Chapter VIII: MISCELLANEOUS.--Fires in London and New York (3)

Here again we are struck by resemblances to the forms that were the subjects of our previous study, we even come across direct transitional forms, which differ from the others only by the lateral curve of the apex of the leaf; sometimes it is the central part, the spadix, that is bent outward, and the very details show a striking agreement with the structure of the aroid inflorescence, so much so that one might regard them as actually copied from them.

This form of ornament has been introduced into Europe since the French expedition to Egypt, owing to the importation of genuine Cashmere shawls. (When it cropped up in isolated forms, as in Venice in the fifteenth century, it appears not to have exerted any influence; its introduction is perhaps rather to be attributed to calico-printing.) Soon afterward the European shawl-manufacture, which is still in a flourishing state, was introduced. Falcot informs us that designs of a celebrated French artist, Couder, for shawl-patterns, a subject that he studied in India itself, were exported back to that country and used there (Fig. 20).

In these shawl-patterns the original simple form meets us in a highly developed, magnificent, and splendidly colored differentiation and elaboration. This we can have no scruples in ranking along with the mediæval plane-patterns, which we have referred to above, among the highest achievements of decorative art.

It is evident that it, at any rate in this high stage of development, resisted fusion with Western forms of art. It is all the more incumbent upon us to investigate the laws of its existence, in order to make it less alien to us, or perhaps to assimilate it to ourselves by attaining to an understanding of those laws. A great step has been made when criticism has, by a more painstaking study, put itself into a position to characterize as worthless ignorantly imitated, or even original, miscreations such as are eternally cropping up. If we look at our modern manufactures immediately after studying patterns which enchant us with their classical repose, or after it such others as captivate the eye by their beautiful coloring, or the elaborative working out of their details, we recognize that the beautifully balanced form is often cut up, choked over with others, or mangled (the flower springing up side down from the leaves), the whole being traversed at random by spirals, which are utterly foreign to the spirit of such a style, and all this at the caprice of uncultured, boorish designers. Once we see that the original of the form was a plant, we shall ever in the developed, artistic form cling, in a general way at least, to the laws of its organization, and we shall at any rate be in a position to avoid violent incongruities.

I had resort, a few years ago, to the young botanist Ruhmer, assistant at the Botanical Museum at Schöneberg, who has unfortunately since died of some chest-disease, in order to get some sort of a groundwork for direct investigations. I asked him to look up the literature of the subject, with respect to the employment of the Indian Araceæ for domestic uses or in medicine. A detailed work on the subject was produced, and establishes that, quite irrespective of species of Alocasia and Colocasia that have been referred to, a large number of Araceæ were employed for all sorts of domestic purposes. Scindapsus, which was used as a medicine, has actually retained a Sanskrit name, "vustiva." I cannot here go further into the details of this investigation, but must remark that even the incomplete and imperfect drawings of these plants, which, owing to the difficulty of preserving them, are so difficult to collect through travelers, exhibit such a wealth of shape, that it is quite natural that Indian and Persian flower-loving artists should be quite taken with them, and employ them enthusiastically in decorative art. Let me also mention that Haeckel, in his '"Letters of an Indian Traveler," very often bears witness to the effect of the Araceæ upon the general appearance of the vegetation, both in the full and enormous development of species of Caladia and in the species of Pothos which form such impenetrable mazes of interlooping stems.

In conclusion, allow me to remark that the results of my investigation, of which but a succinct account has been given here, negative certain derivations, which have been believed in, though they have never been proved; such as that of the form I have last discussed from the Assyrian palmetta, or from a cypress bent down by the wind. To say the least the laws of formation here laid down have a more intimate connection with the forms as they have come down to us, and give us a better handle for future use and development. The object of the investigation was, in general words, to prepare for an explanation of the questions raised; and even if the results had turned out other than they have, it would have sufficed me to have given an impulse to labors which will testify to the truth of the dead master's words:

"Was Du ererbt von deinen Vätern hast,
Erwirb es, um es zu besitzen."

* * * * *

STEPS TOWARD A KINETIC THEORY OF MATTER.

[Footnote: Meeting of the British Association, Montreal. 1884. Section A. Mathematical and Physical science. Opening Address by Prof. Sir William Thomson, M.A., LL.D., D.C.L., F.R.SS.L. and E., F.R.A.S., President of the Section.]

By Sir WILLIAM THOMSON.

