Helmholtz and the British scientific elite: From force conservation to energy conservation

David Cahan


This article discusses the close relationship that developed during the 1850s and 1860s between Hermann von Helmholtz (1821–94), one of the leading German scientists during the second half of the nineteenth century, and the British scientific elite generally. It focuses especially on the importance of the law of conservation of energy to both sides of that relationship as the law emerged and became popularized. In presenting this Anglo-German relationship, the article relates Helmholtz's friendships or acquaintanceships with numerous members of the British elite, including William Thomson, John Tyndall, Henry Enfield Roscoe, Michael Faraday, Edward Sabine, Henry Bence Jones, George Gabriel Stokes, James Clerk Maxwell, Peter Guthrie Tait, George Biddell Airy and James Thomson. It suggests that the building of these social relationships helped create a sense of trust between Helmholtz and the British elite that, in turn, eased the revision of the understanding of the law of conservation of force into that of energy and consolidated its acceptance, and that laid the personal groundwork for Helmholtz's future promotion of Maxwell's electromagnetic theory in Germany and for Anglo-German agreements in electrical metrology.


No foreign man of science had a stronger reputation in Britain during the second half of the nineteenth century than Hermann von Helmholtz, not least because he reinforced it by professional visits to Britain and by building personal and professional friendships with leading British men of science. These visits—there were eight of them all told—were to academic as well as non-academic institutions, including the Royal Institution, the Royal Society of London and two of the annual meetings of the British Association for the Advancement of Science (BAAS), along with one to his great friend William Thomson. Helmholtz, who was ennobled in January 1883 and so then had the ‘von’ added to his name, was especially close with Thomson, John Tyndall and Henry Enfield Roscoe, but he also knew personally many other leading British men of science, including Michael Faraday, Edward Sabine, Henry Bence Jones, George Gabriel Stokes, James Clerk Maxwell, Peter Guthrie Tait, George Biddell Airy and James Thomson. Indeed, perhaps the only senior figure in British scientific life whom Helmholtz did not know personally was Charles Darwin, and it may well be that Darwin's reclusive lifestyle after he moved to Down helps explain their lack of acquaintanceship, for the two men had the highest mutual respect for one another's scientific work.

Helmholtz's work and person effectively constituted a ‘bridge’ between the British scientific elite and himself, if not between British and German science generally. That relationship helped facilitate visits by British men of science (especially younger ones) to him in Heidelberg and Berlin; it greatly facilitated the promotion of Maxwell's electromagnetic theory (and of British physics more generally) in the German-speaking world; it crucially aided in negotiating electrical standards during the last third of the century; and, through Helmholtz's lectures in Britain, it enhanced British appreciation of scientific work in Germany. This article concentrates on the formation of that relationship as it evolved during the 1850s and 1860s around the consolidation and popularization of the law of conservation of force as the latter gradually evolved into and became known as the law of conservation of energy, a law to which Helmholtz, along with several others, made an important, indeed fundamental, contribution. That law was to no small extent an Anglo-German creation, in which individuals on both sides, not to mention several others from elsewhere, made contributions of greater or less importance.

Helmholtz's essay on the conservation of force and its neglect

The ‘discovery’ of the law of conservation of energy has long been a topic of historical dispute, not least because the law stemmed from multiple types of sources and contexts—philosophical, physical, physiological, cultural, technological and political economic—some of which stretched as far back as the seventeenth century. Between the 1820s and 1847 a series of figures throughout Europe—including Sadi Carnot, Carl Friedrich Mohr, Marc Séguin, Faraday, J. Robert Mayer, William Grove, Justus von Liebig, James Prescott Joule, Ludvig Colding, Karl Holtzmann and Helmholtz himself—argued in one way or another that forces could neither be created nor destroyed but instead were subject to conversion or correlation, and in particular that heat and work were convertible and had a more or less precise, quantitative relationship to one another.1 Helmholtz himself borrowed elements for his own theory from numerous physicists, chemists, engineers and philosophers before him. The novelty of his essay on the conservation of force (1847) lay in stating a general framework, in showing the generality of the law throughout physics (and, he hoped, beyond), and in its quantitative specificity for particular physical problems. He argued that physical theorems could be derived from two seemingly disparate but ultimately identical viewpoints: either from the impossibility of a perpetual motion machine (that is, creating an infinite amount of work from a finite amount of force) or from explaining all of nature's effects in terms of attractive and repulsive forces. In good Newtonian and Kantian fashion, he distinguished matter and force as the fundamental abstractions by which science conceived the external world.2

Assuming that no combination of bodies could continuously create force from nothing or, in the language of mechanics, that the quantity of work gained when a system changes from its initial into a second state always equalled the quantity of work lost when the system changed from the second state back to the initial one, no matter how or by what path or at what speed the change was effected, Helmholtz sought to mathematize and generalize the point, calling it the law of the conservation of force: In all cases of the motion of free material points under the influence of their attractive and repulsive forces, whose intensities are dependent only on distance, the loss in the quantity of potential force [Spannkraft] is always equal to the gain in living force [lebendige Kraft], and the gain of the first is the loss of the second. Thus, the sum of the existing living and potential forces is always constant.3Between the early 1850s and 1862 (to anticipate), this ‘potential force’ would become known and understood as potential energy and this ‘living force’ as kinetic energy; however, in 1847 that was language and a conceptual outlook still unknown to Helmholtz and others grounded in a tradition of ‘force’ as change in spatial relationship. (Indeed, strictly speaking, where no motion is produced, force, in contrast to energy, is not conserved at all.4) Helmholtz then applied this law to a variety of mechanical theorems and analysed the force equivalent of a variety of thermal, electrical, and magnetic processes, and towards the end of his essay he briefly mentioned his hope for the law's eventual application to analysing organic life so as to explain the development of heat in plants and animals.5

For aid in getting his manuscript published, Helmholtz turned to the Berlin physicist Gustav Magnus (via the Berlin physiologist Emil du Bois-Reymond). He hoped that Magnus's name, if not his endorsement, would help the manuscript to be accepted by Johann Christian Poggendorff's Annalen der Physik, Germany's premier physics journal. Poggendorff promptly declined to publish it. Although he vaguely conceded its importance, he found it too long for an article for his journal and, more importantly, not devoted to experimental results, which was what, he said, the Annalen principally published. He claimed that to publish the work of ‘the theorizers, … to whom, by the way, I absolutely do not deny my respect and appreciation for their use’ would be tantamount to excluding much work of an experimental nature. His rejection of Helmholtz's manuscript bids well to be among the most egregious rejections of what later proved to be a pathfinding manuscript in the history of science. Helmholtz then turned to Georg Reimer, a well-known publisher, who within 10 weeks published the manuscript. It was not refereed independently and, in fact, du Bois-Reymond intervened with Reimer on Helmholtz's behalf.6 During the next four years, Helmholtz's essay was virtually ignored by the physics and physiological communities in the German states and beyond. Starting in 1851, however, a group of British physicists and engineers gave Helmholtz's essay a rather different reception.

