Thomson, William, Baron Kelvin

(1824-1907), mathematician and physicist

by Crosbie Smith

© Oxford University Press 2004 All rights reserved

Thomson, William, Baron Kelvin (1824-1907), mathematician and physicist, was born on 26 June 1824 at College Square, Belfast, second son among seven children of James Thomson (1786-1849), professor of mathematics in the collegiate department of the Belfast Academical Institution, and his wife, Margaret Gardner (c.1790-1830), whose mother was Elizabeth Patison of Kelvin Grove to the west of Glasgow. After Margaret's death in 1830 James Thomson assumed full responsibility for the education of his children, and two years later took up his appointment to the Glasgow College chair of mathematics. The family lived in the old college off the High Street during the six-month winter sessions but in the summer they moved to rented accommodation at various localities on the Firth of Clyde, most notably Arran. Although William and his elder brother James Thomson had attended some school classes at the Academical Institution (and won first and second prizes respectively in 1831), they had received almost no formal schooling. Having attended as listeners their father's junior class in Glasgow, the brothers matriculated in 1834 when William was just ten.

Making a Cambridge wrangler
For the next six years the brothers were constantly together, James increasingly committed to engineering problems and William to mathematics and natural philosophy. Early in 1835 their older sister Anna reported that 'James and William are quite delighted just now, having been making an electrical machine. It gives strong shocks' (E. King, 135n.). The following year William told his eldest sister, Elizabeth, that 'We have not begun the steam-engine, for papa was not wanting us to do it' (E. King, 138). By the end of the year the brothers had each built an electrical machine, James's machine apparently larger and more carefully finished than his younger brother's but the latter was well satisfied with the utility of his production, its power demonstrated by subjecting other members of the family to frequent shocks. In due course the brothers were allocated a room in the college house where they pursued their mechanical and philosophical researches. In college classes William took first prize, his physically less robust elder brother often coming second.

By May 1839 the brothers were eligible for the degree of BA, but Thomson did not take the degree because he planned to enter Cambridge University as an undergraduate. A further session (1839-40) saw the brothers attending the senior natural philosophy class which, initially under the ailing William Meikleham, passed to the control of John Pringle Nichol, radical professor of astronomy. At the end of the session William won a university medal for an 85-page essay on 'The figure of the earth' which drew on advanced texts by Laplace, Poisson, and Airy. In that summer the Thomsons and the Nichols travelled together to the Rhine. Fired by Nichol's enthusiasm for Joseph Fourier, Thomson took with him a library copy of Fourier's Théorie analytique de la chaleur (1822), and secretly read right through the treatise when he was supposed to be giving his undivided attention to the German language. He nevertheless quickly announced to his incredulous father that the Edinburgh professor of mathematics, Philip Kelland, was mistaken in recent criticisms of Fourier's mathematics. The outcome was the publication of William Thomson's first paper, under the pseudonym 'P. Q. R.', in the Cambridge Mathematical Journal. He had only just turned sixteen.

Thomson was formally entered at Peterhouse on 6 April 1841 but did not come into residence as an undergraduate until the following October. The connections of the mathematical coach, William Hopkins, with Peterhouse probably influenced the choice of college. In any case, Cambridge offered the best mathematical training available anywhere in Britain, training which could open careers in the church and in the legal profession as well as in the universities. Hopkins himself recognized deficiencies in undergraduates who came to Cambridge by way of the Scottish universities with their emphasis on a broad philosophical education rather than on rigorous mathematical practice: 'men from Glasgow and Edinburgh require a great deal of drilling' (Smith and Wise, 55). Only days after arriving in Cambridge, Thomson was singled out as the likely senior wrangler of his year.

Thomson's Cambridge years were lived with characteristic intensity. He quickly made the acquaintance of distinguished Trinity College Scots such as D. F. Gregory (editor of the Cambridge Mathematical Journal) and Archibald Smith (senior wrangler in 1836). With one eye on his father's financial imperatives to avoid dissipation and the other on Cambridge's moral strictures designed to shape its wranglers, he attempted to adhere to highly disciplined routines of reading and exercising. His private diary (1843) suggests a different story. Rising at six or seven on February mornings, his days were filled by passionate rather than disciplined involvement in walking, skating, swimming, reading, and, above all, wide-ranging discussions with a large circle of friends extending well into the night. Against the wishes of his father he became increasingly enthusiastic about rowing. By the end of his second year he had joined the college eight and towards the close of 1843 won the Colquhoun silver sculls for single-seater boats. The family too had been won over. As his sister Anna perceptively observed:

I got your letter today containing all your reasons for having joined the boat races, which has one good effect at least--that of convincing us all that you are a most excellent logician, and that ... you possess the excellent talent of being able to defend yourself most eloquently when anything you do is in the least blamed. (Smith and Wise, 78)
As an enthusiastic musician and player of the cornet, William also became a founder member of the Cambridge University Music Society in the spring of 1844.