The now well known kinetic theory of gases is a step so important in the way of explaining seemingly static properties of matter by motion, that it is scarcely possible to help anticipating in idea the arrival at a complete theory of matter, in which all its properties will be seen to be merely attributes of motion. If we are to look for the origin of this idea we must go back to Democritus, Epicurus, and Lucretius. We may then, I believe, without missing a single step, skip 1800 years. Early last century we find in Malebranche's "Recherche de la Verite," the statement that "la durete de corps" depends on "petits tourbillons." [1] These words, embedded in a hopeless mass of unintelligible statements of the physical, metaphysical, and theological philosophies of the day, and unsupported by any explanation, elucidation, or illustration throughout the rest of the three volumes, and only marred by any other single sentence or word to be found in the great book, still do express a distinct conception which forms a most remarkable step toward the kinetic theory of matter. A little later we have Daniel Bernoulli's promulgation of what we now accept as a surest article of scientific faith--the kinetic theory of gases. He, so far as I know, thought only of Boyle's and Mariotte's law of the "spring of air," as Boyle called it, without reference to change of temperature or the augmentation of its pressure if not allowed to expand for elevation of temperature, a phenomenon which perhaps he scarcely knew, still less the elevation of temperature produced by compression, and the lowering of temperature by dilatation, and the consequent necessity of waiting for a fraction of a second or a few seconds of time (with apparatus of ordinary experimental magnitude), to see a subsidence from a larger change of pressure down to the amount of change that verifies Boyle's law. The consideration of these phenomena forty years ago by Joule, in connection with Bernoulli's original conception, formed the foundation of the kinetic theory of gases as we now have it. But what a splendid and useful building has been placed on this foundation by Clausius and Maxwell, and what a beautiful ornament we see on the top of it in the radiometer of Crookes, securely attached to it by the happy discovery of Tait and Dewar,[2] that the length of the free path of the residual molecules of air in a good modern vacuum may amount to several inches! Clausius' and Maxwell's explanations of the diffusion of gases, and of thermal conduction in gases, their charmingly intelligible conclusion that in gases the diffusion of heat is just a little more rapid than the diffusion of molecules, because of the interchange of energy in collisions between molecules,[3] while the chief transference of heat is by actual transport of the molecules themselves, and Maxwell's explanation of the viscosity of gases, with the absolute numerical relations which the work of those two great discoverers found among the three properties of diffusion, thermal conduction, and viscosity, have annexed to the domain of science a vast and ever growing province.

[Footnote 1: "Preuve de la supposition que j'ay faite: Que la matiere subtile ou etheree est necessairement composee de PETITS TOURBILLONS; et qu'ils sont les causes naturelles de tous les changements qui arrivent a la matiere; ce que je confirme par i'explication des effets les plus generaux de la Physique, tels que sont la durete des corps, leur fluidite, leur pesanteur, legerete, la lumiere et la refraction et reflexion de ses rayons."--Malebranche, "Recherche de la Verite," 1712.]

[Footnote 2: Proc. R.S.E., March 2, 1874, and July 5, 1875.]

[Footnote 3: On the other hand, in liquids, on account of the crowdedness of the molecules, the diffusion of heat must be chiefly by interchange of energies between the molecules, and should be, as experiment proves it is, enormously more rapid than the diffusion of the molecules themselves, and this again ought to be much less rapid than either the material or thermal diffusivities of gases. Thus the diffusivity of common salt through water was found by Fick to be as small as 0.0000112 square centimeter per second; nearly 200 times as great as this is the diffusivity of heat through water, which was found by J.T. Bottomley to be about 0.002 square centimeter per second. The material diffusivities of gases, according to Loschmidt's experiments, range from 0.98 (the interdiffusivity of carbonic acid and nitrous oxide) to 0.642 (the interdiffusivity of carbonic oxide and hydrogen), while the thermal diffusivities of gases, calculated according to Clausius' and Maxwell's kinetic theory of gases, are 0.089 for carbonic acid, 0.16 for common air of other gases of nearly the same density, and 1.12 for hydrogen (all, both material and thermal, being reckoned in square centimeters per second).]

Rich as it is in practical results, the kinetic theory of gases, as hitherto developed, stops absolutely short at the atom or molecule, and gives not even a suggestion toward explaining the properties in virtue of which the atoms or molecules mutually influence one another. For some guidance toward a deeper and more comprehensive theory of matter, we may look back with advantage to the end of last century and beginning of this century, and find Rumford's conclusion regarding the heat generated in boring a brass gun: "It appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner the heat was excited and communicated in these experiments, except it be MOTION;" and Davy's still more suggestive statements: "The phenomena of repulsion are not dependent on a peculiar elastic fluid for their existence." ... "Heat may be defined as a peculiar motion, probably a vibration, of the corpuscles of bodies, tending to separate them." ... "To distinguish this motion from others, and to signify the causes of our sensations of heat, etc., the name _repulsive_ motion has been adopted." Here we have a most important idea. It would be somewhat a bold figure of speech to say the earth and moon are kept apart by a repulsive motion; and yet, after all, what is centrifugal force but a repulsive motion, and may it not be that there is no such thing as repulsion, and that it is solely by inertia that what seems to be repulsion is produced? Two bodies fly together, and, accelerated by mutual attraction, if they do not precisely hit one another, they cannot but separate in virtue of the inertia of their masses. So, after dashing past one another in sharply concave curves round their common center of gravity, they fly asunder again. A careless onlooker might imagine they had repelled one another, and might not notice the difference between what he actually sees and what he would see if the two bodies had been projected with great velocity toward one another, and either colliding and rebounding, or repelling one another into sharply convex continuous curves, fly asunder again.

