All this is exceedingly interesting, for it seems to make clear Lord Kelvin's att.i.tude with respect to the electromagnetic theory of Maxwell, which is now regarded by most physicists as affording on the whole a satisfactory account, if not a dynamical theory in the sense understood by Lord Kelvin, of light-propagation. That there is an electric displacement perpendicular to the direction of propagation and a magnetic displacement (or motion) perpendicular to both seems proved by the experiments of Hertz, and the velocity of propagation of these disturbances has been found to be that of light. Of course it remains to be found out in what the electric and magnetic changes consist, and whether the ether has or has not an atomic structure. Towards the answer to this question on electromagnetic presuppositions some progress has already been made, princ.i.p.ally by Larmor. And, after all, while we may imagine that we know something more definite of dynamical actions on ponderable matter, it is not quite certain that we do: we are more familiar with them, that is almost all. We know, for example, that at every point in the gravitational field of the earth we may set up a gravitation vector, or field-intensity; for a particle of matter there is subjected to acceleration along that direction. But of the rationale of the action we know nothing, or next to nothing. So we set up electric and magnetic vectors in an insulating medium, corresponding to electric and magnetic effects which we can observe; and it is not too much to say that we know hardly less in this case than we do in the other, of the inner mechanism of the action of which we see the effects.

Returning to the difficulty of the elastic solid theory, that while its rigidity is enormous, it offers no obstacle to the planets and other heavenly bodies which move through it, it may be interesting to recall how Lord Kelvin used to deal with it in his elementary lectures. The same discussion was given in the Introductory Lecture at Baltimore. The difficulty is not got over by an explanation of what takes place: it is turned by showing that a similar difficulty exists in reconciling phenomena which can be observed every day with such ordinary materials as pitch or shoemakers' wax. A piece of such wax can be moulded into a tuning-fork or a bell, and will then, if struck, sound a musical note of definite pitch. This indicates, for rapidly alternating deformations started by a force of short duration, the existence of internal forces of the kind called elastic, that is, depending on the amount of deformation caused, not on the rate at which the deformation is increasing or diminishing, as is the case for the so-called "viscous forces" which are usually displayed by such material. But the tuning-fork or bell, if left lying on the table, will gradually flatten down into a thin sheet under only its own weight. Here the deformation is opposed only by viscous forces, which, as the change is very slow, are exceedingly small.

But let a large slab of it, three or four inches thick, be placed in a gla.s.s jar ten or twelve inches in diameter, already partly filled with water, and let some ordinary corks be imprisoned beneath, while some lead bullets are laid on the upper surface. After a month or two it will be found that the corks have disappeared from the water into the wax, and that the orifices which they made in entering it have healed up completely; similarly the bullets have sunk down into the slab, leaving no trace behind. After two or three months more, the corks will be seen to be bursting their way out through the upper surface of the slab, and the bullets will be found in the water below. The very thing has taken place that would have happened if water had been used instead of pitch, only it has taken a very much longer time to bring it about. The corks have floated up through the wax in consequence of hydrostatic upward force exerted by the wax acting as a fluid; and the bullets have sunk down in consequence of the excess of their weights above the upward hydrostatic force exerted on them as on the corks. The motion in both cases has been opposed by the viscous forces called into play.

The application of this to the luminiferous ether is immediate. Let the ether be regarded as a substance which can perform vibrations only "when times and forces are suitable," that is, when the forces producing distortion act for only an infinitesimal time (as in the starting of the tuning-fork by a small blow), and are not too great. Vibrations may be set up locally, and the medium may have a true rigidity by which they are propagated to more remote parts; that is to say, waves travel out from the centre of disturbance. On the other hand, if the forces are long continued, even if they be small, they produce continuously increasing change of shape. Thus the planets move seemingly without resistance.

The conclusion is that the apparently contradictory properties of the ether are no more mysterious than the properties of pitch or shoemakers'

wax. And, after all, matter is still a profound mystery.