From his second undergraduate year Thomson's coaching took the form of constant rehearsals according to Hopkins's training methods. In the summer of 1844 he joined Hopkins's reading party, which included his friends Hugh Blackburn (later professor of mathematics at Glasgow) and W. F. L. Fischer (later professor of natural philosophy at St Andrews), at Cromer in the months leading up to the Senate House examinations. In January 1845, twelve mathematical examination papers later, Thomson emerged as second wrangler, after Stephen Parkinson of St John's College. One of the examiners, R. L. Ellis, remarked to a fellow examiner that 'You and I are just about fit to mend his [Thomson's] pens' (Thompson, 97-8) while William Whewell noted to J. D. Forbes that 'Thomson of Glasgow is much the greatest mathematical genius: the Senior Wrangler was better drilled' (ibid., 103). The fault lay not with Hopkins, however, but with Thomson's irrepressible zeal for physical problems that interested him. In the subsequent Smith's prize examination the order was reversed. By June 1845 he had been appointed a fellow of Peterhouse and in the same year took over as editor of the Cambridge Mathematical Journal which he soon expanded into the Cambridge and Dublin Mathematical Journal.

The mathematical theory of electricity
During his undergraduate years Thomson had published eleven papers in the Journal which, under the editorship of first Gregory and latterly Ellis, represented the young and reforming generation of Cambridge mathematicians. Whigs both in mathematics and politics, as Thomson noted approvingly, the three successive editors regarded Fourier as their inspiration (Smith and Wise, 174). On the basis of Fourier's treatment of heat conduction, Thomson's 'On the uniform motion of heat in homogeneous solid bodies, and its connexion with the mathematical theory of electricity' (1841-2) constructed a mathematical analogy between electrostatic induction and heat conduction. Instead of forces acting at a distance over empty space, he viewed electrical action mathematically as represented by a series of geometrical lines or 'surfaces of equilibrium' intersecting at right angles with the lines of force. These surfaces would later be called equipotential lines or surfaces. At each stage he correlated the mathematical forms in thermal and electrical cases, but avoided any physical inferences about the nature of electricity as an actual contiguous action like fluid flow.

Thomson soon deployed the analogy to reformulate the action-at-a-distance mathematical theory of electricity (developed by Poisson and employed in Robert Murphy's Cambridge textbook on electricity) into Faraday's theory of contiguous action, though without Faraday's quantity-intensity distinction. In the analogy, force at a point was analogous to temperature gradient while specific inductive capacity of a dielectric was analogous to conductivity. Over the next decade or so Thomson would search for the mechanism of propagation, perhaps in terms of an elastic-solid model such as that used to explain the wave nature of light, or in terms of a hydrodynamical model which would show not only electricity, magnetism, and heat, but ponderable matter itself, to result from the motions of an all-pervading fluid medium or ether. This quest for a unified field theory acquired special urgency once he adopted a dynamical theory of heat about 1850. However, Thomson also pursued other analogies as problem-solving geometrical techniques, including the method of images (1847) which deployed a simple analogy from geometrical optics to solve complex problems in electrostatics.

By 1850 Thomson had contributed more than thirty papers to the Cambridge Mathematical Journal; two years later he relinquished its editorship, his strenuous efforts to expand it into a national journal for mathematical sciences having been hampered by what he saw as the stubborn preponderance of contributions from pure mathematicians and correspondingly few papers on physical subjects. With few converts to his own style of electrical science, he especially welcomed in 1854 the enthusiasm of a recent Cambridge graduate and second wrangler, James Clerk Maxwell, for following through Thomson's insights into the mathematical theories of electricity and magnetism.

The Glasgow chair and the motive power of heat
As early as 1843 Thomson's father had begun to prepare him as a potential successor to the Glasgow professor of natural philosophy, Meikleham, who had been unable to conduct the class since 1839. In alliance with Nichol and the new professor of medicine, another William Thomson, James Thomson agreed that a mere mathematician, unskilled in lecture demonstrations, could not command the class. In order to fill this lacuna in his training, Thomson was dispatched to Paris after graduation from Cambridge. His brief was to observe, and if possible to participate in, a full range of experimental practice, from lecture demonstrations by the finest of the French experimentalists to the physical laboratory of Victor Regnault at the Collège de France. Thomson later acknowledged his principal debt to the French physicien as 'a faultless technique, a love of precision in all things, and the highest virtue of the experimenter--patience' (Thompson, 1154).

Regnault's accurate measurements on the properties of steam and other gases were being funded by the French government with a view to improving the efficiency of heat engines. A year earlier James had written from William Fairbairn's Thames shipbuilding works to his younger brother asking if he knew who it was that had offered an account of the motive power of heat in terms of the mechanical effect (or work done) by the 'fall' of a quantity of heat from a state of intensity (high temperature as in a steam-engine boiler) to a state of diffusion (low temperature as in the condenser), analogous to the fall of a quantity of water from a high to a low level in the case of water-wheels. While in Paris, Thomson located Emile Clapeyron's memoir (1834) on the subject but failed to locate a copy of Sadi Carnot's original treatise (1824). At the same time he began to consider solutions to problems in the mathematical theory of electricity (notably that of two electrified spherical conductors, the complexity of which had defied Poisson's attempts to obtain a general mathematical solution) in terms of mechanical effect given out or taken in, analogous to the work done or absorbed by a water-wheel or heat engine. He therefore recognized that measurements of electrical phenomena and of steam were both to be treated in absolute, mechanical and, above all, engineering terms. The contrast to the action-at-a-distance approach of Laplace and Poisson, as well as to Michael Faraday's non-mechanical perspective, was striking.

