# Thomson, William (1824-1907) (DNB12)

**THOMSON**, Sir WILLIAM, first Baron Kelvin of Largs (1824–1907), man of science and inventor, born on 26 June 1824 in College Square East, Belfast, was second son and fourth child of James Thomson (1786-1849) [q. v.], professor of mathematics in the Royal Academical Institution of Belfast, by his wife Margaret, eldest daughter of William Gardiner of Glasgow. The elder brother, James (1822-1892) [q. v.], was professor of engineering, first in Belfast, then in Glasgow. When William was six years old his mother died, and the father himself taught the boys, who never went to school. In 1832, when William was eight, his father moved to Glasgow as professor of mathematics in the university there. In 1834, in his eleventh year, William matriculated in the University of Glasgow. He loved in later life to talk of his student days and of his teachers, William Ramsay, Lushington, Thomas Thomson, Meikleham, and John Pringle Nichol. He early made his mark in mathematics and physical science ; and in 1840 won the university medal for a remarkable essay, 'On the Figure of the Earth.' During his fifth year as a student at Glasgow (1839-40) he received a notable impulse toward physics from the lectures of Nichol and of David Thomson, who temporarily took the classes in natural philosophy during the illness of Meikleham. At the same time he systematically studied the ’Mecanique Analytique' of Lagrange, and the 'Mecanique Celeste' of Laplace, and made the acquaintance — a notable event in his career — of Fourier's ' Theorie Analytique de la Chaleur,' reading it through in a fortnight, and studying it during a three months' visit to Germany. The effect of reading Fourier dominated his whole career. During his last year at Glasgow (1840-1) he communicated to the ’Cambridge Mathematical Journal' (ii. May 1841), under the signature 'P.Q.R.,' an original paper 'On Fourier's Expansions of Functions in Trigonometrical Series,' which was a defence of Fourier's deductions against some strictures of Professor Kelland. The paper is headed 'Frankfort, July 1840, and Glasgow, April 1841.'

He left Glasgow after six years without taking his degree ; and on 6 April 1841 entered as a student at Peterhouse, Cambridge, where he speedily made his mark. An undergraduate of seventeen, he handled methods of difficult integration readily and with mastery, and proved his power in a paper entitled ' The Uniform Motion of Heat in Homogeneous Solid Bodies, and its Connection with the Mathematical Theory of Electricity,' published in the 'Cambridge Mathematical Journal,' vol. iii. 1842. In other papers he announced various important theorems, in some of which he found, however, that he had been anticipated by Sturm, Gauss, and George Green [q. v.], all of them master minds in mathematics. At Cambridge he rowed in the college races of 1844, and won the Colquhoun silver sculls. He also helped to found the Cambridge University Musical Society, and in its first concert, and afterwards in others, played the French horn. His love of good music he retained to the end of his life. He read mathematics with William Hopkins [q. V.]. In January 1845 he came out second wrangler in the mathematical tripos, but he beat the senior wrangler, Stephen Parkinson [q. v.], in the severer test of the competition for Smith's prize.

On leaving Cambridge he visited Faraday's laboratory at the Royal Institution in London. Faraday and Fourier were the chief heroes of his youthful enthusiasm. Then he went to Paris University to work in the laboratory of Regnault with a view to acquiring experimental skill. There he spent four months, and there also he made the acquaintance of Biot, Liouville, Sturm, and Foucault. Returning to Cambridge, he was elected fellow of his college in the autumn of 1845, and became a junior mathematical lecturer and editor of the 'Cambridge Mathematical Journal.'

Thomson at twenty-one years had gained experience in three universities — Glasgow, Cambridge, and Paris — had published a dozen original papers, and had thus established for himself a reputation in mathematical physics. In 1846, at twenty-two, he became professor of natural philosophy in Glasgow on the death of Meikle ham. The subject of his inaugural dissertation (3 Nov. 1846) was ’De Motu Caloris per Terrae Corpus.' He held this professorship till 1899. Admittedly a bad expositor, he proved himself to be a most inspiring teacher and a leader in research. With the slenderest material resources and most inadequate room, he created a laboratory of physics, the first of its kind in Great Britain, where he worked incessantly, gathering around him a band of enthusiastic students to collaborate in pioneering researches in electric measurement and in the investigation of the electro-dynamic and thermoelectric properties of matter. In the lecture theatre his enthusiasm won for him the love and respect of all students, even those who were unable to follow his frequent flights into the more absruse realms of mathematical physics. Over the earnest students of natural philosophy he exercised an influence little short of inspiration, which extended gradually far beyond the bounds of his own university.

