permanent structure. Only the frictionless medium was lacking to fulfil all the conditions of Helmholtz’s indestructible vortices. And at once Lord Kelvin bethought him of the frictionless medium which physicists had now begun to accept–the all-pervading ether. What if vortex rings were started in this ether, must they not have the properties which the vortex rings in air had exhibited–inertia, attraction, elasticity? And are not these the properties of ordinary tangible matter? Is it not probable, then, that what we call matter consists merely of aggregations of infinitesimal vortex rings in the ether?
Thus the vortex theory of atoms took form in Lord Kelvin’s mind, and its expression gave the world what many philosophers of our time regard as the most plausible conception of the constitution of matter hitherto formulated. It is only a theory, to be sure; its author would be the last person to claim finality for it. “It is only a dream,” Lord Kelvin said to me, in referring to it not long ago. But it has a basis in mathematical calculation and in analogical experiment such as no other theory of matter can lay claim to, and it has a unifying or monistic tendency that makes it, for the philosophical mind, little less than fascinating. True or false, it is the definitive theory of matter of the twentieth century.
Quite aside from the question of the exact constitution of the ultimate particles of matter, questions as to the distribution of such particles, their mutual relations, properties, and actions, came in for a full share of attention during the nineteenth century, though the foundations for the modern speculations were furnished in a previous epoch. The most popular eighteenth- century speculation as to the ultimate constitution of matter was that of the learned Italian priest, Roger Joseph Boscovich, published in 1758, in his Theoria Philosophiae Naturalis. “In this theory,” according to an early commentator, “the whole mass of which the bodies of the universe are composed is supposed to consist of an exceedingly great yet finite number of simple, indivisible, inextended atoms. These atoms are endued by the Creator with REPULSIVE and ATTRACTIVE forces, which vary according to the distance. At very small distances the particles of matter repel each other; and this repulsive force increases beyond all limits as the distances are diminished, and will consequently forever prevent actual contact. When the particles of matter are removed to sensible distances, the repulsive is exchanged for an attractive force, which decreases in inverse ratio with the squares of the distances, and extends beyond the spheres of the most remote comets.”
This conception of the atom as a mere centre of force was hardly such as could satisfy any mind other than the metaphysical. No one made a conspicuous attempt to improve upon the idea, however, till just at the close of the century, when Humphry Davy was led, in the course of his studies of heat, to speculate as to the changes that occur in the intimate substance of matter under altered conditions of temperature. Davy, as we have seen, regarded heat as a manifestation of motion among the particles of matter. As all bodies with which we come in contact have some temperature, Davy inferred that the intimate particles of every substance must be perpetually in a state of vibration. Such vibrations, he believed, produced the “repulsive force” which (in common with Boscovich) he admitted as holding the particles of matter at a distance from one another. To heat a substance means merely to increase the rate of vibration of its particles; thus also, plainly, increasing the repulsive forces and expanding the bulk of the mass as a whole. If the degree of heat applied be sufficient, the repulsive force may become strong enough quite to overcome the attractive force, and the particles will separate and tend to fly away from one another, the solid then becoming a gas.
Not much attention was paid to these very suggestive ideas of Davy, because they were founded on the idea that heat is merely a motion, which the scientific world then repudiated; but half a century later, when the new theories of energy had made their way, there came a revival of practically the same ideas of the particles of matter (molecules they were now called) which Davy had advocated. Then it was that Clausius in Germany and Clerk-Maxwell in England took up the investigation of what came to be known as the kinetic theory of gases–the now familiar conception that all the phenomena of gases are due to the helter- skelter flight of the showers of widely separated molecules of which they are composed. The specific idea that the pressure or “spring” of gases is due to such molecular impacts was due to Daniel Bournelli, who advanced it early in the eighteenth century. The idea, then little noticed, had been revived about a century later by William Herapath, and again with some success by J. J. Waterston, of Bombay, about 1846; but it gained no distinct footing until taken in hand by Clausius in 1857 and by Clerk-Maxwell in 1859.
The considerations that led Clerk-Maxwell to take up the computations may be stated in his own words, as formulated in a paper “On the Motions and Collisions of Perfectly Elastic Spheres.”
