TheBaltimore Lectures were delivered in 1884 at Johns Hopkins University, soon after the Montreal meeting of the British Association. The subject chosen was the Wave Theory of Light; and the idea underlying the course was to discuss the difficulties of this theory to "Professorial fellow-students in physical science." A stenographic report of the course was taken by Mr. A. S. Hathaway, and was published soon after. The lectures were revised by Lord Kelvin, and the book now known asThe Baltimore Lectureswas published just twenty years later (in 1904) at the Cambridge University Press. It is absolutely impossible in such a memoir as the present to give any account of the discussions contained in the lectures as now published. The difficulties dealt with can for the most part only be understood by those who are acquainted with the wave theory of light in its details, and such readers will naturally go direct to the book itself.
Some of the difficulties, however, were frequently alluded to in Lord Kelvin's ordinary lectures, and all his old students will remember the animation with which he discussed the apparent anomaly of a medium like the luminiferous ether, which is of such enormous rigidity that (on the elastic solid theory) a wave of transverse oscillation is propagated through it with a speed of3 × 1010centimetres (186,000 miles) per second, and yet appears to offer no impediment to the slow motion of the heavenly bodies. For Lord Kelvin adopted the elastic solid theory of propagation of light as "the only tenable foundation for the wave theory of light in the present state of our knowledge," and dismissed the electromagnetic theory (his words were spoken in 1884, it is to be remembered) with the statement of his strong view that an electric displacement perpendicular to the line of propagation, accompanied by a magnetic disturbance at right angles to both, is inadmissible.
And he goes on to say that "when we have an electromagnetic theory of light," electric displacement will be seen as in the direction of propagation, with Fresnelian vibrations perpendicular to that direction. In the preface, of date January 1904, the insufficiency of the elastic solid theory is admitted, and the question of the electromagnetic theory again referred to. He says there that the object of the Baltimore Lectures was to ascertain how far the phenomena of light could be explained within the limits of the elastic solid theory. And the answer is "everythingnon-magnetic; nothing magnetic." But he adds, "The so-called electromagnetic theory of light has not helped us hitherto," and that the problem is now fully before physicists of constructing a "comprehensive dynamics of ether, electricity, and ponderable matter which shall include electrostatic force, magnetostatic force, electromagnetism, electrochemistry, and the wave theory of light."
All this is exceedingly interesting, for it seems to make clear Lord Kelvin's attitude with respect to the electromagnetic theory of Maxwell, which is now regarded by most physicists as affording on the wholea 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, principally 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 therationaleof 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 LordKelvin 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 glass 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 thebullets 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 illustrations, which old Glasgow students will recognise, appear continually in the lectures. They will remember, almost with affection, the system of threeparticles(7 lb. or 14 lb. weights!) joinedtogether in a vertical row by stout spiral springs of steel, which were always to be taken as massless, and will recall Lord Kelvin's experiments with them, demonstrating the three modes of vibration of a system of three masses, 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 massive 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 shell embedded in the ether as in the simpler case, a second shell 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 phosphorescence 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 toswing 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 analogous to that of phosphorescence.
Fig. 18.Fig. 18.
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 ofinterest 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 class 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 Rücker 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 byLoschmidt 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 (Constitution of Matter) of Lord Kelvin'sPopular Lectures and Addresses, for his Royal Institution 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 coarse-grained than a heap of small shot, but probably less coarse-grained than a heap of cricket-balls."
Of course, it is not intended here to convey the idea that the molecules are spheres like shot or cricket-balls; they undoubtedly have a structure of their own. And no pronouncement 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, andsuo morehe endeavoured to frame dynamical explanations of electronic (or, as hepreferred 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.
Whenthe 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 analysis 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 aconducting bar, or the diffusion of a salt solution along a column of water. The signals are retarded (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 retardation 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 isn, the changes of potential are propagated with velocity 2√(πn⁄cr), wherecandrare the capacity and resistance of the cable, each taken per unit length. In this case, for a long cable, thereis 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.
The first cable of 1858 was laid by the U.S. frigateNiagaraand 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 assistance. 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 variouspractical cases of importance—for example, in the lifting of a cable for repairs.
A first Atlantic cable had been partly laid in 1857 by theNiagara, 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, theAgamemnontowards Valentia, theNiagaratowards Newfoundland. Professor Thomson was engineer in charge of the electrical testing on board of theAgamemnon. 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 pass, 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 shore to shore. 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 manœuvring 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.