From his first days as professor Thomson worked strenuously with fruitful results. By the end of four years (1850), when he was twenty-six, he had pul3lished no fewer than fifty original papers, most of them highly mathematical in character, and several of them in French. Amongst these researches there is a remarkable group which originated in his attendance in 1847 at the meeting at Oxford of the British Association, where he read a paper on electric images. But a more important event of that meeting was the commencement of his friendship with James Prescott Joule [q. v.] of Manchester, who had for several years been pursuing his researches on the relations between heat, electricity, and mechanical work. Joule's epoch-making paper, which he presented on this occasion, on the mechanical equivalent of heat, would not have been discussed at all but for Thomson's observations. Thomson had at first some difficulty in grasping the significance of the matter, but soon threw himself heart and soul into the new doctrine that heat and work were mutually convertible. For the next six or eight years, partly in co-operation with Joule, partly independently, he set himself to unravel those mutual relations.

Thomson was never satisfied with any phenomenon until it should have been brought into the stage where numerical accuracy could be determined. He must measure, he must weigh, in order that he might go on to calculate. ’The first step,' he wrote, 'toward numerical reckoning of properties of matter ... is the discovery of a continuously varying action of some kind, and the means of observing it definitely, and measuring it in terms of some arbitrary unit or scale division. But more is necessary to complete the science of measurement in any department, and that is the fixing on something absolutely definite as the unit of reckoning.' It was in this spirit that Thomson approached the subject of the transformation of heat.

Sadi Camot in 1824 had anticipated Joule in his study of the problem in his 'Reflexions sur la Puissance Motrice du Feu,' where was discussed the proportion in which heat i% convertible into work, and William John Macquom Rankine [q. v.] had carried the inquiry a stage farther in 1849; while Helmholtz in 'Die Erhaltung der Kraft' (1847)— 'On the Conservation of Force' (meaning what we now term Energy) — denied the possibility of perpetual motion, and sought to establish that in all the transformations of energy the sum total of the energies in the universe remains constant. Thomson in June 1848 communicated to the Cambridge Philosophical Society a paper 'On an Absolute Thermometric Scale founded on Camot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations.' There he set himself to answer the question : Is there any principle on which an absolute thermometric scale can be founded ? He arrived at the answer that such a scale is obtained in terms of Camot's theory, each degree being determined by the performance of equal quantities of work in causing one imit of heat to be transformed while being let down through that difference of temperature. This indicates as the absolute zero of temperature the point which would be marked as — 273° on the air thermometer scale. In 1849 he elaborated this matter in a further paper on 'Carnot's Theory,' and tabulated the values of 'Carnot's function' from 1° C. to 231° C. Joule, writing to Thomson in December 1848, suggested that probably the values of 'Carnot's function' would turn out to be the reciprocal of the absolute temperatures as measured on a perfect gas thermometer, a conclusion independently enunciated by Clausius in February 1850.

Thomson zealously continued his investigation. He experimented on the heat developed by compression of air. He verified the prediction of his brother, Professor James Thomson, of the lowering by pressure of the melting-point of ice. He gave a thermodynamic explanation of
the non-scalding property of steam issuing from a high-pressure boiler. He formulated between 1851 and 1854, with scientific precision, in a long communication to the Royal Society of Edinburgh, the two great laws of thermodynamics — (1) the law of equivalence discovered by Joule, and (2) the law of transformation, which he generously attributed to Carnot and Clausius. Clausius, indeed, had done little more than put into mathematical language the equation of the Carnot cycle, corrected by the arbitrary substitution of the reciprocal of the absolute temperature ; but Thomson was never grudging of the fame of independent discoverers. 'Questions of personal priority,' he wrote, 'however interesting they may be to the persons concerned, sink into insignificance in the prospect of any gain of deeper insight into the secrets of nature.' He gave a demonstration of the second law, founding it upon the axiom that *it is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.* Further, by a most ingenious use of the integrating factor to solve the differential equation for the quantity of heat needed to alter the volume and temperature of unit mass of the working substance, he gave precise mathematical proof of the theorem that the efficiency of the perfect engine working between given temperatures is inversely proportional to the absolute temperature. In collaboration with Joule, he worked at the 'Thermal Effects of Fluids in Motion,' the results appearing between 1852 and 1862 in a series of four papers in the 'Philosophical Transactions,' and four others in the 'Proceedings of the Royal Society.' Thus were the foundations of thermodynamics laid. In later years he rounded off his thermodynamic work by enunciating the doctrine of available energy.

