After electing William Thomson to the Glasgow chair of natural philosophy in 1846, the faculty, as part of the formal admission procedure, directed him to prepare and read a dissertation in Latin on the subject “De caloris distributione per terrae corpus”—the distribution of heat within the earth. By marvelous coincidence, this was a subject close to Thomson’s heart. No doubt he or his father put a word in someone’s ear. The dissertation met with the faculty’s entire satisfaction. The question it addressed haunted Thomson until the end of his life.

In one of his dozen undergraduate publications, Thomson had shown that Fourier’s theory of heat flow implied a fundamental difference between past and future. From some initial distribution of temperature within a solid body, heat would flow inexorably as time marched on, ironing out temperature variations until a state of uniformity emerged. Going back in time, therefore, heat distributions necessarily became less uniform. Thomson proved in 1842 that extrapolating a plausible heat distribution backward in time would in general produce, at some point, an unphysical, impermissible pattern. Mathematically, the solution to the equations became discontinuous or double-valued or otherwise pathological. Physically, heat gradients would become infinite or the temperature indeterminate.

Following up this insight, Thomson applied his reasoning in 1844 specifically to the case of the earth. Regarding it simply as a cooling body with no internal source of heat, he showed that it could not have an unlimited past. In his 1846 dissertation to the Glasgow faculty, he developed this argument further. Among other things he explained how careful measurement of heat loss from the earth’s surface could in principle yield estimates of the age of the earth. This was a novel and striking conclusion, but Thomson had no data to apply to the problem. Characteristically, he would not take the matter further until he could find something quantitative to say about the earth’s age, and left the question as one of many that he would pick up again when the time was ripe.

By the mid-1850s he had begun to think about a closely related problem: the origin of the sun’s heat. In this case, calculations could be attempted. From the known distance of the sun to the earth, and from estimates of the candle power of the sun’s heat at the earth’s surface, a rough idea could be obtained of the total amount of heat—now understood as a form of energy—produced by the sun every second. This energy must come from somewhere; it could not appear out of nothing. Either the sun had some initial reserve, which it was gradually using up, or else energy was coming into the sun by some other means so that it could continuously pump out heat at a prodigious rate with no net loss.

One or two scientists had suggested that a stream of meteors falling constantly on the sun’s surface could provide a sufficient source of energy to account for the output of heat. This idea owed something to Joule’s experimental demonstration that the energy of a falling body could turn into heat. Taking up this idea in 1854, Thomson calculated that about 10 pounds per hour (not quite 100 tons per year) of infalling material could supply enough energy to generate the sun’s heat.¹ This mass, added to the sun every year, would not perceptibly increase its size on the sky even over millions of years, he asserted. Without further ado he concluded that the energy of the sun was “undoubtedly meteoric” in origin.

He had second thoughts, though, as soon as he had delivered the first version of this paper to the Royal Society of Edinburgh in April. A series of footnotes added in May brought out a number of difficulties. If the mass added to the sun in the form of meteors came originally from beyond earth’s orbit, then the increased gravity would change the orbit and thus change the length of the year. He calculated it would have shortened by a month and a half since the beginning of the Christian era, which was surely not possible. As the meteors slowed down in the sun’s outer atmosphere, friction (which generated heat) would significantly slow the sun’s rotation in as little as 32,000 years. And if the meteors all spiraled in at the sun’s equator, how would a uniform glow arise across the whole body?

Thomson was by this time in the habit of discussing his scientific proposals in his extensive correspondence with Stokes, who came up with a related difficulty. If meteors drifted toward the sun from beyond Mercury and Venus, the orbits of those planets would change as the mass of the sun increased. This proved to be a fatal problem. In 1859 the French astronomer Urbain Leverrier announced that he had detected a tiny drift in the orientation of Mercury’s slightly elliptical orbit. Contrary to appearances, this was not good news for the meteor theory. Leverrier’s careful observations set precise limits on the extent to which Mercury’s orbit changed from year to year and forced the conclusion that, if a supply of meteors was to produce the sun’s heat, those meteors would have to be contained within the orbit of Mercury from the outset. To have such a large mass of hidden material hanging about so close to the sun, and drifting inward in an orderly manner over perhaps millions of years, was unfeasible for both theoretical and observational reasons.

Not long after his first pronouncements on solar heat, Thomson became entangled with the Atlantic cable project and made no further progress for some years. He had satisfied himself that any conceivable chemical reactions would be too feeble to supply enough energy and that if the sun had been endowed at birth with some quantity of heat, which had been leaking passively away ever since, it would have cooled very rapidly early on and could not possibly maintain its current temperature even for centuries, let alone millennia or longer. And the meteor theory had run into all kinds of difficulties.

During the hiatus between the first and second series of transatlantic ventures, Thomson, in what was becoming his standard scavenging style, took up an idea originally due to Helmholtz, who had suggested that the sun was born through the coagulation of countless small meteors and other rocky bodies into a single gigantic sphere. As numerous bodies, originally scattered far and wide, came together under their own gravitational attraction, they would gather with increasing speed, and as the bodies finally coalesced that kinetic energy would turn into heat. Thus, Helmholtz argued, originally cold matter spread over a large volume of space could create a single condensed hot body.

Thomson at first put this idea aside because he thought the initial charge of heat would dissipate very quickly. But he came to see that continuing slow contraction of the sun under its own immense gravity would convert gravitational energy into heat in a gradual manner. This was the power of thermodynamic argument: Shrinking released gravitational energy, which had to emerge as heat in the end. The details of the transformation were unimportant. In an essay published in 1862 in Macmillan’s Magazine, a journal of general interest, Thomson concluded that slow gravitational contraction could keep the sun in roughly its present state for a period of at least 20 million years, perhaps as much as 100 million, but certainly not as much as 500 million years.

At about the same time, during 1859 and 1860, Thomson got hold of data on heat loss from the earth, which allowed him to obtain numerical estimates of the planet’s age from the methods he had proposed long ago. When the British Association met in Glasgow in 1855, Thomson had urged official endorsement of a program of measurements to establish the gradient of temperature with depth underground. It was well known that coal mines were hotter at greater depths, but Thomson wanted to know how fast the temperature increased with the descent. On his summer trips to Kreuznach, for his wife’s health, he had noticed and pondered the warm water bubbling up from underground. With Thomson’s encouragement, his Edinburgh colleague J. D. Forbes began measuring temperatures at a range of depths in local rock formations. Thomson applied his analytical powers—and, once again, his acute understanding of Fourier’s methods—to estimate from these measurements

the heat conductivity of the rocks and thus the rate at which heat from the earth’s interior was flowing outward at the surface.

Finally, on April 28, 1862, Thomson read to the Royal Society of Edinburgh his account of heat flow from the earth, and his inferences about the planet’s age. His opening sentence plainly declared a broader and fiercer intent: “For eighteen years it has pressed on my mind, that essential principles of Thermo-dynamics have been overlooked by those geologists who uncompromisingly oppose all paroxysmal hypotheses, and maintain not only that we have examples now before us, on the earth, of all the different actions by which its crust has been modified in geological history, but that these actions have never, or have not on the whole, been more violent in the past than they are at present.”

Thomson began here with a characteristic revisionist flourish. “Eighteen years” refers to the 1844 publication of his first thoughts on heat loss from the earth. But to say that for all this time he had been distressed at geologists’ ignorance of thermodynamics was a mite unfair, as the subject itself only came into being around 1850. This is mere rhetoric, however. Thomson’s annoyance is against the geologists’ embrace of unsound science. In the mid-1800s most geologists held to some version of a general philosophy by the name of uniformitarianism, according to which geological change on and within the earth was going on today at the same rate it had always gone on. Erosion of rocks by wind or water was understood as a slow processe that shaped the planet’s topography, so geologists accepted that the earth had not always looked precisely the same as it happened to look in 1862. But broadly speaking they believed that change was slow, so that the planet had never looked qualitatively different. By tacit implication they also believed that the earth’s past was infinite, or at any rate as long as it needed to be. In other words, geologists felt able to draw on an immeasurable account of time past in order to explain how slow processes had produced the modern world.

As a corollary, geologists also rejected the possibility that there had been eras of abrupt, violent, or catastrophic change in the earth’s past. This explains Thomson’s reference to those who opposed what he called “paroxysmal hypotheses.” His argument was simple. Physics, particularly the new science of thermodynamics, dictated that a cooling earth must have a finite age. It simply could not have existed for the amount of time

that geologists complacently assumed. Therefore, if the present appearance of the planet was to be explained as the result of natural processes, those processes must have at some time worked significantly faster than they did at present. “It is impossible,” Thomson declared in his 1862 article, “that hypotheses assuming an equability of sun and storms for 1,000,000 years, can be wholly true.”

Geologists had not altogether ignored this problem. Charles Lyell, whose 1830 Principles of Geology was a bible of uniformitarianism, had tried to explain the earth’s heat by proposing a thermo-electric-chemical mechanism in the interior. Chemical reactions were supposed to generate heat, which would in turn generate electric currents (thermoelectricity, by which junctions of certain dissimilar metals generate electricity when heated, was discovered in 1821), and this electricity would then dissociate the compounds formed in the original reaction, so the cycle could start over again. This proposal Thomson contemptuously but accurately dismissed as a kind of perpetual motion machine, capable of generating heat yet returning to its starting conditions unchanged—further proof, were it needed, that even the greatest of geologists were innocent of the laws of thermodynamics.

Forbes found that the earth’s temperature rose by about 1° Fahrenheit for every 50 feet of depth. Thomson assumed that the earth had long ago been a uniform sphere, at the same temperature throughout, sitting in empty and absolutely cold space. As heat flowed away from the surface, a temperature gradient would develop in the interior, and simple application of Fourier’s method yielded a formula for the surface temperature gradient as a function of elapsed time. For the initial temperature, Thomson chose 7,000°F, which he got from estimates of the melting point of a variety of igneous rocks. If the earth was hotter in the past, then at some point it must have been molten. A molten earth certainly wouldn’t look anything like the earth today, and life on it would have been impossible. There were numerous assumptions and uncertainties in this calculation, particularly concerning the physical state of rock in the earth’s interior and its heat conductivity and capacity at high temperature and pressure. Nevertheless, allowing some reasonable latitude in such parameters, Thomson estimated, from Forbes’s data, a planetary age of between 20 million and 400 million years.