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. Forunless 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 massless 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 expeditionin the U.S. frigateNiagara) 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 glass 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 unretarded 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 wasanticipated 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 assistants 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.
After the earlier Atlantic expeditions Sir William Thomson turned his attention to the construction of navigational instruments, and invented the mariner's compass and wire-sounding apparatus which are now so well known. He had come to the conclusion that the compasses 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 masses of soft-iron to annul the action of the magnetism of the ship.
The compass 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 compass bowl. Eight magnets of glass-hard steel, from 3¼ inches to 2 inches long, and about the thickness of a knitting-needle, which form the compass 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 170½ grains; that is less than2⁄5of 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 ofthe card also causes the error due to friction on the point of support to be very small.
The errors of the compass 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 compass, 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 shore (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 compass 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 compass with their centres in a line transverse to the ship, through the centre of the compass 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 compass. The immensely-too-large magnets used formerly as compass 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 balls, 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 compass 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 coursescan 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 compass is then quite correct.
The theory of deviations of the compass, 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 theAdmiralty Manual of Deviations of the Compass, led to Lord Kelvin's inventions.
Lord Kelvin's compass 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.
The sounding machine is also well known. At first pianoforte wire was used for deep-sea sounding by Commodore Belknap of the U.S. Navy, and by others, on Sir William Thomson's recommendation. Finally, a form of machine was made by which a sinker could be lowered to the bottom of the sea and brought up again in a few minutes; so that it was possible to take a sounding without the long delay involved in the old method with a reel of hemp-rope, which often tempted shipmasters to run risks of going ashore rather than stop the ship for the purpose. The wire offered little resistance to motion through the water, and by a proper winding machine, with brake to prevent the wire from running out too fast and kinking, when it was almost certain to break, one man could quickly sound and heave up again, while another attended to the wire and sinker. A gauge consisting of a long quill-tube closed at the upper end, and coated inside with chromate of silver, showed by the action of thesea-water on the coating how far the water had passed up the tube, compressing the air above it; and from this, by placing the tube along a wooden rule properly graduated, the depth was read off at once. With the improved machine a ship approaching the shore in thick weather could take soundings at short intervals without stopping, and discover at once any beginning of shallowing of the water, and so avoid danger.
The single wire is not now used, as a thin stranded wire is found safer and quite as effective. The gauge also has been improved. The apparatus can be seen in any well-found sea-going vessel; though there are still, or were until not very long ago, steam vessels without this apparatus, though crossing the English Channel with passengers. These depended for soundings on the obsolete hemp-rope, wrapped round an iron spindle held vertically on the deck by members of the ship's company, while the cord was unwound by the descent of the sinker.24
Sir William Thomson's electrical and other inventions are too numerous to specify here, and they are in constant use wherever precision of measurement is aimed at or required. Long ago he invented electrometers for absolute measurements of electrical potential ("electric pressure"); more recently his current-balances have given the same precision to electrodynamic measurement of currents. All his early instruments were made by Mr. James White, Glasgow. Thebusiness founded by Mr. White, and latterly carried on at Cambridge Street, has developed immensely, and is now owned by a limited liability company—Messrs. Kelvin and James White (Limited).
For many years Sir William Thomson was a keen yachtsman, and his schooner yacht, theLalla Rookh, was well known on the Clyde and in the Solent. An expert navigator, he delighted to take deep-sea voyages in his yacht, and went more than once as far as Madeira. Many navigational and hydrodynamical problems were worked out on these expeditions. For a good many years, however, he had given up sea-faring during his times of relaxation, and lived in Glasgow and London and in Largs, Ayrshire, where he built, in 1875, a large and comfortable house, looking out towards the Firth and the Argyleshire lochs he knew and loved so well.
In the course of his deep-sea expeditions in his yacht he became impressed with the utility of Sumner's method of determining the position of a ship. Let us suppose that at a given instant the altitude of the sun is determined from the ship. The Greenwich meantime, and therefore the longitude at which the sun is vertical, is known by chronometer, and the declination of the sun is known from the Nautical Almanac. The point on the earth vertically under the sun can be marked on the chart, and a circle (or rather, what would be a circle on a terrestrial globe) drawn round it from every point of which the sun would have the observed altitude. The ship is at a point on this circle. Some time after the altitude of the sun is observed again, and a new "circle" is drawn. If the first "circle" be bodily shifted on the chart along thedistance run in the interval, it will intersect the second in two points, one of which will be the position of the ship, and it is generally possible to tell which, without danger of mistake.