Joule, Clausius, and Maxwell, and no doubt Daniel Bernoulli himself, and I believe every one who has hitherto written or done anything very explicit in the kinetic theory of gases, has taken the mutual action of molecules in collision as repulsive. May it not after all be attractive? This idea has never left my mind since I first read Davy's "Repulsive Motion," about thirty-five years ago, and I never made anything of it, at all events have not done so until to-day (June 16, 1884)--if this can be said to be making anything of it--when, in endeavoring to prepare the present address, I notice that Joule's and my own old experiments[1] on the thermal effect of gases expanding from a high-pressure vessel through a porous plug, proves the less dense gas to have greater intrinsic _potential_ energy than the denser gas, if we assume the ordinary hypothesis regarding the temperature of a gas, according to which two gases are of equal temperatures [2] when the kinetic energies of their constituent molecules are of equal average amounts per molecule.

[Footnote 1: Republished in Sir W. Thomson's "Mathematical and Physical Papers," vol. i., article xlix., p. 381. ]

[Footnote 2: That this is a mere hypothesis has been scarcely remarked by the founders themselves, nor by almost any writer on the kinetic theory of gases. No one has yet examined the question, What is the condition as regards average distribution of kinetic energy, which is ultimately fulfilled by two portions of gaseous matter, separated by a thin elastic septum which absolutely prevents interdiffusion of matter, while it allows interchange of kinetic energy by collisions against itself? Indeed, I do not know but, that the present is the very first statement which has ever been published of this condition of the problem of equal temperatures between two gaseous masses.]

Think of the thing thus. Imagine a great multitude of particles inclosed by a boundary which may be pushed inward in any part all round at pleasure. Now station an engineer corps of Maxwell's army of sorting demons all round the inclosure, with orders to push in the boundary diligently everywhere, when none of the besieged troops are near, and to do nothing when any of them are seen approaching, and until after they have turned again inward. The result will be that, with exactly the same sum of kinetic and potential energies of the same inclosed multitude of particles, the throng has been caused to be denser. Now Joule's and my own old experiments on the efflux of air prove that if the crowd be common air, or oxygen, or nitrogen, or carbonic acid, the temperature is a little higher in the denser than in the rarer condition when the energies are the same. By the hypothesis, equality of temperature between two different gases or two portions of the same gas at different densities means equality of kinetic energies in the same number of molecules of the two. From our observations proving the temperature to be higher, it therefore follows that the potential energy is smaller in the condensed crowd. This--always, however, under protest as to the temperature hypothesis--proves some degree of attraction among the molecules, but it does not prove ultimate attraction between two molecules in collision, or at distances much less than the average mutual distance of nearest neighbors in the multitude. The collisional force might be repulsive, as generally supposed hitherto, and yet attraction might predominate in the whole reckoning of difference between the intrinsic potential energies of the more dense and less dense multitudes.

It is however remarkable that the explanation of the propagation of sound through gases, and even of the positive fluid pressure of a gas against the sides of the containing vessel, according to the kinetic theory of gases, is quite independent of the question whether the ultimate collisional force is attractive or repulsive. Of course it must be understood that, if it is attractive, the particles must, be so small that they hardly ever meet--they would have to be infinitely small to _never_ meet--that, in fact, they meet so seldom, in comparison with the number of times their courses--are turned through large angles by attraction, that the influence of these surely attractive collisions is preponderant over that of the comparatively very rare impacts from actual contact. Thus, after all, the train of speculation suggested by Davy's "Repulsive Motion" does not allow us to escape from the idea of true repulsion, does not do more than let us say it is of no consequence, nor even say this with truth, because, if there are impacts at all, the nature of the force during the impact and the effects of the mutual impacts, however rare, cannot be evaded in any attempt to realize a conception of the kinetic theory of gases. And in fact, unless we are satisfied to imagine the atoms of a gas as mathematical points endowed with inertia, and as, according to Boscovich, endowed with forces of mutual, positive, and negative attraction, varying according to some definite function of the distance, we cannot avoid the question of impacts, and of vibrations and rotations of the molecules resulting from impacts, and we must look distinctly on each molecule as being either a little elastic solid or a configuration of motion in a continuous all-pervading liquid. I do not myself see how we can ever permanently rest anywhere short of this last view; but it would be a very pleasant temporary resting-place on the way to it if we could, as it were, make a mechanical model of a gas out of little pieces of round, perfectly elastic solid matter, flying about through the space occupied by the gas, and colliding with one another and against the sides of the containing vessel.

This is, in fact, all we have of the kinetic theory of gases up to the present time, and this has done for us, in the hands of Clausius and Maxwell, the great things which constitute our first step toward a molecular theory of matter. Of course from it we should have to go on to find an explanation of the elasticity and all the other properties of the molecules themselves, a subject vastly more complex and difficult than the gaseous properties, for the explanation of which we assume the elastic molecule; but without any explanation of the properties of the molecule itself, with merely the assumption that the molecule has the requisite properties, we might rest happy for a while in the contemplation of the kinetic theory of gases, and its explanation of the gaseous properties, which is not only stupendously important as a step toward a more thoroughgoing theory of matter, but is undoubtedly the expression of a perfectly intelligible and definite set of facts in Nature.