“So many of the properties of matter, especially when in the gaseous form,” he says, “can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity. Daniel Bournelli, Herapath, Joule, Kronig, Clausius, etc., have shown that the relations between pressure, temperature, and density in a perfect gas can be explained by supposing the particles to move with uniform velocities in straight lines, striking against the sides of the containing vessel and thus producing pressure. It is not necessary to suppose each particle to travel to any great distance in the same straight line; for the effect in producing pressure will be the same if the particles strike against each other; so that the straight line described may be very short. M. Clausius has determined the mean length of path in terms of the average of the particles, and the distance between the centres of two particles when the collision takes place. We have at present no means of ascertaining either of these distances; but certain phenomena, such as the internal friction of gases, the conduction of heat through a gas, and the diffusion of one gas through another, seem to indicate the possibility of determining accurately the mean length of path which a particle describes between two successive collisions. In order to lay the foundation of such investigations on strict mechanical principles, I shall demonstrate the laws of motion of an indefinite number of small, hard, and perfectly elastic spheres acting on one another only during impact. If the properties of such a system of bodies are found to correspond to those of gases, an important physical analogy will be established, which may lead to more accurate knowledge of the properties of matter. If experiments on gases are inconsistent with the hypothesis of these propositions, then our theory, though consistent with itself, is proved to be incapable of explaining the phenomena of gases. In either case it is necessary to follow out these consequences of the hypothesis.
“Instead of saying that the particles are hard, spherical, and elastic, we may, if we please, say the particles are centres of force, of which the action is insensible except at a certain very small distance, when it suddenly appears as a repulsive force of very great intensity. It is evident that either assumption will lead to the same results. For the sake of avoiding the repetition of a long phrase about these repulsive bodies, I shall proceed upon the assumption of perfectly elastic spherical bodies. If we suppose those aggregate molecules which move together to have a bounding surface which is not spherical, then the rotatory motion of the system will close up a certain proportion of the whole vis viva, as has been shown by Clausius, and in this way we may account for the value of the specific heat being greater than on the more simple hypothesis.”[1]
The elaborate investigations of Clerk-Maxwell served not merely to substantiate the doctrine, but threw a flood of light upon the entire subject of molecular dynamics. Soon the physicists came to feel as certain of the existence of these showers of flying molecules making up a gas as if they could actually see and watch their individual actions. Through study of the viscosity of gases–that is to say, of the degree of frictional opposition they show to an object moving through them or to another current of gas–an idea was gained, with the aid of mathematics, of the rate of speed at which the particles of the gas are moving, and the number of collisions which each particle must experience in a given time, and of the length of the average free path traversed by the molecule between collisions, These measurements were confirmed by study of the rate of diffusion at which different gases mix together, and also by the rate of diffusion of heat through a gas, both these phenomena being chiefly due to the helter-skelter flight of the molecules.
It is sufficiently astonishing to be told that such measurements as these have been made at all, but the astonishment grows when one hears the results. It appears from Clerk-Maxwell’s calculations that the mean free path, or distance traversed by the molecules between collisions in ordinary air, is about one-half-millionth of an inch; while the speed of the molecules is such that each one experiences about eight billions of collisions per second! It would be hard, perhaps, to cite an illustration showing the refinements of modern physics better than this; unless, indeed, one other result that followed directly from these calculations be considered such–the feat, namely, of measuring the size of the molecules themselves. Clausius was the first to point out how this might be done from a knowledge of the length of free path; and the calculations were made by Loschmidt in Germany and by Lord Kelvin in England, independently.
The work is purely mathematical, of course, but the results are regarded as unassailable; indeed, Lord Kelvin speaks of them as being absolutely demonstrative within certain limits of accuracy. This does not mean, however, that they show the exact dimensions of the molecule; it means an estimate of the limits of size within which the actual size of the molecule may lie. These limits, Lord Kelvin estimates, are about the one- ten-millionth of a centimetre for the maximum, and the one-one-hundred-millionth of a centimetre for the minimum. Such figures convey no particular meaning to our blunt senses, but Lord Kelvin has given a tangible illustration that aids the imagination to at least a vague comprehension of the unthinkable smallness of the molecule. He estimates that if a ball, say of water or glass, about “as large as a football, were to be magnified up to the size of the earth, each constituent molecule being magnified in the same proportion, the magnified structure would be more coarse-grained than a heap of shot, but probably less coarse-grained than a heap of footballs.”
Several other methods have been employed to estimate the size of molecules. One of these is based upon the phenomena of contact electricity; another upon the wave-theory of light; and another upon capillary attraction, as shown in the tense film of a soap-bubble! No one of these methods gives results more definite than that due to the kinetic theory of gases, just outlined; but the important thing is that the results obtained by these different methods (all of them due to Lord Kelvin) agree with one another in fixing the dimensions of the molecule at somewhere about the limits already mentioned. We may feel very sure indeed, therefore, that the molecules of matter are not the unextended, formless points which Boscovich and his followers of the eighteenth century thought them. But all this, it must be borne in mind, refers to the molecule, not to the ultimate particle of matter, about which we shall have more to say in another connection. Curiously enough, we shall find that the latest theories as to the final term of the series are not so very far afield from the dreamings of the eighteenth-century philosophers; the electron of J. J. Thompson shows many points of resemblance to the formless centre of Boscovich.