Sir William Thomson printed tables for facilitating the calculations in the use of Sumner's method, and continually used them in his own voyages. He was well versed in seamanship of all kinds, and used his experience habitually to throw light on abstruse problems of dynamics. Some of these will be found in "Thomson and Tait"; for instance, in Part I, § 325, where a number of nautical phenomena are cited in illustration of an important principle of hydrodynamics. The fifth example stated is as follows: "In a smooth sea, with moderate wind blowing parallel to the shore, a sailing ship heading towards the shore, with not enough of sail set, can only be saved from creeping ashore by setting more sail, and sailing rapidly towards the shore, or the danger that is to be avoided, so as to allow her to be steered away from it. The risk of going ashore in fulfilment of Lagrange's equations is a frequent incident of 'getting under way' while lifting anchor or even after slipping from moorings." His seamanship was well known to shipmasters, with whom he had much intercourse, and whose intelligence and practical skill he held in very high regard.
Itis impossible to convey to those who never studied at Glasgow any clear conception of Thomson as he appeared to students whom he met daily during the session. His appearance at meetings of the British Association, and his vivacious questionings of the various authors of papers, his absorption in his subject and oblivion to the flight of time when he read a paper himself, will long be remembered by scientific men: but though they suffice to suggest what he was like in his own lecture-room, the picture lacks the setting of furniture, apparatus, assistants, and students, which all contributed to the unique impression made by his personality on his pupils. The lecture-table—with long straight front and ends refracted inward, flanked by higher small round tables supported on cylindrical pillars—laden with instruments; the painted diagrams of the solar spectrum and of the paths of coloured rays through a prism, hung round the walls; the long wire with the cylindrical vibrator attached, for experiments on torsion, and the triple spiral spring vibrator, which hung at the two ends of the long blackboard; the pendulum thirty feet long, consisting of a steel wire and a twelve-pound cannon-ball as bob, suspended from the apex of the dome-roof above the lecture-table; the large iron wheel in the beautifuloriel window on the right of the lecturer, and the collection of optical instruments on the table in front of the central window spaces, from which the small iron-framed panes—dear to the heart of the architect—had been removed; the clock on either side of the room, one motionless, the other indicating the time, and having attached to it the alarm which showed when the "angry bell" outside had ceased to toll; the ten benches of eager and merry students, which filled the auditorium; all these combined to form a scene which every student fondly recalls, and which cannot be adequately described. A similar scene, with some differences of arrangement and having its own particular associations, will occur to every student who attended in the Old College.
The writer will never forget the lecture-room when he first beheld it, from his place on Bench VIII, a few days after the beginning of session 1874-5. Sir William Thomson, with activity emphasised rather than otherwise by his lameness, came in with the students, passed behind the table, and, putting up his eye-glass, surveyed the apparatus set out. Then, as the students poured in, an increasing stream, the alarm weight was released by the bell-ringer, and fell slowly some four or five feet, from the top of the clock to a platform below. By the time the weight had descended the students were in their places, and then, as Thomson advanced to the table, all rose to their feet, and he recited the third Collect from the Morning Service of the Church of England. It was the custom then, and it is still one better honoured in the observance than in the breach (which has become rather common) to open all the first and second classesof the day with prayer; and the selection of the prayers was left to the discretion of the professors. Next came the roll-call by the assistant; each name was called in its English, or Scottish (for the clans were always well represented) form, and the answer "adsum" was returned.
Then the Professor began his lecture, generally with the examination of one of the students, who rose in his place when his name was called. Thomson, as the quotation in Chapter VI from the Bangor Address shows, was fond of oral examination, and after the second hour had begun to decline as one of regular attendance, habitually devoted ten or fifteen minutes to asking questions and criticising the answers. The names of the students to be questioned were selected at random from the class register, or by a kind of lottery, carried out by placing a small card for each student in a box on the table, and drawing a name whenever a member of the class was to be examined. The interest in the drawing each day was intense, for there was a glorious uncertainty as to what might be the line of examination adopted. Sometimes, in the midst of a criticism of an answer, an idea would suddenly occur to the Professor, and he would enlarge upon it, until the forgotten examinee slipped quietly back into his seat, to be no more disturbed at least for that day! And how great the relief if the ordeal was well passed and the card was placed in that receptacle of the blessed, the compartment reserved for those who had been called and duly passed the assize! But there was a third compartment reserved for the cards of those unfortunates who failed to satisfy the judge! The reader may haveanticipated the fact that the three divisions of this fateful box were commonly known to students by the names of the three great habitations of spirits described in theDivina Commediaof Dante.
