William Thomson

http://id.loc.gov/authorities/names/n79139223

Crosbie Smith, ‘Thomson, William, Baron Kelvin (1824–1907)’, Oxford Dictionary of National Biography, Oxford University Press, 2004; online edn, Jan 2011 [http://proxy.bostonathenaeum.org:2055/view/article/36507, accessed 30 Aug 2017]

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 [see North British network]. 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