Chapter 7

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.

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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.

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FIRES IN LONDON AND NEW YORK.

When the chief of the London Fire Brigade visited the United States in 1882, he was, as is the general rule on the other side of the Atlantic, "interviewed"--a custom, it may be remarked, which appears to be gaining ground also in this country. The inferences drawn from these interviews seem to be that the absence of large fires in London was chiefly due to the superiority of our fire brigade, and that the greater frequency of conflagrations in American cities, and particularly in New York, was due to the inferiority of their fire departments. How unjust such a comparison would be is shown in a paper presented by Mr. Edward B. Dorsey, a member of the American Society of Civil Engineers, to that association, in which the author discusses the comparative liability to and danger from conflagrations in London and in American cities. He found from an investigation which he conducted with much care during a visit to London that it is undoubtedly true that large fires are much less frequent in the metropolis than in American cities; but it is equally true that the circumstances existing in London and New York are quite different. As it is a well-known fact that the promptness, efficiency, and bravery of American firemen cannot be surpassed, we gladly give prominence to the result of the author's investigations into the true causes of the great liability of American cities to large fires. In a highly interesting comparison the writer has selected New York and London as typical cities, although his observations will apply to most American and English towns, if, perhaps, with not quite the same force. In the first place, the efforts of the London Fire Brigade receive much aid from our peculiarly damp climate. From the average of eleven years (1871-1881) of the meteorological observations made at the Greenwich Observatory, it appears that in London it rains, on the average, more than three days in the week, that the sun shines only one-fourth of the time he is above the horizon, and that the atmosphere only lacks 18 per cent. of complete saturation, and is cloudy seven-tenths of the time. Moreover, the humidity of the atmosphere in London is very uniform, varying but little in the different months. Under these circumstances, wood will not be ignited very easily by sparks or by contact with a weak flame. This is very different from the condition of wood in the long, hot, dry seasons of the American continent. The average temperature for the three winter months in London is 38.24 degrees Fahr.; in New York it is 31.56 degrees, or 6.68 degrees lower. This lower range of temperature must be the cause of many conflagrations, for, to make up for the deficiency in the natural temperature, there must be in New York many more and larger domestic fires. The following statistics, taken from the records of the New York Fire Department, show this. In the three winter months of 1881, January, February, and December, there were 522 fire alarms in New York, or an average per month of 174; in the remaining nine months 1,263, or an average per month of 140. In the corresponding three winter months of 1882 there were 602 fire alarms, or an average per month of 201; in the remaining nine months 1,401, or an average per month of 155. In round numbers there were in 1881 one-fourth, and in 1882 one-third more fire alarms in the three winter months than in the nine warmer months. We are not aware that similar statistics have ever been compiled for London, and are consequently unable to draw comparison; but, speaking from recollection, fires appear to be more frequent also in London during the winter months.