As has been stated, the oral examination with which the lectures opened was the cause of a good deal of excitement, which was added to by the element of chance introduced by drawing the names from the purgatorial compartment of the box. The ordeal was dreaded by backward students, whom Thomson found, as he said, aphasic, when called on to answer in examination, but who certainly were anything but aphasic in more congenial circumstances. Occasionally they abstained from responding to their names, modestly seeking the seclusion of the crowd, and some little time would be spent in ascertaining whether the examinee-designate was present. When at last he was discovered, he generally rose with a fervent appeal to his fellows on either side to help him in his need.
McFarlane used to tell of an incident which illustrated the ingenuity with which it was sometimes attempted to evade the ordeal of theviva voceexamination. One afternoon, when he was busily preparing the lecture-illustrations for next day, a student came into the class-room, and engaging him in conversation on some point of dynamics, regarding which he professed to have a difficulty, hovered round the box which contained the three compartments popularly known as Purgatory, Heaven, and Hell! Always when McFarlane left the room to bring something from the adjoining cabinet of apparatus, he found, when he returned, his inquiring friend hurriedly quitting the immediate vicinity of the box. At last the studenttook leave, with many apologies for giving so much trouble. As McFarlane suspected would be the case, the ticket bearing the name of that student was no longer to be found! He used to conclude the story as follows: "I just made a new ticket for him, and placed it on the top of the other tickets, and next day Sir William called him, the very first time." What were his feelings, who had fondly thought himself safe for the session, and now found himself subjected to a "heckling" which he probably expected would be repeated indefinitely, may be imagined.
The subject of the first lecture which the writer attended was simple harmonic motion, and was illustrated by means of pendulums, spiral springs with weights, a long vertical rod of steel tipped with an ivory ball and fastened to a heavy base, tuning-forks, etc.
The motion was defined as that of a particle moving along the diameter of a circle—the "auxiliary circle," Thomson called it—so as always to keep pace, as regards displacement in the direction along that diameter, with a particle moving with uniform speed in the circle. Then the velocity and acceleration were found, and it was shown that the particle was continually accelerated towards the centre in proportion to the distance of the particle from that point. The constant ratio of acceleration to displacement was proved to be equal to the square of the angular velocity in the auxiliary circle, and from this fact, and the particular value of the acceleration when the particle was at either end of its range of motion, an expression for the period in terms of the speed and radius of the auxiliary circle was deduced. Then the ordinary simple pendulum formula was obtained.
This mode of treatment of an elementary matter, so entirely different from anything in the ordinary text-books, arrested the attention at once, and conveyed, to some at least of those present, an idea of simple harmonic motion which was directly applicable to all kinds of cases, such as the motion of the air in a sound wave, or of the medium which conveys the waves of light.
The subject of Kepler's laws was dealt with in the early lectures of every course, and Newton's deductions were insisted on as containing the philosophy of the whole question, leading, as they did, to the single principle from which the laws could be deduced, and the third law corrected when the mass of the planet was comparable with that of the sun. Sometimes Thomson would read the remarkable passage in Hegel'sLogik, in which he refers to the Newtonian theory of gravitation and says, "The planets are not pulled this way and that, they move along in their orbits like the blessed gods," and remark upon it. On one occasion his remark was, "Well, gentlemen, if these be his physics, what must his metaphysics be?" And certainly that aphilosophershould deny, as Hegel seemed to do, all merit to the philosophical setting in which Newton placed the empirical results of Kepler, is a very remarkable phenomenon.