This brilliant development and generalisation of the subject did not content Thomson. He inquired into its applications to human needs and to the cosmic consequences it involved. Thus he not only suggested the process of refrigeration by the sudden expansion of compressed cooled air, but propounded the doctrine of the dissipation of energy. If the availability of the energy in a hot body be proportional to its absolute temperature, it follows that as the earth and the sun — indeed, the whole solar system itself — cool down towards one uniform level of temperature, all life must perish and all energy become unavailable. This far-reaching conclusion once more suggested the question of a beginning of the Cosmos, a question which had arisen in the consideration of the Fourier doctrine of the flow of heat. His note-books of this time show that he had also been applying Fourier's equations to a number of outlying problems capable of similar mathematical treatment, such as the diffusion of fluids and the transmission of electric signals through long cables.

In 1852 Thomson married his second cousin Margaret, daughter of Walter Crum, F.R.S., and resigned his Cambridge fellowship. His wife's precarious health necessitated residence abroad at various times. In the summer of 1855, while they stayed at Kreuznach, Thomson sent to Helmholtz, whose acquaintance he desired to make, an invitation to come to England in September to attend the 'British Association meeting at Glasgow. On 29 July Helmholtz arrived at Kreuznach to make Thomson's acquaintance before his journey to England. On 6 August Hebnholtz wrote to his wife of the deep impression that Thomson, 'one of the first mathematical physicists of Europe,' made on him. 'He far exceeds all the great men of science with whom I have made personal acquaintance, in intelligence, and lucidity, and mobility of thought, so that I felt quite wooden beside him sometimes.' A year later Helmholtz again met Thomson at Schwalbach and described him as 'certainly one of the first mathematical physicists of the day, with powers of rapid invention such as I have seen in no other man.' Subsequently Helmholtz visited Thomson in Scotland many times, and his admiration grew steadily.

The utilisation of science for practical ends was Thomson's ambition through life. 'There cannot,' he said in a lecture to the Institution of Civil Engineers in May 1883, 'be a greater mistake than that of looking superciliously upon practical applications of science. The life and soul of science is its practical application ; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind' (see *Popular Lectures and Addresses,* i. 79).
Hitherto Thomson's work had lain mainly in pure science ; hut while still engaged on his thermodynamic studies, he was drawn toward the first of those practical applications that made him famous. Early in 1853 he had communicated to the Glasgow Philosophical Society a paper 'On Transient Electric Currents,' in which he investigated mathematically the discharge of a Leyden jar through circuits possessing self-induction as well as resistance. He founded his solution on the equation of energy, ingeniously building up the differential equation and then finding the integral. The result was remarkable. He discovered that a critical relation occurred if the capacity in the circuit was equal to four times the coefficient of self-induction divided by the square of the resistance. If the capacity was less than this the discharge was oscillatory, passing through a series of alternate maxima and minima before dying out.
If the capacity was greater than this the discharge was non-oscillatory, the charge dying out without reversing. This beautiful bit of mathematical analysis passed almost unnoticed at the time, but it laid the foundation of the theory of electric oscillations subsequently studied by Oberbeck, Schiller, Hertz, and Lodge, and forming the basis of wireless telegraphy. Fedderssen in 1859 succeeded in photographing these oscillatory sparks, and sent photographs to Thomson, who with great delight gave an account of them to the Glasgow Philosophical Society.

At the Edinburgh meeting of the British Association in 1854 Thomson read a paper 'On Mechanical Antecedents of Motion, Heat, and Light.' Here, after touching on the source of the sun's heat and the energy of the solar system, Thomson reverted to his favourite argument from Fourier according to which, if traced backwards, there must have been a beginning to which there was no antecedent.