But alas for our mechanical model consisting of the cloud of little elastic solids flying about among one another. Though each particle have absolutely perfect elasticity, the end must be pretty much the same as if it were but imperfectly elastic. The average effect of repeated and repeated mutual collisions must be to gradually convert all the translational energy into energy of shriller and shriller vibrations of the molecule. It seems certain that each collision must have something more of energy in vibrations of very finely divided nodal parts than there was of energy in such vibrations before the impact. The more minute this nodal subdivision, the less must be the tendency to give up part of the vibrational energy into the shape of translational energy in the course of a collision; and I think it is rigorously demonstrable that the whole translational energy must ultimately become transformed into vibrational energy of higher and higher nodal subdivisions if each molecule is a continuous elastic solid. Let us, then, leave the kinetic theory of gases for a time with this difficulty unsolved, in the hope that we or others after us may return to it, armed with more knowledge of the properties of matter, and with sharper mathematical weapons to cut through the barrier which at present hides from us any view of the molecule itself, and of the effects other than mere change of translational motion which it experiences in collision.

To explain the elasticity of a gas was the primary object of the kinetic theory of gases. This object is only attainable by the assumption of an elasticity more complex in character, and more difficult of explanation, than the elasticity of gases--the elasticity of a solid. Thus, even if the fatal fault in the theory, to which I have alluded, did not exist, and if we could be perfectly satisfied with the kinetic theory of gases founded on the collisions of elastic solid molecules, there would still be beyond it a grander theory which need not be considered a chimerical object of scientific ambition--to explain the elasticity of solids. But we may be stopped when we commence to look in the direction of such a theory with the cynical question, What do you mean by explaining a property of matter? As to being stopped by any such question, all I can say is that if engineering were to be all and to end all physical science, we should perforce be content with merely finding properties of matter by observation, and using them for practical purposes. But I am sure very few, if any, engineers are practically satisfied with so narrow a view of their noble profession. They must and do patiently observe, and discover by observation, properties of matter and results of material combinations. But deeper questions are always present, and always fraught with interest to the true engineer, and he will be the last to give weight to any other objection to any attempt to see below the surface of things than the practical question, Is it likely to prove wholly futile? But now, instead of imagining the question, What do you mean by explaining a property of matter? to be put cynically, and letting ourselves be irritated by it, suppose we give to the questioner credit for being sympathetic, and condescend to try and answer his question. We find it not very easy to do so. All the properties of matter are so connected that we can scarcely imagine one _thoroughly explained_ without our seeing its relation to all the others, without in fact having the explanation of all; and till we have this we cannot tell what we mean by "explaining a property" or "explaining the properties" of matter. But though this consummation may never be reached by man, the progress of science may be, I believe will be, step by step toward it, on many different roads converging toward it from all sides. The kinetic theory of gases is, as I have said, a true step on one of the roads. On the very distinct road of chemical science, St. Claire Deville arrived at his grand theory of dissociation without the slightest aid from the kinetic theory of gases. The fact that he worked it out solely from chemical observation and experiment, and expounded it to the world without any hypothesis whatever, and seemingly even without consciousness of the beautiful explanation it has in the kinetic theory of gases, secured for it immediately an independent solidity and importance as a chemical theory when he first promulgated it, to which it might even by this time scarcely have attained if it had first been suggested as a probability indicated by the kinetic theory of gases, and been only afterward confirmed by observation. Now, however, guided by the views which Clausius and Williamson have given us of the continuous interchange of partners between the compound molecules constituting chemical compounds in the gaseous state, we see in Deville's theory of dissociation a point of contact of the most transcendent interest between the chemical and physical lines of scientific progress.

To return to elasticity: if we could make out of matter devoid of elasticity a combined system of relatively moving parts which, in virtue of motion, has the essential characteristics of an elastic body, this would surely be, if not positively a step in the kinetic theory of matter, at least a fingerpost pointing a way which we may hope will lead to a kinetic theory of matter. Now this, as I have already shown,[1] we can do in several ways. In the case of the last of the communications referred to, of which only the title has hitherto been published, I showed that, from the mathematical investigation of a gyrostatically dominated combination contained in the passage of Thomson and Tait's "Natural Philosophy" referred to, it follows that any ideal system of material particles, acting on one another mutually through massless connecting springs, may be perfectly imitated in a model consisting of rigid links jointed together, and having rapidly rotating fly wheels pivoted on some or on all of the links. The imitation is not confined to cases of equilibrium. It holds also for vibration produced by disturbing the system infinitesimally from a position of stable equilibrium and leaving it to itself. Thus we may make a gyrostatic system such that it is in equilibrium under the influence of certain positive forces applied to different points of this system; all the forces being precisely the same as, and the points of application similarly situated to, those of the stable system with springs. Then, provided proper masses (that is to say, proper amounts and distributions of inertia) be attributed to the links, we may remove the external forces from each system, and the consequent vibration of the points of application of the forces will be identical. Or we may act upon the systems of material points and springs with any given forces for any given time, and leave it to itself, and do the same thing for the gyrostatic system; the consequent motion will be the same in the two cases. If in the one case the springs are made more and more stiff, and in the other case the angular velocities of the fly wheels are made greater and greater, the periods of the vibrational constituents of the motion will become shorter and shorter, and the amplitudes smaller and smaller, and the motions will approach more and more nearly those of two perfectly rigid groups of material points moving through space and rotating according to the well known mode of rotation of a rigid body having unequal moments of inertia about its three principal axes. In one case the ideal nearly rigid connection between the particles is produced by massless, exceedingly stiff springs; in the other case it is produced by the exceedingly rapid rotation of the fly wheels in a system which, when the fly wheels are deprived of their rotation, is perfectly limp.