Dynamical ill.u.s.trations, which old Glasgow students will recognise, appear continually in the lectures. They will remember, almost with affection, the system of three particles (7 lb. or 14 lb. weights!) joined together in a vertical row by stout spiral springs of steel, which were always to be taken as ma.s.sless, and will recall Lord Kelvin's experiments with them, demonstrating the three modes of vibration of a system of three ma.s.ses, each of which influenced those next it on the two sides. Here they will find the problem solved for any number of particles and intervening springs, and the solution applied to an extension of the ma.s.sive molecule which von Helmholtz imbedded in the elastic ether, and used to explain anomalous dispersion. A highly complex molecule is suggested, consisting of an outer sh.e.l.l embedded in the ether as in the simpler case, a second sh.e.l.l within that connected to the outer by a sufficient number of equal radial springs, a third within and similarly connected to the second by radial springs, and so on. This molecule will have as many modes of vibration as there are sets of springs, and can therefore impart, if it is set into motion, a complex disturbance to the ether in which it is imbedded.

The modification of this arrangement by which Lord Kelvin explained the phosph.o.r.escence of such substances as luminous paint is also described, and will be recognised by some as an old friend. A number, two dozen or so, of straight rods of wood eighteen inches long are attached to a steel wire four or five inches apart, like steps on a ladder made with a single rope along the centres of the steps. The wire is so attached to each rod that the rod must turn with the wire if the latter is twisted round. Each rod is loaded with a piece of lead at each end to give it more moment of inertia about the wire. The wire, with this "ladder"

attached to it, is rigidly attached to the centre of a cross-bar at the top, which can be made to swing about the wire as an axis and so impart twisting vibrations to the wire in a period depending on this driver.

Sliding weights attached to the bar enable its moment of inertia to be changed at pleasure. The lower end of the wire carries a cross-bar with two vanes, immersed in treacle in a vessel below. When the period of the exciter was very long the waves of torsion did not travel down the "ladder," but when the period was made sufficiently short the waves travelled down and were absorbed in the treacle below. In the former case the vibrations persisted; the case was a.n.a.logous to that of phosph.o.r.escence.

[Ill.u.s.tration: FIG. 18.]

Incidentally a full and very attractive account of the elastic solid theory is given in these lectures, accompanied as it is by characteristic digressions on points of interest which suggest themselves, and on topics on which the lecturer held strong opinions, such, for example, as the absurd British system of weights and measures.

The book reads in many places like a report of some of the higher mathematical lectures which were given every session at Glasgow; and on that account, if on no other, it will be read by the old students of the higher cla.s.s with affectionate interest. But the discussions of the great fundamental difficulty presented at once by dispersion--the fact, that is, that light of different wave lengths has different velocities in ordinary transparent matter--the discussions of the various theories of dispersion that have been put forward, the construction of the molecules, gyrostatic and non-gyrostatic, with all their remarkable properties, which Lord Kelvin invents in order to frame a dynamical mechanism which will imitate the action of matter as displayed in the complex manifestations of the optical phenomena, not only of isotropic matter, but of crystals, will ever afford instruction to every mathematician who has the courage to attack this subject, and remain as a monument to the extraordinary genius of their author.

A subject is touched on in these lectures which has not been dealt with in the present review of Lord Kelvin's work. By four lines of argument--by the heat of combination of copper and zinc, together with the difference of electric potential developed when these metals are put in contact, from the thickness of a capillary film of soap and water (measured by Rucker and Reinold) just before it gives way, and the work spent in stretching it, from the kinetic theory of gases and the estimated length of free path of a particle (given also by Loschmidt and by Johnstone Stoney), and from the undulatory theory of light--Lord Kelvin estimated superior and inferior limits to the "size of the atoms"

of bodies, or, more properly speaking, of the molecular structure of the matter. We cannot discuss these arguments--and they can be read at leisure by any one who will consult Volume I (Const.i.tution of Matter) of Lord Kelvin's _Popular Lectures and Addresses_, for his Royal Inst.i.tution Lecture on the subject, there given in full--but we may state his conclusion. Let a drop of water, a rain drop, for example, be magnified to the size of the earth, that is, from a sphere a quarter of an inch, or less, in diameter to a sphere 8000 miles in diameter, and let the dimensions of the molecular structure be magnified in the same proportion. "The magnified structure would be more coa.r.s.e-grained than a heap of small shot, but probably less coa.r.s.e-grained than a heap of cricket-b.a.l.l.s."