After returning to Cambridge, Thomson bided his time by coaching four or five pupils during the long vacation and then taking on the duties of college lecturer in mathematics from October 1845. The death of Professor Meikleham the following May publicly opened the campaign for the succession, a competition which ended with the unanimous election of Thomson to the Glasgow chair on 11 September 1846. Six years later, in September 1852, he married his second cousin, Margaret Crum, daughter of the prosperous cotton manufacturer and calico-printer Walter Crum FRS, of Thornliebank, who had a strong interest in industrial chemistry. The Crums had always been closely associated with the Thomsons and the couple had known each other since childhood. Soon after the marriage, however, Margaret's health broke down and she remained, despite all attempts at finding a cure, an invalid until her death in 1870.

The focal point of Thomson's academic life was the natural philosophy classroom. Filling a chair which had been largely neglected for the seven years since he himself had attended the class as an undergraduate, the 22-year-old professor's most immediate challenge was to fashion his authority over a class of more than 100 students and to establish his credibility within a college still largely ruled by a 75-year-old principal, Duncan Macfarlan, who deployed all his power to oppose academic and political reform. Yet the election had actually tipped the numerical balance of reforming over tory professors within the college, and the reformers therefore gave the young professor a practical vote of confidence when they won financial backing from the college for the rapid replacement of the existing stock of physical apparatus. Thomson immediately embarked on an investment programme which, over the first few years, saw the classroom equipped with the latest and finest electrical, acoustical, and optical apparatus and instruments from prestigious instrument makers such as Watkins and Hill in London and Pixii in Paris. Travelling to London and Paris in the summer following his first session with the class, he told his brother James that he aimed to see for himself the kind of apparatus, 'on the best possible scale for a lecture room', deployed by celebrated natural philosophers such as Faraday (Thompson, 202).

Early in 1847 Thomson rediscovered a model air engine, presented to the college classroom in the late 1820s by its designer, Robert Stirling, but long since clogged with dust and oil. Having joined his elder brother as a member of the Glasgow Philosophical Society in December 1846, Thomson addressed the society the following April on issues raised by the engine when considered as a material embodiment of the Carnot-Clapeyron account of the motive power of heat. If, he suggested, the upper part of the engine were maintained at the freezing point of water by a stream of water and if the lower part were held in a basin of water also at the freezing point, the engine could be cranked forward without the expenditure of mechanical effect (other than to overcome friction) because there existed no temperature difference. The result, however, would be the transference of heat from the basin to the stream and the gradual conversion of all the water in the basin into ice. Such considerations raised two fundamental puzzles: on the one hand, the production of seemingly unlimited quantities of ice without work, and on the other hand the seeming 'loss' of work which might have been produced from heat generated at high temperature if that heat were instead used to melt ice. As he explained the second puzzle to J. D. Forbes:

It seems very mysterious how power can be lost in such a way [by the conduction of heat from hot to cold], but perhaps not more so than that power should be lost in the friction of fluids (a plumb line with the weight in water for instance) by which there does not seem to be any heat generated, nor any physical change effected. (Smith and Wise, 294)
At the close of his first Glasgow College session Thomson attended the Oxford meeting of the British Association for the Advancement of Science. He had long been acquainted with these annual spectacles--as long before as 1840 he and James had played supporting roles during the association's Glasgow meeting. However, 1847 marked his first appearance as a professor of natural philosophy and author of a string of avant-garde articles on electricity. It also marked his first encounter with James Prescott Joule who had been arguing since 1843 for the mutual convertability of work and heat according to an exact mechanical equivalence. Thomson immediately recognized in Joule's claim for the conversion of work into heat an answer to the puzzle of what happened to the seeming 'loss' of that useful work which might have been done but which was instead 'wasted' in conduction and fluid friction. Unconvinced by Joule's complementary claim that such heat could in principle be converted into work, Thomson remained deeply perplexed by what seemed to him the irrecoverable nature of that heat. Furthermore, he could not accept Joule's rejection of the Carnot-Clapeyron theory, with its 'fall' of heat from high to low temperature, in favour of mutual convertibility.

With regard to the first puzzle raised by the Stirling engine, however, James Thomson quickly pointed out the implication that, since ice expands on freezing, it could be made to do useful work: in other words, the arrangement would function as a perpetual source of power, long held to be impossible by almost all orthodox engineers and natural philosophers. He therefore concluded that avoidance of this implication would require that the freezing point be lowered with increase of pressure. His prediction, and its subsequent experimental confirmation in William Thomson's laboratory, did much to persuade the brothers of the value of the Carnot-Clapeyron theory.

