unless we adopt the ether-squirts theory: on that hypothesis it is a plausible explanation.
I should add that Maclaurin implies (An Account of Sir Isaac Newton's Philosophical Discoveries, London, 1748, p. 111.) that though the above explanation was Newton's early opinion, yet his final view was that he could not devise any tenable hypothesis about the cause of gravitation.
(2) In 1782 Le Sage of Geneva suggested (Mémoires de l'Académie des Sciences for 1782, Berlin, 1784, pp. 404--432: see also the first two books of his Traité de Physique, Geneva, 1818.) that gravity was caused by the bombardment of streams of ultramundane corpuscles. These corpuscles are supposed to come in all directions from space and to be so small that inter-collisions are rare.
A body by itself in space would receive on an average as many blows on one side as on another, and therefore would have no tendency to move. But, if there are two bodies, each will screen the other from some of the bombarding corpuscles. Thus each body will receive more blows on the side remote from the other body than on the side turned towards it. Hence the two bodies will be impelled each towards the other.
In order to make this force between two particles vary directly as the product of their masses and inversely as the square of the distance between them, Le Sage showed that it was sufficient to suppose that the mass of a body was proportional to the area of a section at right angles to the direction in which it was attracted. This requires that the constitution of a body shall be molecular, and that the distances between consecutive molecules shall be very large compared with the sizes of the molecules. On the vortex hypothesis we may suppose that the ultramundane corpuscles are vortex rings.
This is ingenious, and it is possible that if the corpuscles were perfectly elastic the theory might be tenable (See a paper by Sir William Thomson (Lord Kelvin) in the Proceedings of the Royal Society of Edinburgh, Dec. 18, 1871, vol. vii, pp. 577--589.). But
the results of Maxwell's numerical calculation show, first, that the particles must be imperfectly elastic; second, that merely to produce the effect of the attraction of the earth on a mass of one pound would require that Le Sage's corpuscles should expend energy at the rate of at least billions (I use billion with the English (and not the French) meaning, that is, a billion =10^12 .) of foot-pounds per second; and third, that it is probable that the effect of such a bombardment would be to raise the temperature of all bodies beyond a point consistent with our experience. Finally, it seems probable that the distance between consecutive molecules would have to be considerably greater than is compatible with the results given below.
Tait summed up the objections to these two hypotheses by saying (Properties of Matter, London, 1885, art. 164.), "One common defect of these attempts is that they all demand some prime mover, working beyond the limits of the visible universe or inside each atom: creating or annihilating matter, giving additional speed to spent corpuscles, or in some other way supplying the exhaustion suffered in the production of gravitation. Another defect is that they all make gravitation a mere difference-effect, as it were; thereby implying the presence of stores of energy absolutely gigantic in comparison with anything hitherto observed, or even suspected to exist, in the universe; and therefore demanding the most delicate adjustments, not merely to maintain the conservation of energy which we observe, but to prevent the whole solar and stellar systems from being instantaneously scattered in fragments through space. In fact, the cause of gravitation remains undiscovered."
(3) There is another conjecture on the cause of gravity which I may mention (See an article by myself in the Messenger of Mathematics, Cambridge, 1891, vol. xxi, pp. 20--24.). It is possible that the attraction of one particle on another might be explained if both of them rested on a homogeneous elastic body capable of transmitting
energy. This is the case if our three-dimensional universe rests in the direction of a fourth dimension on a four-dimensional homogeneous elastic body (which we may call the ether) whose thickness in the fourth dimension is small and constant.
The results of spectrum analysis lead us to suppose that every molecule of matter in our universe is in constant vibration. On the above hypothesis these vibrations would cause a disturbance in the supporting space, in the ether. This disturbance would spread out uniformly in all directions; the intensity diminishing as the square of the distance from the centre of vibration, but the rate of vibration remaining unaltered. The transmission of light and radiant heat may be explained by such vibrations transversal to the direction of propagation. It is possible that gravity may be caused by vibrations in the supporting space which are wholly longitudinal or are compounded of vibrations which are partly longitudinal and partly transversal in any of the three directions at right angles to the direction of propagation. If we define the mass of a molecule as proportional to the intensity of these vibrations caused by it, then at any other point in space the intensity of the vibration there would vary as the mass of the molecule and inversely as the square of the distance from the molecule; hence, if we may assume that such vibrations of the medium spreading out from any centre would draw to that centre a particle of unit mass at any other point with a force proportional to the intensity of the vibration there, then the Newtonian law of attraction would follow. This conjecture is consistent either with Boscovich's hypothesis or with the vortex theory. It would be interesting if the results of a branch of pure mathematics so abstract as the theory of hyperspace should be found to be closely connected with one of the most fundamental problems of material science
.
