TRANSACTIONS OF THE SECTIONS.

SECTION A.-MATHEMATICAL AND PHYSICAL SCIENCE. PRESIDENT OF THE SECTION-Professor W. M. HICKS, M.A., D.Sc., F.R.S.

THURSDAY, SEPTEMBER 12.

THE President delivered the following Address :

In making a choice of subject for my address the difficulty is not one of finding material but of making selection. The field covered by this Section is a wide one. Investigation is active in every part of it, and is being rewarded with a continuous stream of new discoveries and with the growth of that co-ordination and correlation of facts which is the surest sign of real advancement in science. The ultimate aim of pure science is to be able to explain the most complicated phenomena of nature as flowing by the fewest possible laws from the simplest fundamental data. A statement of a law is either a confession of ignorance or a mnemonic convenience. It is the latter if it is deducible by logical reasoning from other laws. It is the former when it is only discovered as a fact to be a law. While, on the one hand, the end of scientific investigation is the discovery of laws, on the other, science will have reached its highest goal when it shall have reduced ultimate laws to one or two, the necessity of which lies outside the sphere of our cognition. These ultimate laws-in the domain of physical science at least-will be the dynamical laws of the relations of matter to number, space, and time. The ultimate data will be number, matter, space, and time themselves. When these relations shall be known, all physical phenomena will be a branch of pure mathematics. We shall have done away with the necessity of the conception of potential energy, even if it may still be convenient to retain it; and-if it should be found that all phenomena are manifestations of motion of one single continuous medium -the idea of force will be banished also, and the study of dynamics replaced by the study of the equation of continuity.

Before, however, this can be attained, we must have the working drawings of the details of the mechanism we have to deal with. These details lie outside the scope of our bodily senses; we cannot see, or feel, or hear them, and this, not because they are unseeable, but because our senses are too coarse-grained to transmit impressions of them to our mind. The ordinary methods of investigation here fail us; we must proceed by a special method, and make a bridge of communication between the mechanism and our senses by means of hypotheses. By our imagination, experience, intuition we form theories; we deduce the consequences of these theories on phenomena which come within the range of our senses, and reject or modify and try again. It is a slow and laborious process. The wreckage of rejected theories is appalling; but a knowledge of what actually goes on behind what we can see or feel is surely if slowly being

attained. It is the rejected theories which have been the necessary steps towards formulating others nearer the truth. It would be an extremely interesting study to consider the history of these discarded theories; to show the part they have taken in the evolution of truer conceptions, and to trace the persistence and modification of typical ideas from one stratum of theories to a later. I propose, however, to ask your attention for a short time to one of these special theories or rather to two related theories-on the constitution of matter and of the ether. They are known as the vortex atom theory of matter, and the vortex sponge theory of the ether. The former has been before the scientific world for a quarter of a century, since its first suggestion by Lord Kelvin in 1867, the second for about half that time. In what I have to say I wish to take the position not of an advocate for or against, but simply as a prospector attempting to estimate what return is likely to be obtained by laying down plant to develop an unknown district. This is in fact the state of these two theories at present. Extremely little progress has been made in their mathematical development, and until this has been done more completely we cannot test them as to their powers of adequately explaining physical phenomena.