Within a year Thomson had added another feature to the Carnot-Clapeyron construction, namely, an absolute scale of temperature. In presentations to the Glasgow and Cambridge philosophical societies in 1848 he explained that an air-thermometer scale provided 'an arbitrary series of numbered points of reference sufficiently close for the requirements of practical thermometry'. In an absolute thermometric scale 'a unit of heat descending from a body A at the temperature T° of this scale, to a body B at the temperature (T-1)°, would give out the same mechanical effect [motive power or work], whatever be the number T'. Its absolute character derived from its being 'quite independent of the physical properties of any specific substance' (Thomson, 1.104). In other words, unlike the air-thermometer which depended on a particular gas, he deployed the waterfall analogy to establish a scale of temperature independent of the working substance.

The Glasgow College natural philosophy classroom had long been complemented by an adjacent professor's room and apparatus room for the storage of instruments and the preparation of lecture demonstration apparatus. Having worked with his brother James since childhood on mechanical and philosophical apparatus in the college, and having participated himself in the Parisian physical laboratory of Regnault, Thomson also used these spaces for the production of new scientific knowledge, aided by his classroom assistant Robert Mansell and, increasingly, by enthusiastic students. The location of the college near the heart of a growing industrial city also provided Thomson with many material resources for experimental work. Indeed, he later declined the offer of the new Cambridge chair of experimental physics on the grounds that 'the convenience of Glasgow for getting mechanical work done' gave him 'means of action which I could not have in any other place' (Thompson, 563).

Thomson's lectures to the experimental natural philosophy class became increasingly linked to the experimental practices of the 'apparatus room'. Thus in the 1849/50 session he instructed his class on the skills required for thermometry, insisting that, for instruments of the highest precision, accurate testing of the suitability of the glass tube in the laboratory was necessary before the thermometer was made by the instrument maker. Indeed, such testing, calibration, and standardization soon became another characteristic function of the Glasgow research and teaching programme. The professor and his assistant deployed one such highly sensitive thermometer to investigate the depression of the freezing point of ice under pressure. The results, confirming his brother's prediction of the lowering of the freezing point in accordance with Carnot's theory, were announced to the class and to his opposite number in Edinburgh, J. D. Forbes, prior to being made public at a meeting of the Royal Society of Edinburgh.

When Thomson acquired from his colleague Lewis Gordon (professor of civil engineering and mechanics) a copy of the very rare Carnot treatise, he presented an exposition, especially in the light of the issues raised by Joule, to the Royal Society of Edinburgh. In particular, Thomson read Carnot as claiming that any work obtained from a cyclical process can only derive from transfer of heat from high to low temperature. From this claim, together with a denial of perpetual motion, it followed that no engine could be more efficient than a perfectly reversible engine (Carnot's criterion for a perfect engine). It further followed that the maximum efficiency obtainable from any engine operating between heat reservoirs at different temperatures would be a function of those temperatures (Carnot's function).

The science of energy
Prompted by the competing investigations of Macquorn Rankine and Rudolf Clausius, Thomson finally laid down two propositions in 1851, the first a statement of Joule's mutual equivalence of work and heat and the second a statement of Carnot's criterion for a perfect engine. His long-delayed acceptance of Joule's proposition rested on a resolution of the problem of the irrecoverability of mechanical effect lost as heat. He now believed that work 'is lost to man irrecoverably though not lost in the material world'. Thus although:

no destruction of energy can take place in the material world without an act of power possessed only by the supreme ruler, yet transformations take place which remove irrecoverably from the control of man sources of power which ... might have been rendered available. (Smith and Wise, 329)
In other words, God alone could create or destroy energy (i.e., energy was conserved in total quantity) but human beings could make use of transformations of energy, for example in water-wheels or heat-engines.In a private draft Thomson referred these transformations to a universal statement that 'Everything in the material world is progressive' (Smith and Wise, 330). On the one hand, this statement expressed the geological directionalism of Cambridge dons such as Hopkins and Adam Sedgwick in opposition to the steady-state uniformitarianism of Charles Lyell, but on the other it could be read as agreeing with the radical evolutionary doctrines of the subversive Vestiges of Creation (1844). In his published statement, Thomson opted instead for universal dissipation of energy, a doctrine which reflected the presbyterian (Calvinist) views of a transitory visible creation rather than a universe of ever-upwards progression. Work dissipated as heat would be irrecoverable to human beings, for to deny this principle would be to imply that they could produce mechanical effect by cooling the material world with no limit except the total loss of heat from the world.

This reasoning crystallized in what later became the canonical 'Kelvin' statement of the second law of thermodynamics, first enunciated by Thomson in 1851: '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' (Thomson, 1.179). This statement provided Thomson with a new demonstration of Carnot's criterion of a perfect engine. Having resolved the recoverability issue, he also quickly adopted a dynamical theory of heat, making it the basis of Joule's proposition of mutual equivalence and abandoning the Carnot-Clapeyron notion of heat as a state function (with the corollary that in any cyclic process the change in heat content is zero).