In the same year, in the 'Proceedings of the Royal Society,' appeared the result of Thomson's investigation of cables under the title 'On the Theory of the Electric Telegraph.' Faraday had predicted that there would be retardation of signals in cables owing to the coating of gutta-perclia acting like the glass of a Leyden jar. Forming the required differential equation, and applying Fourier's integration of it, Thomson drew the conclusion that the time required for the current at the distant end to reach a stated fraction of its steady value would be proportional both to the resistance and to the capacity ; and as both of these are proportional to the length of the cable, the retardation would be proportional to the square of the length. This famous law of squares provoked much controversy. It was followed by a further research, 'On Peristaltic Induction of Electric Currents,' communicated to the British Association in 1855, and afterward in more complete mathematical form to the Royal Society.

Submarine telegraphy was now becoming a practical problem of the day [see Bright, Sib Charles Tilstok, Suppl. I]. Sea cables were laid in 1851 between England and France, in 1853 between Holyhead and Howth, and in 1856 across the Gulf of St. Lawrence. In the last year the Atlantic Telegraph Company was formed, with capital mostly subscribed in England, with a view to joining Ireland to Newfoundland. Bright was engineer; Whitehouse (a retired medical practitioner) was electrician ; Thomson (of 2 The College, Glasgow) was included in the list of the directors. In a pamphlet issued by the company in July 1857 it was stated that 'the scientific world is particularly indebted to Professor W. Thomson, of Glasgow, for the attention he has given to the theoretical investigation of the conditions under which electrical currents move in long insulated wires, and Mr. Whitehouse has had the advantage of this gentleman's presence at his experiments, and counsel, upon several occasions.' As a matter of fact Whitehouse had previously questioned Thomson's ’law of squares' at the British Association meeting of 1856, declaring that if it was true Atlantic telegraphy was hopeless. He professed to refute it by experiments. Thomson effectively replied in two letters in the 'Athenæum.' He pointed out that success lay primarily in the adequate section of the conductor, and hinted at a remedy (deduced from Fourier's equations) which he later embodied in the curb signal transmitter. Thomson steadily tested his theories in practice. In December 1856 he described to the Royal Society his device for receiving messages, namely a sort of tangent galvanometer, with copper damper to the suspended needle, the deflections being observed by watching through a reading telescope the image of a scale reflected from the polished side of the magnet or from a small mirror carried by it. Subsequently he abandoned this subjective method for the objective plan in which a spot of light from a lamp is reflected by the mirror upon a scale. It is probably true that the idea of thus using the mirror arose from noticing the reflection of light from the monocle which Thomson, being short-sighted, wore round his neck on a ribbon.

The first attempt to lay the Atlantic cable was made in 1857 and failed, and in subsequent endeavours Thomson played a more active part. His discovery that the conductivity of copper was greatly affected — to an extent of 30 or 40 per cent. — by its purity led him to organise a system of testing conductivity at the factory where the additional lengths were being made, and he was in charge of the test-room on board the Agamemnon, which in 1858 was employed in cable-laying in the Atlantic. Whitehouse was unable to join the expedition, and Thomson, at the request of the directors, also undertook the post of electrician without any recompense, though the tax on his time and energies was great.

After various mishaps, success crowned the promoters' efforts. Throughout the voyage Thomson's mirror galvanometer was used for the continuity tests and for signalling to shore, with a battery of seventy-five Daniell's cells. The continuity was reported perfect, and the insulation improved on submersion. On 5 Aug. the cable was handed over to Whitehouse and reported to be in perfect condition. Clear messages were interchanged, but the insulation was soon found to be giving way, and on 20 Oct., after 732 messages had been conveyed, the cable spoke no more. The cause of the collapse was the mistaken use in defiance of Thomson's tested conclusions, by Whitehouse, of induction coils working at high voltage. Thomson's self-abnegation and forbearance throughout this unfortunate afiair are almost beyond belief. He would not suffer any personal slight to interfere with his devotion to a scientific enterprise.

During the next eight years Thomson sought to redeem the defeat. Throughout the preparations for the cables of 1865 and 1866, the preliminary trials, the interrupted voyage of 1865 when 1000 miles were lost, the successful voyage of 1866, when the new cable was laid and the lost one recovered and completed, Thomson was the ruling spirit, and his advice was sought and followed. On his return from the triumphant expedition he was knighted. He had in the meantime made further improvements in conjunction with Cromwell Fleetwood Varley [q. v.]. In 1867 he patented the siphon recorder, and, in conjunction with Fleeming Jenkin [q. v.], the curb-transmitter. He was consulted on practically every submarine cable project from that time forth. In 1874 Thomson was elected president of the Society of Telegraph Engineers, of which, in 1871, he had been a foundation member and vice-president. In 1876 he visited America, bringing back with him a pair of Graham Bell's earliest experimental telephones. He was president of the mathematical and physical section of the British Association of that year at Glasgow. In the winter of 1860-1 Thomson had met with a severe accident. He fell on the ice when curling at Largs, and broke his thigh. The accident left him with a slight limp for the rest of his life.