A certain amount of educated guesswork went into these numbers. Even so, they came out compellingly similar to the numbers Thomson had produced for the age of the sun. He was onto something. The solar system—at least one containing a warm sun and a habitable earth—was around 100 million years old. This was all the geologists could have. It was all physics would give them.

Adding to Thomson’s irritation was the incursion of biology into his subject, in the person of Charles Darwin, whose Origin of Species appeared in 1859. Darwin did not much discuss the amount of time he thought the process of evolution required, but he recognized in a qualitative way that it was a slow business and leaned toward Lyell’s view of an essentially infinite past. In one of the lesser parts of his revolutionary treatise, Darwin undertook the ill-advised task of estimating, from geological analyses of rates of deposition and weathering, the age of the Weald, a sedimentary rock formation in the southeastern corner of England where Darwin had settled after his strenuous travels on the Beagle. The Weald was about 300 million years old, he reckoned, and if so modest a geological feature had so great an age, Darwin felt no unease at assuming much longer periods for the earth as a whole.

In his 1862 paper on the age of the sun, Thomson took a swipe at Darwin’s presumptuousness. The Weald estimate rested on the uniformitarian assumption that present rates of erosion were unchanging throughout geological history, and he showed in any case that even within its limited scope it wasn’t a very astute calculation. Five years later Thomson’s friend Fleeming Jenkin wrote a long review of the Origin of Species and dismissed Darwin’s attempt at quantitative geology as a calculation of the kind engineers refer to as “guess at the half and multiply by two.” By that time, however, Darwin’s book had gone through several editions in the course of which discussion of the age of the Weald had been quietly shelved. Darwin still wanted a long time for evolutionary history, but admitted defeat on this instance. This minor error of Darwin’s forever after colored Thomson’s view of the man and his theories.

Even by the mid-1860s, however, Thomson’s arguments about the age of the earth had produced little change among geologists, who were not quantitative scientists in the modern way. It disturbed him that his

rock-solid thermodynamic arguments were blatantly ignored on the grounds, it seemed, that physics was physics and geology was geology and never the twain shall meet. In 1867, when the British Association met at Dundee, Thomson accosted the geologist Andrew Ramsay, who professed he could happily contemplate 1 billion years, 10 billion if necessary, for the life of the sun. Thomson objected that the sun, being a finite body, could not possibly shine forever. Ramsay responded as if this point of physics had nothing to do with him: “I am as incapable of estimating and understanding the reasons which you physicists have for limiting geological time as you are incapable of understanding the geological reasons for our unlimited estimates.” Thomson rejoined that “you can understand physicists’ reasoning perfectly if you give your mind to it.” It was another example of what he called aphasia, the habit of switching off one’s mind as soon as mathematics was mentioned. So far as he was concerned, Thomson was not telling geologists how to conduct their science, only that their theorizing could not disregard the laws of thermodynamics. It took some time for this elementary point to be appreciated, no matter how hard Thomson pressed it.

***

On the east coast of Scotland in July and August, daylight comes early and leaves late. Every year from 1868 until the close of the century, if the weather was even halfway decent, a tall, rugged man was generally to be found at half past six on these summer mornings, marching determinedly around the windswept links of the venerable golf course at St. Andrews, whacking and walloping a golf ball as he went. He was frequently on his own, getting in a round before his colleagues were up and about, so that he was ready to join them for a second round when they were blearily beginning their first. On a good day he could squeeze in five rounds of 18 holes before twilight stopped him.

A close observer would discover that this man talked to himself a great deal as he went—didn’t talk, rather, but sang or recited or chanted. He knew by heart considerable stretches of Greek and Latin verse and for reasons known only to himself found declamations from Horace or Homer the ideal accompaniment to solo golf. When the classics palled,

he tried a song of his own devising, modeled on the popular ditty “Star of the Evening”:²

and so on for nine verses.

This man, six feet two and a half inches in his boots, with thick beard and high forehead, was Peter Guthrie Tait, professor of natural philosophy at the University of Edinburgh. He had taken up the position in 1860, when Forbes retired. J. M. Barrie, the author of Peter Pan and a former Edinburgh student, recalled Tait’s fearsomeness in the lecture room: “The small twinkling eyes had a fascinating gleam in them; he could concentrate them until they held the object looked at; when they flashed round the room he seemed to have drawn a rapier. I have seen a man fall back in alarm under Tait’s eyes, though there were a dozen benches between them.” On the links at St. Andrews, Tait golfed with speed and determination and nary a second thought; he picked a shot, hit it firmly, and went on to the next one. He wrote mathematics and physics the same way. Seven years younger than William Thomson, he had enthusiastically embraced the new style of mathematical physics that was coming of age as he acquired an education. Like Thomson, he embraced the principle of energy conservation not merely as a law of physics but as a foundation stone to all of science.

Tait, born and raised in Edinburgh, had been senior wrangler at Cambridge in 1852. Never was the title more appropriately bestowed. Nothing gave him more joy than a fierce dispute, and he would turn even small points of scientific disagreement into full-blown wrangles if he could find a way. The argument over the age of the earth suited him perfectly, setting as it did the hard principles of mathematical science against the lax and ignorant speculations of geologists. Through the late

1860s, a frustrated Thomson had repeated his charge against uniformitarianism, with little perceptible effect. At the end of 1865 he had read to the Royal Society of Edinburgh a short paper, “The ‘Doctrine of Uniformity’ in Geology Briefly Refuted.” Brief refutation indeed: Geologists assumed an infinite past; physics dictated it must be finite. He presented once again his proof that the earth must have been molten around 20 million years ago. This remonstration drew little response.

In February 1868 he tried again with a lecture, “On Geological Time,” delivered to the Geological Society of Glasgow. He began bluntly: “A great reform in geological speculation seems now to have become necessary.” Once again he talked of the cooling of the earth and of the impossibility of the sun shining forever. He tried out a new, more complex argument, which he said he had first heard from his brother James, though it seemed to go back ultimately to the observation by Kant that ocean tides, through friction, would slow the earth’s rotation. Making quantitative use of this undoubted fact was tricky. Thomson reasoned that if the earth was originally molten and spinning, it would have assumed a slight nonspherical shape, flattened at the poles and bulging at the equator. If it then solidified and remained rigid that original figure would stay the same. From measurements of the known departure of the planet from strict spherical form, Thomson hoped to deduce the original rate of rotation when it was born and use estimates of tidal friction to calculate how long it would take to slow down to the present rate of rotation, once every 24 hours. He claimed to get a limit on the age of the earth consistent with his other calculations.

This was further demonstration that the uniformitarian assumption must be mistaken. He returned in conclusion to his original arguments about energy loss from the sun and the earth, which he regarded as unanswerable. “Now, if the sun is not created a miraculous body, to shine on and give out heat for ever, we must suppose it to be a body subject to the laws of matter…. Imagine it as we please, we cannot estimate more on any probable hypothesis, than a few million years of heat. When I say a few millions, I must say at the same time that I consider one hundred millions as being a few.” He would concede 100 million years but drew the line at 500 million.

Perhaps because he at last spoke directly to an audience of geologists, Thomson finally drew a response, though not for almost a year later and

not from a scientist intimately associated with geological thinking. Thomas H. Huxley had earned the sobriquet “Darwin’s Bulldog” for his tenacious debating on behalf of evolutionary theory, particularly in his contest with Bishop “Soapy Sam” Wilberforce at the 1860 British Association meeting in Oxford, when he famously declared that if he could choose his ancestors he would take an ape over the bishop. Huxley thought of himself as a generalist and an orator, but his first interest remained the biological sciences. It was Thomson’s complaint about Darwin rather than uniformitarianism that mostly captured Huxley’s attention. In letters to colleagues Darwin confided that “Thomson’s views of the recent age of the world have been for some time one of my sorest troubles” and when thinking of the long periods of time evolution required, he noted ruefully, “then comes Sir W. Thomson, like an odious spectre.”

In February 1869 Huxley used his presidential address to the London Geological Society to take up Thomson’s challenge directly and defend the honor of the geologists and the biologists. He seized on Thomson’s changing theories of the origin of the sun’s heat and on admitted uncertainties in estimates of the age to suggest that the physical arguments were not nearly as secure as Thomson claimed. He explained that in any case Thomson was fighting a straw man: No modern geologist, Huxley asserted, hewed to the strict uniformitarian line anymore. He mentioned Thomson’s limit of 100 million years and asked rhetorically whether any geologist had ever wanted more than this. This was a little slick, since Darwin himself had wanted 300 million years for the age of the Weald, though that number was no longer mentioned.

For all his eloquence, however, Huxley was out of his depth in dealing with mathematical physics and the laws of thermodynamics, and he resorted more than once to meaningless bluster. “The rotation of the earth may be diminishing, … the sun may be waxing dim … the earth itself may be cooling. Most of us, I suspect, are Gallios, ‘who care for none of these things,’ being of the opinion that, true or fictitious, they have made no practical difference to the earth, during the period of which a record is preserved in stratified deposits.”³ Not unlike Whitehouse when

attacking Thomson’s theory of the submarine telegraph, Huxley hinted that niceties of academic theory were somehow inapplicable to the practical world of geology and biology. He concluded with a fine flourish: “I speak with more than the sincerity of a mere advocate when I express the belief that the case against has entirely broken down. The cry for reform which has been raised without, is superfluous, inasmuch as we have long been reforming from within with all needful speed. And the critical examination of the grounds upon which the very grave charge of opposition to the principles of Natural Philosophy has been brought against us rather shows that we have exercised a wise discrimination in declining to meddle with our foundations at the bidding of the first passer-by who fancies our house is not so well built as it might be.”