Whatever the exact form of the molecule, its outline is subject to incessant variation; for nothing in molecular science is regarded as more firmly established than that the molecule, under all ordinary circumstances, is in a state of intense but variable vibration. The entire energy of a molecule of gas, for example, is not measured by its momentum, but by this plus its energy of vibration and rotation, due to the collisions already referred to. Clausius has even estimated the relative importance of these two quantities, showing that the translational motion of a molecule of gas accounts for only three-fifths of its kinetic energy. The total energy of the molecule (which we call “heat”) includes also another factor–namely, potential energy, or energy of position, due to the work that has been done on expanding, in overcoming external pressure, and internal attraction between the molecules themselves. This potential energy (which will be recovered when the gas contracts) is the “latent heat” of Black, which so long puzzled the philosophers. It is latent in the same sense that the energy of a ball thrown into the air is latent at the moment when the ball poises at its greatest height before beginning to fall.
It thus appears that a variety of motions, real and potential, enter into the production of the condition we term heat. It is, however, chiefly the translational motion which is measurable as temperature; and this, too, which most obviously determines the physical state of the substance that the molecules collectively compose–whether, that is to say, it shall appear to our blunt perceptions as a gas, a liquid, or a solid. In the gaseous state, as we have seen, the translational motion of the molecules is relatively enormous, the molecules being widely separated. It does not follow, as we formerly supposed, that this is evidence of a repulsive power acting between the molecules. The physicists of to-day, headed by Lord Kelvin, decline to recognize any such power. They hold that the molecules of a gas fly in straight lines by virtue of their inertia, quite independently of one another, except at times of collision, from which they rebound by virtue of their elasticity; or on an approach to collision, in which latter case, coming within the range of mutual attraction, two molecules may circle about each other, as a comet circles about the sun, then rush apart again, as the comet rushes from the sun.
It is obvious that the length of the mean free path of the molecules of a gas may be increased indefinitely by decreasing the number of the molecules themselves in a circumscribed space. It has been shown by Professors Tait and Dewar that a vacuum may be produced artificially of such a degree of rarefaction that the mean free path of the remaining molecules is measurable in inches. The calculation is based on experiments made with the radiometer of Professor Crookes, an instrument which in itself is held to demonstrate the truth of the kinetic theory of gases. Such an attenuated gas as this is considered by Professor Crookes as constituting a fourth state of matter, which he terms ultra- gaseous.
If, on the other hand, a gas is subjected to pressure, its molecules are crowded closer together, and the length of their mean free path is thus lessened. Ultimately, the pressure being sufficient, the molecules are practically in continuous contact. Meantime the enormously increased number of collisions has set the molecules more and more actively vibrating, and the temperature of the gas has increased, as, indeed, necessarily results in accordance with the law of the conservation of energy. No amount of pressure, therefore, can suffice by itself to reduce the gas to a liquid state. It is believed that even at the centre of the sun, where the pressure is almost inconceivably great, all matter is to be regarded as really gaseous, though the molecules must be so packed together that the consistency is probably more like that of a solid.
If, however, coincidently with the application of pressure, opportunity be given for the excess of heat to be dissipated to a colder surrounding medium, the molecules, giving off their excess of energy, become relatively quiescent, and at a certain stage the gas becomes a liquid. The exact point at which this transformation occurs, however, differs enormously for
different substances. In the case of water, for example, it is a temperature more than four hundred degrees above zero, centigrade; while for atmospheric air it is one hundred and ninety-four degrees centigrade below zero, or more than a hundred and fifty degrees below the point at which mercury freezes.
Be it high or low, the temperature above which any substance is always a gas, regardless of pressure, is called the critical temperature, or absolute boiling- point, of that substance. It does not follow, however, that below this point the substance is necessarily a liquid. This is a matter that will be determined by external conditions of pressure. Even far below the critical temperature the molecules have an enormous degree of activity, and tend to fly asunder, maintaining what appears to be a gaseous, but what technically is called a vaporous, condition–the distinction being that pressure alone suffices to reduce the vapor to the liquid state. Thus water may change from the gaseous to the liquid state at four hundred degrees above zero, but under conditions of ordinary atmospheric pressure it does not do so until the temperature is lowered three hundred degrees further. Below four hundred degrees, however, it is technically a vapor, not a gas; but the sole difference, it will be understood, is in the degree of molecular activity.