Meanwhile much beside the submarine cable occupied Thomson's fertile mind, and his researches were incessant. In 1859-60 he was studying atmospheric electricity. For this end he invented the water-dropping collector, and vastly improved the electrometer, which he subsequently developed into the elaborate forms of the quadrant instrument and other types. He also measured electro-statically the electromotive force of a Daniell's cell, and investigated the potentials required to give sparks of different lengths in the air. At the same time he urged the application of improved systems of electric measurement and the adoption of rational units. In 1861 he cordially supported the proposal of Bright and Clark to give the names of ohm, volt, and farad to the practical units based on the centimetre-gramme-second absolute system, and on his initiative was formed the Committee of Electrical Standards of the British Association, which afterwards went far in perfecting the standards and the methods of electrical measurement. He was largely responsible for the international adoption of the system of units by his advocacy of them at the Paris Congress in 1881. He was an uncompromising advocate of the metric system, and lost no opportunity of denouncing the 'absurd, ridiculous, time-wasting, brain-destroying British system of weights and measures.'

A long research on the electrodynamic qualities of metals, thermoelectric, thermo-elastic, and thermomagnetic, formed the subject of his Bakerian lecture of 1856, which occupies 118 pages of the reprinted 'Mathematical and Physical Papers.' He worked long also at the mathematical theory of magnetism in continuation of Faraday's labours in diamagnetism. Thomson set himself to investigate Faraday's conclusions mathematically. As early as 1849 and 1850, with all the elegance of a mathematical disciple of Poisson and Laplace, he had discussed magnetic distributions by aid of the hydrodynamic equation of continuity. To Thomson are due the now familiar terms 'permeability' and 'susceptibility' in the consideration of the magnetic properties of iron and steel. In these years Thomson was also writing on the secular cooling of the earth, and investigating the changes of form during rotation of elastic spherical shells. At the same time he embarked with his friend Professor Peter Guthrie Tait [q. v. Suppl. II] on the preparation of a text-book of natural philosophy. Though the bulk of the writing was done by Tait, the framework of it thought and its most original parts are due to Thomson. The first part of the first volume of Thomson and Tait's 'Treatise on Natural Philosophy' was published in 1867, the second part only in 1874. No more was published, though the second edition of the first part was considerably enlarged. The book had the effect of revolutionising the teaching of natural philosophy.

Thomson's contributions to the theory of elasticity are no less important than those he made to other branches of physics. In 1867 he communicated to the Royal Society of Edinburgh a masterly paper 'On Vortex Atoms' ; seizing on Hehnholtz's proof that closed vortices could not be produced in a liquid perfectly devoid of internal friction, Thomson showed that if no such vortex could be artificially produced, then if such existed it could not be destroyed, but that being in motion and having the inertia of rotation, it would have elastic and other properties. He showed that vortex rings (like smokerings in air) in a perfect medium are stable, and that in many respects they possess qualities essential to the properties of material atoms — permanence, elasticity, and power to act on one another through the medium at a distance. The different kinds of atoms known to the chemist as elements were to be regarded as vortices of different degrees of complexity. The vortex-atom theory was linked to Ms other important researches on gyrostatic problems. Though he came to doubt whether the vortex-atom hypothesis was adequate to explain all the properties of matter, the conception bears witness to his great mental power.

In 1870 Lady Thomson, whose health had been failing for several years, died. In the same year the University of Glasgow was removed to the new buildings on Gilmore Hill, overlooking the Kelvin River. Thomson had a house here in the terrace assigned for the residences of the professors, adjoining his laboratory and lecture-room.