[Footnote 1: Paper on "Vortex Atoms," _Proc_. R.S.E. February. 1867: abstract of a lecture before the Royal Institution of Great Britain, March 4, 1881, on "Elasticity Viewed as possibly a Mode of Motion"; Thomson and Tait's "Natural Philosophy," second edition, part 1, §§ 345 viii. to 345 xxxvii.; "On Oscillation and Waves in an Adynamic Gyrostatic System" (title only), _Proc_. R.S.E. March, 1883.]

The drawings (Figs. 1 and 2) before you illustrate two such material systems.[1] The directions of rotation of the fly-wheels in the gyrostatic system (Fig. 2) are indicated by directional ellipses, which show in perspective the direction of rotation of the fly-wheel of each gyrostat. The gyrostatic system (Fig. 2) might have been constituted of two gyrostatic members, but four are shown for symmetry. The inclosing circle represents in each case in section an inclosing spherical shell to prevent the interior from being seen. In the inside of one there are fly-wheels, in the inside of the other a massless spring. The projecting hooked rods seem as if they are connected by a spring in each case. If we hang any one of the systems up by the hook on one of its projecting rods, and hang a weight to the hook of the other projecting rod, the weight, when first put on, will oscillate up and down, and will go on doing so for ever if the system be absolutely unfrictional. If we check the vibration by hand, the weight will hang down at rest, the pin drawn out to a certain degree; and the distance drawn out will be simply proportional to the weight hung on, as in an ordinary spring balance.

[Footnote 1: In Fig. 1 the two hooked rods seen projecting from the sphere are connected by an elastic coach-spring. In Fig. 2 the hooked rods are connected one to each of two opposite corners of a four-sided jointed frame, each member of which carries a gyrostat so that the axis of rotation of the fly-wheel is in the axis of the member of the frame which bears it. Each of the hooked rods in Fig. 2 is connected to the framework through a swivel joint, so that the whole gyrostatic framework may be rotated about the axis of the hooked rods in order to annul the moment of momentum of the framework about this axis due to rotation of the fly-wheels in the gyrostat.]

Here, then, out of matter possessing rigidity, but absolutely devoid of elasticity, we have made a perfect model of a spring in the form of a spring balance. Connect millions of millions of particles by pairs of rods such as these of this spring balance, and we have a group of particles constituting an elastic solid; exactly fulfilling the mathematical ideal worked out by Navier, Poisson, and Cauchy, and many other mathematicians, who, following their example, have endeavored to found a theory of the elasticity of solids on mutual attraction and repulsion between a group of material particles. All that can possibly be done by this theory, with its assumption of forces acting according to any assumed law of relation to distance, is done by the gyrostatic system. But the gyrostatic system does, besides, what the system of naturally acting material particles cannot do--it constitutes an elastic solid which can have the Faraday magneto-optic rotation of the plane of polarization of light; supposing the application of our solid to be a model of the luminiferous ether for illustrating the undulatory theory of light. The gyrostatic model spring balance is arranged to have zero moment of momentum as a whole, and therefore to contribute nothing to the Faraday rotation; with this arrangement the model illustrates the luminiferous ether in a field unaffected by magnetic force. But now let there be a different rotational velocity imparted to the jointed square round the axis of the two projecting hooked rods, such as to give a resultant moment of momentum round any given line through the center of inertia of the system; and let pairs of the hooked rods in the model thus altered, which is no longer a model of a mere spring balance, be applied as connections between millions of pairs of particles as before, with the lines of resultant moment of momentum all similarly directed. We now have a model elastic solid which will have the property that the direction of vibration in waves of rectilinear vibrations propagated through it shall turn round the line of propagation of the waves, just as Faraday's observation proves to be done by the line of vibration of light in a dense medium between the poles of a powerful magnet. The case of wave front perpendicular to the lines of resultant moment of momentum (that is to say, the direction of propagation being parallel to these lines) corresponds, in our mechanical model, to the case of light traveling in the direction of the lines of force in a magnetic field.