I should sum up the effect of this discussion on gravity on the relative probabilities of the hypotheses as to the constitution of matter enumerated above, by saying that it does not enable us to discriminate between them.
Conjectures to explain the finite number of species of AtomsFinite number of kinds of Matter The fact that the number of kinds of matter (chemical elements) is finite and the consequences of spectrum analysis are closely related and may be treated together. The results of spectrum analysis show that every molecule of any species of matter, such as hydrogen, vibrates with (so far as we can tell) exactly equal sets of periods of vibration. This then is one of the characteristics of the particular kind of matter, and it is probable that any explanation of why the molecules of each kind have a definite set of periods of vibration will account also for the fact that the number of kinds of matter is finite.
Various attempts to explain why the molecules of matter are capable only of certain definite periods of vibration have been made, and it may be interesting if I give them briefly.
(1) To begin with, I may note the conjecture that it depends on properties of time. This, however, is impossible, for the continuity of certain spectra proves that in these cases there is nothing which prevents the period of vibration from taking any one of millions of different values: thus no explanation dependent on the nature of time is permissible.
(2) It has been suggested that there may have been a sorting agency, and only selected specimens of the infinite number of species formed originally have got into our universe. The objection to this is that no explanation is offered as to what has become of the excluded molecules.
(3) The finite number of species might be explained by supposing a physical connection to exist between all the molecules in the universe, just as two clocks whose rates are nearly the same tend to go at the same rate if their cases are connected.
Maxwell's objection to this is that we have no other reason for supposing that such a connection exists, but if we are living in a space of four dimensions as suggested above in chapter xii, this connection does exist, for all the molecules rest on one and the same body. This body is capable of transmitting vibrations, hence, no matter how the molecules were set vibrating originally, they would fall into certain groups,
and all the members of each group would vibrate at the same rate. It was the possibility of obtaining thus a physical connection between the various particles in our universe that first suggested to me the idea of a supporting medium in a fourth dimension.
(4) If we accept Boscovich's hypothesis or that of an elastic solid ether, and if we may lay it down as axiomatic that the mass of every sub-atom is the same, we may conceive that the number of ways of combining the sub-atoms into a permanent system is limited, and that the period of vibration depends on the form in which the sub-atoms are combined into an atom. This view is not inconsistent with any known facts. I may add that it is probable that the chemical atom is the essential vibrating system, for the sodium spectrum, to take one instance, is the same as that of all its compounds.
(5) In the same way we may suppose that the vortex rings are formed so that they can have only a definite number of stable forms produced by interlinking or kinking.
(6) Similarly we may modify the popular hypothesis by treating the atoms as indivisible aggregates of sub-atoms which are in all respects equal and similar, and can be combined in only a limited number of forms which are permanent. But most of the old difficulties connected with the atoms arise again in connection with the sub-atoms.
(7) I am not aware that Maxwell discussed any other hypotheses in connection with this point, but it has been suggested recently that, if the various forms of matter were evolved originally out of some one primitive material, then there may have been periodic disturbances in this matter when the atoms were being formed, such that they were produced only at some definite phase in the period (See Crookes on Mendeléeff's periodic law, Nature, Sept. 2, 1886, vol. xxxiv, pp. 423--432.).
Thus, if the disturbance is represented by the swinging of a pendulum in a resisting medium, it might be supposed that
the atoms were formed at the points of maximum amplitude, and we should expect that the atoms successively thrown off would form a series having the properties of its successive members connected by a regular periodic law. This conjecture, when worked out in some detail, led to the conclusion that some elements which ought to have appeared in the series were missing, but it was possible to predict their properties and to suggest the substances with which they were most likely to be found in combination. Guided by these theoretical conclusions a careful chemical analysis revealed the fact that such elements did exist.
That this hypothesis has led to new discoveries is something in its favour, but I do not wish to be understood to say that it is a theory which leads to results that have been verified subsequently. I should say rather that we have obtained an analogy which is sufficiently like the truth to suggest new discoveries. Such analogies are often the precursors of laws, so that it is not unreasonable to hope that ere long our knowledge of this border-land of chemistry and physics may be more definite, and thus that molecular physics may be brought within the domain of mathematics. It is however very remarkable that J.J. Thomson's conclusions on the stability of the orbital systems he devised should agree so closely with Mendeléeff's periodic law.