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The theory of the rigid atom has been a very fruitful one, especially in explaining the properties of matter in the gaseous state; but it gives no explanation of the apparent forces which hold atoms together, and in many other respects it requires supplementing. The elastic solid ether explained much, but there are difficulties connected with it-especially in connection with reflection and refraction —which decide against it. The mathematical rotational ether of MacCullagh is admirably adapted to meet these difficulties, but he could give no physical conception of its mechanism. Maxwell and Faraday proposed a special ether for electrical and magnetic actions. Maxwell's identification of the latter with the luminiferous ether, his deduction of the velocity of propagation of light and of indices of refraction in terms of known electrical and magnetic constants, will form one of the landmarks in the history of science. This ether requires the same mathematical treatment as that of MacCullagh. Lord Kelvin's gyrostatic of an ether is also of the MacCullagh type. Lastly, we have Lord Kelvin labile ether, which again avoids the objections to the elastic solid ether. In MacCu type of ether the energy of the medium when disturbed depends only on the produced in it. This ether has recently been mathematically discussed b ena Larmor, who has shown that it is adequate to explain all the various pheno of light, electricity, and magnetism. To this I hope to return later. Meanw ile, it may be borne in mind that the vortex sponge ether belongs to MacCull type. Already before a formal theory of a fluid ether had been attempted, Kelvin had proposed his theory of vortex atoms. The permanence of a vo filament with its infinite flexibility, its fundamental simplicity with its poter capacity for complexity, struck the scientific imagination as the thing which 18wanted. Unfortunately the mathematical difficulties connected with the disc sion of these motions, especially the reactions of one on another, have retarded full development of the theory. Two objections in chief have been raised st it, viz. the difficulty of accounting for the densities of various kinds of matter, ad the fact that in a vortex ring the velocity of translation decreases as the en gy increases. There are two ways of dealing with a difficulty occurring in a ger ral theory-one is to give up the theory, the other is to try to see if it can be r dified to get over the difficulty. Such difficulties are to be welcomed as mea is of help in arriving at greater exactness in details. It is a mistake to subm too readily to crucial experiments. The very valid crucial objection of Stoles to MacCullagh's ether is a case in point. It drew away attention from a heory which, in the light of later developments, gives great hope of leading us to correct ideas. As Larmor has pointed out, this objection vanishes when we have intrinsic rotations in the ether itself. A special danger to guard against is the importation into one theory of ideas which have grown out of one essentially different.

1 Vortex Atoms,' Proc. Roy. Soc. Edin., vi. 94; Phil. Mag. (4), 34.

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remark has reference to the apparent difficulty of decrease of velocity with increased energy.

Maxwell was, I believe, the first to point out the difficulty of explaining the masses of the elements on the vortex atom hypothesis. To me it has always appeared one of the greatest stumbling-blocks to the acceptance of the theory. We have always been accustomed to regard the ether as of extreme tenuity, as of a density extremely though not infinitely smaller than that of gross matter, and we carry in our minds that Lord Kelvin has given an inferior limit of about 10-19. There are two directions in which to seek a solution. The first is to cut the knot by supposing that the atoms of gross matter are composed of filaments whose rotating cores are of much greater density than the ether itself. The second is to remember that Lord Kelvin's number was obtained on the supposition of elastic solid ether, and does not necessarily apply to the vortex sponge. Unfortunately, however, for the first explanation, the mathematical discussion shows that a ring cannot be stable unless the density of the fluid outside the core is equal to, or greater than, that inside. This instability also cannot be cured by supposing an additional circulation added outside the core. Unless, therefore, some modification of the theory can be made to secure stability, this idea of dense fluid cores must be given up.

We seem, therefore, forced back to the conclusion that the density of the ether must be comparable with that of ordinary matter. The effective mass of any atom is not composed of that of its core alone, but also of that portion of the surrounding ether which is carried along with it as it moves through the medium. Thus a rigid sphere moving in a liquid behaves as if its mass were increased by half that of the displaced liquid. In the case of a vortex filament the ratio of effective to actual mass may be much larger. In this explanation the density of the matter composing an atom is the same for all, whilst their masses depend on their volumes and configurations combined. Now the configuration alters with the energy, and this would make the mass depend to some extent at least on the temperature. However repugnant this may be to current ideas, we are not entitled to deny its possibility, although such an effect must be small or it would have been detected. Such a variation, if it exists, is not to be looked for by means of the ordinary gravitation balance, but by the inertia or ballistic balance. The mass of the core itself remains, of course, constant, but the effective mass-that which we can measure by the mechanical effects which the moving vortex produces-is a much more complicated matter, and requires much fuller consideration than has been given to it.

The conditions of stability allow us to assume vacuous cores or cores of less density than the rest of the medium. If we do this then the density of the ether itself may be greater than that of gross matter. Until, however, we meet with phenomena whose explanation requires this assumption, it would seem preferable to take the density everywhere the same. In this case the density of the ether must be rather less than the apparent density of the lightest of any of the elements, taking the apparent density to mean the effective mass of a vortex atom per its volume. This will probably be commensurable with the density of the matter in its most compressed state, and will lie between 5 and 1-comparable, that is to say, with the density of water. Larmor, from a special form of hypothesis for a magnetic field in the rotationally elastic ether, is led to assign a density of the same order of magnitude. If the density be given it is easy to calculate the intrinsic energy per c.c. in the medium. The velocity of propagation of light in a vortex sponge ether, as deduced by Lord Kelvin,3 is 47 times the mean square

'An error in the expression on p. 768 of ' Researches in the Theory of Vortex Rings,' Phil. Trans., pt. ii. 1885, vitiates the conclusion there drawn. If this be corrected the result mentioned above follows. See also Basset, Treatise on Hydrodynamics, § 338, and Amer. Jour. Math.