In these illustrations and models we have different portions of ideal rigid matter acting upon one another, by normal pressure at mathematical points of contact--of course no forces of friction are supposed. It is exceedingly interesting to see how thus, with no other postulates than inertia, rigidity, and mutual impenetrability, we can thoroughly model not only an elastic solid, and any combination of elastic solids, but so complex and recondite a phenomenon as the passage of polarized light through a magnetic field. But now, with the view of ultimately discarding the postulate of rigidity from all our materials, let us suppose some to be absolutely destitute of rigidity, and to possess merely inertia and incompressibility, and mutual impenetrability with reference to the still remaining rigid matter. With these postulates we can produce a perfect model of mutual action at a distance between solid particles, fulfilling the condition, so keenly desired by Newton and Faraday, of being explained by continuous action through an intervening medium. The law of the mutual force in our model, however, is not the simple Newtonian law, but the much more complex law of the mutual action between electro magnets--with this difference, that in the hydro-kinetic model in every case the force is opposite in direction to the corresponding force in the electro-magnetic analogue. Imagine a solid bored through with a hole, and placed in our ideal perfect liquid. For a moment let the hole be stopped by a diaphragm, and let an impulsure pressure be applied for an instant uniformly over the whole membrane, and then instantly let the membrane be dissolved into liquid. This action originates a motion of the liquid relatively to the solid, of a kind to which I have given the name of "irrotational circulation," which remains absolutely constant however the solid be moved through the liquid. Thus, at any time the actual motion of the liquid at any point in the neighborhood of the solid will be the resultant of the motion it would have in virtue of the circulation alone, were the solid at rest, and the motion it would have in virtue of the motion of the solid itself, had there been no circulation established through the aperture. It is interesting and important to remark in passing that the whole kinetic energy of the liquid is the sum of the kinetic energies which it would have in the two cases separately. Now, imagine the whole liquid to be inclosed in an infinitely large, rigid, containing vessel, and in the liquid, at an infinite distance from any part of the containing vessel, let two perforated solids, with irrotational circulation through each, be placed at rest near one another. The resultant fluid motion due to the two circulations, will give rise to fluid pressure on the two bodies, which, if unbalanced, will cause them to move. The force systems--force-and-torques, or pairs of forces--required to prevent them from moving will be mutual and opposite, and will be the same as, but opposite in direction to, the mutual force systems required to hold at rest two electromagnets fulfilling the following specification: The two electro magnets are to be of the same shape and size as the two bodies, and to be placed in the same relative positions, and to consist of infinitely thin layers of electric currents in the surfaces of solids possessing extreme diamagnetic quality--in other words, infinitely small permeability. The distribution of electric current on each body may be any whatever which fulfills the condition that the total current across any closed line drawn on the surface once through the aperture is equal to ¼ [pi] of the circulation[1] through the aperture in the hydro-kinetic analogue.

[Footnote 1: The integral of tangential component velocity all round any closed curve, passing once through the aperture, is defined as the "cyclic-constant" or the "circulation" ("Vortex Motion," § 60 (a), _Trans_. R.S.E., April 29, 1867). It has the same value for all closed curves passing just once through the aperture, and it remains constant through all time, whether the solid body be in motion or at rest.]

It might be imagined that the action at a distance thus provided for by fluid motion could serve as a foundation for a theory of the equilibrium, and the vibrations, of elastic solids, and the transmission of waves like those of light through an extended quasi-elastic solid medium. But unfortunately for this idea the equilibrium is essentially unstable, both in the case of magnets and, notwithstanding the fact that the forces are oppositely directed, in the hydro-kinetic analogue also, when the several movable bodies (two or any greater number) are so placed relatively as to be in equilibrium. If, however, we connect the perforated bodies with circulation through them in the hydro-kinetic system, by jointed rigid connecting links, we may arrange for configurations of stable equilibrium. Thus, without fly-wheels, but with fluid circulations through apertures, we may make a model spring balance or a model luminiferous ether, either without or with the rotational quality corresponding to that of the true luminiferous ether in the magnetic fluid--in short, do all by the perforated solids with circulations through them that we saw we could do by means of linked gyrostats. But something that we cannot do by linked gyrostats we can do by the perforated bodies with fluid circulation: we can make a model gas. The mutual action at a distance, repulsive or attractive according to the mutual aspect of the two bodies when passing within collisional distance[1] of one another, suffices to produce the change of direction of motion in collision, which essentially constitutes the foundation of the kinetic theory of gases, and which, as we have seen before, may as well be due to attraction as to repulsion, so far as we know from any investigation hitherto made in this theory.

[Footnote 1: According to this view, there is no precise distance, or definite condition respecting the distance, between two molecules, at which apparently they come to be in collision, or when receding from one another they cease to be in collision. It is convenient, however, in the kinetic theory of gases, to adopt arbitrarily a precise definition of collision, according to which two bodies or particles mutually acting at a distance may be said to be in collision when their mutual action exceeds some definite arbitrarily assigned limit, as, for example, when the radius of curvature of the path of either body is less than a stated fraction (one one-hundredth, for instance) of the distance between them.]