At last Thomson had an opponent willing to speak out. Reading of Huxley’s dismissal of the case, he responded in April at the Geological Society of Glasgow, lamenting once again that “so many geologists are contented to regard the general principles of natural philosophy, and their application to terrestrial physics, as matters quite foreign to their ordinary pursuits.” He dredged up remarks from a number of recent geological writings to show that, in some quarters anyway, belief in the possible infiniteness of the past still existed. He had nothing new to say scientifically but bristled at Huxley’s accusation of meddling: “I cannot pass from Professor Huxley’s last sentence without asking, Who are the occupants of ‘our house,’ and who is the ‘passer-by’? Is geology not a branch of physical science? Are investigations experimental and mathematical, of underground temperature, not to be regarded as an integral part of geology? … For myself, I am anxious to be regarded by geologists, not as a mere passer-by, but as one constantly interested in their grand subject, and anxious, in any way, however slight, to assist them in their search for truth.”

Into this more or less gentlemanly contest the rumbustious Professor Tait now inserted himself. In a lengthy review of the addresses by Thomson and Huxley, along with some other contributions, Tait

marched in with all the unsubtlety he could muster. He faulted Thomson only for responding in “the mildest and meekest spirit” to Huxley’s charges; this, Tait feared, “weakens, not his cause but, his chance of a hearing by not sufficiently showing his teeth.” Tait had no such reservations. To Huxley’s suggestion that application of mathematical methods to geology was somehow inappropriate, he responded scornfully: “Mathematics … cannot be usefully introduced until we have arrived at something a little beyond what may be called the mere ‘beetle-hunting’ or ‘crab-catching’ stage…. Let us then hear no more nonsense about the interference of mathematicians in matters with which they have no concern; rather let them be lauded for condescending from their proud pre-eminence to help out of a rut the too ponderous waggon of some scientific brother.”

Huxley’s address, according to Tait, was “clever, dashing, and plausible; but when perused with attention it is found to be seriously illogical.” He noted that geologists varied widely in the length of the past they desired; Huxley even seemed to think that the 100 million years Thomson would allow was not so bad. But then, Tait wondered, why did Huxley side against Thomson with those geologists who persisted in thinking the past infinite? He had a nice answer: “As we have but too lately seen, when two Irish mobs are engaged in the sweet pastime of murdering one another, the interference of the police at once reconciles the hostile factions into one great brotherhood.”

From time to time Tait paused to inject a compliment toward Huxley as one of the foremost men of his discipline, but these pleasantries only served to introduce further insults and charges of scientific ignorance. Having laid waste to the foolish and insupportable beliefs of geologists and biologists, as opposed to the clear-eyed facts that Thomson had set before them, Tait closed his review of the subject by tightening the screws further: “In truth, when we come to examine the question as a whole, giving its full weight to each of the separate details, we find that we may, with considerable probability, say that Natural Philosophy already points to a period of some ten or fifteen millions of years as all that can be allowed for the purposes of the geologist and paleontologist; and that it is not unlikely that, with better experimental data, this period may be still farther reduced.”

Now this was remarkable. Having thoroughly castigated Huxley and the rest for offering hopeful opinions instead of mathematically precise arguments, Tait finished with an embellishment of Thomson’s reasoning drawn from thin air. He had no reason to say 10 million years rather than 100 million, apart from his eagerness to make life uncomfortable for the geologists. And his judgment that new data, as yet unknown, would most likely reduce the number further is as pure a piece of illogic as anything he criticized in Huxley. If Huxley was Darwin’s bulldog, Tait was aiming to be Thomson’s terrier. A few years later, in lectures intended for a general audience, Tait reiterated his severe views: “We cannot give more scope for [geologists’] speculation than about ten or (say at most) fifteen millions of years.” If geologists found this irksome “so much the worse for geology…. [P]hysical considerations from various independent points of view render it utterly impossible that more than ten or fifteen millions of years can be granted.”

Tait even managed to suggest that 10 million years might be generous, using an exaggerated version of the tidal friction argument in which he assumed that the earth solidified instantly when it had cooled sufficiently and remained absolutely rigid thereafter. For neither of these extreme assumptions did he have any good grounds, but they produced a small age and that was recommendation enough.

Thomson himself never insisted on an age unequivocally less than 100 million years, yet he never clearly dissociated himself from his friend Tait’s opinion that anything more than 15 million years was “utterly impossible.” Plenty of geologists could see that Tait’s vehemence was mostly hot air—Darwin thought his views “monstrous”—but they lacked the mathematical and physical skill to take him on. Tait succeeded in making the battle fierce and uncompromising, which was greatly to his liking, but his strategy in the end backfired. Compared to Tait’s shrill prosecutions, Thomson’s admonitions began to seem reasonable, and his allowance of 100 million years generous. That, perhaps, was a period of time the geologists could work with.

***

This was not the first time Tait had taken up the cudgels on behalf of his excessively polite friend Thomson. In 1862 the two had written an

article entitled “Energy” for the magazine Good Words, which was edited by Thomson’s friend the Reverend Norman Macleod. Ostensibly the authors wished to bring to a general audience the new and essential scientific concept of energy, but what impelled them to put pen to paper was an article published earlier that year arguing that credit for demonstrating the equivalence of mechanical work and heat, and by extension credit for what had become the general law of energy conservation, should go not to Thomson’s close friend Joule but to an obscure German physician by the name of Julius Robert Mayer.

This allegation had come up before. Writing to Thomson in December 1848, Joule had mentioned that “a German of the name of Mayer has set up a claim for the discovery of the equivalent upon the ground that he asserted in 1842 that the heat produced by compressing air was the equivalent to the force employed although he made no experiments to prove it. This is disagreeable to me as it has involved the necessity of writing in reply to the Comptes Rendus [the journal of the French Academy of Sciences] but I will not be drawn into a controversy on the subject of priority beyond one rejoinder. I do not want to monopolize. The merit will belong to all those who have worked out the doctrine.”

A modest and unassuming man, Joule told Thomson: “I have not the slightest wish to detract from Mayer’s real merits, and I hope I have said nothing which may be thought acrimonious or unfair.” Mayer responded in turn to Joule, who refused to be drawn. As he explained to Thomson, his view was that while Mayer had undoubtedly proposed an equivalence between mechanical work and heat, he had offered no empirical evidence to back up the assertion. Joule, painstakingly, had done numerous experiments to demonstrate the equivalence, and as he said in another letter to Thomson, “I have not pursued the controversy further because the facts are before the scientific world and I shall be perfectly satisfied with its verdict, whatever it may be.”

Joule’s reticence had the desired effect. The Comptes Rendus published a handful of brief communications, no one else weighed in, and there the matter rested. Until June 6, 1862, that is, when John Tyndall, Faraday’s assistant at the Royal Institution, gave a public lecture in which he reiterated Mayer’s claim and hinted that credit was not being given because Mayer was both a foreigner and an outsider, not part of the inner

circle of reputable scientists. The lecture appeared a little later in the Philosophical Magazine, where it came to the attention of Thomson and Tait.

Like Tait, Tyndall had a habit of contentiousness. His grandfather, for obscure reasons, had disinherited his father out of some modest property in County Carlow, Ireland, south of Dublin, leaving the younger Tyndalls to fend for themselves and bestowing on John, it would seem, a permanent sense of grievance against privilege and establishment. Learning mathematics from the books of Professor James Thomson, Tyndall found work as a surveyor first in Ireland and then in England in the railway boom of the early 1840s. He got himself sacked for protesting about pay and conditions on behalf of the junior employees. “I suffer in a righteous cause,” he recorded in his diary, and when his father suggested he might be wise to moderate his passions he shot back, “I am not stubborn, but what do you want me to do? Is it to unsay what I have said? I have said nothing but the truth. Shall I crawl like a guilty reptile to the knees of Captain Tucker and stain my conscience with a falsehood by telling that I am sorry for what I have done? … If I be wrong, you should not have taught me to be honest, as honesty and truth have been my guiding light in this transaction.” He was 23 at the time, fired with youthful passion for the underdog.

For a few years he bounced from one railway job to another, more than once losing a position amid the numerous legal disputes that raged between companies seeking regional rights and monopolies. By 1847 railway mania was collapsing, and Tyndall found a position as a teacher at Queenwood, a Quaker school in southern England that had started life as Harmony Hall, an educational institution for workers founded by the socialist pioneer Robert Owen. There Tyndall discovered a talent for teaching and an appetite for science, and at the urging of one of his fellow teachers went to the University of Marburg, Germany, to study with the chemist Robert Bunsen. Over the next several years he shuttled between England and Germany, publishing experimental researches mainly in the Philosophical Magazine, getting to know Faraday, Huxley, and a few other London luminaries, but maintaining close ties also with the German academic world.

In 1853 he gave a successful popular lecture at the Royal Institution,

earning an invitation to give four more at £5 each. Later that year he won permanent appointment to the Royal Institution and remained there the rest of his life. Tyndall scraped together a living from his modest salary, along with fees for lecturing, writing, and translating. In later years he wrote books that brought in extra income. He made a few modest experimental discoveries but was by no means a remarkable or original scientist, tending to throw out qualitative ideas on general grounds rather than work out fine details. Some saw him as an opportunist and self-promoter, though he had an ally in Huxley, who likewise contributed more to science as a disseminator and interpreter than as an innovator. In 1853 Tyndall was told informally he would be awarded one of the Royal Society’s annual research medals, but several fellows grumbled that other scientists had greater claims to priority, and Tyndall angrily withdrew his name rather than be the subject of back-room bickering.

Tyndall’s enemies may have seen this as a piece of rough justice, since Tyndall had already started to make a name for himself as a man eager to engage in priority battles, usually on behalf of continental scientists whose work was unknown or ignored in Britain. In 1852, at the British Association meeting in Belfast, he made a favorable impression with an account of his recent work on the magnetic properties of certain crystals, but also publicly criticized William Thomson’s theoretical opinions on the subject, and for good measure told the assembled scientists that the theory of solar prominences advanced by their countryman Charles Piazzi Smyth had been enunciated earlier by the German astronomer Feilitzsch.