2A Dynamical Theory of the Electric and Luminiferous Medium,' Phil. Trans., 1894, A. p. 779.

On the Propagation of Laminar Motion through a Turbulently Moving Inviscid Liquid,' Phil. Mag., October 1887.

velocity of the intrinsic motion of the medium. This gives for the mean square velocity 6.3 x 1010 cm. per second. If we follow Lord Kelvin and use for comparison the energy of radiation per c.c. near the sun, or say 18 erg per c.c., the resulting density will be 10-21. The energy per c.c. in a magnetic field of 15,000 c.g.s. units is about 1 joule. If we take this for comparison we get a density of 10-14. But the intrinsic energy of the fluid must be extremely great compared with the energy it has to transmit. If it were a million times greater the density would still only amount to 10-8-comparable with the density of the residual gas in our highest vacua. To account for the density of gross matter on the supposition that it is built up out of the same material as the ether leads to a density between 5 and 1. This gives the enormous energy of 1014 joules per c.c. In other words, the energy contained in one cubic centimetre of the ether is sufficient to raise a kilometre cube of lead 1 metre high against its weight. Thus the difficulty in explaining the mass of ordinary matter seems to reduce itself to a difficulty in believing that the ether possesses such an enormous store of energy. It may be that there are special reasons against such a large density. Larmor refers to the large forcives which would be called into play by hydrodynamical motions. Perhaps an answer to this may be found in the remark that where all the matter is of the same density the motions are kinematically deducible from the configuration at the instant, and are independent of the density. It is only where other causes act, such, e.g., as indirectly depend on the mean pressure of the fluid or where vacuous spaces occur, that the actual value of the density may modify the measurable forcives.

Ever since Professor J. J. Thomson proved that a vortex atom theory of matter is competent to serve as a basis of a kinetic theory of gases, it has been urged by various persons as a fatal objection that the translation velocity of the atoms falls off as the temperature rises. I must confess this objection has never appealed to me. Why should not the velocity fall off? The velocity of gaseous molecules has never been directly observed, nor has it been experimentally proved that it increases with rise of temperature. We have no right to import ideas based on the kinetic theory of hard discrete atoms into the totally distinct theory of mobile atoms in continuity with the medium surrounding them. Doubtless the molecules of a gas effuse through a small orifice more quickly as the temperature rises, but it is natural to suppose that a vortex ring would do the same as its energy increases. To make the objection valid, it is necessary to show that a vortex ring passing through a small tube, comparable with its own diameter, would pass through more slowly the greater its energy. It is not, however, necessarily the case that in every vortex aggregate the velocity decreases as the energy increases. The mathematical treatment of thin vortex filaments is comparatively easy, and little attention has been paid to other cases. Let us attempt to trace the life history as to translation velocity and energy of a vortex ring. We start with the energy large; the ring now has a very large aperture, and has a very thin filament. As the energy decreases the aperture becomes smaller, the filament thicker, and the velocity of translation greater. We can trace quantitatively the whole of this part of its history until the thickness of the ring has increased to about four times the diameter of the aperture, or perhaps a little further. Then the mathematical treatment employed fails us or becomes very laborious to apply. Till eighteen months ago, this was the only portion of its history we could trace. Then Professor M. J. M. Hill 1 published his beautiful discovery of the existence of a spherical vortex. This consists of a spherical mass of fluid in vortical motion and moving bodily through the surrounding fluid, precisely as if it were a rigid sphere. This enables us to catch a momentary glimpse as it were of our vortex ring sonie little time after it has passed out of our ken. The aperture has gone on contracting, the ring thickening, and altering the shape of its cross section in a manner whose exact details have not yet been calculated. At last we just catch sight of it again as the aperture closes up. We find the ring has changed into a spherical ball, with still further diminished energy and increased velocity. We then lose sight of it again, but it now lengthens 'On a Spherical Vortex,' Phil. Trans., 1894.