The British transformation of Helmholtz's law: from force to energy

In 1850–51, Helmholtz announced the invention of the ophthalmoscope, an instrument for viewing the living human retina. This achievement rapidly transformed him from an obscure if able physiologist in distant Königsberg into a well-known and leading figure in European science and medicine. He began to travel professionally, including a trip to the Hull meeting (1853) of the BAAS. On his first morning in Hull he met Stokes, ‘a young man, yet one of the highest, most excellent abilities’, as he told his wife, and who was in fact a leading mathematical physicist and the Lucasian Professor of Natural Philosophy at Cambridge.7 He also met several other leading figures ‘whose acquaintance I very much wanted [to make]’, including Grove, ‘a lawyer and important physicist from London’, best known for giving one of the first versions of the law of correlation of forces as well as for his work in electrochemistry, and Thomas Andrews, the professor of chemistry at Belfast who specialized in thermochemistry.8 At the opening, plenary session that evening, William Hopkins, the much-respected mathematical coach at Cambridge, geologist, and president of the BAAS, reviewed the principal ‘progress’ in science during the past year, and the secretary, Sabine, read aloud the names of all foreigners present, including Helmholtz's, ‘who has made some of the most important progress of continental science’. Helmholtz was surprised to learn that ‘[m]y conservation of force [essay] is better known here than in Germany and better known than my other works’.9

How did his essay become better known in Britain than in the German states and better known there than his physiological studies? For four years it had lain fallow. The change was due in part to the attention that his physiological studies (especially his invention of the ophthalmoscope) meant for his general scientific standing. But there was also another, more direct, reason why the essay suddenly drew attention in Britain, and one perhaps related to why Helmholtz chose to visit Britain and meet some of its men of science. In late January 1851 the young Thomson, who had recently begun thinking about physics in terms of ‘energy’, read Helmholtz's essay and by March had publicly expressed his admiration of it.10 During the next two decades he led a group of north British physicists and engineers—including his brother James, Joule, W. J. M. Rankine, Maxwell, Tait and Fleeming Jenkin—into transforming Helmholtz's law of conservation of force into that of conservation of energy.11 By the spring of 1853, an English language version of Helmholtz's essay had appeared; its translator and co-editor was Tyndall.12 Helmholtz's essay was reborn in Britain. However, there were important philosophical differences between him and these north British physicists and engineers. As Crosbie Smith has argued, whereas Helmholtz constructed a deterministic account of the role of force in a mechanical universe, one rooted in eighteenth-century Laplacian physics and centred on attractive and repulsive forces, the British built an indeterministic one that eschewed action-at-a-distance and discrete particles moving in space, and instead posited a Creator who had established a continuum of matter and energy and who left room for human will to intervene. The British effectively re-read Helmholtz's ‘force’ into their ‘energy’. Both Helmholtz and his British interpreters largely glossed over these differences as together they promoted what gradually became the law of conservation of energy. It was thus more than semantics (‘force’ versus ‘energy’) that separated him from them, even as he and they allied to promote their common cause and move it beyond philosophical battles within physics and physiology and beyond its British industrial and professional contexts.13

Helmholtz's popularization of conservation of force/energy

In the very year (1854) in which Thomson created a new name (‘thermodynamics’) for the study of heat, Helmholtz began to popularize the subject. He gave the first of numerous popular lectures on the conservation of force—that was the term (Kraft in German), not energy, that he still used—and he brought the subject to the educated world and beyond. That year, before the Physical-Economic Society in Königsberg, he declared that there was ‘a new, general law of nature’ in physics, one ‘of very general interest’. It concerned the mutual relationship of all forces of nature with one another, he said, and was thus of importance for understanding nature theoretically as well as for its ‘technical application’. He argued against the possibility of a perpetual motion machine. His general scientific analysis of machinery, work, force and money came as the German economy was beginning to ‘take off’. It was just the sort of talk that listeners in commercial Königsberg and readers throughout the economically booming German states could well appreciate.14 He noted, too, that a series of natural philosophers and physicists—he named, among others, Mayer15—had in one form or another recognized the proposition that all forces could be transformed into one another, and he reported that in England during the previous summer he had found growing interest among men of science in the law of conservation of force. Joule and others had confirmed the theory experimentally, and Victor Regnault, ‘the most important of the French physicists’, had used it as the basis for investigating the specific heats of gases. Although Helmholtz conceded that more proof was still needed, he nonetheless thought the theory was sufficiently confirmed to merit presentation before ‘a non-scientific public’. He also drew implications from force conservation for understanding such phenomena as the formation of the Solar System, the effects of the Sun on the Earth's atmosphere, geological formations, and movement and work in organic beings. The law of conservation of force, he declared, had given humankind a long though not an immortal history.16 He presented a naturalistic, evolutionary and non-Christian analysis of Earth's and humankind's history.