Of course, it is not intended here to convey the idea that the molecules are spheres like shot or cricket-b.a.l.l.s; they undoubtedly have a structure of their own. And no p.r.o.nouncement is made as to the divisibility or non-divisibility of the molecules. All that is alleged is that if the division be carried to a minuteness near to or beyond that of the dimensions of the structure, portions of the substance will be obtained which have not the physical properties of the substance in bulk.

The recent interesting researches of chemists and physicists into phenomena which seem to demonstrate the disintegration, not merely of molecules, but even of the atomic structure of matter, attracted Lord Kelvin's attention in his last years, and _suo more_ he endeavoured to frame dynamical explanations of electronic (or, as he preferred to call it, "electrionic") action. But though keenly interested in all kinds of research, he turned again and again to the older theories of light, and his dynamical representations of the ether and of crystals, with renewed vigour and enthusiasm.

CHAPTER XV

SPEED OF TELEGRAPH SIGNALLING--LAYING OF SUBMARINE CABLES--TELEGRAPH INSTRUMENTS--NAVIGATIONAL INSTRUMENTS, COMPa.s.s AND SOUNDING MACHINE

THEORY OF SIGNALLING

When the question of laying an Atlantic cable began to be debated in the middle of the nineteenth century, Professor Thomson undertook the discussion of the theory of signalling through such a cable. It was not generally understood by practical telegraphists that the conditions of working would be very different from those to which they were accustomed on land lines, and that the instruments employed on such lines would be useless for a cable. Such a cable consists of a copper conductor separated from the sea-water by a coating of gutta-percha; it forms an elongated Leyden jar of very great capacity, which, when a battery is connected to one end of the conducting core, is gradually charged up, first at that end, and later and later at greater distances from it, and then is gradually discharged again when the battery is withdrawn and the end of the conductor connected to earth. Here, again, an application of Fourier's a.n.a.lysis solved the problem, which, with certain modifications, and on the supposition that the working is slow, is essentially the same problem as the diffusion of heat along a conducting bar, or the diffusion of a salt solution along a column of water. The signals are r.e.t.a.r.ded (and this was one of the results of the investigation) in such a manner "that the time required to reach a stated fraction of the maximum strength of current at the remote end,"

when a given potential difference is applied at the other, or home end, is proportional to the product of the capacity and resistance of the cable, each taken per unit of the length, and also proportional to the square of the length of cable. In other words, the r.e.t.a.r.dation is proportional to the product of the resistance of the copper conductor and the total capacity of the cable. This gave a practical rule of great importance for guidance in the manufacture of submarine cables. The conductor should have the highest conductivity obtainable, and should therefore be of pure copper; the insulating covering should, while forming a nearly absolutely non-conducting sheath, have as low a specific inductive capacity as possible. The first of these conditions ran counter to some views that had been put forward, to the effect that it was only necessary to have the internal conductor highly conducting on its surface; and some controversy on the subject ensued. The inverse square law, as it was called, was vehemently called in question, from a mistaken interpretation of some experiments that were made to test it.

For if the potential at the home end be regularly altered, according to the simple harmonic law, so that the number of periods of oscillation in a second is n, the changes of potential are propagated with velocity 2v(pn?cr), where c and r are the capacity and resistance of the cable, each taken per unit length. In this case, for a long cable, there is a velocity of propagation independent of the length; and this fact seems to have misled the experimenters. Thomson's view prevailed, and the result was the establishment, first by Thomas Bolton & Sons, Stoke-on-Trent, of mills for the manufacture of high conductivity copper, which is now a great industry.