Thomson’s ideas on magnetism were evolving during this period, and a few years later he had come around to an interpretation more in line with Faraday’s thinking. Tyndall recorded in his diary the dim view he took of this: “Thomson completely backed out of the position which he had assumed in Belfast, and completely disowned the interpretation of his own views as stated in Faraday’s lecture. Thomson has in fact backed out of every position he has assumed in regard to the phenomena of diamagnetism and magne-crystallic action. And he has done so, leaving the public to suppose that he had been misconstrued or misapprehended; which tact may generally increase his reputation with the general public,

but in the private opinion of me at least does not add a whit to his nobleness.”

Thomson could change his mind, of course. Any good scientist must abandon old and incorrect ideas in favor of new and better ones. What rankled with Tyndall, though, was Thomson’s habit of speaking as if his earlier views belonged to some forgotten and unimportant era, or hinting that the erroneous ideas he once held were not genuinely wrong but merely inarticulate stumblings toward the more sophisticated opinions he now embraced. Worse, Thomson had a way of picking up all manner of ideas and hints from whatever he read and whomever he spoke to, recasting these bits and pieces into a finished theory, then talking as if he had come up with the whole thing himself. Tyndall saw dishonesty in this, but Tait, who had on occasion seen his own suggestions to Thomson bounced back at him later as Thomson’s own, interpreted his friend’s character benignly. He is a “most absolutely honest man,” Tait wrote. “There is no doubt that he cannot distinguish between what he thinks, and what he hears;—for he never pays full attention to anything, he is always also thinking on something else; so that what he hears gets mixed with what he thinks; and he takes it for his own.”

Tyndall, at any rate, was primed for battle when the question of Mayer’s priority came to his attention. Tyndall’s closest friend described him as sometimes “peremptory, abrupt and dogmatic…. He enjoys an intellectual fence for its own sake, and I am not sure that his own dexterity in inflicting sharp lashes is not a source of amusement to him.”

In 1825, Faraday had begun a series of Friday evening public lectures at the Royal Institution, which served both to bring scientific innovation to a larger audience and to bring money to the struggling institution. Tyndall, who like Faraday was a lively lecturer and demonstrator of scientific experiments, continued the tradition and in 1862 decided to discourse on heat. Understanding of heat, energy, and mechanical work had revolutionized science thoroughly, but the concepts were little appreciated or understood in the world at large.

Tyndall asked Clausius for advice on the origins of the modern theory, and Clausius sent a bundle of papers, including Mayer’s as well as his own contributions. This, it seems, was the first time Clausius had bothered to look closely at Mayer’s writings. He was, he wrote to Tyndall,

“astonished at the multitude of beautiful and correct thoughts they contain.” Tyndall likewise was taken aback to find, in Mayer’s little-known paper of 1842, a comprehensive statement of the equivalence of physical action, whether of chemical, electrical, gravitational, or mechanical form, and of the further equivalence of heat to all these phenomena. Mayer had concluded with an estimate of the mechanical equivalent of heat—the number that Joule had worked so hard to find out and which he had first published a year later, in 1843. In another paper came the suggestion from Mayer that meteors falling into the sun provided its heat.

Accordingly, in his 1862 lecture, Tyndall talked of the work needed to raise a body against gravity, the heat released by the same body when it fell and slammed into the earth, the ability of electric currents to make magnets move, the energy generated in a chemical reaction, and so on. He described the universal concept of energy underlying all these seemingly distinct phenomena and asked rhetorically, “To whom, then, are we indebted for the striking generalizations of this evening’s discourse? All that I have laid before you is the work of a man of whom you have scarcely ever heard. All that I have brought before you has been taken from the labours of a German physician, named Mayer. Without external stimulus, this man was the first to raise the conception of the interaction of natural forces to clearness in his own mind. And yet he is scarcely ever heard of in scientific lectures, and even to scientific men his merits are but partially known.”

Tyndall went on to mention Joule’s “beautiful researches … quite independent of Mayer” but emphasized again that Mayer had calculated the mechanical equivalent of heat a year earlier. He talked of a meteoric origin for the sun’s heat, and how in 1854 “Professor William Thomson applied his admirable mathematical powers to the development of the theory; but six years previously the subject had been handled in a masterly manner by Mayer, and all that I have said on the subject has been derived from him.”

Tyndall’s fiery sense of justice led him to a vigorous endorsement of Mayer: “Here was a man of genius working in silence, animated solely by a love of his subject, and arriving at the most important results some time in advance of those whose lives were entirely devoted to Natural Philosophy.” No doubt Mayer’s work had been neglected, and no doubt too

Tyndall’s effort to reinstate him was sincere. But in repeatedly stressing the German’s priority over both Joule and Thomson, he went out of his way to needle the big names of British science.

This attempt to put Mayer ahead of Joule came to Thomson’s attention during the summer of 1862, when Tait was visiting him on the Isle of Arran. In writing a rebuttal they were obliged to face an inconvenient fact: Mayer had indeed published a statement of the equivalence of heat and other forms of energy, along with a calculation of the mechanical equivalent of heat, in 1842, a year before Joule. With Thomson’s malleable view of history bolstered by Tait’s pugnacity and adaptable sense of logic, their article on energy tried to set matters straight. “We were certainly amazed,” they began, “to find in a recent number of a popular magazine, and in an article specially intended for popular information, that one great branch of our present subject, which we had been accustomed to associate with the great name of Davy, was in reality discovered so lately as twenty years ago by a German physician.”

Bringing Humphry Davy into the argument was a smart dodge. Davy had allegedly, in the early years of the 19th century, tried an experiment of rubbing two pieces of ice together to see if heat from friction would melt them. It is very hard to imagine how this experiment could have been done convincingly. Davy apparently held the ice by tongs but still, heat could have conducted down them into the ice. Ideally he should have done his experiment under vacuum, so that heat from the air would not melt the ice. In his long account of 1851 on the new theory of heat and work, Thomson had begun by briefly mentioning Davy and also Count Rumford, born in prerevolutionary Massachusetts as Benjamin Thompson, who as a military engineer in Bavaria had noted as early as 1798 the generation of heat by drill bits used to bore out cannons.

Both Davy and Rumford, Thomson said, had provided evidence for heat being a dynamical phenomenon, not an intangible fluid, but it seems that these early ideas only impressed themselves on Thomson’s attention after he had belatedly accepted Joule’s evidence for the dynamical nature of heat. Nonetheless, in their 1862 article on energy, Thomson and Tait now declared firmly that the relationship of heat and motion “remained a conjecture, unsupported by scientific evidence, until the proof was furnished by Davy…. But it is not to be imagined that for all this the

pleasant fiction called Caloric was to be abandoned; and consequently, for upwards of forty years after Davy’s proof of its non-existence, caloric was believed in, written about, and taught, all over the world.”

Breathtakingly absent from this summary is any hint that among those who clung for years to a belief in the “pleasant fiction called Caloric” was Thomson himself. The authors moved swiftly on: “The founder of the modern dynamical theory of the heat, an extension immediately beyond anything previously surmised, is Joule. As early as 1840 we find him investigating the heat generated by electric currents, and in 1841 he published researches which contain the germ of the vast developments of dynamical science as applied to chemical actions. In 1843 he published the results of a well planned and executed series of experiments, by which he ascertained that a pound of water is raised one degree Fahrenheit in temperature by 772 foot-pounds of mechanical work done upon it.”

This elaborate recitation is intended to make clear that, although Joule had not published his work until 1843, he had working up to it for a number of years before that. But of course! And so, one may equally well imagine, had Mayer been thinking about the matter for some time before 1842. But that was of no concern to Thomson and Tait, who finally mention Mayer’s 1842 paper only to say that in it “the results obtained by preceding naturalists are stated with precision—among them the fundamental one of Davy—new experiments are suggested, and a method for finding the dynamical equivalent of heat is propounded. On the strength of this publication an attempt has been made to claim for Mayer the credit for being the first to establish in its generality the principle of the Conservation of Energy.” It was true that Mayer mentioned Davy’s alleged experiment, as an example of the general principle he was discussing, but the implication that Davy had prefigured the general idea of the conservation of energy is entirely misleading.

All in all, Thomson and Tait’s account is astonishingly dishonest. They are careful not to say anything demonstrably untrue, but pick and choose from scientific history and allow the reader to conclude that Mayer, far from saying anything new, merely summarized what was already well known in 1842. The tendency to interpret the past fluidly is perhaps Thomson’s; the belligerence and elision of inconvenient facts are no doubt Tait’s. The purpose of the article is not to review the origin of

the conservation of energy; it is to place Joule above Mayer by whatever means lend themselves.

Why the great animus against Mayer? Two reasons stand out, one personal and the other philosophical. Thomson had for some years resisted Joule’s argument that mechanical work could create heat, but once convinced, he had all the zeal of the convert and praised Joule above everyone else—Joule being the greatest precisely because he had succeeded in changing Thomson’s mind. Conversely, to accept that someone else besides Joule had made the connection clear would be to imply that Thomson ought to have seen the truth sooner than he did.

The philosophical reason has more substance. Mayer’s 1842 paper contained a great deal more vaporous rhetoric than rational analysis. Although he adduced various examples of physical phenomena, his case rested on a vaguely Kantian assertion that all natural events must have true and proximate causes, that nothing uncaused could happen, and that therefore physical “effects” of any sort could not appear and disappear spontaneously. The language of energy did not yet exist. A thinker as illustrious as Helmholtz, in 1847, talked of the conservation of “force,” that term being used interchangeably for the distinct concepts now labeled force and energy. Mayer thus spoke of something being conserved without any precise sense of what that something was.

His calculation of the mechanical equivalent of heat Thomson and Tait attacked vigorously. Take away this numerical estimate and Mayer’s paper was nothing but windy prose and metaphysics. Mayer imagined a volume of mercury falling in a glass column, compressing and heating the air beneath it, thus turning the energy of the fall into heat. From simple mechanics and the approximately known properties of air, Mayer came up with a number that was, unhappily for Thomson and Tait, not far from the right answer. Their complaint was that Mayer gave no good reason for assuming that all the energy of a falling weight would go into heating the compressed volume of air. For an ideal gas this would be the result, though whether Mayer knew that is unclear. Air is not an ideal gas—but it’s close enough.