Thomson's 'On a universal tendency in nature to the dissipation of mechanical energy' took the new 'energy' perspective to a wide audience. In this short paper for the Philosophical Magazine the term 'energy' achieved public prominence for the first time and the dual principles of conservation and dissipation of energy were made explicit: 'As it is most certain that Creative Power alone can either call into existence or annihilate mechanical energy, the "waste" referred to cannot be annihilation, but must be some transformation of energy' (Thomson, 1.511). Now the dynamical theory of heat, and with it a whole programme of dynamical (matter-in-motion) explanation, went unquestioned; and now, too, the universal primacy of the energy laws opened up fresh questions about the origins, progress, and destiny of the solar system and its inhabitants. Two years later Thomson told the Liverpool meeting of the British Association that Joule's discovery of the conversion of work into heat by fluid friction, the experimental foundation of the new energy physics, had 'led to the greatest reform that physical science has experienced since the days of Newton' (Thomson, 1.34).

From the early 1850s the Glasgow professor and his new ally in engineering science, Macquorn Rankine, began replacing an older language of mechanics with terms such as 'actual' ('kinetic' from 1862) and 'potential energy'. Within a few years they had been joined by like-minded scientific reformers, most notably the Scottish natural philosophers James Clerk Maxwell and Peter Guthrie Tait and the engineer Fleeming Jenkin. With strong links to the British Association, this informal grouping of 'North British' physicists and engineers was primarily responsible for the construction and promotion of the 'science of energy', inclusive of nothing less than the whole of physical science. Natural philosophy or physics was thus redefined as the study of energy and its transformations. It was a programme which served a wide range of functions. At the level of the Glasgow classroom, consisting largely of students destined for the ministry of the Scottish kirk, Thomson could represent the new physics as a counter to the seductions of enthusiast biblical revivals on the one hand and of evolutionary materialism on the other at a time of considerable instability in Scottish society. At a national level Thomson and his friends could offer through the British Association a powerful rival reform programme to that of the metropolitan scientific naturalists (including T. H. Huxley and John Tyndall) who aimed at a professionalized science free from the perceived shackles of Anglican theology.

To these ends Thomson examined the principal source of all the mechanical effect on earth. Arguing that the sun's energy was too great to be supplied by chemical means or by a mere molten mass cooling, he at first suggested that the sun's heat was provided by vast quantities of meteors orbiting round the sun but inside the earth's orbit. Retarded in their orbits by an etherial medium, the meteors would progressively spiral towards the sun's surface in a cosmic vortex analogous to James's vortex turbines (horizontal water-wheels). As the meteors vaporized by friction, they would generate immense quantities of heat. In the early 1860s, however, he adopted Hermann Helmholtz's version of the sun's heat whereby contraction of the body of the sun released heat over long periods. Either way, the sun's energy was finite and calculable, making possible order-of-magnitude estimates of the limited past and future duration of the sun. In response to Charles Darwin's demand for a much longer time for evolution by natural selection and in opposition to Charles Lyell's uniformitarian geology upon which Darwin's claims were grounded, Thomson deployed Fourier's conduction law to make similar estimates for the earth's age. The limited time-scale of about 100 million years (later reduced) approximated to estimates for the sun's age, but the new cosmogeny was itself evolutionary, offering little or no comfort to strict biblical literalists within the Scottish kirk, especially the recently founded Free Church of Scotland.

The most celebrated textual embodiment of the 'science of energy' was Thomson and Tait's Treatise on Natural Philosophy (1867). Originally intending to treat all branches of natural philosophy, Thomson and Tait in fact produced only the first volume of the Treatise. Taking statics to be derivative from dynamics, they reinterpreted Newton's third law (action-reaction) as conservation of energy, with action viewed as rate of working. Fundamental to the new energy physics was the move here to make extremum conditions, rather than point forces, the theoretical foundation of dynamics. The tendency of an entire system to move from one place to another in the most economical way would determine the forces and motions of the various parts of the system. Variational principles (especially least action) thus played a central role in the new dynamics.

Although never published in treatise form, Thomson's subsequent attempts to produce a unified theory of matter and ether at first centred on the 'vortex atom' which also had a powerful practical foundation in James Thomson's vortex turbines and pumps. From 1867 Thomson drew extensively on Hermann Helmholtz's mathematical work on vortex motion and on Tait's experimental demonstrations of smoke rings. The theory supposed matter to consist of rotating portions of a perfect (that is, frictionless) fluid which continuously filled space. Without internal friction the fluid and everything therein would require a creative act for the production or destruction of rotation and hence of matter. Although the model seemed ideal for simple thermodynamic systems, stability remained a serious problem.

In the wake of Maxwell's electromagnetic theory of light, Thomson defended an elastic-solid model for light waves and remained for the most part highly sceptical of the work of Maxwell's scientific heirs. Grounding his criticism upon the practical success of his own telegraph theory, he continually argued against any methodology which dealt in theoretical entities without a basis in direct sensory perception. These views were forcefully expressed in his Baltimore Lectures, delivered to a distinguished academic audience at Johns Hopkins University in 1884, when he famously asserted: 'I can never satisfy myself until I can make a mechanical model of a thing ... and that is why I cannot get the electro-magnetic theory'. For him, Maxwell's 'beautiful theory of electro displacements' had no foundation in such sensory reality (Smith and Wise, 470).

