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[PDF page 324] 308 MATTER AND ETHER THEORIES. [CH. XIV Vortex rings—though, since friction is brought into play, of an im- perfect 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 op- posite 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* showed that a closed vortex filament in a perfect fluid is indestructible and retains certain characteristics always unaltered. In 1867 Sir William Thomson propounded† 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 than1014. By a development of this hypothesis Prof. J.J. Thomson‡showed, some years ago, that chemical combination may be explained. He sup- posed that a molecule of a compound is formed by the linking together of vortex filaments representing atoms of different elements: this ar- rangement 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 chemi- cal combination on the vortex atom hypothesis has been suggested by W.M. Hicks. It is known§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. * Crelle’s Journal, 1858, vol.l v, pp. 25–55; translated by Tait in thePhilosophical Magazine, June, 1867, supplement, series 4, vol.xxxiii, pp. 485–512. † Proceedings of the Royal Society of Edinburgh, Feb. 18, 1867, vol.vi, pp. 94–105. ‡ A Treatise on the Motion of Vortex Rings, Cambridge, 1883. § See a memoir by M.J.M. Hill in the Philosophical Transactions of the Royal Society, London, 1894, part i, pp. 213–246.

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[PDF page 325] CH. XIV] MATTER AND ETHER THEORIES. 309 (ii) The Vortex Sponge Hypothesis. Any vortex atom hypothe- sis 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 transver- sal radiations Sir William Thomson suggested what has been termed, not perhaps very happily, the vortex sponge hypothesis*: this rests on the assumption that laminar motion can be propagated through a turbulently moving inviscid liquid. The mathematical difficulties con- nected 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 in- destructibility 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. (iii) The Ether-Squirts Hypothesis. Prof. Karl Pearson†has sug- gested another dynamical theory in which an atom is conceived as a point at which ether is pouring into our space from space of four di- mensions. 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 * Philosophical Magazine, London, October, 1887, series 5, vol.xxiv, pp. 342–353. † American Journal of Mathematics, 1891, vol.xiii, pp. 309–362.

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[PDF page 326] 310 MATTER AND ETHER THEORIES. [CH. XIV hypothesis rests on the assumption of the existence of a world beyond our senses. (iv) 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 re- sist rotation. This suggestion has been recently modified and extended by Dr J. Larmor*, 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 intro- duces monad electric elements orelectrons, 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 consid- erations 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 possi- ble 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, ofnucleiofstrainintheether, whicharesupposedtobeinincessantand 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. 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 thirtyyearsagoClerkMaxwellhadshownthatlightandelectricitywere closely connected phenomena. It was then believed that both were due to waves in the hypothetical ether, but it was supposed that the phe- * Philosophical Transactions of the Royal Society, London, 1894, pp. 719–822; 1895, pp. 695–743.

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[PDF page 327] CH. XIV] MATTER AND ETHER THEORIES. 311 nomena 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 ura- nium 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 oxy- gen. 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 repre- sented 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

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[PDF page 328] 312 MATTER AND ETHER THEORIES. [CH. XIV 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 cor- responding 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 cor- puscles 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. (v) The Bubble Hypothesis*. The difficulty of conceiving the mo- tion 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 par- ticles 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 * O. Reynolds, Submechanics of the Universe, Cambridge, 1903.

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[PDF page 329] CH. XIV] THE CAUSE OF GRA VITY 313 than 5 ×10−18 centimetres, and that the pressure in the medium would be about 104 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. 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*, “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†, “’Tis inconceivable, that inanimate brute matter should (without the mediation of something elsewhichisnotmaterial)operateuponandaffectothermatterwithout 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 * Letter dated Jan. 17, 1693. I quote from the original, which is in the Library of Trinity College, Cambridge; it is printed in theLetters to Bentley, London, 1756, p. 20. † Letter dated Feb. 25, 1693;ibid., pp. 25, 26.

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[PDF page 330] 314 MATTER AND ETHER THEORIES. [CH. XIV 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 depen- dent 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 hisOpticks, where he suggested as a possible explanation the existence of a stress in the ether surrounding a particle of matter*. This has been elaborated on a statical basis by Maxwell, who showed† that the stress would have to be at least 3000 times greater than that which the strongest steel would support. Sir William Thom- son (Lord Kelvin) has suggested‡ 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 pro- portional 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 New- ton’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§that though the above expla- nation 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∥ that gravity was caused by the bombardment of streams of ultramundane corpuscles. These * Quoted by S.P. Rigaud in hisEssay on thePrincipia, Oxford, 1838, appendix, pp. 68–70. On other guesses by Newton see Rigaud, text, pp. 61–62, and refer- ences there given. † Article Attraction, in Encyclopaedia Britannica, or Collected Works, vol. ii, p. 489. ‡ Proceedings of the Royal Society of Edinburgh, Feb. 7, 1870, vol.vii, pp. 60–63. § An Account of Sir Isaac Newton’s Philosophical Discoveries, London, 1748, p. 111. ∥ Mémoires de l’Académie des Sciencesfor 1782, Berlin, 1784, pp. 404–432: see also the first two books of hisTraité de Physique, Geneva, 1818.

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[PDF page 331] CH. XIV] THE CAUSE OF GRA VITY 315 corpuscles are supposed to come in all directions from space and to be so small that inter-collisions are rare. Abodybyitselfinspacewouldreceiveonanaverageasmanyblows 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 per- fectly elastic the theory might be tenable*. 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†of foot-pounds per second; and third, that it is probable that the effect of such a bombard- ment 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 say- ing‡, “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 exhaus- tion suffered in the production of gravitation. Another defect is that * See a paper by Sir William Thomson (Lord Kelvin) in theProceedings of the Royal Society of Edinburgh, Dec. 18, 1871, vol.vii, pp. 577–589. † I use billion with the English (and not the French) meaning, that is, a billion = 10 12. ‡ Properties of Matter, London, 1885, art. 164.

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[PDF page 332] 316 MATTER AND ETHER THEORIES. [CH. XIV they all make gravitation a mere difference-effect, as it were; thereby implying the presence of stores of energy absolutely gigantic in com- parison 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 instan- taneously 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*. 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,i.e. 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 re- maining unaltered. The transmission of light and radiant heat may be explained by such vibrations transversal to the direction of propaga- tion. 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 vibra- tion there, then the Newtonian law of attraction would follow. This conjecture is consistent either with Boscovich’s hypothesis or with the * See an article by myself in the Messenger of Mathematics, Cambridge, 1891, vol. xxi, pp. 20–24.

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[PDF page 333] CH. XIV] FINITE NUMBER OF KINDS OF MATTER 317 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. 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 capa- ble 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 supposingthatsuchaconnectionexists, butifwearelivinginaspaceof