The Fourier mathematics of the conduction of heat along a bar suffices to solve the problem, so long as the signalling is so slow as not to bring into play electromagnetic induction to any serious extent. For rapid signalling in which very quick changes of current are concerned the electromotive forces due to the growth or dying out of the current would be serious, and the theory of diffusion would not apply. But ordinary cable working is quite slow enough to enable such electromotive forces to be disregarded.

LAYING OF FIRST AMERICAN CABLES

The first cable of 1858 was laid by the U.S. frigate Niagara and H.M.S.

Agamemnon, after having been manufactured with all the precautions suggested by Professor Thomson's researches. It is hard to realise how difficult such an enterprise was at the time. The manufacture of a huge cable, the stowage of it in cable tanks on board the vessels, the invention of laying and controlling and picking-up machinery had to be faced with but little experience to guide the engineers. Here again Thomson, by his knowledge of dynamics and true engineering instinct, was of great a.s.sistance. In 1865 he read a very valuable paper on the forces concerned in the laying and lifting of deep-sea cables, showing how the strains could be minimised in various practical cases of importance--for example, in the lifting of a cable for repairs.

A first Atlantic cable had been partly laid in 1857 by the Niagara, when it broke in 2000 fathoms of water, about 330 miles from Valentia, where the laying had begun. An additional length of 900 miles was made, and the enterprise was resumed. This time it was decided that the two vessels, each with half of the cable on board, should meet and splice the cable in mid-ocean, and then steam in opposite directions, the Agamemnon towards Valentia, the Niagara towards Newfoundland. Professor Thomson was engineer in charge of the electrical testing on board of the Agamemnon. After various mishaps the cable was at last safely laid on August 6, 1858, and congratulations were shortly after exchanged between Great Britain and the United States. On September 6 it was announced that signals had ceased to pa.s.s, and an investigation of the cause of the stoppage was undertaken by Professor Thomson and the other engineers. The report stated that the cable had been too hastily made, that, in fact, it was not good enough, and that the strains in laying it had been too great and unequal. It was found impossible to repair it, so that there was no option but to abandon it.

This cable probably suffered seriously from the violent means which seem to have been employed to force signals through it. Now only a very moderate difference of potential is applied to a cable at the sending end, and speed of signalling is obtained by the use of instruments, the moving parts of which have little inertia, and readily respond to only an exceedingly feeble current.

A second cable was made and laid in 1865 by the Great Eastern, which could take on board the whole at once and steam from sh.o.r.e to sh.o.r.e. It was also well adapted for cable work through having both screw and paddles. As Thomson points out, "steerage way" could be got on the vessel by driving the screw ahead, so as to send a stream of water astern towards the rudder, while the paddles were driven astern to prevent the ship from going ahead. This was of great advantage in manuvring on many occasions.

This cable also broke, but a third was laid successfully in 1866 by the same vessel, and the second was recovered and repaired, so that two good cables were secured for commercial working. On both expeditions Professor Thomson acted as electrical engineer, and received the honour of knighthood and the thanks of the Anglo-American Telegraph Company on his return home, when he was also presented with the freedom of the city of Glasgow.

He afterwards acted as engineer for the French Atlantic Cable, for the Brazilian and River Plate Company, and for the Commercial Company, whose two new Atlantic cables were laid in 1882-4.

MIRROR GALVANOMETER AND SIPHON RECORDER

Since whatever the potential applied at the sending end of the cable might be (and, of course, as has been stated, this potential had to be kept to as low a value as possible) the current at the receiving end only rose gradually, it was necessary to have as delicate a receiving instrument as possible, so that it would quickly respond to the growing and still feeble current. For unless the cable could be worked at a rate which would permit of charges per word transmitted which were within the reach of commercial people, it was obvious that the enterprise would fail of its object. And as a cable could not cost less than half a million sterling, the revenue to be aimed at was very considerable. This problem Thomson also solved by the invention of his mirror galvanometer. The suspended magnet was made of small pieces of watch-spring cemented to a small mirror, so that the whole moving part weighed only a grain or two. Its inertia, or resistance to being set into motion, was thus very small, and it was hung by a single fibre of silk within a closed chamber at the centre of the galvanometer coil. A ray of light from a lamp was reflected to a white paper scale in front of the mirror, which as it turned caused a spot of illumination to move along the paper. A motion of this long ma.s.sless index to the left was regarded as a dot, a motion to the right as a dash, and the Morse alphabet could therefore be employed. This instrument was used in the 1858 cable expedition, and a special form of suspension was invented for it by Thomson, to enable it to be used on board ship. The suspension thread, instead of being held at one end only, was stretched from top to bottom of the chamber in which the needle hung, and kept tight by being secured at both ends. Thus the minimum of disturbance was caused to the mirror by the rolling or pitching of the ship.