On 17 June 1874 he married Prances Anna, daughter of Charles F. Blandy of Madeira, whom he had met on cable-laying expeditions. In 1875 he built at Netherhall, near Largs, a mansion in the Scottish baronial style ; and in his later life, though he had a London house in Eaton Place, Netherhall was his chief home. From his youth he had been fond of the sea, and had early owned boats on the Qyde. For many years his sailing yacht the Lalla Rookh was conspicuous, and he was an accomplished navigator. His experiences at sea in cable-laying had taught him much, and in return he was now to teach science in navigation. Between 1873 and 1878 he reformed the mariners' compass, on which he undertook to write a series of articles in 'Good Words' in 1873 ; he lightened the moving parts of the compass to avoid protracted oscillations, and to facilitate the correction of the quadrantal and other errors arising from the magnetism of the ship's hull. At first the Admiralty would have none of it. Even the astronomer royal condemned it. 'So much for the astronomer royal's opinion,' he ejaculated. But the compass won its way ; and until recently was all but universally adopted both in the navy and in the mercantile marine (see, for Thomson's contributions to navigation, his *Popular Lectures*, vol. iii., and the Kelvin Lecture (1910) of Sir J. A. Ewing).

Dissatisfied with the clumsy appliances used in sounding, when the ship had to be stopped before the sounding line could be let down, Thomson devised in 1872 the well-known apparatus for taking flying soundings by using a line of steel piano wire. He had great faith in navigating by use of sounding fine, and delighted to narrate how, in 1877, in a time of continuous fog, he navigated his yacht all the way across the Bay of Biscay into the Solent trusting to soundings only. He also published a set of Tables for facilitating the use of Sumner's method at sea. He was much occupied with the question of the tides, not merely as a sailor, but because of the interest attending their mathematical treatment in connection with the problems of the rotation of spheroids, the harmonic analysis of their complicated periods by Fourier's methods, and their relation to hydrodynamic problems generally. He invented a tide-predicting machine, which will predict for any given port the rise and fall of the tides, which it gives in the form of a continuous curve recorded on paper ; the entire curves for a whole year being inscribed by the machine automatically in about four hours. Further than this, adopting a mechanical integrator, the device of his ingenious brother, James Thomson, he invented a harmonic analyser — the first of its kind — capable not only of analysing any given periodic curve such as the tidal records and exhibiting the values of the coefficients of the various terms of the Fourier series, but also of solving differential equations of any order.

Wave problems always had a fascination for Thomson, and he was familiar with the work of the mathematicians Poisson and Cauchy on the propagation of wave-motion. In 1871 Helmholtz went with him on the yacht Lalla Rookh to the races at Inverary, and on some longer excursions to the Hebrides. Together they studied the theory of waves, 'which he loved,' says Helmholtz, 'to treat as a race between us.' On calm days he and Helmholtz experimented on the rate at which the smallest ripples on the surface of the water were propagated. Almost the last publications of Lord Kelvin were a series of papers on 'Deep Sea Ship Waves,' communicated between 1904 and 1907 to the Royal Society of Edinburgh. He also gave much attention to the problems of gyrostatics, and devised many forms of gyrostat to elucidate the problems of kinetic stability. He held that elasticity was explicable on the assumption that the molecules were the seat of gyrostatic motions. A special opportunity of practically applying such theories was offered him by his appointment as a member of the admiralty committee of 1871 on the designs of ships of war, and of that of 1904-5 which resulted in the design of the Dreadnought type of battleship.

In 1871 he was president of the British Association at its meeting in Edinburgh. His presidential address ranged luminously over many branches of science and propounded the suggestion that the germs of life might have been brought to the earth by some meteorite. With regard to the age of the earth he had already from three independent lines of argument inferred that it could not be finite, and that the time demanded by the geologists and biologists for the development of life must be finite. He himself estimated it at about a hundred million of years at the most. The naturalists, headed by Huxley, protested against Thomson's conclusion, and a prolonged controversy ensued. He adhered to his propositions with unrelaxing tenacity but unwavering courtesy. 'Gentler knight there never broke a lance,' was Huxley's dictum of his opponent. His position was never really shaken, though the later researches of John Perry, and the discovery by R. J. Strutt of the degree to which the constituent rocks of the earth contain radioactive matter, the disgregation of which generates internal heat, may so far modify the estimate as somewhat to increase the figure which he assigned. In his presidential address to the mathematical and physical section of the British Association at York in 1881 he spoke of the possibility of utilising the powers of Niagara in generating electricity. He also read two papers, in one of which he showed mathematically that in a shunt dynamo best economy of working was attained when the resistance of the outer -circuit was a geometric mean between the resistances of the armature and of the shunt. In the other he laid down the famous law of the economy of copper lines for the transmission of power.