In the spring of 1859, Thomson invited Helmholtz to attend the BAAS meeting in Aberdeen that coming September. He sought to entice him by offering private quarters with a relative (James Crum), by noting that Queen Victoria and the Prince Consort, Albert, would attend (with the prince serving as the BAAS's president) and by inviting him to join him on the Isle of Arran. Thomson, who had not seen Helmholtz for ‘a long time’, said they had much to talk about. In the meantime he had studied Helmholtz's paper on rotary motion in fluids ‘with great interest’, and made progress on improving both resistance standards and on his marine and land galvanometers.17 However, for a variety of reasons—his wife's poor and declining health that summer and the associated dangers in Baden due to the recent war in northern Italy between Austria on the one hand, and France and Italy on the other—Helmholtz felt that he could not leave his family alone in Heidelberg and go to Britain (Aberdeen). Both he and Thomson were disappointed.18 On 28 December 1859, Helmholtz's wife died.

Six months later, Helmholtz had recovered sufficiently from his mourning and depression such that in August 1860 he could indeed visit Thomson on the Isle of Arran in Scotland.19 The sea and the air helped his health, not least by largely ridding him of the headaches ‘and other small illnesses’ that had plagued him during the previous winter.20 He visited Walter Crum, an industrial chemist in Glasgow, who was also Thomson's father-in-law, and he met William Barton Rogers, the American natural philosopher, who the following year became the founding President of the Massachusetts Institute of Technology (1861–70, and again 1879–81).21

In late 1860, three leaders of the Royal Institution—Faraday, Bence Jones and William Benjamin Carpenter (the Fullerian Professor of Physiology, and in general a supporter of the popularization of science)—induced Helmholtz to lecture there in the following spring. The Royal Institution was, of course, Britain's central theatre for popular lectures on science, above all thanks to its Friday Evening Discourses. These attracted London's intellectual and social elites, not least for the style and grace of their evenings. Lecturers stimulated and entertained London's intelligentsia and literati with the latest, most interesting developments in science. At mid-century—under the tripartite leadership of old Faraday, young Tyndall, who since 1853 held the chair of natural philosophy, and the chemist Edward Frankland—the Royal Institution experienced a golden age: its lectures were well attended (about 400–500 ladies and gentlemen) and were published and distributed throughout the world. Many notable figures in mid-Victorian scientific life—not only Faraday and Tyndall, but also Charles Lyell, Richard Owen, T. H. Huxley, Lyon Playfair and Thomson, to name only the most prominent—gave these Discourses, as did a few select foreigners, including Helmholtz.22

Bence Jones and Faraday wanted Helmholtz to lecture above all on the conservation of force, and he agreed to give three lectures, one of which, the Friday Evening Discourse, was expected to attract perhaps 1000 or more attendees and for which the Royal Institution paid him nothing. The organizers, and Faraday in particular, especially wanted the lecture to be on the law of conservation of force ‘in its application to life’, a topic, Bence Jones said, that ‘will interest us all and get us out of the metaphysical groove into which this subject has got here.’ The other two lectures would be more specialized and Helmholtz would be compensated for them (to the tune of £20).23 In truth, Helmholtz preferred not to lecture on the conservation of force at all, but because Bence Jones and Faraday insisted on this and because the Institution was paying for his other two lectures (both on the physiological foundations of music), he was forced to agree.24

Helmholtz spent about a month in London, and everybody there and beyond wanted to see him. Carpenter gave an evening party for him, which Maxwell attended, as did Thomas Archer Hirst, a minor British mathematician but one who was well connected with the British scientific elite, including the leaders of the Royal Society. Hirst ‘had long conversations’ with both Helmholtz and Maxwell at the evening party: ‘[t]he former is a little reserved the latter talkative with a Scotch brogue.’25 Thomson, who was ill and so could not travel, and Roscoe invited Helmholtz to visit them in Glasgow and Manchester, respectively, but he had to decline.26 William Sharpey, an anatomist and physiologist, and a Secretary of the Royal Society, also looked forward to Helmholtz's London visit and wanted to know whether Helmholtz, a Foreign Member (since 1860) of the Society, would also be willing to give that year's Croonian Lecture. The lectureship, he explained, had originally (in 1738) been meant to advance understanding of ‘the nature and laws of muscular motion’, but Helmholtz could speak on any topic in physiology or anatomy that he cared to.27 Helmholtz declined the honour, for now.

Helmholtz's Friday Evening Discourse was entitled ‘On the Application of the Law of the Conservation of Force to Organic Nature’. In it he argued that the law ‘embraces and rules all the various branches of physics and chemistry’. It was important not only for understanding ‘the nature of forces’, he said, but also for understanding ‘immediate and practical questions in the construction of machines’. Following Rankine, he thought that the law of conservation of force might well be called ‘the conservation of energy’, yet he himself nearly always spoke of ‘force’ rather than ‘energy’. Furthermore, he explained that Joule had determined the mechanical equivalent of heat, and that heat, as a motive power, could be converted into mechanical power, such as in a steam engine through the chemical process of burning fuel. He also explained the law's use in understanding the cosmological formation of the Solar System, and the strong effect that the Sun's radiation had on shaping meteorological phenomena and on plants and animals. He thought it understandable that the law had been ‘detected by natural philosophers or engineers’ in England, with its ‘more practical interests of engineering’, and also by medical men or physiologists (namely Mayer and himself) in the German states, who generalized the law. There was a very strong analogy, he said, between the living body and a steam engine. Animals consume food (fuel) and breathe oxygen from the air, which is similar to the sources that give steam engines their power. An animal can do a certain amount of mechanical work, expressed either in the form of heat or work as muscular exertion. Still, the analogy between the body and a steam engine remained just that, and Helmholtz concluded that there was as yet no proof that the laws of animal life agreed with the conservation of force. What was not open for discussion, he said, was any doubt that the agents or inorganic forces operating within the body did so by necessity, without arbitrariness of action.28 His broadly determinist and reductionist outlook stood in opposition to the role allotted to free will in nature by his Scottish friends and colleagues. By contrast, Tyndall, whose views and efforts were repeatedly attacked or belittled by Thomson and Tait, expressed scientific naturalist views.29

Hirst, who attended one of Helmholtz's specialized lectures (that on vowel sounds), met him again at a dinner party, where the guests included Roscoe, Thomas Graham—the chemist and Master of the Mint (1855–69)—and Carpenter. Hirst also attended Helmholtz's Discourse lecture, which he found ‘instructive but not as interesting as I anticipated.’30 Bence Jones saw it more positively. He told his (and Helmholtz's) good friend du Bois-Reymond: ‘Helmholtz did very well; not splendidly [but] his Friday evening was very good & I had it reported & will send you a verbatim report.’ He hoped to ‘persuade him to come’ again.31