The galvanometer was also enclosed in a thick iron case to guard it against the magnetic field due to the iron of the ship. The "iron-clad galvanometer" first used in submarine telegraphy (on the 1858 expedition in the U.S. frigate Niagara) is in the collection of historical apparatus in the Natural Philosophy Department of the University of Glasgow.

The mirror galvanometer then invented has become one of the most useful instruments of the laboratory. Mirror deflection is now used also for the indicators of many kinds of instruments.

The galvanometer was replaced later by another invention of Professor Thomson--the siphon recorder. Here a small and delicate pen was formed by a piece of very fine gla.s.s tube (vaccination tubing, in fact) in the form of a siphon, of which the shorter end dipped into an ink-bottle, while the other end wrote the message in little zig-zag notches on a ribbon of paper drawn past it by machinery. The siphon was moved to and fro by the signalling currents, which flowed in a small coil hung between the poles of an electromagnet, excited by a local battery, and the ink was spirted in a succession of fine drops from the pen to the paper. This was accomplished by electrifying the ink-bottle and ink by a local electrical machine, and keeping the paper in contact with an uninsulated metal roller. Electric attraction between the electrified ink and the unelectrified paper thus drew the ink-drops out, and the pen, which never touched the paper, was quite unr.e.t.a.r.ded by friction.

Both these instruments had the inestimable advantage that the to and fro motions of the spot of light or the pen took place independently of ordinary earth-currents through the cable.

The arrangement of magnet and suspended coil in this instrument has become widely known as that of the "d'Arsonval galvanometer." This application was antic.i.p.ated by Thomson, and is distinctly mentioned in his recorder patent, long before such galvanometers were ever used. It was later proposed by several experimenters before M. d'Arsonval.

It is not too much to say that, by his discussion of the speed of signalling, his services as an electrical engineer, and especially by his invention of instruments capable of responding to very feeble currents, Thomson made submarine telegraphy commercially possible. Later he entered into partnership with Mr. C. F. Varley and Professor Fleeming Jenkin. A combination of inventions was made by the firm: Varley had patented a method of signalling by condensers, and Jenkin later suggested and patented an automatic key for "curb-sending" on a cable--that is, signalling by placing one pole of the battery for an interval a little shorter than the usual one to the line, and then reversing the battery for the remainder. This gave sharper signals, as the reversal helped to discharge the cable more rapidly than it would have been by the mere connection to earth between two signals. The firm of Thomson, Varley & Jenkin took a prominent part in cable work; and Thomson and Jenkin acted as engineers for many large undertakings. They employed a staff of young electricians at the cable-works at Millwall and elsewhere, keeping watch over the cable during manufacture, and sent them to sea as representatives and a.s.sistants to perform similar duties during the process of cable-laying. On their staff were many men who have come to eminence in electrical and engineering pursuits in later life.

MARINERS' COMPa.s.s AND SOUNDING MACHINE

After the earlier Atlantic expeditions Sir William Thomson turned his attention to the construction of navigational instruments, and invented the mariner's compa.s.s and wire-sounding apparatus which are now so well known. He had come to the conclusion that the compa.s.ses in use had much too large needles (some of them bar-magnets seven or eight inches long!) to respond quickly and certainly to changes of course, and, what was still more serious, to admit of the application of correcting magnets, and of ma.s.ses of soft-iron to annul the action of the magnetism of the ship.