Towards a system of electrical standards
Thomson's energy physics had its focal point in the physical laboratory. Ever since his participation in Regnault's laboratory practice in 1845 he had resolved to make physical measurements in absolute or mechanical measures. This commitment derived from a realization that electricity could be measured simply in terms of the work done by the fall of a quantity of electricity through a potential just in the way that work was done by the fall of a mass of water through a height. His absolute scale of temperature utilized the same notion of absolute measurement in the case of heat. His first public commitment to a system of absolute units for electrical measurement coincided both with his reading of Wilhelm Weber's contribution 'On the measurement of electric resistance according to an absolute standard' to Poggendorff's Annalen (1851) and with his own 'Dynamical theory of heat' series. In contrast to Weber's system founded on absolute measures of electromotive forces and intensities, Thomson's approach continued to be grounded on measurements of mechanical effect or work. His 1851 paper on the subject deployed Joule's mechanical equivalent to calculate the heat produced by the work done in an electrical circuit. Further applying Joule's earlier relationship of heat to current and resistance squared yielded an expression for resistance in absolute measure.

Production of knowledge in this manner, and the establishment of new functions for laboratory work, led to an increasing number of student volunteer assistants whose labour was divided into a range of skills from basic measurement techniques to involvement in the most advanced experimental practice. By the winter session of 1860 the number of such volunteers had risen to about twenty, a large proportion of whom were deployed on telegraphic work which from the mid-1850s formed an integral part of the laboratory. By 1857, after resistance to further territorial expansion had been overcome, Thomson gained official recognition for the 'physical laboratory' which was now centred in a converted ground-floor space beneath the classroom but which was expanded by the early 1860s by annexation of the redundant Blackstone examination room, also on the ground floor and beneath the apparatus room. Even the college tower, however, was secured for experiments where a long perpendicular drop was required. Constituting the first university physical laboratory in Britain, Thomson's college spaces were replaced by a new, purpose-built laboratory when the whole University of Glasgow transferred to its Gilmorehill site in 1870.

Laboratory concerns with measurement of physical properties of matter soon connected directly with a matter of national importance. Unforeseen retardation effects upon signalling in long submarine telegraph cables threatened the viability of several ambitious projects aimed at giving rapid communication, and hence physical unity, to the scattered British empire. Faraday's qualitative diagnosis of the problem as one of treating underwater cables as Leyden jars of vast capacity for electric charge inspired Thomson's mathematical analysis, using Fourier's techniques, in 1854. His resulting law of the squares showed the dependence of the retardation effect on resistance and inductive capacity and suggested optimum dimensions for the planned Atlantic telegraph. His approach facilitated a new demand for accurate measurement of electrical quantities and his physical laboratory became a major source for the supply of such data. Employing his 1851 method of determining resistances in absolute measure, for example, he drew attention to the great variation in the resistance of different specimens of supposedly pure copper wire manufactured by different firms for use in telegraph cables. The effects on the commercial transmission of signals over long distances would be to reduce profitability and perhaps even render the project unworkable. Accurate measurement of resistances during manufacture would introduce quality control, and hence greater commercial stability, into the highly volatile telegraph business.

Submarine telegraphy
By 1856 Thomson had been made a director of the newly formed Atlantic Telegraph Company. He accompanied the first expedition in 1857 but the parting of the cable after only a few hundred miles had been laid halted the project. The following year he again joined the cable-laying ships, taking with him a new instrument, the marine mirror galvanometer, which he had recently invented and developed in Glasgow. The company's electrician, W. O. W. Whitehouse, remained ashore and Thomson took charge of the electrical test-room aboard HMS Agamemnon, monitoring the condition of the cable. Soon after completion, however, signals became more and more unreliable, culminating in the total failure of communication. Other long-distance cables of the period suffered similar fates. A joint Board of Trade/Atlantic Telegraph Company inquiry published its findings in 1861. Given the scientific representation on the committee, it was not surprising that Whitehouse was portrayed as representing a discredited 'trial-and-error' approach and thus the principal scapegoat for telegraphic failures. The inquiry came down strongly in favour of Thomson's laboratory-centred methods, characterized by accurate measurement and absolute units.

Unable to attend the 1861 Manchester meeting of the British Association on account of a broken thigh sustained while curling on ice at Largs, Thomson had nevertheless been working vigorously behind the scenes to secure the appointment of a committee on standards of electrical resistance. Fleeming Jenkin, only recently introduced to Thomson, handled on his behalf the delicate negotiations among practical electricians and natural philosophers. The outcome was a committee, already heavily weighted towards scientific men, which eventually included most members of the North British energy group: Thomson, Jenkin, Joule, Balfour Stewart, and Maxwell. Throughout the 1860s Thomson played a leading role both in shaping the design of measuring apparatus and in promoting the adoption of an absolute system of physical measurement such that all the units (including resistance) of the system should bear a definite relation to the unit of work, 'the great connecting link between all physical measurements' (Smith and Wise, 687).