That is precisely what happened. Less than two years later Helmholtz was invited back to the Royal Institution to lecture again on the conservation of energy and its applications. The entrepreneur behind this second invitation was Bence Jones, who had heard about Helmholtz's recent lectures on the general results of the natural sciences; that is, either a course of popular lectures that he gave in 1862–63 at Heidelberg, where in 1858 he had become Professor of Physiology, or, what was probably the same thing, a series of eight weekly lectures that he held in Carlsruhe that same winter.32 Bence Jones hoped that Helmholtz could hold a similar set of lectures in the spring of 1864 at the Royal Institution, and Helmholtz accommodated him with a set of suggested lecture topics: 1) Exposition of the Principle of Conservation; 2) Mechanical Energy of the Stellar System; 3) Stellar and Solar Heat; 4) Formation of the Earth; 5) Motions of Atmosphere and Ocean; 6) Circulation of Water on the Earth; 7) Food of Plants and Animals; 8) Mechanical Energy of Plants and Animals.33Bence Jones said that the Royal Institution wanted him to give the eight lectures in April 1864; that the general subject and theme would be conservation of energy; and that Helmholtz would receive £80 for his effort.34 In the event, Helmholtz held six lectures on conservation of energy (including its ramifications into fields beyond physics) at the Royal Institution that April.35 That the Institution's leadership again wanted Helmholtz to lecture on energy conservation indicates that ‘energy physics’ was a subject that the general public was then still very much just learning about. But it also suggests that, in view of a controversy that erupted in 1862–63 over the historical origins of the conservation of energy, between Tyndall on the one hand and Thomson and Tait on the other, the Institution's leadership may have seen Helmholtz as a well-informed and perhaps even impartial judge, as someone who was at once an outsider and an insider in this matter. Helmholtz, for his part, agreed to lecture on energy conservation partly because he needed money to help pay for equipping his new physiological institute in Heidelberg; as he told du Bois-Reymond, he ‘treats the conservation of force like a nourishing cow’. However, he also envisioned his London lectures ‘mainly as a cheap and advantageous way to get into close contact with London savants and English circumstances’. He expected England to offer him ‘a sort of intellectual mineral-water cure that would shake up the mind's activity’, and so be an antidote to sleepy southern Germany.36

Helmholtz planned to arrive in London in mid March and spend much of the next 30 days residing alternately with Bence Jones, the Enfields (Henry Roscoe's sister) and Carpenter, who also planned a dinner party for him. Among other things, Helmholtz was keen to participate in meetings of the Royal Society.37 The Thomsons invited him to their place in Glasgow for late March. Thomson wanted ‘to have a great deal of conversation with you [Helmholtz] on many subjects’.38 To do so, Helmholtz had to give up his original plans to visit Cambridge, not least to see Stokes, whom he now hoped instead to see in London at the Royal Society or in Cambridge on another occasion.39 Helmholtz's visit, Tyndall told him, was much anticipated.40 In all, Helmholtz spent six weeks in Britain, again delivering a series of invited lectures at the Royal Institution on conservation of force but also delivering the Croonian Lecture, and visiting friends in London, Oxford, Glasgow and Manchester.41

In London, that ‘gigantic Babel’, Helmholtz went first to the Royal Institution, where he sought in vain to see Tyndall but did manage to find Faraday, who ‘as in the old days, was extremely charming’. Faraday told him that, because of memory loss, he himself had given up lecturing. Helmholtz dined that evening at the Philosophical Club in St James's Hotel, ‘where rather the most interesting members of the Royal Society came together’. After dinner, the group went to hear Tyndall lecture at the Society. Helmholtz found its quarters to be ‘extremely sumptuous’ and he was especially impressed by ‘the powerful golden mace’ that symbolized the Society's royal privileges. Late that same evening he and Bence Jones called on William Gladstone, one of the leaders of the Liberal Party, the Chancellor of the Exchequer, the future Prime Minister, and a man who knew many leading British men of science, including Huxley, Joseph Dalton Hooker and Darwin, and who himself had published on human colour vision and had numerous scientific interests, including Helmholtz's work on vowel sounds.42

While in London, Helmholtz made three brief side trips: to Oxford, where among others he saw Friedrich Max Müller, the comparative philologist and orientalist; to Glasgow, where he visited Thomson; and to Manchester, where his friend Roscoe of Owens College had invited him to stay in his home.43 He had been keen to experience Manchester's urban, commercial life.44 At Roscoe's country house he dined with Joule, the ‘principal discoverer of conservation of energy [Kraft]’, to use Helmholtz's own words, and with Robert Bellamy Clifton, a former student of Stokes's, and the first (and young) Professor of Natural Philosophy at Owens College. (In 1865, the promising and socially well-connected Clifton would be elected the new Professor of Experimental Philosophy (that is, physics) at Oxford.)45 Helmholtz noted that the Roscoes, unlike the Thomsons, had completely done away with pre-meal blessings, and he judged that England was rapidly becoming liberal in religious matters. He was impressed with Roscoe's ‘well-equipped laboratory’. After two days in Manchester he returned to London, where he stayed at the Athenaeum, visited Carpenter and talked with Faraday again at the Royal Institution as he prepared his forthcoming lectures.46

Helmholtz's Croonian Lecture at the Royal Society (14 April) was devoted to human eye movements and their relations to perceptions. He thought his subject, which was limited to relating his own results, was of interest not only in terms of understanding the eye's physiology but also in terms of voluntary muscular movement in general. He hoped his subject might interest physiologists, medical men and ‘every scientific man who desires to understand the mechanism of the perceptions of our senses’.47 In contrast to his popular lectures at the Royal Institution, at the Royal Society he spoke without notes and for more than an hour, and he thought that approach made his lecture noticeably better. His talk was apparently well received, because Sabine, the Society's President (1861–71), praised his English and insisted that he continue, which he did for another half hour, and because several listeners made comments that supported his views.48 Among those in attendance was the science writer and editor Edward William Brayley, of the London Institution. Brayley had written the article on the correlation of physical forces for the English Cyclopedia, and there he reported on Helmholtz's essay on conservation of energy, although he told him that he had done justice neither to it nor, especially, to the work of Mayer, whose views ‘were scarcely known in England when I wrote’.49 Helmholtz also spent an ‘amusing’ evening with Tyndall and others at the Athenaeum. On the following morning he had breakfast with Bence Jones, and hoped that the Italian revolutionary, Giuseppe Garibaldi, who was then also in London, would attend a dinner party to which both men had been invited.50