It thus appeared that the prevalence of water in a vaporous and liquid rather than in a “permanently” gaseous condition here on the globe is a mere incident of telluric evolution. Equally incidental is the fact that the air we breathe is “permanently” gaseous and not liquid or solid, as it might be were the earth’s surface temperature to be lowered to a degree which, in the larger view, may be regarded as trifling. Between the atmospheric temperature in tropical and in arctic regions there is often a variation of more than one hundred degrees; were the temperature reduced another hundred, the point would be reached at which oxygen gas becomes a vapor, and under increased pressure would be a liquid. Thirty-seven degrees more would bring us to the critical temperature of nitrogen.
Nor is this a mere theoretical assumption; it is a determination of experimental science, quite independent of theory. The physicist in the laboratory has produced artificial conditions of temperature enabling him to change the state of the most persistent gases. Some fifty years since, when the kinetic theory was in its infancy, Faraday liquefied carbonic-acid gas, among others, and the experiments thus inaugurated have been extended by numerous more recent investigators, notably by Cailletet in Switzerland, by Pictet in France, and by Dr. Thomas. Andrews and Professor James Dewar in England. In the course of these experiments not only has air been liquefied, but hydrogen also, the most subtle of gases; and it has been made more and more apparent that gas and liquid are, as Andrews long ago asserted, “only distant stages of a long series of continuous physical changes.” Of course, if the temperature be lowered still further, the liquid becomes a solid; and this change also has been effected in the case of some of the most “permanent” gases, including air.
The degree of cold–that is, of absence of heat– thus produced is enormous, relatively to anything of which we have experience in nature here at the earth now, yet the molecules of solidified air, for example, are not absolutely quiescent. In other words, they still have a temperature, though so very low. But it is clearly conceivable that a stage might be reached at which the molecules became absolutely quiescent, as regards either translational or vibratory motion. Such a heatless condition has been approached, but as yet not quite attained, in laboratory experiments. It is called the absolute zero of temperature, and is estimated to be equivalent to two hundred and seventy- three degrees Centigrade below the freezing-point of water, or ordinary zero.
A temperature (or absence of temperature) closely approximating this is believed to obtain in the ethereal ocean of interplanetary and interstellar space, which transmits, but is thought not to absorb, radiant energy. We here on the earth’s surface are protected from exposure to this cold, which would deprive every organic thing of life almost instantaneously, solely by the thin blanket of atmosphere with which the globe is coated. It would seem as if this atmosphere, exposed to such a temperature at its surface, must there be incessantly liquefied, and thus fall back like rain to be dissolved into gas again while it still is many miles above the earth’s surface. This may be the reason why its scurrying molecules have not long ago wandered off into space and left the world without protection.
But whether or not such liquefaction of the air now occurs in our outer atmosphere, there can be no question as to what must occur in its entire depth were we permanently shut off from the heating influence of the sun, as the astronomers threaten that we may be in a future age. Each molecule, not alone of the atmosphere, but of the entire earth’s substance, is kept aquiver by the energy which it receives, or has received, directly or indirectly, from the sun. Left to itself, each molecule would wear out its energy and fritter it off into the space about it, ultimately running completely down, as surely as any human-made machine whose power is not from time to time restored. If, then, it shall come to pass in some future age that the sun’s rays fail us, the temperature of the globe must gradually sink towards the absolute zero. That is to say, the molecules of gas which now fly about at such inconceivable speed must drop helpless to the earth; liquids must in turn become solids; and solids themselves, their molecular quivers utterly stilled, may perhaps take on properties the nature of which we cannot surmise.
Yet even then, according to the current hypothesis, the heatless molecule will still be a thing instinct with life. Its vortex whirl will still go on, uninfluenced by the dying-out of those subordinate quivers that produced the transitory effect which we call temperature. For those transitory thrills, though determining the physical state of matter as measured by our crude organs of sense, were no more than non-essential incidents; but the vortex whirl is the essence of matter itself. Some estimates as to the exact character of this intramolecular motion, together with recent theories as to the actual structure of the molecule, will claim our attention in a later volume. We shall also have occasion in another connection to make fuller inquiry as to the phenomena of low temperature.