Thomson's lively interest in the practical — indeed the commercial — application of science, led him to study closely the first experiments in electric lighting. Such details as fuses and the suspension pulleys with differential gearing by which incandescent lamps can be raised or lowered absorbed some of his attention. He gave evidence before the parliamentary committee on electric fighting of 1879, and discussed the theory of the electric transmission of power, pointing out the advantage of high voltages. The introduction into England in 1881 of the Faure battery accumulator by which electricity could be economically stored excited him greatly. Thomson's various inventions — electrometers, galvanometers, siphon-recorders, and his compasses were at first made by James White, an optician of Glasgow. In White's firm, which became Kelvin & White, Limited, he was soon a partner, taking the keenest commercial interest in its operations, and frequenting the factory daily to superintend the construction. To meet demands for new measuring instruments he devised from time to time potential galvanometers, ampere gauges, and a whole series of standard electric balances for electrical engineers. His patented inventions thus grew very numerous. Up to 1900 they numbered fifty-six. Of these eleven related to telegraphy, eleven to compasses and navigation apparatus, six to dynamo machines or electric lamps. twenty-five to electric measuring instruments, one to the electrolytic production of alkali, and two to valves for fluids. Helmholtz, visiting Thomson in 1884, found him absorbed in regulators and measuring apparatus for electric lighting and electric railways. 'On the whole,' Helmholtz wrote, 'I have an impression that Sir William might do better than apply his eminent sagacity to industrial undertakings ; his instruments appear to me too subtle to be put into the hands of uninstructed workmen and officials. . . . He is simultaneously revolving deep theoretical projects in his mind, but has no leisure to work them out quietly.' But he shortly added ' I did Thomson an injustice in supposing him to be wholly immersed in technical work ; he was full of speculations as to the original properties of bodies, some of which were very difficult to follow ; and, as you know, he will not stop for meals or any other consideration.'

Thomson's teaching was always characterised by a peculiar fondness for illustrating recondite notions by models. The habit was possibly derived from Faraday ; but he developed it beyond precedent. 'I never satisfy myself,' he wrote,. 'until I can make a mechanical model of a thing. If I can make a mechanical model, I can understand it. As long as I cannot make a mechanical model all the way through I cannot understand it.' He built up chains of spinning gyrostats to show how the rigidity derived from the inertia of rotation might illustrate the property of elasticity. The vortex-atom presented a dynamical picture of an ideal material system. He strung together little balls and beads with sticks and elastic bands to demonstrate crystalline dynamics. Throughout all his mathematical speculation his grip of the physical reality never left him, and he associated every mathematical process with a physical significance.

In 1893 Lord Kelvin astonished the audience at the Royal Institution by a discourse on 'Isoperimetrical Problems,' endeavouring to give a popular account of the mathematical process of determining a maximum or minimum, which he illustrated by Dido's task of cutting an ox- hide into strips so as to enclose the largest piece of ground ; by Horatius Codes' prize of the largest plot that a team of oxen could plough in a day ; and by the problem of running the shortest railway fine between two given points over uneven country. On another occasion he entertained the Royal Society with a discourse on the 'Homogeneous Partitioning of Space,' in which the fundamental packing of atoms was geometrically treated, and he incidentally propounded the theory of the designing of wall-paper patterns.

In 1884 Thomson delivered at Baltimore twenty lectures 'On Molecular Dynamics and the Wave Theory of Light.' His hearers, mostly accomplished teachers and professors, numbered twenty-six. The lectures, reported verbatim at the time, were issued with many revisions and additions in 1904. They show Thomson's speculative genius in full energy and brilliance. Ranging from the most recondite problems of optics to speculations on crystal rigidity, the tactics of molecules and the size of atoms, they almost embody a new conception of the ultimate dynamics of physical nature. Thomson accepted little external guidance. He never accepted Maxwell's classical generalisation that the waves of fight were essentially electro-magnetic displacements in the ether, although in 1888 he gave a nominal adhesion to the theory, and in his preface in 1893 to Hertz's 'Electric Waves,' he used the phrase 'the electromagnetic theory of fight, or the undulatory theory of magnetic disturbance.' But later he withdrew his adhesion, preferring to think of things in his own way. Yet to the last he took an intense interest in the most recent discoveries. He discussed the new conception of electrons — or 'electrions,' as he called them — and read again and again Mr. Ernest Rutherford's book on 'Radioactivity' (1904). He objected, however, in toto to the notion that the atom was capable of division or disintegration. In 1903, in a paper called ' Æpinus Atomized,' he reconsidered the views of Æpinus and Father Boscovich from the newest standpoint, modifying the theory of Æpinus to suit the notion of 'electrions.'