It was Joule, Thomson and Tait insisted, who had performed careful experiments to establish that mechanical energy turned into heat with a consistent conversion factor, and from this empirical basis he had argued

for the universality of energy. This was how science must proceed: from observation and experiment to theoretical principle. Mayer had it backwards. He had assumed, on dubious metaphysical grounds, a theoretical principle, then had made an unjustifiable calculation of the mechanical equivalent of heat, which by pure luck gave the correct answer. This, above all, Thomson and Tait found intolerable. Mayer had not done the work or propounded good science; he didn’t deserve credit for making a lucky guess.

Inevitably, Tyndall had to reply to Thomson and Tait, and Tait could not resist replying again for his side. The Philosophical Magazine carried charges and rebuttals and countercharges for several months. Joule wrote briefly, in his levelheaded way, to say that Mayer indeed deserved more recognition than he had received but that “to give to Mayer, or indeed any single individual, the undivided praise of propounding the dynamical theory of heat, is manifestly unjust.” For himself he claimed the first “decisive proof” of the dynamical nature of heat, but no more than that. Tyndall responded that he didn’t mean to detract from Joule’s merit, but defended Mayer against the charge that he didn’t know what he was doing. He made some captious remarks about Thomson and Tait putting a scientific question before the readership of Good Words, as if the general public was somehow to adjudicate the dispute. Tait responded that the magazine published one scientific article in every issue, and anyway Tyndall was in no position to talk, seeing that he had published essays in Macmillan’s Magazine, alongside articles on “Water Babies, Sunken Rocks, and Women of Italy.” (Of course, Thomson had published one of his serious discussions on the age of the earth in Macmillan’s; Tait did not mention that.)

Tyndall translated Mayer’s papers and arranged for their publication in the Philosophical Magazine, of which he had been an editor for some years now. Having earlier stated his admiration and respect for Joule, he now noted that Joule’s initial determinations of the mechanical equivalent of heat “were so discordant that nobody attached any value to them” and that Helmholtz (Thomson’s great friend—a nice touch!) had in 1847 paid little attention to Joule’s work for precisely that reason. Tait responded brusquely that the correct value could, even so, be found in a footnote to Joule’s first paper. Tyndall, slightly abashed, admitted that he

hadn’t noticed this footnote until now, but in any case, what about all the other discrepant numbers in the body of the paper?

These exchanges make immensely tedious reading. Several other names came up: Sèguin and Verdet, both French, and Colding, a Dane, had all made statements sounding like inarticulate versions of a law of conservation of energy before Mayer came into it. Tait, stretching his powers of interpretation to the limit, wanted Tyndall to admit that Isaac Newton himself had understood energy conservation, or rather would have, had he understood heat and light and electricity and magnetism better than he could have done at the time.⁴ Tait wrote with belligerence and bluster to cover up the holes in his logic. Tyndall responded with Victorian high dudgeon: “What you have the hardihood to affirm, you certainly must have the goodness to prove or the manliness to retract.”

Over about a year the debate fizzled, neither side admitting defeat or acknowledging agreement. Thomson contributed only once. Tyndall on one occasion addressed Thomson rather than Tait, implying none too delicately that he wished to speak to the organ grinder not the monkey. Thomson replied in a brief letter to the editors, objecting to being addressed over Tait’s head, saying he did not wish to participate in the discussion but professing full confidence in whatever his colleague said. “Allow me to say I consider a great injury to myself that I should be made even apparently the medium of the statements which Dr Tyndall addresses to me regarding my friend Professor Tait,” he concluded, withdrawing from the discussion.

Apart from possible therapeutic benefits to Tyndall and Tait, the controversy achieved little. As Joule had said at the outset, no one person deserves credit for formulating the principle of energy conservation. In vague and speculative form, the idea had been around for some time. As different forms of energy and their interrelationship were understood, the notion grew clearer. Helmholtz, in his 1847 essay, contributed little that was original, but stated a number of points more precisely and sys-

tematically than had been done before. Historian of science Clifford Truesdell has argued, on the other hand, that the first incontrovertible and mathematically correct statement of a true conservation law came from William Thomson himself, as late as 1851.

The point is a perhaps an excessively sophisticated one. When Clausius, in 1850, modified Carnot’s reasoning by allowing heat and work to interconvert, he had in mind that gas was a collection of atoms or molecules, so that heat was their energy of motion. But he also recognized that there could be forces of attraction or repulsion between these molecules. In that case, when energy was used to compress a gas, say, some of it would go not into a change of temperature but into overcoming intermolecular forces. To accommodate this possibility Clausius invented what is now called “internal energy,” which became part of the accounting needed to depict the thermodynamic state of a gas. However, Clausius seems to have decided, on the basis of his molecular picture of a gas, that the internal energy would have the properties it needed to have to make his revised version of Carnot’s argument come out right.

Thomson, in his series of papers “On The Dynamical Theory of Heat,” took up this question with more care. He saw that he couldn’t found a rigorous set of thermodynamic laws if he depended on the wholly unproven hypothesis that a gas consisted of molecules. Instead, he was able to show on quite general grounds, and independent of any assumption about the true constitution of gases, not only that the internal energy must exist but that it had all the correct mathematical properties and relationships to other properties to allow it to serve as a genuine thermodynamic function.

Truesdell argues that this was the real foundation of a rigorously stated law of conservation of energy. Then again, one might say that energy conservation as an overarching concept was established by this time and that Thomson’s achievement here was to demonstrate exactly what form the first law of thermodynamics, as a particular instance of energy conservation, must take.

These are academic arguments, in both the good and bad senses. That such niceties remain debatable today illustrates the hopelessness of trying to apportion credit among the many scientists who contributed to the formulation of the laws of energy conservation and thermodynamics.

Tyndall’s estimation of Mayer was excessive. Tait’s position, both variable and extreme in that he would give pride of place sometimes to Joule, or to Davy, or to Newton, but never to a German, was absurd. Thomson’s opinion on the matter remains enigmatic. He praised Joule unceasingly, rarely pushed hard for his own case (unless writing with Tait), and even after the spat with Tyndall could be generous to Mayer. In his 1868 lecture “On Geological Time,” he made passing reference to “Mayer, the great German advocate of the modern theory of heat, who did so much to urge the reception of the idea of an equivalence between heat and mechanical power.” This reinforces a suspicion that the harsh words against Mayer in “Energy” came mostly from Tait, admittedly with Thomson’s acquiescence. Thomson didn’t care much for history, his own or anyone else’s. He was inclined to say, and probably even believe, whatever seemed appropriate or congenial at the time.

***

Through these years Margaret Thomson remained an invalid, often housebound though accompanying her husband on summer trips to Arran or to Kreuznach, where the waters failed to cure her. Late in 1862 she suffered a fall that did her no physical harm but left her shocked and nervous. Poems from later years record episodes when death, her angel, fluttered closer. From August 20, 1866:

Struggle, submit, yield: she survived anyway. In 1868 the Thomsons spent some weeks at Bellagio, on Lake Como in northern Italy, before retreating over the Alps to Bad Kissingen, whose waters had been recommended for Lady Thomson, as a change, presumably, from the waters at Kreuznach. The same doctor told Thomson his lame leg would benefit from immersion, but as much as he hoped for a miraculous cure for his wife, he had little time for dubious treatments on his own account. As he told his sister Elizabeth, “I have commenced trying [the waters], but my

faith is not so great in their efficacy.” Even so he wrote to Helmholtz that “my wife has been feeling much better and able to walk since she came here, and it seems as if she had derived real benefit from the waters.”

Thomson maintained constant hope for improvement in Margaret’s condition, despite all evidence to the contrary. Friends and colleagues testified occasionally to Margaret’s lively intelligence and charm. Her poems spoke otherwise. From Bellagio in 1868, from the sun and the warmth and the soothing, gorgeous landscape of Italy, she concluded an ode to death thus:

In the second half of 1869 her health became decidedly worse, to the point where her doctors would not allow travel at all. That winter Thomson took his wife to the Scottish coast at Largs, away from the smoke and grime of their Glasgow residence, where they still lived in one of the old college houses squeezed among the city’s slums. He refused to teach the spring classes, so that he could stay with her in the fresh sea air. The university engaged a substitute teacher for that session. Margaret’s health declined steadily, but Thomson took her occasional rallies as slight cause for optimism. Though Margaret’s sister and others assisted him, he spent many hours at his wife’s bedside. He could sleep apparently at will and got up at three every morning to take over nursing duties. Margaret Thomson died on June 17, 1870, bringing to a close the 17 years of nameless ill health she had endured since overtaxing herself on her honeymoon tour.

Thomson’s commitment to his wife had been one of uncomplaining devotion rather than passion. Her loss created an absence in his life—an absence not so much of emotion as of occupation. His immediate solution was work and travel. Although the Atlantic expedition of 1858 and the tussle with Whitehouse had demonstrated the virtues of his mirror galvanometer, Thomson had long sought to remedy its one flaw: It needed an operator to stand by at all times and record the flickering motion of

the light beam as it registered incoming signals. Electromechanical devices of the old Morse type had evolved into machines that punched marks onto a paper tape, but these instruments demanded bigger electric pulses than long oceanic telegraphs could provide. Thomson tried for a while to build a device that would record electric sparks as scorch marks on paper strips, but failed to produce a reliable or sensitive system.

In 1867 he took out a patent on a new instrument, which he called his siphon recorder. A fine stream of ink passed down a narrow glass needle, which Thomson adapted from needles used to administer vaccines. As in the mirror galvanometer, this “siphon” was connected to a small magnet that moved from side to side in response to electrical signals. A paper tape ran beneath the tip of the needle. The important innovation in the siphon recorder was that Thomson devised a system to electrically charge the ink in its reservoir, so that electrical repulsion constituted an internal pressure driving the ink through the needle. This was an electric rather than a mechanical pump, pushing a finely controllable ink jet from the end of the siphon.