As his stay began drawing to a close, Helmholtz became busier than ever in London. He attended a lecture at the Royal Institution on guncotton, and afterwards dined with several Frenchmen. He had breakfast the following morning at Carpenter's, where he met James Martineau (a Unitarian minister and a professor at London's Manchester College, and a brother of Harriet Martineau, the writer and feminist), James Joseph Sylvester, the distinguished mathematician, and, at last, Stokes, ‘one of the leading mathematical physicists’. Afterwards he prepared his Croonian Lecture for publication, and then went to Maxwell's place in Kensington for lunch, when, as Maxwell put it, ‘we can have light to analyze’. Maxwell had finally got his colour-mixing instruments in sufficient order to be able to invite him, as well as William Pole, the civil engineering professor and musician, who was colour-blind, for lunch. Maxwell showed Helmholtz his ‘beautiful apparatus for [understanding] colour theory’, and the two performed experiments on Pole. ‘We had there’, Helmholtz said, ‘a splendid lunch with champagne and every imaginable delicious item.’51

In his fifth lecture at the Royal Institution, Helmholtz focused on the importance of the law of conservation of energy for physiology,52 and in his sixth and final lecture he discussed the human body's output of energy (that is, mechanical effects and heat). Although he could not prove it, his broad point was that the quantity of heat developed in the interior of the body is the same as the heat of combustion. When work is being done by the human body, then work must be done at the expense of a part, at least, of the heat given out by the body.More or less with that, he brought to a close his survey of the law of the conservation of energy and its various ramifications in the inorganic and organic worlds.53

Helmholtz arrived back in Heidelberg on 23 April 1864. He reported to du Bois-Reymond that in London he had ‘seen a lot of interesting things, and I find that a stay in London from time to time is always stimulating and pleasant.’ As for the popular lectures at the Royal Institution, he had adopted du Bois-Reymond's view: he would think twice before again agreeing to give such lectures. To be sure, he was more than satisfied with their ‘outward success’: he had attracted about 300 attendees per lecture, he said, ‘and had amongst them a great many scientifically educated men’.54 He subsequently told du Bois-Reymond that he ‘himself was dissatisfied with my lectures’, even as he was ‘very much amused’ in London.55

Between 1853 and 1864 Helmholtz met (with the exception of Darwin) virtually every leading British man of science of the day and visited numerous British scientific institutions. The old Faraday, the leading British chemist and physicist of his generation, had served him coffee as he wrote his lectures. Thomson and Maxwell, the leading British physicists of their generation, invited him into their homes to socialize and experiment. He also attended meetings of the BAAS, lectured at the Royal Institution, visited the Royal Society as well as universities in Cambridge, Oxford, London, Manchester and Glasgow. Between giving lectures to hundreds in London, being reported on in newspapers, and touring the country, he had come to know personally virtually everyone of scientific consequence in Britain. Perhaps no other foreign scientist ever received such a warm reception in Britain as Helmholtz had in these years. By the same token, he had learned from the British and felt warmth towards them. He wrote to Alexander William Williamson, Professor of Chemistry at University College London, and Roscoe's former teacher, in 1867: ‘I owe a great deal to England for my own intellectual education. Grown up among the traditions of high-flown metaphysics, I have learned to value the reality of facts in opposition to theoretical probabilities by the great example of English science.’56 Yet despite several new invitations, he would not return to Britain until 1871, a full seven years later. From the late 1860s onwards he would become much concerned with variously understanding, articulating and promoting Maxwell's electromagnetic theory, just as from the 1870s onwards he would become a key figure in Germany's efforts to establish electrical units and standards and to reach agreements with Britain and other national groups. His sensitivity to the importance of Maxwell's work and his leadership in delicate Anglo-German metrological issues owed no small amount to the social experiences and personal connections that he had made in Britain during the 1850s and 1860s.


I would like to thank two anonymous referees for their helpful comments in revising this essay.


  • 1 Thomas S. Kuhn, ‘Energy conservation as an example of simultaneous discovery’, in Critical problems in the history of science (ed. Marshall Clagett), pp. 321–356 (University of Wisconsin Press, Madison, WI, 1959). In addition to Kuhn's classic article, see also Yehuda Elkana, ‘The conservation of energy: a case study of simultaneous discovery?’, Arch. Int. Hist. Sci. 23, 31–60 (1970); idem, ‘Helmholtz’ Kraft: An Illustration of Concepts in Flux', Hist. Stud. Phys. Sci. 2, 263–299 (1970); idem, The discovery of the conservation of energy (Harvard University Press, Cambridge, MA, 1974); Kenneth L. Caneva, Robert Mayer and the conservation of energy (Princeton University Press, 1993); Peter Heimann, ‘Conversion of forces and the conservation of energy’, Centaurus 18, 147–161 (1974); Geoffrey Cantor, ‘William Robert Grove, the correlation of forces, and the conservation of energy’, Centaurus 19, 273–290 (1976); P. M. Harman, ‘Helmholtz: the principle of the conservation of energy’, in P. M. Harman, Metaphysics and natural philosophy: the problem of substance in classical physics (Harvester Press, Brighton, 1982), pp. 105–126; Richard Lynn Kremer, ‘The thermodynamics of life and experimental physiology, 1770–1880’, PhD thesis, Harvard University (1984) (reprinted by Garland, New York (1990)); Donald S. L. Cardwell, James Joule. A biography (Manchester University Press, 1989), pp. 57 and 93–95; Fabio Bevilacqua, ‘Helmholtz's Ueber die Erhaltung der Kraft: The emergence of a theoretical physicist’, in Hermann von Helmholtz and the foundations of nineteenth-century science (ed. David Cahan), pp. 291–333 (University of California Press, Berkeley, CA, 1993); Olivier Darrigol, ‘God, waterwheels, and molecules: Saint-Venant's anticipation of energy conservation’, Hist. Stud. Phys. Sci. 31, 285–353 (2001). See also the references in notes 2 and 4.

