CM. XXl] MATTER AND ETHER THEORIES 469

and eight groups. All the elements since discovered have fallen into place in the sequence, and possess properties in general accordance with his grouping, but helium, argon, and other similar inactive elements, constitute a ninth or zero group.
In this scheme hydrogen, with an atomic weight 1*008, is in the first series and first group. It has the lowest atomic weight of any element yet known, but there may be lighter elements, ex. gr. one in the first series and zero group. Mendelejcv has however suggested that just as a zero group has been now discovered so there may be a zero series ; and that the element (if there is one) in the zero group and zero series might be expected to possess properties closely resembling those of the hypothetical ether. It would be the lightest and simplest form of matter, of great elasticity, and with an atomic weight of perhaps about 1/10^ as compared with hydrogen. The velocity of its atoms would be so great as to make it all pervading, and it would appear to be capable of doing all that is required fi:om the mysterious ether. The hypothesis is attractive and intelligible.
(viii) The Bubble Hypothesis''^, 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 gi-ains piled together so closely that they cannot change their neigh- bours, 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
* 0. Reynolds, Submechanics of the Universe, Cambridge, 1903.
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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 x 10~^^ centimetres, and that the pressure in the medium would be about 10^ tons per square centimetre. This theory is in itself more plausible than the electron hypothesis, but its consequences have not 3^et 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 h5rpotheses 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 correspondence with Bentley, while declaring his ignorance of the cause of gravity, refused to admit the possi- bility 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
* Letter dated Jan. 17, 1693. 1 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.
CH. XXl] MATTER AND ETHER THEORIES 471
place he v/rote*, "'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 philo- sophical 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 matterf.
This was elaborated on a statical basis by Clerk Maxwell, who showedj that the stress would have to be at least 3000 times as great as that which the strongest steel would support. Sir William Thomson suggested § a dynamical way of producing the stress by supposing that space is filled with an incom- pressible fluid, constantly being amiihilated by each atom of matter at a rate proportional to its mass, a constant supply
♦ Letter dated Feb. 25, 1693 ; Letters to Bentley, London, 1756, pp. 25, 26.
+ 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.
Ij: 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,
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being kept up at an infinite distance. It is true that this avoids Clerk 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* 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 suggestedf 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 pro- portional 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.
* An Account of Sir Isaac Neiotonh Philosophical Discoveries, London, 1748, p. 111.
t Memoires de VAcademie des Sciences for 1782, Berlin, 1784, pp. 404—432 : see also the first two books of his Traite de Physique, Geneva, 1818.
CH. XXl] MATTER AND ETHER THEORIES 473
This is ingenious, and it is possible that if the corpuscles were perfectly elastic the theory might be tenable*. But the results of Clerk 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 f 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 mole- cules would have to be considerably greater than is compatible with the results given below.
Tait summed up the objections to these two hypotheses by sayingj:, "One common defect of these attempts is... that they all demand gome prime mover, working beyond the limits of the visible universe or inside each atom: creating or annihilating matter, giving additional speed to spent cor- puscles, 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 sys- tems 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 §. It is possible that the attraction of one particle on another might be explained if both of them
* See a paper by Sir William Thomson in the Proceedings of the Royal Society of Edinburgh, Dec. 18, 1871, vol. vii, pp. 577 — 589.
t I use billion with the English (and not the French) meaning, that is, a billion = 10^2.
:J: Properties of Matter, London, 1885, art. 164.
§ See an article by myself in the Messenger of Mathematics, Cambridge, 1891, vol. XXI, pp. 20 — 24.
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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 vibra- tion. 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 remaining un- altered. 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 h3rpothesis or with the vortex theory. It would be interesting if the results of a branch of pure mathematics so abstract as the theory of hyper-space 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.
CH. XXl] MATTER AND ETHER THEORIES 475
The fact that the number of kinds of matter (chemical elements) is finite and the consequences of spectrum analysis are closely related. 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 explana- tion 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 mole- cules 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.
Clerk 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