This new technology was ingenious but delicate. It took Thomson two years of fiddling to make a prototype good enough to install at a telegraph station, where it could be tested alongside the mirror galvanometer. In fact, one might argue it took around 120 years of development for the siphon recorder to graduate to a trustworthy piece of technology. The modern inkjet printer, which became affordable and dependable only in the late 1980s, uses essentially the trick that Thomson dreamed up in the 1860s.

By the summer of 1870, following Margaret’s death, Thomson was eager to take to the seas again to try out the latest version of his siphon recorder. The operators of the French Atlantic cable, which ran from Brest to St. Pierre, had been using siphon recorders with mixed success for about a year. A long cable from Falmouth, on the southwestern coast of England, to Bombay began transmitting in April 1870, and the Prince of Wales, among other distinguished guests, saw messages arrive in London on one of Thomson’s siphon recorders.

Thomson spent several weeks in Cornwall tinkering with his siphon recorder at the English end of the India cable. From there he wrote optimistically to his wife’s sister that “the days of signalling by the ‘spot of

light’ are numbered, and a luminous electrified pen will succeed the mirror.” This was premature. Though the siphon recorder enjoyed some success, it was never the unqualified triumph that the mirror galvanometer had been a decade earlier. Telegraph companies hoped it would allow a reduction in manpower, since it recorded messages without an operator, but its mechanism proved in practice so delicate that a technician generally had to stand by to keep it running correctly. More than two years later, Thomson was sent copies of reports from telegraph company men testifying to the siphon recorder’s balkiness. From Bombay, in September 1872, complete with misspellings: “The signals are, comparitively, not so distinct on Recorder as on Mirror…. Will you kindly point this out to Sir William Thompson to see if he can remedy it.” From Aden on the Arabian Peninsula: “I am sorry to say however the Recorder has only worked here with varying success, and in no way to justify any one in reccommending for you a staff reduction…. Close connection with the Instrument does not dispel the opinion that I formed when I first saw it i.e. that as a Telegraph Instrument it had too many things to get out of order.” The correspondent explained that in damp conditions the ink stopped flowing, and they had to dry the machine at the kitchen fire. He continued: “We loose in speed by it and the signals not being too distinct the speed is still further reduced by repititions being necessary…. I hope when Sir William Thomson’s assistant Mr. Leitch returns here and gives us the benefit of his advice and experience that I shall be able to report that we are making progress.”

Mr. Leitch, who had assisted Thomson in Cornwall in 1870 and then headed out to the Far East, unfortunately died of dysentery in Alexandria at the end of 1872, though not before making the siphon recorder at Suez work tolerably well. After a year of trials in Bombay, operators concluded that the recorder worked better than the mirror galvanometer from October to May, but that during the monsoon season the constant humidity drained away electric charge from the ink, and they had to return to the mirror instrument instead. From balmier Mediterranean climes, on the other hand, came a ringing endorsement: “At Malta, the Mirror is a thing of the past…. The Recorder has undoubtedly tended to lessen greatly, the number of errors.” Happily for the telegraph com-

pany, this report also noted a reduction in staff numbers at Malta because of the recorder’s satisfactory functioning.

The siphon recorder, despite its delicacy, added to Thomson’s reputation and to his wealth. The devices were made in Glasgow by his long-time instrument maker, James White, who formed a company with Thomson as senior partner. Thomson asked for, and received, licensing fees of £1,000 a year from each company using the siphon recorder—several times his professorial salary.

Thomson never went in for ostentatious displays of affluence, but he showed a taste for some of the things that money could buy. Late in the summer of 1870, a few months after his wife’s death, and having spent some time again at sea on cabling business, he decided he needed a boat of his own. It was no mere weekend pleasure craft he chose. During the course of a trip to London on telegraph business, he consulted his old colleague, the Glasgow mathematician turned lawyer Archibald Smith, a sailing man himself, about a vessel he had heard of. Smith wrote a few days later: “You quite take away my breath by your plans for a schooner of 120 tons.” The craft in question was at Cowes, on the Isle of Wight, and after seeing it Thomson described it to his brother James, in tones reminiscent of the letter he had written years ago to his father justifying the purchase of the “funny” at Cambridge: “It is the Lalla Rookh⁵ 126 tons vessel of 17 years old but of oak & very strong and in perfect condition, also a very good model & said to be a fast sailer, that I have bought.”

Thomson engaged a captain and crew and sailed his new boat around the coast to Glasgow. After a few local jaunts he put it up for the winter and started planning nautical excursions for the following year, fondly imagining his scientific friends would eagerly join him. From his seafaring connections sprang new work and interests. In September 1870, as he was purchasing the Lalla Rookh, the Royal Navy was conducting trials of the 7,000-ton H.M.S. Captain, the prototype of a modern design of gunship intended to carry British seapower and political might around the world. But in a sharp storm at Vigo Bay, on the northwestern tip of

Spain, the Captain capsized with the loss of all aboard, almost 500 men, including its designer. The Admiralty, counter to long-standing habit, thought it wise to obtain technical expertise in its investigation of the catastrophe and accordingly asked Thomson as well as his colleague William Rankine (who was by this time professor of engineering at Glasgow) to serve on a committee of inquiry. The two contributed an analysis of the dynamical stability of ships against rolling due to wind and waves. They concluded that the Captain carried such a quantity of turreted weaponry that it became top heavy and therefore unstable even in moderate seas. Once it tipped more than nine degrees away from vertical, they estimated, it could not have righted itself. Thomson’s work on this committee (he traveled from Glasgow to London every other week throughout the spring of 1871) contributed to the establishment of elementary principles of physics in ship design and to criteria that any new design must meet. As always this was, for him, no distraction from real science but a vital aspect of what science must do. Well into the second half of the 19th century the point needed still to be made that scientific laws were not restricted to the laboratory and the ivory tower but had an essential role in the industrial and military prowess of Great Britain.

Thomson, still only in his mid-40s, was racing incessantly about Britain by sea and rail, consulting on cable ventures, meeting with Admiralty officials, dealing with lawyers and businessmen on patent rights and licensing fees, and darting off to Oxford or Cambridge or some other academic institution to discuss pure science. C. G. Knott, a student of Tait’s and later his biographer, recalled an occasion when Thomson stopped in at Tait’s lab in Edinburgh on his way to London in order to get some experimental data he needed. “Full of impatience and excitement Thomson kept moving to and fro between the slabs on which the instruments stood, suggesting new combinations and jotting down in chalk on the blackboard the readings we declared. Tait stood by, assisting and at the same time criticizing some of the methods. At length Sir William went to the further side of the lecture table and copied into his note book the columns of figures on the blackboard. After a few hasty calculations he said: ‘That will do, it is just what I expected.’ Then off he hurried for a hasty lunch at Tait’s before the start for London where during the next week he was to give expert evidence in a law case. As they with-

drew, Tait looked back at us with a laugh and said ‘There’s experimenting for you.’”

Amid all this activity and traveling Thomson was still, from November to May each year, professor of natural philosophy at Glasgow University, with a complement of courses to teach. Telegraph and other business he mostly managed to conduct during the long summers (when cabling voyages invariably took place), but when the Admiralty summoned him to assist Her Majesty’s government on matters of national importance university lectures took second place. By this time his nephew James Thomson Bottomley, born in 1845 to his since deceased sister Anna, had trained as a physicist himself and had become his assistant. Bottomley took classes with increasing frequency as official duties called Thomson elsewhere.

Throughout 1870 Thomson was largely absent during a momentous period in the university’s history. After years of planning, the university relocated to a new building, designed in high Victorian style by George Gilbert Scott, who had been responsible a few years earlier for that most magnificent of Victorian buildings, St. Pancras railway station in London. The new Glasgow University rose up in a more salubrious part of the city, west of the old site. As long ago as 1845, James Thomson had written to his son in Cambridge to say that the railway company had agreed to buy the old college site for £30,000, in order to build a new railway station for Glasgow, and would kick in another £70,000 to help the university move. But the railway boom came to a bust a few years later, and the deal fell through. In 1863 the City of Glasgow Union Railway Company made a similar proposal, now offering £100,000 for the old site. Much more was required to build a new college, but with a combination of government money and funds raised by public subscription (in those days commercial men took civic pride in the great city universities), ground was broken for the new university in 1867, with the move completed in time for the start of the 1870-1871 session.

That year, however, Thomson attended his dying wife in Largs and rarely came to Glasgow. During the summer he worked on his siphon recorder, in Cornwall and London, and bought the Lalla Rookh. He did not attend the inauguration of the new buildings, saying he was still officially in mourning. He taught the first part of the 1870-1871 session, but during the second part was frequently away for the Captain inquiry.

Out of a mix of loyalty, affection, and pragmatism, Thomson remained a Glasgow man. By 1869 Cambridge University had finally worked its way around to seeing the value of experimental physics and approached Thomson, who had been teaching the subject at Glasgow for almost a quarter of a century, about coming down to Cambridge to instruct students there in the novelties of experiments and data. His wife’s illness prevented him from making any commitment, though clearly the prospect tempted him. The Duke of Devonshire (who had been second wrangler in his day and was then chancellor of the university) offered money for the construction and endowment of a physical laboratory at Cambridge in memory of his great-uncle, the accomplished amateur scientist Henry Cavendish, who among other things had calibrated Newton’s inverse square law of gravity by measuring the force between two large masses.

