On the dynamical theory of heat, with numerical results deduced from Mr Joule’s equivalent of a thermal unit and M. Regnault’s observations on steam. [Bound with:] On a method of discovering experimentally the relation between the mechanical work spent, and the heat produced by the compression of a gaseous fluid. [Together two offprints from Transactions of the Royal Society of Edinburgh, Vol. XX, Part II, 1851].

Edinburgh: Printed for the Society by Neill and Co., 1851.

First edition, the extremely rare offprints, of these groundbreaking papers in which Kelvin outlined the view, as based on recent experiments by Joule and others, that “heat is not a substance [‘caloric’], but a dynamical form of mechanical effect; we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect.” “His great paper on The Dynamical Theory of Heat, published in the Transactions of the Royal Society of Edinburgh in 1851, fully established the bases of thermodynamics” (Wyllie, p. 89). “In 1851 he laid down two fundamental propositions, the first a statement of Joule’s proposition of the mutual equivalence of work and heat, and the second a statement of Carnot’s criterion for a perfect engine… [He] accepted as a fundamental principle what he soon termed the universal dissipation of energy… This reasoning provided the basis for Kelvin’s ‘second law of thermodynamics’: ‘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’” (Companion to the History of Modern Science, p. 334). “In these papers, Thomson outlined the basic principles of the new science of thermodynamics that had emerged from his attempts at making sense of Carnot and Joule’s apparently contradictory positions. Over the next few decades, Thomson, Joule, and others would succeed in placing this new thermodynamic science at the very heart of 19th-century physics” (Morus, p. 122). COPAC lists one copy only (Cambridge); ABPC/RBH list only the Plotnick copy (in modern boards) (sold Christie’s 2002, lot 271, $1135).


“In 1847 William presented to the Glasgow Philosophical Society A Notice of Stirling’s Air Engine, a subject already well known but not well understood. At this time the only lucid, though incomplete, account of the principles of heat engines was that produced by the French engineer, Sadi Carnot, in 1824 [Réflexions sur la puissance motrice du feu et sur les machines propres a développer cette puissance] which Thomson probably knew through an even less complete account by Emile Clapeyron. Carnot’s theory was based on an analogy with hydraulic engines in which he supposed that the work done by a heat engine was to be drawn from the fall of heat from higher to lower temperature without loss of heat, just as work done by a water wheel is drawn from the fall of water from an upper to a lower level without loss of matter. In spite of the falsity of this supposed conservation of heat, Carnot and his successors contrived to give a correct account of a number of phenomena, and these successes made it hard to accept the contrary rule, that in an ideal heat engine the work done is in an invariable proportion to the heat which disappears.


“Already in 1847, James Prescott Joule had presented to the British Association meeting at Oxford the results of his careful experiments which showed that, in dissipative fluid flow, the energy lost reappeared as an equivalent amount of heat. Thomson was present during Joule’s talk and was deeply impressed by the potential importance of the result; however, it seems that his reservations about its accuracy were only finally dispelled by the repetition of some of Joule’s results in his own laboratory.


“In 1848 Thomson obtained a copy of Carnot’s original memoir from Lewis Gordon, professor of engineering at Glasgow. One consequent suggestion was that it should be possible using a reversible engine as a heat pump to freeze large amounts of water at freezing point without expenditure of energy. In late 1847 or early 1848, James [Thomson, William’s elder brother] had remarked that since water expands on freezing, work would be done by that expansion against the ambient pressure, and deduced that the freezing point of water should be lowered by applied pressure. William subsequently designed an ether thermometer to measure the small temperature shift and succeeded in verifying the effect. In 1849 he also presented a full and clear account of Carnot’s theory to the Royal Society of Edinburgh.


“Joule’s careful work had now convinced the Thomson brothers that dissipated mechanical or electrical energy was transformed to heat in unvarying proportion but they remained unconvinced of the reverse. On the other hand, a general law of conservation of energy, now formulated as the First Law of Thermodynamics, was a speculative commonplace with European thinkers and it was Rudolf Clausius in 1850 who combined that with the statement that ‘heat cannot of itself pass from a cooler to a hotter body’ to formulate a correct theory of thermodynamics. Thomson was happy then and later to admit Clausius’ priority in publication, but insisted, probably correctly, that he had independently reached equivalent conclusions before reading Clausius’ paper” (Wyllie, pp. 87-88).