The vivacity and enthusiasm of the Professor at that time were very great. The animation of his countenance as he looked at a gyrostat spinning, standing on a knife-edge on the glass plate in front of him, and leaning over so that its centre of gravity was on one side of the point of support; the delight with which he showed that hurrying of the precessional motion caused the gyrostat to rise, and retarding the precessionalmotion caused the gyrostat to fall, so that the freedom to "precess" was the secret of its not falling; the immediate application of the study of the gyrostat to the explanation of the precession of the equinoxes, and illustration by a model of a terrestrial globe, arranged so that the centre should be a fixed point, while its axis—a material spike of brass—rolled round a horizontal circle, the centre of which represented the pole of the ecliptic, and the diameter of which subtended an angle at the centre of the globe of twice the obliquity of the ecliptic; the pleasure with which he pointed to the motion of the equinoctial points along a circle surrounding the globe on a level with its centre, and representing the plane of the ecliptic, and the smile with which he announced, when the axis had rolled once round the circle, that 26,000 years had elapsed—all these delighted his hearers, and made the lecture memorable.
Then the gyrostat, mounted with its axis vertical on trunnions on a level with the fly-wheel, and resting on a wooden frame carried about by the professor! The delight of the students with the quiescence of the gyrostat when the frame, gyrostat and all, was carried round in the direction of the spin of the fly-wheel, and its sudden turning upside down when the frame was carried round the other way, was extreme, and when he suggested that a gyrostat might be concealed on a tray of glasses carried by a waiter, their appreciation of what would happen was shown by laughter and a tumult of applause.
Some would have liked to follow the motions of spinning bodies a little more closely, and to have made out clearly why they behaved as they did. ApparentlyThomson imagined the whole affair was self-evident, for he never gave more than the simple parallelogram diagram showing the composition, with the already existing angular momentum about the axis of the top, of that generated about another axis, in any short time, by the action of gravity.
As a matter of fact, the stability and instability of the gyrostat on the tray give the best possible illustration of the two different forms of solution of the differential equation, Ӫ + μӨ = 0, according as μ is positive or negative; though it is also possible to explain the inversion very simply from first principles. All this was no doubt regarded by Thomson as obvious; but it was far from being self-evident to even good students of the ordinary class, who, without exception, were beginning the study of dynamics.
Thomson's absorption in the work of the moment was often very great, and on these occasions he much disliked to be brought down to sublunary things by any slight mischance or inconvenience. Examples will occur to every old pupil of the great emphasis with which he commanded that precautions should be taken to prevent the like from happening again. Copies of Thomson and Tait'sNatural Philosophy—"T and T'" was its familiar title—and of other books, including Barlow's Tables and other collections of numerical data, were always kept on the lecture-table. But occasionally a laboratory student would stray in after everything had been prepared for the morning lecture, and carry offBarlowto make some calculation, and of course forget to return it. Next morning some number would be wanted fromBarlowin a hurry, and the book would be missing. Then Thomson wouldorder thatBarlowshould be chained to the lecture-table, and enjoin his assistant to see that that was done without an hour's delay!
On one occasion, after working out part of a calculation on the long fixed blackboard on the wall behind the table, his chalk gave out, and he dropped his hand down to the long ledge which projected from the bottom of the board to find another piece. None was just there; and he had to walk a step or two to obtain one. So he enjoined McFarlane, his assistant, who was always in attendance, to have a sufficient number of pieces on the ledge in future, to enable him to find one handy wherever he might need it. McFarlane forgot the injunction, or could not obtain more chalk at the time, and the same thing happened next day. So the command was issued, "McFarlane, I told you to get plenty of chalk, and you haven't done it. Now have ahundredpieces of chalk on this ledge to-morrow; remember, ahundredpieces; I will count them!" McFarlane, afraid to be caught napping again, sent that afternoon for several boxes of chalk, and carefully laid the new shining white sticks on the shelf, all neatly parallel at an angle to the edge. The shelf was about sixteen feet long, so that there was one piece of chalk for every two inches, and the effect was very fine. The class next morning was delighted, and very appreciative of McFarlane's diligence. Thomson came in, put up his eye-glass, looked at the display, smiled sweetly, and, turning to the applauding students, began his lecture.
From time to time there were special experiments, which excited the interest of the class to an extraordinary degree. One was the determination of thevelocity of a bullet fired from a rifle into a Robins ballistic pendulum. The pendulum, consisting of a massive bob of lead attached to a rigid frame of iron bars turning about knife-edges, was set up behind the lecture-table, and the bullet was fired by Thomson from a Jacob rifle into the bob of the pendulum. The velocity was deduced from the deflection of the pendulum, its known moment of inertia about the line of the knife-edges, the distance of the line of fire from that line, and the mass of the bullet.