Cookson, Thomson’s tutor of three decades ago and now master of Peterhouse, tried to draw him down from Scotland. But Thomson had begun to settle into his spacious laboratory in the new Glasgow buildings, and the prospect not only of moving but of starting an entire new Cambridge course, in a laboratory yet to be built or equipped, did not attract him. He confessed to Cookson an anxiety about taking on new responsibilities, especially when set against “the great advantages I have here in the new College, the apparatus and assistance provided, the convenience for getting mechanical work done” (the latter referring to his long-standing relationship with the instrument maker James White). Thomson, in short, was comfortable at Glasgow and had built a life combining scientific work, teaching, inventing, business, advising, and so on, which he could not imagine disrupting. Cambridge would make new demands, and the purer academic environment of that place was, at this point in Thomson’s life, far less attractive, narrower, and less thrilling perhaps than it had seemed to him at the age of 20. He stayed in Glasgow, and in the course of his life refused the Cavendish professorship three times. Cambridge appointed James Clerk Maxwell instead, who had for the previous five years abandoned professorial life to be a country squire in the Scottish lowlands, at his modest Galloway estate, although he never ceased to work at mathematics and physics.

Maxwell, though he stands as the greatest theoretical physicist of the

19th century, had been instrumental in working out the practicalities of the BA system of electrical units. Probably it was good for Cambridge that they got him and not Thomson, who as he admitted to Cookson had too full and complex a life to devote himself entirely to the creation from scratch of a wholly new laboratory. Possibly it was not such a good thing for Maxwell, though. Diligent as always, he set the Cavendish Laboratory on the road to becoming for a considerable stretch of time the premier experimental venue in the world. He spent an inordinate amount of his time collecting and editing the scientific papers of Henry Cavendish, when more papers from James Clerk Maxwell would have bestowed greater benefit on the world. In 1879, still producing works of enormous profundity and promise, Maxwell died of intestinal cancer, at the age of 48.

***

“I am very glad Maxwell is standing for the professorship,” Thomson had written to Stokes in March 1871, perhaps partly out of relief that he could set the matter behind him. Thomson and Maxwell knew each other but were never particularly close. Maxwell, a loner with a cryptic and “pawky” Scots sense of humor, lived a largely detached life. Jemima Blackburn, the wife of Thomson’s Cambridge friend and Glasgow colleague Hugh Blackburn, professor of mathematics in succession to his father, was a cousin of Maxwell’s. She was well known in her lifetime for her drawings and watercolors of nature, especially of birds, and made the acquaintance of a number of Victorian luminaries outside the scientific world, notably Anthony Trollope and William Thackeray. She had early encouragement in her artistic endeavors from the great critic Ruskin. The Blackburns entertained numerous visitors and parties at their homes (they had a house in Glasgow and a rambling mansion on the Moidart peninsula, on the west coast of Scotland, looking out toward the islands of Rum, Muck, and Eigg). Thomson, especially before he was married, spent a great deal of time with his friends, and so too for a while did James Clerk Maxwell. When the teenaged Maxwell attended the Edinburgh Academy, before going to Cambridge, he lived in Edinburgh with his father’s sister Mrs. Wedderburn, Jemima’s mother. He and Jemima played and made toys together. Jemima recorded a few charming sketches of

James, both in Edinburgh and at his father’s small estate, where the Wedderburns visited.

As an adult, though, James Clerk Maxwell was far less at ease in the boisterous Blackburn household than was William Thomson, who had a splendid time amusing the numerous Blackburn children. Thomson was a bluff, engaging, straightforward fellow, but Maxwell was by nature an ironist and an observer. A watercolor by Jemima shows Maxwell sitting silently to one side, looking away, while Hugh Blackburn and Thomson lark about with the youngsters. Maxwell’s withdrawal from social life was completed when he married a woman whom, according to Jemima, no one liked, possibly not even Maxwell himself. Katherine Dewar was several years older than her husband, and the daughter of the principal of Marischal College in Aberdeen, where Maxwell was professor from 1857 to 1860. In Jemima’s words, “The lady was neither pretty, nor healthy, nor agreeable, but much enamored of him. It was said that her sister had brought about the match by telling him how much she was in love with him, and being of a very affectionate tender disposition [Maxwell] married her out of gratitude. Her mind afterwards became unsettled but he was always most kind to her, and put up with it all. She alienated him from his friends, and was a suspicious and jealous nature.” As a cousin and childhood friend displaced by a wife, Jemima had reason to be irked, but similar accounts come from other acquaintances. A student at Aberdeen described Maxwell as “the most delightful and sympathetic of beings” but said he had a “terrible wife.” There is a Cambridge anecdote that she fetched her husband away from a social gathering once by announcing loudly, “James, it’s time you went home, you are beginning to enjoy yourself.” The son of one physicist said that “Mrs. Maxwell, although she no doubt had her points was, to put it bluntly, a difficult woman.” Another Cambridge physicist advised new arrivals that Maxwell, when he was a professor there, was always eager to talk to his colleagues at the laboratory, but warned them they should not call on him at home.

Maxwell, like Thomson, belongs to the rank of distinguished scientists who managed only second place in the wrangler competition. Maxwell lost in 1854 to E. J. Routh, who went on to become a moderately well known applied mathematician and a notable coach of more wran-

glers. Already acquainted with Thomson through the Blackburns, Maxwell had studied closely Thomson’s early work on the analogies between electric lines of force and heat flow and wrote to him in February 1854 asking for advice on how to proceed. “Suppose a man to have a popular knowledge of electrical show experiments and a little antipathy to Murphy’s Electricity [a textbook of the day that did not impress Maxwell], how ought he to proceed in reading & working so as to get a little insight into the subject wh may be of use…. If he wished to read Ampere and Faraday &c how should they be arranged, and at what stage and in what order might he read your articles in the Cambridge Journal?”

In the mid-1850s Thomson had published his innovative papers on electricity and magnetism, the main achievement of which had been to cast in mathematical form Faraday’s qualitative ideas about lines of force and the state of “electrotonic” tension that Faraday believed to pervade electrified space. Digesting these works, Maxwell conceived that Thomson had more or less evolved a full theory of electromagnetism, but being a busy man of diverse interests had not yet got around to assembling it all in publishable form. By the end of 1854 Maxwell was telling Thomson that he had “been rewarded of late by finding the whole mass of confusion beginning to clear up under the influence of a few simple ideas.” In this endeavor he was, he said, “greatly aided by the analogy of the conduction of heat, wh: I believe is your invention at least I never found it elsewhere…. This is a long screed of electricity, but I find no other man to apply to on the subject so I hope you may not find it difficult to see my drift.”

A little less than a year later, in September 1855, Maxwell was eager to start publishing his own ideas and discoveries but remained cautious about encroaching on Thomson’s territory. “I would be much assisted by your telling me whether you have not the whole draught of the thing lying in loose papers and neglected only till you have worked out Heat or got a little spare time,” he wrote. “As there can be no doubt that you have the mathematical part of the theory in your desk all that you have to do is to explain your results with reference to electricity. I think that if you were to do so publicly it would introduce a new set of electrical notions into circulation & save much useless speculation. I do not know the Game-laws and Patent-laws of science…. I certainly intend to poach

among your electrical images, and as for the hints you have dropped about the ‘higher’ electricity, I intend to take them.”

In fact, Maxwell was mistaken. Thomson had no theory, in loose papers or otherwise, waiting to be published. In 1855 Maxwell wrote the first of his great papers on electromagnetic theory, entitled “On Faraday’s Lines of Force.” This was not yet a theory of electromagnetism. Maxwell had worked out a full mathematical treatment of lines of force on Faraday’s model, but did not link these notions to the movement of electric charges or variations in magnetic fields.

As different as were their personalities, Maxwell and Thomson diverged too in their views of mathematical science. Maxwell aimed to capture electromagnetism in mathematical form, finding relationships between the spatial distribution of charges and magnets and the fields they produced, their variation with time, and (as Faraday had so triumphantly demonstrated) the generation of currents by moving lines of magnetic force. This grand synthesis Maxwell eventually created, but not for another 10 years, and by that time Thomson resisted the theory Maxwell gave to the world. Thomson had the same goal but wanted to get there by a different route. For him, mathematics was to be trusted only if it emerged from a tangible physical model. As early as 1847 he had published a paper in which he tried to portray electric and magnetic influences by analogy to the behavior of solid materials with specific properties. He imagined an elastic material with some rigidity, capable of being deformed by external forces but also resisting such forces and returning to its normal disposition when unstressed.

As with his earlier analogies between electric lines of forces and lines of heat flow according to Fourier, Thomson believed that mathematical similarity betokened an underlying physical connection, in the sense that different phenomena appeared to follow the same kinds of law. Such thinking bolstered his entire approach to electromagnetism. He wished to discover what properties a physical solid would need—density, rigidity, elasticity—in order to provide a complete and consistent model for the behavior and interrelationship of electric and magnetic effects. His early work didn’t do this. It suggested three different analogies for electric forces, electric currents, and magnetic forces. But it was a step in the right direction, Thomson believed. Find a plausible physical solid that con-

tained an analogy to all electromagnetic phenomena at the same time, and you will have found a full and satisfactory theory of electromagnetism. Such a theory would not, in the modern sense, give much clue as to the elementary nature of electromagnetism, but that was entirely in keeping with Thomson’s distaste for “metaphysics.” Find the right analogy, obtain the correct equations, and you have found all you can need or want, so he fiercely believed. This belief never left him. Maxwell may have started out thinking along the same lines, but his genius led him to see, after many years of cogitation, that the mathematical laws governing electromagnetism must be sui generis, laws that correctly accounted for electromagnetic phenomena and interrelationships, without any necessary connection or analogy to other parts of physics.

Indeed, Maxwell’s finished theory of 1865 contained elements that Thomson disliked precisely because they had no analogy to the behavior of any known kind of physical solid. Maxwell built a theory of mathematical relationships between charges, currents, and what we now recognize as the electromagnetic field. But Thomson saw this as abstract mathematics, divorced from direct physical meaning. There was no model, no tangible, palpable elastic substance underlying the quantities Maxwell defined. He accepted that Maxwell had found an important link between the propagation of electromagnetic influences and the speed of light, but he saw that as an isolated triumph within a theory that was, to him, no theory at all.