  • 2 Hermann Helmholtz, Ueber die Erhaltung der Kraft. Eine physikalische Abhandlung (G. Reimer, Berlin, 1847); reprinted in idem, Wissenschaftliche Abhandlungen (Johann Ambrosius Barth, Leipzig, 1882–83, 1895), vol. 1, pp. 12–75. In an addendum of 1881, Helmholtz distanced himself from this Kantian outlook on causality and phenomena. (See ibid., pp. 68–75, at p. 68.) Compare, in this regard, especially Edward Jurkowitz, ‘Helmholtz's early empiricism and the Erhaltung der Kraft’, Ann. Sci. 67, 39–78 (2010).

  • 3 Helmholtz, op. cit. (note 2), pp. 17–18 and 24–25.

  • 4 Crosbie Smith, The science of energy: a cultural history of energy physics in Victorian Britain (University of Chicago Press, 1998), pp. 126–149, 176–177 and 185–186; Crosbie Smith and M. Norton Wise, Energy and empire: a biographical study of Lord Kelvin (Cambridge University Press, 1989), pp. 617–619 and cf. 626.

  • 5 Helmholtz, op. cit. (note 2), p. 66; Bevilacqua, op. cit. (note 1), pp. 319–332.

  • 6 J. C. Poggendorff to Gustav Magnus, 1 August 1847, draft, Nachlaß Hermann von Helmholtz, Nr. 537, Berlin-Brandenburgische Akademie der Wissenschaften, Akademiearchiv, Berlin (hereafter abbreviated as HN); Hermann Helmholtz to G. A. Reimer, 14 and 20 August and 6 November 1847, Walter de Gruyter & Co. (the successor firm to Georg Reimer), Berlin, Archiv, Helmholtz Letters. Regarding du Bois-Reymond's intervention, see Helmholtz in Hanns von Zobeltitz, ‘Eine Stunde bei Prof. v. Helmholtz’, Daheim: ein deutsches Familienblatt mit Illustrationen, vol. 27 (1891), pp. 768–770; and Emil du Bois-Reymond, ‘Gedächtnisrede auf Hermann von Helmholtz’ (1895), in Reden von Emil du Bois-Reymond (ed. Estelle du Bois-Reymond), 2nd enl. edn (Veit, Leipzig, 1912), vol. 2, pp. 516–570, at p. 524.

  • 7 Hermann Helmholtz to Olga Helmholtz, 8 September 1853, in Letters of Hermann von Helmholtz to his wife 1847–1859 (ed. Richard L. Kremer) (Franz Steiner Verlag, Stuttgart, 1990), pp. 125–131, at p. 131 (and nn. 18 and 20).

  • 8 Hermann Helmholtz to Olga Helmholtz, 14 September 1853, in Helmholtz, op. cit. (note 7), pp. 132–137, at p. 133.

  • 9 Hermann Helmholtz to Olga Helmholtz, 8 September 1853, in Helmholtz, op. cit. (note 7), pp. 130–131 (and n. 16).

  • 10 William Thomson, ‘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’, in William Thomson, Mathematical and Physical Papers, vols 4 and 5 (ed. Joseph Larmor), (Cambridge University Press, 1880–1905), pp. 174–316, at pp. 182–183n; originally in Trans. R. Soc. Edinb. 20, 261–298, 475–482 (March 1851) and Phil. Mag. 4, 8–21, 105–117, 168–176; 9, 523–531 (1852); and see Silvanus P. Thompson, The life of William Thomson, Baron Kelvin of Largs (Macmillan Thompson, London, 1910), vol. 1, pp. 288 and 308.

  • 11 Smith, op. cit. (note 4), pp. 126–149, 178–179 and passim; Smith and Wise, op. cit. (note 4), pp. 282–395; Olivier Darrigol, ‘La termodinamica’, in Storia della scienza, vol. 7 (Istituto della Enciclopedia Italiana, Rome, 2003), pp. 470–481, at pp. 475–477.

  • 12 Hermann Helmholtz, ‘On the Conservation of Force; A Physical Memoir’, in Scientific Memoirs, selected from the transactions of foreign academies of science, and from foreign journals. Natural Philosophy (ed. John Tyndall and William Francis), pp. 114–162 (Taylor & Francis, London, 1853).

  • 13 Smith, op. cit. (note 4), pp. 2, 13, 127–128, 132–135, 138–139 and 249.

  • 14 Hermann Helmholtz, ‘Über die Wechselwirkung der Naturkräfte und die darauf bezüglichen neuesten Ermittelungen der Physik’, in Hermann Helmholtz, Vorträge und Reden, 5th edn (Friedrich Vieweg & Sohn, Braunschweig, 1903), vol. 1, pp. 49–83, at pp. 51–54 and 57–59 (quotations on p. 51). This version, first published in 1884, contains a few changes from the identically titled essay that appeared as a separate pamphlet in 1854 and again in 1872 in his Populäre wissenschaftliche Vorträge, Heft 2. (Ibid., pp. ix–x.) On the boom, see W. O. Henderson, The rise of German industrial power 1834–1914 (University of California Press, Berkeley, CA, 1975), pp. 111–129.

  • 15 Already in 1850, in Die Fortschritte der Physik, Helmholtz had acknowledged Mayer's work, and he did so again in 1852, 1853 and 1855. (Jacob J. Weyrauch (ed.), Kleinere Schriften und Briefe von Robert Mayer. Nebst Mittheilungen aus seinem Leben (J. G. Cotta, Stuttgart, 1893), pp. 316–321.)

  • 16 Helmholtz, op. cit. (note 14), pp. 61–63 (quotations on p. 63), 65 and 73–83.