In some of the notices of Lord Kelvin that have appeared in the newspapers, the imagination of the writers has converted the Jacob rifle into one which Professor Thomson carried in the early years of the volunteer movement, as a member of a Glasgow corps. It is still used in the Natural Philosophy Department for the same experiment, and is a muzzle-loading rifle of large calibre, which throws an ounce bullet. It was invented by the well-known Indian sportsman, Colonel Jacob, for big-game shooting in India. Thomson held a commission as captain in the K (or University) Company of rifle volunteers, and so did not shoulder a rifle, except when he may have indulged in target practice.
The front bench students were always in a state of excitement, mingled in some cases perhaps with a little trepidation. For the target was very near them, and though danger was averted by placing a large wooden screen in front of the bob, to prevent splinters of the bullet from flying about in the event of its missing the target and striking the iron casing of the bob, there was a slight amount of nervousness as to what might happen. The rifle, loaded by McFarlane,who had weighed out the charge of powder (so many drams) from a prescription kept in a cavity of the stock, was placed on the table, and two rests, provided withVnotches to receive the rifle, were placed in the proper position to enable a bull's eye to be obtained. Thomson generally produced a small box of cotton wool, and inserted a little in each of his ears to prevent injury to the tympanum from the report, and advised the spectators to do the same. Then, adjusting his eye-glass, he bent down, placed the rifle in position, and fired, and the solemn stillness with which the aiming and adjustments had been witnessed was succeeded by vociferous applause. The length of tape drawn out under a light spring was read off by McFarlane, who had already placed on the blackboard the formula for calculation of the velocity, with the factor by which the length of tape had to be multiplied to give the velocity in feet per second. Then, with the intimation that a question involving numerical calculation would be set on the subject, in the ensuing Monday morning examination paper, the lecture generally closed, or was rounded off with some further observations on angular (or, as Thomson always preferred to call it, moment of) momentum.
Long after in the course of a debate in the House of Lords on a proposal to make the use of the metric system of weights and measures compulsory, Lord Kelvin told their lordships how he had weighed out the powder to charge this rifle, and, mistaking the weights, had loaded the rifle with an amount of powder which would have been almost certain to burst the piece, but had happily paused before firing it off.
He often interrupted the course of a lecture with adenunciation of the British "no-system of weights and measures"—"insane," "brain-wasting," "dangerous," were among the mildest epithets he applied to it, and he would deeply sympathise with the student whose recollection of avoirdupois weight, troy weight, apothecaries' weight, etc., was somewhat hazy. The danger of the system consisted mainly in the fact that the apothecaries' dram is 60 grains, while the avoirdupois dram is 271⁄3grains. Thus so many drams of powder required to charge a rifle is a very much larger quantity when reckoned in apothecaries' drams than when reckoned in avoirdupois. As a rule he left the loading of the rifle, like all the other lecture-room experiments, to his assistants.
Another experiment which caused a great sensation was that known as the "dew-drop"! A funnel of brass, composed of a tube about 30 inches long and an inch wide, and a conical mouth about ten inches wide, had a piece of stout sheet India-rubber stretched, as tightly as it could be by hand, across its mouth, and made water-tight by a serving of twine and cement round the edge. A wire soldered round the outside of the lip gave a good hold for this serving and made all perfectly secure. On the plane surface of the sheet geometrical figures were drawn in ink, so that their distortion could be afterwards studied. The funnel was then hung by a strong support in an inverted position behind the table, and water poured gently into it from a rubber supply pipe connected with the water-main. As the water was allowed to accumulate—very slowly at first—the sheet of rubber gradually stretched and bulged out, at first to a flat lens-shape, and gradually more and more, till an immense water-drop had been formed, 15 or 18 inches in horizontal diameter, and of still greater vertical dimensions. The rubber film was now, at the place of greatest tension, quite thin and transparent, and its giving way was anticipated by the students with keen enjoyment. A large tub had been placed below to receive the water, but the deluge always extended over the whole floor space behind the table, and was greeted with rapturous applause.
Before the drop burst, and while it was forming, Thomson discoursed on surface tension, emphasising the essential difference between the tension in the rubber-film and the surface-film of a dewdrop, and pointing out how the geometrical figures had changed in shape. Then he would poke it with the pointer he held in his hand, and, turning to the class, as the mass quivered, remark, "The trembling of the dewdrop, gentlemen!"