In 1865 the largest ship in the world, Isambard Kingdom Brunel's Great Eastern, had been converted for the laying of a new Atlantic cable. Although the cable parted in mid-ocean, the Great Eastern laid another new cable the following season before recovering and completing the severed original. Thomson's direct involvement in the two expeditions brought him a knighthood. Meanwhile, he had secured his first joint telegraphic patent with Jenkin. By 1865 the partnership included the telegraph engineer Cromwell Varley. This pooling of patent property enabled the partners, after protracted legal negotiations, to win favourable financial terms from the Atlantic telegraph companies--£7000 initially to the partners, with a guaranteed £2500 per annum for ten years thereafter. Many other patents followed, including in 1867 that for Thomson's 'siphon recorder' which, by the automatic recording of telegraph signals on moving paper tape, served to minimize waste of time and improve economy of working. Thomson's involvement with ocean telegraphy continued: in 1869, for example, he and Varley were consulting electricians for the French Atlantic cable project. Thomson indeed later claimed that between 1866 and 1883 all signalling on ocean telegraphs was carried out with his instruments.

The instruments of navigation
With the wealth generated by telegraph patents Thomson purchased the 126 ton schooner-rigged yacht Lalla Rookh in 1870, a few months after the death of his wife, Margaret. Laid up during the six-month Glasgow session, the Lalla Rookh served as Thomson's floating laboratory and home throughout the summer as she voyaged among the Western Isles or made much longer cruises to Lisbon (1871), Gibraltar (1872), and Madeira (1874 and 1877). His absences from more familiar workplaces prompted his friend G. G. Stokes to remark that it was 'not easy to say where to find a man who owns a yacht' (Smith and Wise, 736). However, Thomson was never idle. By the early 1870s he was testing both a new sounding apparatus (using pianoforte wire) and a new design of dry-card magnetic compass. The original sounding apparatus aided the cable ship Hooper in the laying of the Brazilian cable in 1873. As the Hooper lay at Madeira for sixteen days, Thomson made the acquaintance of the Blandy family, who lived on the island; he returned aboard the Lalla Rookh a year later and proposed to Frances Anna Blandy (c.1838-1916), who became his second wife in June 1874. There were no children from either of his marriages. During a voyage to North America in 1876 aboard the Cunard liner Russia, Thomson carried out extensive trials with both sounding machine and compass for navigational purposes. Patents quickly followed and soon he was marketing sounder and compass to the prestigious mail-liner companies of the empire, including Cunard, White Star, P. & O., and British India. Thanks to the vigorous support of Jacky Fisher (later first sea lord) the Admiralty in 1889 adopted as its standard compass Thomson's design which retained its naval pre-eminence until the Admiralty began switching to liquid compasses in the 1900s.

Although the laboratory and the Lalla Rookh remained the principal sites for invention, the expansion into manufacturing of telegraphic and navigational instruments required the construction of a separate factory. Thomson's association with the Glasgow instrument maker James White dated from about 1854 and had developed especially during the peak of telegraphic work in the 1860s. By the 1880s the business had been transformed into a large-scale instrument factory, effectively under Thomson's control and devoted to the production of his instruments. By 1900 the firm took the formal title of Kelvin and James White Ltd, with a rigorous division of labour among its 400-strong labour force from drawing office to polishing shop. The firm typically produced some 400 compasses per annum in the 1890s. With the growth of electric lighting and power in the 1880s, the firm added electrical measuring instruments to its production. Thomson, meanwhile, became directly involved in numerous electrical projects which ranged from electric traction for trams and trains to the production of hydroelectric power from Niagara and in the Scottish highlands (especially for the large-scale smelting of aluminium at Foyers by Loch Ness). By the end of his life he had a total of some seventy patents to his credit, either separately or jointly with his business partners.

Politics and peerage
A lifelong Liberal in politics, Thomson split with the Liberal Party at the time of Gladstone's first Home Rule Bill (1886). As president of the West of Scotland Liberal Unionist Association between 1886 and 1892, he therefore took an active role in opposing the moves for an Irish parliament. He firmly believed that liberal values of free trade, equality before the law, and freedom of religion were best preserved within a United Kingdom of Great Britain and Ireland and that local rule was a sure guarantee of sectarian strife, fruitless factionalism among parties, and the stifling of free commerce under protectionist legislation. Through his friendship with Liberal Unionist aristocrats such as Lord Hartington (eighth duke of Devonshire from 1891) and the duke of Argyll, Thomson was well placed for elevation to the peerage in 1892, the first scientist to be thus honoured. With maternal connections to Kelvin Grove and with the university's location adjacent to the River Kelvin since 1870, it was appropriate that William Thomson should have become Baron Kelvin of Largs. Begun in the 1870s, his country seat, Netherhall, near Largs, provided the new peer with a permanent residence, although in his later years he and his wife would frequently travel to their London home at 15 Eaton Place.

The very high level of national and international credibility which Lord Kelvin had built up through his 53-year reign as Glasgow professor meant that he wielded immense scientific authority, but for the new generation, his views looked increasingly anachronistic. As younger groups of physicists grew more enthusiastic about Maxwell's electromagnetic theory of light, for instance, so Kelvin's resistance to Maxwellian approaches and his own commitment to elastic-solid models made him appear increasingly conservative. Likewise, his reluctance to abandon his age-of-the-earth estimates (based on secular cooling of an originally molten earth) presented advocates of radioactivity (based on the generation of heat by radioactive elements distributed in the earth's crust) with a serious obstacle to easy acceptance of the new views. Even his representation of his dry-card compass as a major Admiralty reform came to be seen as a barrier to the introduction of liquid compasses in the 1900s.