  • 17 William Thomson to Hermann Helmholtz, 12 May 1859, HN 464; and O. J. R. Howarth, The British Association for the Advancement of Science: a retrospect 1831–1921 (published by the Association at its Office, London 1922), p. 286 (for Albert as president).

  • 18 William Thomson to Hermann Helmholtz, 11 July and 18 August 1859, and 6 October 1859, both in HN 464; and Hermann Helmholtz to William Thomson, 30 August 1859, Cambridge University Library, Department of Manuscripts and University Archives, Thomson Papers, Add 7342 H65.

  • 19 Thompson, op. cit. (note 10), vol. 1, p. 411.

  • 20 Hermann Helmholtz to Mrs. William Thomson, 16 January 1861, Thomson Papers, Add 7342 H66.

  • 21 William Barton Rogers to Henry Rogers, 19 October and 27 November 1860, in William Barton Rogers, Life and Letters of William Barton Rogers (edited by his wife) (Houghton, Mifflin, Boston, 1896), vol. 2, p. 43 and pp. 52–54, at p. 53, respectively; see also William Barton Rogers to Henry Rogers, 13 October 1862, in ibid., vol. 2, pp. 133–134, at p. 134.

  • 22 Frank James, ‘Running the Royal Institution: Faraday as an administrator’, in ‘The common purposes of life’: science and society at the Royal Institution of Great Britain (ed. Frank A. J. L. James), pp. 119–146 (Ashgate, Aldershot, 2002), at pp. 136–140; Iwan Morus, Simon Schaffer and Jim Secord, ‘Scientific London’, in London—world city 1800–1840 (ed. Celina Fox), pp. 129–142 (Yale University Press, New Haven, CT, in association with the Museum of London, 1992), at p. 130; Gwendy Caroe, The Royal Institution: an informal history (John Murray, London, 1985), pp. 76 and 126–129.

  • 23 Henry Bence Jones to Hermann Helmholtz, 23 November 1860?, HN 222; Henry Bence Jones to Hermann Helmholtz, 5 and 21 December 1860, and 4 March 1861, HN 222 (quotation in letter of 5 December 1860); Anna Helmholtz to Mary von Mohl, [sometime between 2 and 17] March 1861, in Anna von Helmholtz. Ein Lebensbild in Briefen (ed. Ellen von Siemens-Helmholtz), vol. 1, pp. 76–77 (Verlag für Kulturpolitik, Berlin, 1929), at p. 76; Henry Bence Jones to Emil du Bois-Reymond, 15 February [1861], Bl. 311–313, SD 3 k 1852 (3), Handschriftenabteilung, Haus 2, Staatsbibliothek Preussischer Kulturbesitz.

  • 24 Hermann Helmholtz to Emil du Bois-Reymond, 2 March 1861, in Dokumente einer Freundschaft. Briefwechsel zwischen Hermann von Helmholtz und Emil du Bois-Reymond 1846–1894 (ed. Christa Kirsten et al.), pp. 196–197 (Akademie-Verlag, Berlin, 1986).

  • 25 William H. Brock and Roy M. MacLeod (eds), Natural knowledge in social context: the journals of Thomas Archer Hirst FRS (Mansell, n.p., 1980), diary entry for 24 March 1861, folio 1572. On Hirst, see also William H. Brock, ‘The spectrum of science patronage’, in The patronage of science in the nineteenth century (ed. G. L'E. Turner), pp. 173–206 (Noordhoff, Leiden, 1976); J. Helen Gardner and Robin J. Wilson, ‘Thomas Archer Hirst—mathematician xtravagant. I’, Am. Math. Mthly 100, 435–441, 531–538, 619–625, 723–731, 827–834, 907–915 (1993).

  • 26 Mrs. Thomson to Hermann Helmholtz, 4 April 1861, in Thompson, op. cit. (note 10), vol. 1, p. 416; Henry Enfield Roscoe to Hermann Helmholtz, 1 April 1861, HN 385.

  • 27 William Sharpey to Hermann Helmholtz, 6 March 1861, HN 402.

  • 28 Hermann Helmholtz, ‘On the Application of the Law of the Conservation of Force to Organic Nature’, Not. Proc. Meet. Memb. R. Instn Gt Br. 3, 347–357 (1861), reprinted in Helmholtz, op. cit. (note 2), vol. 3, pp. 565–580, quotations on pp. 565, 572–573 and 578–579.

  • 29 Smith and Wise, op. cit. (note 4), pp. 617–619, and cf. p. 626; Smith, op. cit. (note 4), pp. 171–172 and 253.

  • 30 Brock and MacLeod (eds), op. cit. (note 25), diary entry for 14 April 1861, folio 1575.

  • 31 Henry Bence Jones to Emil du Bois-Reymond, 7 July 1861, Bl. 314–316, SD 3 k 1852 (3), Handschriftenabteilung, Haus 2, Staatsbibliothek Preussischer Kulturbesitz.

  • 32 Hermann Helmholtz, ‘Über die Erhaltung der Kraft (1862–63). Einleitung zu einem Cyclus von Vorlesungen, gehalten zu Karlsruhe im Winter 1862–63’, in Helmholtz, op. cit. (note 14), vol. 1, pp. 186–229.

  • 33 Henry Bence Jones to Hermann Helmholtz, 12 April 1863, HN 222; Helmholtz, op. cit. (note 32). This latter was only the introductory lecture to the series of lectures that he held first in Carlsruhe and then at the Royal Institution. It first appeared as ‘Lectures on the Conservation of Energy. By Professor Helmholtz. Delivered at the Royal Institution on April 5, 7, 12, 14, 19 and 21, 1864’, Med. Times Gaz. 1, 385–388, 415–418, 443–446, 471–474, 499–501, 527–530 (1864); cf. Helmholtz, op. cit. (note 14), vol. 1, pp. x–xii.

  • 34 Henry Bence Jones to Hermann Helmholtz, 1 June 1863, HN 222.

  • 35 Helmholtz, op. cit. (note 33).

  • 36 Hermann Helmholtz to Emil du Bois-Reymond, 26 February 1864, in Kirsten et al. (eds), op. cit. (note 24), pp. 207–208 (quotations on p. 207).