Vibrations of elastic solids were illustrated in various ways, frequently by means of a symmetrical shape of calves'-foot jelly, at the top of which a coloured marble had been imbedded as a molecule, the motions of which could be followed. And then he would discourse on the Poisson-Navier theory of isotropic solids, and the impossibility of the fixed relation which that theory imposed between the modulus of rigidity and the modulus of compression; and refer with approval to the series of examples of "perfectly uniform, homogeneous, isotropic solids," which Stokes had shown could be obtained by making jellies of different degrees of stiffness. Another example, frequently adduced as indicating the falsity of the theory, was the entirely different behaviour of blocks of India-rubber andcork, under compression applied by a Bramah press. The cork diminished in thickness without spreading out laterally; the rubber, being very little compressible, bulged out all round as its thickness was diminished.
The lectures on acoustics, which came late in the course, were also exceedingly popular. Two French horns, with all their crooks and accessories, were displayed, and sometimes, to the great delight of the class, Thomson would essay to show how the pitch of a note could be modified by means of the keys, or by the hand inserted in the bell. The determination by the siren of the pitch of the notes of tuning-forks excited by a 'cello bow, and the tuning of a major third by sounding at the same time the perfect fifth of the lower note, were often exhibited, and commented on with acute remarks, of which it is a pity no statement was ever published.25
The closing lecture of the ordinary course was usually on light, and the subject which was generally the last to be taken up—for as the days lengthened in spring, it was possible sometimes to obtain sunlight for the experiments—was often relegated to the last day or two of the session. So after an hour's lecture Thomson would say, "As this is the last day of the session, I will go on for a little longer, after those who have to leave have gone to their classes." Then he would resume after ten o'clock, and go on to eleven, when another opportunity would be given for students to leave, and the lecture would be again resumed. Messengers wouldbe sent from his house, where he was wanted for business of different sorts, to find out what had become of him, and the answer brought would be, hour after hour, "He is still lecturing." At last he would conclude about one o'clock, and gently thank the small and devoted band who had remained to the end, for their kind and prolonged attention.
In the course of his lectures Thomson continually called on his assistants for data of all kinds. In the busiest time of his life—the fifteen years from 1870 to 1885—he trusted to his assistants for the preparation of his class illustrations, and it was sometimes a little difficult to anticipate his wishes, for without careful rehearsal it is almost impossible to make sure that in an experimental lecture everything will go without a hitch. The digressions, generally most interesting and instructive, in which he frequently indulged, almost always rendered it necessary to bring some experiment before the class which had not been anticipated, and all kinds of things were kept in readiness, lest they should be wanted suddenly.
It has often been asserted that Thomson appealed to his assistant for information contained in the multiplication-table, and could not perform the ordinary operations of arithmetic. His active mind, working on ahead of the statements he was making at the moment, often could not be brought back to the consideration of the value of 9 times 6, and the like; but it was quite untrue that he was incapable of making calculations. His memory was good, and though he never could be, for example, sure whether the aqueous humour was before or behind the crystalline in the eye, he was generally able at once to tell when a misstatement hadbeen made as to any numerical question regarding the subject under discussion.
In the higher mathematical class, to which he lectured on Wednesdays, at noon, Thomson was exceedingly interesting. There he seemed to work at the subject as he lectured; new points to be investigated continually presented themselves, and the students were encouraged to work them out in the week-long intervals between his lectures. Always the physical interpretation of results was aimed at, even intermediate steps were discussed. Thus the meaning of the mathematical processes was ever kept in view, and the men who could follow were made to think while they worked, and to regard the mathematical analysis as merely an aid, not an end in itself. "A little expenditure of chalk is a saving of brains;" "the art of reading mathematical books is judicious skipping," were remarks he sometimes made, and illustrate his view of the relative importance of mathematical work when he regarded it as the handmaid of the physical thinker. Yet he valued mathematics for its own sake, and was keenly alive to elegance of form and method, as readers of such great mathematical discussions as the "Appendix on Spherical Harmonics," in Thomson and Tait, will observe. He spoke with unqualified admiration of the work of Green and Stokes, of Cauchy's great memoir on Waves, and of Hamilton's papers on Dynamics. But no form of vector-analysis, neither the Quaternions of Hamilton nor the Vectors of Willard Gibbs and Heaviside, appealed to him, and the example of his friend and co-worker, Tait, had no effect in modifying his adverse verdict regarding this department of mathematics,a verdict which in later years became only more emphatic.