The compa.s.s card consists of a paper ring, on which the "points" and degrees are engraved in the ordinary way, and is kept circular by a light ring of aluminium. Threads of silk extend radially from the rim to a central boss of aluminium in which is a cap of aluminium. In the top of the cap is a sapphire bearing, which rests on an iridium point projecting upward from the compa.s.s bowl. Eight magnets of gla.s.s-hard steel, from 3 inches to 2 inches long, and about the thickness of a knitting-needle, which form the compa.s.s needle, are strung like the steps of a rope ladder, on two silk threads attached to four of the radial threads.

The weight of the card is extremely small--only 170 grains; that is less than ? of an ounce. But the matter is not merely made small in amount; it is distributed on the whole at a great distance from the axis; consequently the period of free vibration is long, and the card is very steady. The great lightness of the card also causes the error due to friction on the point of support to be very small.

The errors of the compa.s.s in an iron ship are mainly the semicircular error and the quadrantal error. We can only briefly indicate how these arise and how they are corrected. The ship's magnetism may be considered as partly permanent, and partly inductive. The former changes only very slowly, the latter alters as the ship changes course and position. For the ship is a combination of longitudinal, transverse, and vertical girders and beams. As a whole it is a great iron or steel girder, but its structure gives it longitudinal, transverse, and vertical magnetisation. This disturbs the compa.s.s, which is also affected by the magnetisation of the iron or steel masts and spars, or of iron or steel carried as cargo.

The semicircular error is due to a great extent to permanent magnetism, but also in part to induced magnetism. It is so called because when the ship's head is turned through 360, the error attains a maximum on two courses 180 apart. It may amount to over 20 in an ordinary iron vessel, and to 30 or 40 in an armour-clad. It is corrected by two sets of steel magnets placed with their centres under the needle in the binnacle. One set have their lengths fore and aft, the others in the thwart-ship direction. These magnets annul the error on the north and south and on the east and west courses, due to the two horizontal components of magnetic force produced mainly by the permanent magnetism of the ship. A regular routine of swinging the ship when marks on the sh.o.r.e (the true bearings of which from the ship are known) are available, is followed for the adjustment.

The quadrantal error is so called because its maxima are found on four compa.s.s courses successively a quadrant, or 90, from one another. It amounts in general to from 5 to 10 at most. It is due to induced magnetism, and is corrected by a pair of soft-iron spheres, placed on the two sides of the compa.s.s with their centres in a line transverse to the ship, through the centre of the compa.s.s needle. There are, however, exceptional cases in which they are placed in the fore and aft line one afore, the other abaft, the needle. When the quadrantal error has once been annulled it is always zero, for as the induced magnetism changes, so does that of the spheres, and the adjustment remains good. In a new ship the permanent magnetism slowly alters, and so the semicircular correction has to be improved from time to time by changing the magnets.

These adjustments are not quite all that have to be made; but enough has been stated to show how the process of compensation can be carried out with the Thomson compa.s.s. The immensely-too-large magnets used formerly as compa.s.s needles, through a mistaken notion, apparently, that more directive force would be got by their means, rendered the quadrantal adjustment an impossibility. The card swinging round brought the large needles into different positions relatively to the iron b.a.l.l.s, when these were used, and exerted an inductive action on them which reacted on the needles, producing more error, perhaps, than was corrected.

Thomson invented also an instrument called a "deflector," by which it is possible to adjust a compa.s.s when sights of sun or stars, or bearings of terrestrial objects, cannot be obtained. By means of it the directive forces on the needles on different courses can be compared. Then the adjustment is made by placing the correctors so that the directive force is as nearly as may be the same on all courses. The compa.s.s is then quite correct.

The theory of deviations of the compa.s.s, it is right to say, was discussed first partially by Poisson, but afterwards very completely and elegantly by the late Mr. Archibald Smith of Jordanhill, whose memoirs, now incorporated in the _Admiralty Manual of Deviations of the Compa.s.s_, led to Lord Kelvin's inventions.

Lord Kelvin's compa.s.s is now almost universally in use in the merchant service of this country, and in most of the navies of the world. It has added greatly to the certainty and safety of navigation.