APPENDIX
REFERENCE-LIST
CHAPTER I
THE SUCCESSORS OF NEWTON IN ASTRONOMY [1] (p. 10). An Account of Several Extraordinary Meteors or Lights in the Sky, by Dr. Edmund Halley. Phil. Trans. of Royal Society of London, vol. XXIX, pp. 159-162. Read before the Royal Society in the autumn of 1714. [2] (p. 13). Phil. Trans. of Royal Society of London for 1748, vol. XLV., pp. 8, 9. From A Letter to the Right Honorable George, Earl of Macclesfield, concerning an Apparent Motion observed in some of the Fixed Stars, by James Bradley, D.D., Astronomer Royal and F.R.S.
CHAPTER II
THE PROGRESS OF MODERN ASTRONOMY
[1] (p. 25). William Herschel, Phil. Trans. for 1783, vol. LXXIII.
[2] (p. 30). Kant’s Cosmogony, ed. and trans. by W. Hartie, D.D., Glasgow, 900, pp. 74-81.
[3] (p. 39). Exposition du systeme du monde (included in oeuvres Completes), by M. le Marquis de Laplace, vol. VI., p. 498.
[4] (p. 48). From The Scientific Papers of J. Clerk-Maxwell, edited by W. D. Nevin, M.A. (2 vols.), vol. I., pp. 372-374. This is a reprint of Clerk-Maxwell’s prize paper of 1859.
CHAPTER III
THE NEW SCIENCE OF PALEONTOLOGY
[1] (p. 81). Baron de Cuvier, Theory of the Earth, New York, 1818, p. 98.
[2] (p. 88). Charles Lyell, Principles of Geology (4 vols.), London,
1834.
(p. 92). Ibid., vol. III., pp. 596-598. [4] (p. 100). Hugh Falconer, in Paleontological Memoirs, vol. II., p. 596.
[5] (p. 101). Ibid., p. 598.
[6] (p. 102). Ibid., p. 599.
[7] (p. 111). Fossil Horses in America (reprinted from American Naturalist, vol. VIII., May, 1874), by O. C. Marsh, pp. 288, 289.
CHAPTER IV
THE ORIGIN AND DEVELOPMENT OF MODERN GEOLOGY
[1] (p. 123). James Hutton, from Transactions of the Royal Society of Edinburgh, 1788, vol. I., p. 214. A paper on the “Theory of the Earth,” read before the Society in 1781.
[2] (p. 128). Ibid., p. 216.
[3] (p. 139). Consideration on Volcanoes, by G. Poulett Scrope, Esq., pp. 228-234.
[4] (p. 153). L. Agassiz, Etudes sur les glaciers, Neufchatel, 1840, p. 240.
CHAPTER V
THE NEW SCIENCE OF METEOROLOGY
[1] (p. 182). Theory of Rain, by James Hutton, in Transactions of the Royal Society of Edinburgh, 1788, vol. 1 , pp. 53-56.
[2] (p. 191). Essay on Dew, by W. C. Wells, M.D., F.R.S., London, 1818, pp. 124 f.
CHAPTER VI
MODERN THEORIES OF HEAT AND LIGHT
[1] (p. 215). Essays Political, Economical, and Philosophical, by Benjamin Thompson, Count of Rumford (2 vols.), Vol. II., pp. 470-493, London; T. Cadell, Jr., and W. Davies, 1797. [2] (p. 220). Thomas Young, Phil. Trans., 1802, p. 35. [3] (p. 223). Ibid., p. 36.
CHAPTER VII
THE MODERN DEVELOPMENT OF ELECTRICITY AND MAGNETISM
[1] (p. 235). Davy’s paper before Royal Institution, 1810. [2] (p. 238). Hans Christian Oersted, Experiments with the Effects of the Electric Current on the Magnetic Needle, 1815. [3] (p. 243). On the Induction of Electric Currents, by Michael Faraday, F.R.S., Phil. Trans. of Royal Society of London for 1832, pp. 126-128.
[4] (p. 245). Explication of Arago’s Magnetic Phenomena, by Michael Faraday, F.R.S., Phil. Trans. Royal Society of London for 1832, pp. 146-149.
CHAPTER VIII
THE CONSERVATION OF ENERGY
[1] (p. 267). The Forces of Inorganic Nature, a paper by Dr. Julius Robert Mayer, Liebig’s Annalen, 1842. [2] (p. 272). On the Calorific Effects of Magneto-Electricity and the Mechanical Value of Heat, by J. P. Joule, in Report of the British Association for the Advancement of Science, vol. XII., p. 33.
CHAPTER IX
THE ETHER AND PONDERABLE MATTER
[1] (p. 297). James Clerk-Maxwell, Philosophical Magazine for January and July, 1860.
END OF VOL. III