On the whole Maxwell thought that the phenomena point to a common origin of all molecules of the same kind, that this was an event not belonging to that order of nature under which we live, but must have originated when or before the existing order was established, and that so long as the present order exists it is immutable.
This is equivalent to saying that we have arrived at a point beyond which our limited experience does not enable us to carry the explanation.
The Size of Molecules of Matter. Size of the molecules of bodies That we should be able to form an approximate idea of
the size of the molecules of matter is a testimony to the
extraordinary advance which mathematical physics has made recently.
Sir William Thomson, now Lord Kelvin, whose ingenuity seems to know no limits--has suggested (See Nature, March 31, 1870, vol. i, pp. 531--553; and Tait's Recent Advances, pp. 303--318. The fourth method had been proposed by Loschmidt in 1863.) four distinct methods of attacking the problem. They lead to results which are not very different.
The first of these rests on an assertion of Cauchy that the phenomena of prismatic colours show that the distance between consecutive molecules of matter is comparable with the wave-lengths of light. Taking the most unfavourable case this would seem to indicate that in a transparent homogeneous solid or liquid medium there are not more than 64 × 10^24 molecules in a cubic inch, that is, that the distance between consecutive molecules is greater than 1/(4 × 10^8) th of an inch.
The second method is founded on the amount of work required to draw out a film of liquid, such as a soap-bubble, to a given thickness. This can be calculated from experiments in a capillary tube, and it is found that, if a soap-bubble could be drawn out to a thickness of 1/10^8 th of an inch there would be but a few molecules in its thickness. This method is not quantitative.
Thirdly, Sir William Thomson proved that the contact phenomena of electricity require that in an alloy of brass the distance between two molecules, one of zinc and one of copper, shall be greater than 1/(7 × 10^8) th of an inch; hence the number of molecules in a cubic inch of zinc or copper is not greater than 35 × 10^25.
Lastly, the kinetic theory of gases
leads to the conclusion that certain phenomena of temperature and viscosity depend, inter alia, on inter-molecular collisions, and so on the sizes and velocities of the molecules, while the average velocity
with which the molecules move increases with the temperature. This leads to the conclusion that the distance between two consecutive molecules of a gas at normal pressure and temperature is greater than 1/(6 × 10^6) th of an inch, and is less than 1/10^7 th of an inch; while the actual size of the molecule is a trifle greater than 1/(3 × 10^20) th of a cubic inch; and the number of molecules in a cubic inch is about 3 × 10^20.
Thus it would seem that a cubic inch of gas at ordinary pressure and temperature contains about 3 × 10^20 molecules, all similar and equal, and each molecule has a volume of about 1/(3 × 10^25) th of a cubic inch; while a cubic inch of the simplest solid or liquid contains rather less than 10^27 molecules, and perhaps each molecule has a volume of about 1/(3 × 10^26) th of a cubic inch. For instance, if a pea or a drop of water whose radius is 1/16 th inch was magnified to the size of the earth, then there would be about thirty molecules in every cubic foot of it, and probably the size of a molecule would be about the same as that of a fives-ball. The average size of the minute drops of water in a very light cloud can be calculated from the coloured rings produced when the sun or moon shines through it. The radius of a drop is about 1/30000 th of an inch. Such a drop therefore would contain about 2 × 10^13 separate molecules. In gases and vapours, the number of atoms required to make up one of these molecules can be estimated, but in liquids the number is not as yet known.
Loschmidt asserted that a cube whose side is 1/4000 th of a millimetre is the smallest object which can be made visible at the present time. Such a cube of oxygen or nitrogen would contain from 60 to 100 millions of molecules of the gas. Also on an average about 50 elementary molecules of the so-called elements are required to constitute one molecule of organic matter. At least half of every living organism consists of water, and we may for the moment suppose that the remainder consists of organic matter. Hence the smallest living being which is visible under the microscope contains
from 30 to 50 millions of elementary molecules which are combined in the form of water, and from 30 to 50 millions of elementary molecules which are combined so as to make not more than one million organic molecules.
Hence a very simple organism might be built up out of as few as a million similar organic molecules. Maxwell did not consider that this was sufficient to justify the current conclusions of physiologists, and said that they must not suppose that structural details of infinitely small dimensions can furnish by themselves an explanation of the variety known to exist in the properties and functions of the most minute organisms; but physiologists have replied that whether their conjectures be right or wrong Maxwell's argument is vitiated by his non-consideration of differences due to the physical (as opposed to the chemical) structure of the organism and the consequent motions of the component parts.
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