During his life, Lord Kelvin received some twenty-one honorary doctorates from universities around the world (including Princeton, Yale, Toronto, and Heidelberg). He was a member or honorary member of nearly ninety learned societies and academies. Elected fellow of the Royal Society in 1851, he was awarded its Copley medal in 1883 and served as its president from 1890 until 1895. He was also president of the British Association in 1871 and president of the Society of Telegraph Engineers in 1874. In 1881 he was made commander of the French Légion d'honneur, and he became a grand officer eight years later. He was made knight of the Prussian order of merit in 1884. He served on Admiralty committees in 1871 (for designs of ships of war) and in 1904-5 (for designs of the new dreadnought battleships and battle cruisers). He was appointed to the Order of Merit and was sworn of the privy council in 1902. Lord Kelvin retired from the Glasgow chair in 1899, but became chancellor of the university in 1904 and continued working right up to his death, from a severe chill, at Netherhall on 17 December 1907. His funeral and burial took place in Westminster Abbey two days before Christmas.


C. Smith and M. N. Wise, Energy and empire: a biographical study of Lord Kelvin (1989)
E. King, Lord Kelvin's early home (1909)
S. P. Thompson, The life of William Thomson, Baron Kelvin of Largs, 2 vols. (1910)
J. L. [J. Larmor], PRS, 81A (1908), iii-lxxvi
A. Grey, Lord Kelvin: an account of his scientific life and work (1909)
A. G. King, Kelvin the man (1925)
C. Smith, '"Nowhere but in a great town": William Thomson's spiral of classroom credibility', Making space for science, ed. C. Smith and J. Agar (1998), 118-46
W. Thomson, Mathematical and physical papers, 6 vols. (1882-1911)

CUL, corresp. and papers
Mitchell L., Glas., Glasgow City Archives, letters relating to Atlantic telegraph cable; testamentary papers
NL Scot., corresp. with instrument makers; letters and notes to scientific-instrument makers
NMM, letters and reports
NRA Scotland, priv. coll., corresp. relating to laboratory supplies
Royal Institution of Great Britain, London, letters to Royal Institution
U. Glas., Archives and Business Records Centre, business papers relating to patent compass
U. Glas. L., corresp. and papers; lecture notes |  Balliol Oxf., letters to Sir John Conroy
CUL, letters to his sister, Elizabeth King
CUL, corresp. with James Clerk Maxwell
ICL, letters to Silvanus Thompson
Inst. EE, letter to Oliver Heaviside
Inst. EE, letter to Sir William Henry Preece
MHS Oxf., corresp. with Frederick J. J. Smith
Mitchell L., Glas., Glasgow City Archives, corresp with Walter Crum and the Crum family
NL Scot., letters to Bottomley and Barlow families
PRO, corresp. with Balfour Stewart, BJ1
RS, letters to Sir Arthur Schuster
Trinity Cam., scientific corresp. with Sir Joseph John Thomson
U. Aberdeen L., letters to David Thompson
U. Glas., Archives and Business Records Centre, corresp. with David Reid
U. St Andr. L., letters to James David Forbes
UCL, letters to Sir Oliver Lodge  SOUND  Sci. Mus.

E. King, pencil drawing, 1840, NPG
L. C. Dickinson, oils, 1869, Peterhouse, Cambridge [see illus.]
E. T. King, oils, 1886-7, NPG
H. von Herkomer, oils, 1891, U. Glas.
A. M. Shannan, bronze bust, 1896, Scot. NPG
W. Q. Orchardson, oils, exh. RA 1899, RS
Elliott & Fry, photograph, 1900, NPG
W. W. Ouless, oils, exh. RA 1902, Clockmakers' Company, London
W. Rothestein, pastel drawing, 1904, Scot. NPG
statue, 1910, Botanical Gardens, Belfast
Annan & Sons, photogravure photograph (after photograph by Elliott & Fry), NPG
Berlin Photographic Co., photogravure photograph, NPG
Dickinson, photogravure photograph, NPG
W. & D. Downey, woodburytype photograph, NPG; repro. in W. Downey and D. Downey, The cabinet portrait gallery, 3 (1892)
H. Furniss, pen-and-ink sketch for a caricature, NPG
M. M. Giles, wax medallion, NPG
E. T. King, oils, Scot. NPG
E. King & A. G. King, sketch, NPG
E. G. Lewis, oils, Inst. EE
London Stereoscopic Co., photographs, NPG
W. Q. Richardson, charcoal drawing, Scot. NPG
Spy [L. Ward], watercolour study for a caricature, NPG; repro. in VF (29 April 1897)
medallion on decorative frieze, School of Science and Art, Stroud
statue, Kelvingrove Park, Glasgow
woodburytype photograph, NPG

Wealth at death  
£128,925 0s. 7d.: confirmation, 10 April 1908, CCI

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