One session he began the first lecture of the higher class by writingdx⁄dtin the middle of the blackboard, and demanding of each of the ten or a dozen students present, some of them distinguished graduates, what it meant! One student described it as the limiting value of the ratio of the increment of the dependent variablexto the increment of the independent variablet, when the latter increment is made indefinitely small. He retorted, "That's what Todhunter would say!" The others gave various slightly different versions of the same definition. At last he impatiently remarked, "Does nobody know thatdx⁄dtmeans velocity?" Here the physical idea as a whole was before his mind; and he did not reflect that iftdenoted time andxdistance in any direction, the explanation given by the student did describe velocity with fair accuracy.
An embarrassing peculiarity of his mathematical discussions was his tendency, when a difficulty of symbolisation occurred, to completely change the notation. Also he was not uniformly accurate in analytical work; but he more than made up for this by the faculty he had of devising a test of the accuracy of the result and of divining the error which had crept in, if the test was not satisfied.
The subjects he treated were always such great branches of mathematics as the theory of the tides—he discussed the tidal phenomena of the English Channel in one course—the general theory of vibrations, Fourier analysis, the theory of waves in water, etc., etc. A very good idea of the manner and matterof his mathematical prelections can be obtained from a perusal of theBaltimore Lectures.
In the physical laboratory he was both inspiring and distracting. He continually thought of new things to be tried, and interrupted the course of the work with interpolated experiments which often robbed the preceding sequence of operations of their final result. His ideas were on the whole better worked out by a really good corps of students when he was from home, and could only communicate by letter his views on the work set forth in the daily reports which were forwarded to him.
He insisted with emphasis that a student who found that a quadrant electrometer would not work well should take it to pieces to ascertain what was the matter. This of course generally resulted in the return of the instrument to White's shop to be put together again and adjusted. But, as he said, there was a cause for every trouble of that kind, and the great thing was to find out at once what it was.
Thomson's concentration on the work in hand, and his power of simply taking possession of men, even mere spectators, and converting them into assistants, was often shown in the laboratory. Several men who have since become eminent were among the assistants enrolled from the laboratory students. Professor W. E. Ayrton and, later, Professor John Perry, were students at Glasgow for a time, and rendered the most able and willing help in the researches which were then proceeding. This power was, no doubt, the secret of his success in gathering round him an enthusiastic corps of laboratory workers in the early years of his professorship, and it was shown also bythe ease with which he annexed the Blackstone examination-room and, later, various spaces in the new University buildings. There, after a time, the Natural Philosophy rooms were found by the senatus to include not only the original class-room, laboratory, etc., but also all the spare attics and corridors in the neighbourhood, and even the University tower itself! One of his colleagues, who venerated him highly, remarked recently, "He had a great faculty for annexation!"
The incident referred to occurred while he was preparing the article onHeatfor the ninth edition of theEncyclopædia Britannica. It seemed at first a pity that Thomson should undertake to write such articles; but in the course of their preparation he came upon so many points on which experimental information was wanting, and instituted so many researches to answer his questions, that the essays took very much the character of original papers. In the article onHeat(he also wroteElasticity), will be found a long account of "Steam Thermometry," that is, of thermometers in which the indicating substance was to be the saturated vapours of different substances, water, sulphurous acid, etc., etc., for he did not limit the term "steam" to water-vapour. For some time every one in the laboratory was employed in making sulphurous acid, by heating copper in sulphuric acid in the usual way, and condensing the gas in tubes immersed in freezing mixtures; and the atmosphere of the room was of a sort which, however noxious to germs of different kinds, it was a little difficult to breathe. One morning, when all were thus occupied, an eminent chemist, who had just come home from the south for a vacation, called to pay his respects. After a word or two ofinquiry as to how his young friend was prospering in his new post, Thomson said, "We are all very busy brewing liquid sulphurous acid, for use in sulphurous acid steam thermometers; we want a large quantity of the liquid; would you mind helping us?" So, desiring an assistant to find a flask and materials, he enrolled this new and excellent recruit on the spot; and what was intended to be a mere call, was prolonged into a long day of ungrudging work at an elementary chemical exercise!