  • 37 William Benjamin Carpenter to Hermann Helmholtz, 29 February 1864, HN 85; Hermann Helmholtz to William Benjamin Carpenter, 6 March 1864, Bodleian Library, University of Oxford, MS d.36, f.152.

  • 38 William Thomson to Hermann Helmholtz, 16 March 1864 (quotation), HN 464; Margaret Thomson to Hermann Helmholtz, 25 March [1864], in Thompson, op. cit. (note 10), vol. 1, p. 429. (Thompson misdated this letter as 1863.)

  • 39 Hermann Helmholtz to George Gabriel Stokes, 27 March 1864, Cambridge University Library, Add 7656 H88.

  • 40 John Tyndall to Hermann Helmholtz, 16 January 1864, HN 477.

  • 41 Hermann Helmholtz to Emil du Bois-Reymond, 15 May 1864, in Kirsten et al. (eds), op. cit. (note 24), pp. 208–209.

  • 42 Hermann Helmholtz to Anna Helmholtz, 19 March 1864, in Siemens-Helmholtz (ed.), op. cit. (note 23), vol. 1, pp. 113–115 (quotations on pp. 113–114); Michael Faraday to Hermann Helmholtz, 7 April [1864?], HN 141; John Morley, The life of William Ewart Gladstone (Macmillan, New York, 1903), vol. 2, pp. 536–537; Elizabeth Henry Bellmer, ‘The statesman and the ophthalmologist: Gladstone and Magnus on the evolution of human colour vision, one small episode of the nineteenth-century Darwinian debate’, Ann. Sci. 56, 25–45 (1999).

  • 43 Henry Enfield Roscoe to Hermann Helmholtz, 28 February and 23 March 1864, HN 385; Hermann Helmholtz to Anna Helmholtz, [no day] March 1864; 19, 22, 25 and 31 March 1864; and 2, 5, [no day; probably between 8 and 10], [15], 19 and 20 April 1864, all in Siemens-Helmholtz (ed.), op. cit. (note 23), vol. 1, pp. 113, 113–115, 115–116, 116–117, 117–118, 118, 118–119, 119–120, 120–122, 122–123 and 123, respectively.

  • 44 Hermann Helmholtz to Henry Roscoe, 6 March 1864, Royal Society of Chemistry, London, Library, Henry Roscoe Collection.

  • 45 Hermann Helmholtz to Anna Helmholtz, 5 April 1864, in Siemens-Helmholtz (ed.), op. cit. (note 23), vol. 1, pp. 118–119, at p. 118 (quotation): Helmholtz reports that he met Clifton and Joule at Roscoe's in Manchester. For Clifton, see Robert Fox, ‘The context and practices of Oxford physics, 1839–77’, in Physics in Oxford 1839–1939. Laboratories, learning and college life (ed. Robert Fox and Graeme Gooday), pp. 24–79 (Oxford University Press, 2005), at pp. 42–79; and Graeme Gooday, ‘Robert Bellamy Clifton and the ‘depressing influence’ of the Clarendon Laboratory, 1877–1919’, ibid., pp. 80–118.

  • 46 Hermann Helmholtz to Anna Helmholtz, 5 April 1864, in Siemens-Helmholtz (ed.), op. cit. (note 23), vol. 1, pp. 118–119 (quotation on p. 118). Roscoe and Joule were close friends. Twenty years later, in April 1884, while Helmholtz and his daughter Ellen were again visiting Roscoe in Manchester, Roscoe took Helmholtz to see Joule, who was then 65 years old and unable to work; Joule suffered from ‘extreme shyness and reserve’ and from ‘mental weakness’, and had become ‘a recluse’. Roscoe said that the meeting between Helmholtz and Joule was ‘pathetic’, and that Helmholtz was greatly disappointed. (See Henry Enfield Roscoe to Hermann von Helmholtz, 2 April 1884, HN 385; Hermann von Helmholtz to Anna von Helmholtz, 6 April 1884, in Siemens-Helmholtz (ed.), op. cit. (note 23), vol. 1, pp. 276–277; Henry Enfield Roscoe, The life & experiences of Sir Henry Enfield Roscoe, D.C.L., LL.D., FRS written by himself (Macmillan, London, 1906), p. 120 (for the quotations).)

  • 47 Hermann Helmholtz, ‘On the Normal Motions of the Human Eye in Relation to Binocular Vision’, Proc. R. Soc. Lond. 13, 186–199 (1863–64); reprinted in Helmholtz, op. cit. (note 2), vol. 3, pp. 25–43, quotation on p. 25.

  • 48 Hermann Helmholtz to Anna Helmholtz, [15] April 1864, in Siemens-Helmholtz (ed.), op. cit. (note 23), vol. 1, pp. 120–122, at p. 121.

  • 49 Edward William Brayley to Hermann Helmholtz, 21 April 1864, HN 65.

  • 50 Hermann Helmholtz to Anna Helmholtz, 20 April 1864, in Siemens-Helmholtz (ed.), op. cit. (note 23), vol. 1, p. 123.

  • 51 For the Maxwell quotation see James Clerk Maxwell to Hermann Helmholtz, 12 April 1864, HN 305; for the other quotations see Hermann Helmholtz to Anna Helmholtz, 19 April 1864, in Siemens-Helmholtz (ed.), op. cit. (note 23), vol. 1, pp. 122–123.

  • 52 Helmholtz, op. cit. (note 33), pp. 499–501.

  • 53 Helmholtz, op. cit. (note 33), pp. 527–530, quotation on p. 529.

  • 54 Hermann Helmholtz to Emil du Bois-Reymond, 15 May 1864, in Kirsten et al. (eds), op. cit. (note 24), pp. 208–209.

  • 55 Hermann Helmholtz to Emil du Bois-Reymond, 11 January 1866, in Kirsten et al. (eds), op. cit. (note 24), pp. 219–221, quotation on p. 220.

  • 56 Printed in part in George Haines IV, German influence upon English education and science, 1800–1886 (Connecticut College, New London, CT, 1957), pp. 16–17, citing William A. Tilden, Famous chemists (E. P. Dutton, New York, 1930), p. 239.

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