In the present paper, Kelvin “acknowledged the contributions of Rankine and Clausius at the outset. He then spelled out what he called two propositions. The first, which he attributed to Joule, was that whenever heat is produced from thermal sources, or lost in thermal effects, equal amounts of heat are put out of existence or generated. He, thus, completely abandoned the caloric theory, accepting Joule’s ideas in their entirety, and becoming perhaps the main advocate from that moment of what he called the dynamical theory of heat …

“The second proposition, attributed by William to Carnot and Clausius, states that the most efficient engine acting between particular temperatures of source and refrigerator is a reversible one. William expressed this proposition in his own terms a little later in the paper: ‘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’. This became his famous statement of the second law of thermodynamics.

“So far he had broadly repeated the concepts of Clausius, and to an extent, of Rankine. But the difference between them was that Clausius’s interests were rather narrow, being largely restricted to the theory of heat engines; it might be said that his paper was an admittedly brilliant but technical solution to a technical problem. Rankine too was a comparative newcomer to the topic. William, in contrast, had spent the best part of a decade worrying practically incessantly about the conceptual and cosmological significance of the problems he had been considering. With the solutions now understood in principle, he had much to say about their implications. He began in the remainder of this paper, and continued for the rest of his life.

“First, he became the apostle for the new idea of energy. Until that time, physics had been constructed around the Newtonian idea of force, which was immensely useful in mechanics but not so useful elsewhere in physics. With the understanding that heat, light, sound, electricity and magnetism could all be expressed in terms of energy, with the full appreciation of what we now call kinetic and potential energy, and paying regard to the idea of transformations between the various types of energy, it became clear, at least to William, that all the various areas in physics could very fruitfully be discussed in the new paradigm of energy. The treatise he and Tait wrote together is a celebration of this new belief, and today their evangelism has been so successful that it is almost regarded as tautological to describe physics as the science of energy.

“Even more significant was William’s long concern, together with James, with the question of waste. What for Clausius was little more than a logical explanation of what happened when heat could have produced work but had failed to do so – extra heat was deposited in the cold reservoir, for William became the solution to his central conceptual problems, and the key to his new worldview. This heat was not lost in the material world, thus satisfying William’s demand that only God could create or destroy. Nevertheless, this energy is ‘lost to man irrecoverably’. Thus, William’s worldview was one of dissipation and irreversibility, with an arrow of time leading to the so-called heat death, where everything is at the same temperature, and any interesting features in the universe have been lost. It was a most beautiful solution to the worries that William and James had shared over many years, and this major conceptual development played a deservedly large part in building up William’s towering reputation through the second half of the nineteenth century” (Whittaker, pp. 86-87).

The first offered paper is divided into 60 sections and three parts, the first six sections comprising the introduction. Part I, ‘Fundamental principles in the theory of the motive power of heat,’ comprises sections 7 – 23; Part II, ‘On the motive power of heat through finite ranges of temperature,’ sections 24 – 43; and Part III, ‘Application of the dynamical theory to establish relations between the physical properties of all substances,’ sections 44 – 60. The second paper has sections numbered 1 – 20, but in a subsequent paper published in the same volume of the Edinburgh Transactions, ‘On the dynamical theory of heat. Part 5. On the quantities of mechanical energy contained in a fluid in different states, as to temperature and density,’ Kelvin tells us that the second offered paper should be considered as Part IV and its sections should have been numbered 61 – 80: “A preceding communication (April 21, 1851) published, in the Transactions (Vol. xx., Part ii.), under the title, “On a Method, of Discovering Experimentally the Relation between the Mechanical Work spent, and. the Heat produced, by the Compression of a Gaseous Fluid,” will be referred to as Part IV of a series of Papers on the Dynamical Theory of Heat; and the numbers of its sections will be altered accordingly, so that its first section will be referred to as § 61, and its 20th and last, as § 80.” A sixth part, which dealt with thermoelectric currents, followed in 1854, and a seventh, on thermoelastic and thermomagnetic properties of matter, was mostly written in 1855, though it was first published in Kelvin’s collected papers. It is worth noting that the imprint of these offprints is different from that of the journal volume in which they appeared: the latter is Edinburgh: Robert Grant & Son, 1853. The often thorny question of whether the journal issue or offprint of a paper takes precedence is thus settled clearly in this case in favour of the offprint.


Morus, “A Dynamical Form of Mechanical Effect’: Thomson's Thermodynamics,’ pp. 122-139 in Kelvin: Life, Labours and Legacy, Flood et al. (eds.), 2008; Whittaker, ‘James and William Thomson: the creation of thermodynamics,’ Chapter 3 in Kelvin, Thermodynamics and the Natural World, Collins et al. (eds.), 2015; Wyllie, ‘William Thomson, Lord Kelvin,’ in No Mean Society: 200 Years of the Royal Philosophical Society of Glasgow, 2003.

4to (290 x 227 mm), pp. [ii], 261-288; [ii], 289-298. Original plain wrappers, title in manuscript on front wrapper.

Item #4028

Price: $3,000.00