There remains, however, as we have seen before, the difficulty of providing for the case of actual impacts between the solids, which must be done by giving them massless spring buffers or, which amounts to the same thing, attributing to them repulsive forces sufficiently powerful at very short distances to absolutely prevent impacts between solid and solid; unless we adopt the equally repugnant idea of infinitely small perforated solids, with infinitely great fluid circulations through them. Were it not for this fundamental difficulty, the hydro-kinetic model gas would be exceedingly interesting; and, though we could scarcely adopt it as conceivably a true representation of what gases really are, it might still have some importance as a model configuration of solid and liquid matter, by which without elasticity the elasticity of true gas might be represented.

But lastly, since the hydro-kinetic model gas with perforated solids and fluid circulations through them fails because of the impacts between the solids, let us annul the solids and leave the liquid performing irrotational circulation round vacancy,[1] in the place of the solid cores which we have hitherto supposed; or let us annul the rigidity of the solid cores of the rings, and give them molecular rotation according to Helmholtz's theory of vortex motion. For stability the molecular rotation must be such as to give the same velocity at the boundary of the rotational fluid core as that of the irrotationally circulating liquid in contact with it, because, as I have proved, frictional slip between two portions of liquid in contact is inconsistent with stability. There is a further condition, upon which I cannot enter into detail just now, but which may be understood in a general way when I say that it is a condition of either uniform or of increasing molecular rotation from the surface inward, analogous to the condition that the density of a liquid, resting for example under the influence of gravity, must either be uniform or must be greater below than above for stability of equilibrium. All that I have said in favor of the model vortex gas composed of perforated solids with fluid circulations through them holds without modification for the purely hydro-kinetic model, composed of either Helmholtz cored vortex rings or of coreless vortices, and we are now troubled with no such difficulty as that of the impacts between solids. Whether, however, when the vortex theory of gases is thoroughly worked out, it will or will not be found to fail in a manner analogous to the failure which I have already pointed out in connection with the kinetic theory of gases composed of little elastic solid molecules, I cannot at present undertake to speak with certainty. It seems to me most probable that the vortex theory cannot fail in any such way, because all I have been able to find out hitherto regarding the vibration of vortices,[2] whether cored or coreless, does not seem to imply the liability of translational or impulsive energies of the individual vortices becoming lost in energy of smaller and smaller vibrations.

[Footnote 1: Investigations respecting coreless vortices will be found in a paper by the author, "Vibrations of a Columnar Vortex," _Proc_. R.S.E., March 1, 1880; and a paper by Hicks, recently read before the Royal Society.]

[Footnote 2: See papers by the author "On Vortex Motion." _Trans_. R.S.E. April, 1867, and "Vortex Statics," _Proc_. R.S.E. December, 1875; also a paper by J.J. Thomson, B.A., "On the Vibrations of a Vortex Ring," _Trans_. R.S. December, 1881, and his valuable book on "Vortex Motion."]

As a step toward kinetic theory of matter, it is certainly most interesting to remark that in the quasi-elasticity, elasticity looking like that of an India-rubber band, which we see in a vibrating smoke-ring launched from an elliptic aperture, or in two smoke-rings which were circular, but which have become deformed from circularity by mutual collision, we have in reality a virtual elasticity in matter devoid of elasticity, and even devoid of rigidity, the virtual elasticity being due to motion, and generated by the generation of motion.

* * * * *

APPLICATION OF ELECTRICITY TO TRAMWAYS.

By M. HOLROYD SMITH.

Last year, when I had the pleasure of reading a paper before you on my new system of electric tramways, I ventured to express the hope that before twelve months had passed, "to be able to report progress," and I am happy to say that notwithstanding the wearisome delay and time lost in fruitless negotiations, and the hundred and one difficulties within and without that have beset me, I am able to appear before you again and tell you of advance.

Practical men know well that there is a wide difference between a model and a full sized machine; and when I decided to construct a full sized tramcar and lay out a full sized track, I found it necessary to make many alterations of detail, my chief difficulty being so to design my work as to facilitate construction and allow of compensation for that inaccuracy of workmanship which I have come to regard as inevitable.

In order to satisfy the directors of a tramway company of the practical nature of my system before disturbing their lines, I have laid, in a field near the works of Messrs. Smith, Baker & Co., Manchester, a track 110 yards long, 4 ft. 8½ in. gauge, and I have constructed a full sized street tramcar to run thereon. My negotiations being with a company in a town where there are no steep gradients, and where the coefficient of friction of ordinary wheels would be sufficient for all tractive purposes, I thought it better to avoid the complication involved in employing a large central wheel with a broad surface specially designed for hilly districts, and with which I had mounted a gradient of one in sixteen.