Honours fell thickly on Thomson in his later life. He was thrice offered and thrice declined the Cavendish professorship of physics at Cambridge. He had been made a fellow of the Royal Society in 1851, and in 1883 had been awarded the Copley medal. He was president from 1890 to 1894. He was raised to the peerage in 1892 under the style and title of Baron Kelvin of Largs in the county of Ayr. On 15-17 June 1896 the jubilee of his Glasgow professorship was impressively celebrated by both the town and university m the presence of guests who included the chief men of science of the world. He resigned his professorship in 1899. He was one of the original members of the Order of Merit founded in 1902, was a grand officer of the Legion of Honour, and held the Prussian Order Pour le Mérite. In 1902 he was named a privy councillor. In 1904 he was elected chancellor of the University of Glasgow and published his installation address. He was a member of every foreign academy, and held honorary degrees from almost every university.

After taking part in the British Association meeting of 1907 at Leicester, where he lectured on the electronic theory of matter and joined with keenness in discussions of radioactivity and kindred questions, he went to Aix-les-Bains for change. He had barely reached his home at Largs in September when Lady Kelvin was struck down with a paralytic seizure. Lord Kelvin's misery at her helpless condition was intense, and his vitality was greatly diminished. He had himself suffered for fifteen years from recurrent attacks of facial neuralgia, and a year before underwent a severe operation. A chill now seized him, and after a fortnight's prostration he died on 17 Dec. He was buried in Westminster Abbey on 23 Dec. 1907. Lady Kelvin survived him.

In politics he was, up to 1885, a broad liberal; but as an Ulsterman he became an ardent unionist on the introduction of the home rule bill in 1886, and spoke at many political meetings in the West of Scotland in the years which followed. In religion Kelvin was an Anglican — at least from his Cambridge days — but when at Largs attended the Presbyterian Free Church. A simple, unobtrusive, but essential piety was never clouded. He had a deep detestation of ritualism and sacerdotalism, and he denounced spiritualism as a loathsome and vile superstition. But his studies led him again and again to contemplate a beginning to the order of things, and he more than once publicly professed his belief in creative design. Kindly hearted and exceptionally modest, he carried through life intense love of truth and insatiable desire for the advancement of natural knowledge. His high ideals led him to underrate his achievements. 'I know,' he said at his jubilee, 'no more of electric and magnetic force, or of the relation between ether, electricity, and ponderable matter, or of chemical affinity, than I knew and tried to teach to my students in my first session.'

He strove whole-heartedly through life to reach a great comprehensive theory of matter. If he failed to find in the equations of dynamics an adequate and necessary foundation for the theories of electricity and magnetism, or to assign a dynamical constitution to the luminiferous ether, it is because the physical nature of electricity and of ether is probably more fundamental than that of matter itself. But he never allowed his intellectual grasp of physical matters to be clouded by metaphysical cobwebs, and insistently strove for precision of language.

Lord Kelvin's portrait was painted by Lowes Dickinson in 1869 for Peter house. Another portrait by (Sir) Hubert von Herkomer, R.A.,was presented to Glasgow University in 1892. A third portrait by Sir W. Q. Orchardson was presented to the Royal Society by the fellows in 1899. A fourth portrait, by Mr. W. W. Ouless, R.A., was exhibited at the Royal Academy in 1902. A statue was erected in Belfast in 1910. A Kelvin lectureship in his memory was funded in 1908 at the Institution of Electrical Engineers, and lectures have been given by S. P. Thompson (1908), Sir J. A. Ewing (1910), and H. G. J. Du Bois (1912).

To scientific societies' proceedings or journals Kelvin contributed 661 papers between 1841 and 1908. In 1874 he collected his papers in 'Electrostatics and Magnetism.' In 1882 he began to collect and revise his scattered mathematical and physical papers. Three volumes were issued before his death, and the collection was completed in five volumes (1882-1911) under the editorship of Sir Joseph Larmor. Thomson also wrote for the 'Encyclopædia Britannica' of 1879 the long and important articles on Elasticity and on Heat.