But as the line in question was laid with all the curves unnecessarily quick, even those in the "pass-bies," I thought it expedient to employ differential gear, as illustrated at D, Fig. 1, which is a sketch plan showing the mechanism employed. M is a Siemens electric motor running at 650 revolutions per minute; E is a combination of box gearing, frictional clutch, and chain pinion, and from this pinion a steel chain passes around the chain-wheel, H, which is free to revolve upon the axle, and carries within it the differential pinion, gearing with the bevel-wheel, B², keyed upon the sleeve of the loose tram-wheel, T², and with the bevel-wheel, B¹, keyed upon the axle, to which the other tram-wheel, T¹, is attached. To the other tram-wheels no gear is connected; one of them is fast to the axle, and the other runs loose, but to them the brake is applied in the usual manner.

The electric current from the collector passes, by means of a copper wire, and a switch upon the dashboard of the car, and resistance coils placed under the seats, to the motor, and from the motor by means of an adjustable clip (illustrated in diagram, Fig. 2) to the axles, and by them through the four wheels to the rails, which form the return circuit.

I have designed many modifications of the track, but it is, perhaps, best at present to describe only that which I have in actual use, and it is illustrated in diagram, Fig. 3, which is a sectional and perspective view of the central channel. L is the surface of the road, and SS are the sleepers, CC are the chairs which hold the angle iron, AA forming the longitudinally slotted center rail and the electric lead, which consists of two half-tubes of copper insulated from the chairs by the blocks, I, I. A special brass clamp, free to slide upon the tube, is employed for this purpose, and the same form of clamp serves to join the two ends of the copper tubes together and to make electric contact. Two half-tubes instead of one slotted tube have been employed, in order to leave a free passage for dirt or wet to fall through the slot in the center rail to the drain space, G. Between chair and chair hewn granite or artificial stone is employed, formed, as shown in the drawing, to complete the surface of the road and to form a continuous channel or drain. In order that this drain may not become choked, at suitable intervals, in the length of the track, sump holes are formed as illustrated in diagram, Fig. 4 These sump holes have a well for the accumulation of mud, and are also connected with the main street drain, so that water can freely pass away. The hand holes afford facility for easily removing the dirt.

In a complete track these hand holes would occasionally be wider than shown here, for the purpose of removing or fixing the collector, Fig. 5, which consists of two sets of spirally fluted rollers free to revolve upon spindles, which are held by knuckle-joints drawn together by spiral springs; by this means the pressure of the rollers against the inside of the tube is constantly maintained, and should any obstruction occur in the tube the spiral flute causes it to revolve, thus automatically cleansing the tubes.

The collector is provided with two steel plates, which pass through the slit in the center rail; the lower ends of these plates are clamped by the upper frame of the collector, insulating material being interposed, and the upper ends are held in two iron cheeks. Between these steel plates insulated copper strips are held, electrically connected with the collector and with the adjustable clip mounted upon the iron cheeks; this clip holds the terminal on the end of the wire (leading to the motor) firmly enough for use, the cheeks being also provided with studs for the attachment of leather straps hooked on to the framework of the car, one for the forward and one for backward movement of the collector. These straps are strong enough for the ordinary haulage of the collector, and for the removal of pebbles and dirt that may get into the slit; but should any absolute block occur then they break and the terminal is withdrawn from the clip; the electric contact being thereby broken the car stops, the obstruction can then be removed and the collector reconnected without damage and with little delay.

In order to secure continuity of the center rail throughout the length of the track, and still provide for the removal of the collector at frequent intervals, the framework of the collector is so made that, by slackening the side-bolts, the steel plates can be drawn upward and the collector itself withdrawn sideways through the hand holes, one of the half-tubes being removed for the purpose.

Fig. 6 illustrates another arrangement that I have constructed, both of collector and method of collecting.

As before mentioned, the arrangement now described has been carried out in a field near the works of Messrs. Smith, Baker & Co., Cornbrook Telegraph Works, Manchester, and its working efficiency has been most satisfactory. After a week of rain and during drenching showers the car ran with the same speed and under the same control as when the ground was dry.

This I account for by the theory that when the rails are wet and the tubes moist the better contact made compensates for the slight leakage that may occur.

At the commencement of my paper I promised to confine myself to work done; I therefore abstain from describing various modifications of detail for the same purpose. But one method of supporting and insulating the conductor in the channel may be suggested by an illustration of the plan I adopted for a little pleasure line in the Winter Gardens, Blackpool.

Fig. 7. There the track being exclusively for the electric railway, it was not necessary to provide a center channel; the conductor has therefore been placed in the center of the track, and consists of bar iron 1¼ in. by ½ in., and is held vertically by means of studs riveted into the side; these studs pass through porcelain insulators, and by means of wooden clamps and wedges are held in the iron chairs which rest upon the sleepers. The iron conductors were placed vertically to facilitate bending round the sharp curves which were unavoidable on this line.

The collector consists of two metal slippers held together by springs, attached to the car by straps and electrically connected to the motor by clips in the same manner as the one employed in Manchester.

I am glad to say that, notwithstanding the curves with a radius of 55 feet and gradients of 1 in 57, this line is also a practical success.

* * * * *

FIRES IN LONDON AND NEW YORK.