Such reservations were not unique to Thomson. This was, after all, something new in physics. Maxwell’s was the first modern field theory, rendering in precise mathematical form Faraday’s extraordinary vision of electric and magnetic influences pervading space. In 1855, according to his niece, Faraday felt isolated in his views on electromagnetism. “How few understand the physical lines of force!” he said to her. “Thompson [sic] of Glasgow seems almost the only one who acknowledges them. He is perhaps the nearest to understanding what I meant.” Then Maxwell took up the cause, acknowledging his initial debt to Thomson, whose early analogy between heat flow and electric tension was, he said, “one of the most valuable of these truly scientific, or science-forming ideas.” Subsequent work too he “considered as a development of Thomson’s idea.”

But over the years Maxwell drifted further from Thomson’s concep-

tion of a theory of electromagnetism, while remaining always true to Faraday’s vision. He wrote to Faraday in 1857 that “as far as I know you are the first person in whom the idea of bodies acting at a distance by throwing the surrounding medium into a state of constraint has arisen, as a principle actually to be believed in…. Nothing is clearer than your descriptions of all sources of force keeping up a state of energy in all that surrounds them, which state by its increase or diminution measures the work done by any change in the system.” This “state of constraint” or “state of energy” was Maxwell’s way of reaching toward what we now understand as the electromagnetic field.

Faraday, who had long complained of difficulties with memory, was by this time in his late 60s and beginning to lose his mental powers. He stopped writing to friends because he could not finish a sentence without losing his train of thought. Reluctantly, he resigned his lifelong position from the Royal Institution in October 1861, telling the board members: “I have been most happy in your kindness, and in the fostering care which the Royal Institution has bestowed on me…. My life has been a happy one and all I desired…. I desire therefore to lay down this duty; and I may truly say, that such has been the pleasure of the occupation to me, that my regret must be greater than yours can or need be.”

In his final years, Faraday became silent and motionless. He lived with his wife at Hampton Court, in a “grace and favour” apartment at Queen Victoria’s disposal. In one of his last letters to an old friend, he had written of his sustaining faith: “I am, I hope, very thankful that in the withdrawal of the power and things of this life,—the good hope is left with me, which makes the contemplation of death a comfort—not a fear. Such peace is alone in the gift of god, and as it is he who gives it, why shall we be afraid? His unspeakable gift in his beloved son is the ground of no doubtful hope; and there is the rest for those who like you and me are drawing near the latter end of our terms here below.” He died in 1867, never knowing of the way in which Maxwell had succeeded in casting his vision of the electromagnetic field into a mathematical form that other scientists would slowly accept. After Maxwell’s death in 1879 it was not until 1888, when Heinrich Hertz succeeded in creating and detecting radio waves, that the scientific world began to embrace wholeheartedly Maxwell’s views.

Even then, Thomson refused to see the physics in Maxwell’s elegant mathematics and worked endlessly on alternative theories that would produce the right results on a quite different physical basis. He did not succeed, but neither, even at the end of his life, did he accept that Maxwell’s theory would do.

***

From the time of Newton and Galileo until the startling innovations of the early 20th century, modern theoretical physics emerged by evolution more than revolution. Around 1860, soon after they first met, Thomson and Tait conceived the idea of writing a textbook, in several volumes, in order to lay out the mathematical principles of “natural philosophy” that they both saw as the model for a finished science of the inanimate universe. At this time there was nothing we would now recognize as a general textbook of physics. There were volumes of mathematics, in Cantabrigian or French style (although the two were gradually becoming closer), but these were essentially axiomatic exercises in applied philosophy. Ludwig Fischer, Thomson’s undergraduate rival who had become a professor at St. Andrews, wrote to him in 1855 asking, in a postscript, “Do you know of any elementary work on Mechanics starting with the idea of ‘mechanical energy’ or ‘work’?” No such book existed. Thomson and Tait wanted to start from the new conception of energy, in all its generality, and show how the rules of physical interaction followed ineluctably from the crucial law of conservation. Not only did this simplify the concepts of mechanics, but it allowed mechanical laws to connect to all other branches of physics, as long as the concept of energy was held foremost.

But their textbook was to be furthermore a practical compendium of physics, allowing the student who mastered its techniques to apply them not simply to idealized laboratory examples and Cambridge tripos questions but also to electric telegraph cables and steam engines and ship design. At end of 1861, Tait was writing to Thomson with the broad outline of a plan and concluded: “I fancy that we might easily give in three moderate volumes a far more complete course of Physics Experimental & Mathematical than exists (to my knowledge) either in French or German. As to English, there are none.” A couple of weeks later he

listed his idea of chapter titles, moving from basic kinematics and dynamics, to hydrostatics and hydromechanics (that is, the behavior and motion of fluids), to the properties of matter, on to sound, light, and heat, then to electricity and magnetism, culminating in a final discussion of that essential principle, the conservation of energy. The modern student will recognize this list as forming the backbone of that time-honored subject, classical physics. One may easily get the impression that classical physics had been around for dusty generations before the beginning of the 20th century and the emergence of quantum mechanics and relativity. In fact, it is a product of the late 19th century, and Thomson and Tait’s textbook marks as well as anything its formal appearance. Thomson and Tait were not simply the first to think of putting all these subjects between one set of covers. Rather, they were the first to see these subjects as subparts of a single discipline, elements of a conceptual whole.

Concept was one thing, execution another. As Thomson gallivanted around Britain and further afield on scientific, commercial, and government business, and organized sailing expeditions on the Lalla Rookh, it was Tait’s task to get the book written. In what turned out to be a woefully premature pronouncement, he advised Thomson on Christmas Day in 1861 that completion of the first volume by the following May seemed altogether feasible. “Let us apportion our work, and fall to. An average of three or 4 (or less) hours a day would give us the volume in 6 weeks,” he announced. The most attractive aspect of Tait’s character is that he could be as abrupt and unappeasable toward Thomson, for whom his admiration bordered on besotment, as he was toward enemies such as Tyndall. Thomson began by proposing more subjects and suggesting three or four volumes of experimental matters alone. Tait expressed his alarm at this, not least because of “the expense to the students, especially the Scotch ones. We may mulct & bleed Oxford and Cambridge & Rugby &c &c to any extent, but how about our own classes? What we want at once is not the fame of authorship, but the supply of a want of elementary teaching.”

By the middle of January they were still haggling about the list of contents. Tait’s difficulties with his coauthor became evident: “I will shortly send you the revised headings, that you may see whether they correspond with your ideas, which I confess I have but vaguely gleaned from your notes.” Thomson sent Tait bits and scraps and sketches, which

Tait assembled into some form of continuous text, and returned these products to Thomson, who rather than refining and polishing began adding whole new sections and offshoots in the margins. Thomson in any case did not respond promptly, and Tait had to plead constantly to get anything out of his coauthor: “I wish you would send back my sketch of the Chap. on Prop[erties] of Matter with your amendments &c, & I will have it written as soon as is consistent with care and completeness.” The next day, on another aspect of the book, he urged “at all events act speedily.”

To no avail. More than two years later, in May 1864, Tait was writing thus: “D^r T, Do look alive with my MSS. It should have been all in type this week.” They had taken to addressing each other as T and T′, apparently a shorthand begun by Maxwell, who also referred to them sometimes as the archiepiscopal pair, having discovered to his amusement that the archbishops of York and Canterbury at that time were also Thomson and Tait. (Archibald Campbell Tait, the archbishop of Canterbury, had attended Edinburgh Academy some 15 years before Tait and Maxwell.)

A month later Tait became more peremptory still: “I wish you would go ahead. I am getting quite sick of the great Book…. If you send only scraps and these at rare intervals, what can I do? You have not given me even a hint as to what you want done in our present Chapter about Statics of Liquids and Gases! …. Now all this is very pitiable: I declare you did twice as much during the winter as you are doing now. I sent you a great bundle of proof sheets only ten days ago, but you have taken no notice of them whatever. You proposed certain preposterous problems which I could not be bothered working out.” Each year from 1861 Tait urged Thomson to make haste so they could have at least a small installment of their text printed by September, ready for the incoming class of university students. Each year the book failed to materialize.

Thomson published scientific papers and reviews at a great rate throughout his life, but his productivity came from working on so many projects at once that he could easily pick up another when he tired momentarily of one. Stokes, as editor of the Philosophical Transactions of the Royal Society in London, had encountered the difficulty: “You are a terrible fellow and I must write you a scolding. The vol of the Phil. Trans. ought to have been out by the 30th of Nov^r and here’s your paper won’t

be ready for a month yet.” Thomson responded to this and other scoldings with invariable good humor, which may not have pleased his correspondents, since he carried on as dilatory as before, only more amused.

Tait found, as others had found before him, that it was impossible to chide Thomson to any effect. In his obituary notice for Tait many years later, Thomson recalled that “the making of the first part of ‘T and T′’ was treated as a perpetual joke, in respect to the irksome details for the interchange of drafts for ‘copy’, amendments in type, and final corrections of proofs. It was lightened by the interchange of visits between Greenhill Gardens, or Drummond Place, or George Square, and Largs, or Arran, or the old and new College of Glasgow; but of necessity it was largely carried on by post. Even the postman laughed when he delivered one of our missives, about the size of a postage stamp, out of a pocket handkerchief, in which he had tied it to make sure of not dropping it on the way.” All this to-ing and fro-ing may not have appeared to Tait quite as much of a joke as it did to Thomson. At any rate, having existed in a sort of samizdat form for years, circulating among the undergraduates of Edinburgh and Glasgow as proof sections in various states of completion, the Treatise on Natural Philosophy by Sir William Thomson and P. G. Tait appeared, at over 700 pages long, in October 1867.

After its difficult gestation, the book did well. Reviewers liked it, Helmholtz quickly arranged for a German translation, and reprintings and revisions were soon in demand. Undergraduates bought it at a smart pace, although J. M. Barrie remarked that it was “better known in my year as the ‘Student’s First Glimpse of Hades.’” Commenting in Nature on an updated version published in 1879, Maxwell identified the greatest virtue of the Treatise as the liberation of arcane mathematical propositions in abstract dynamics into the world of practical scientists and even engineers. “The credit of breaking up the monopoly of the great masters of the spell, and making all their charms familiar to our ears as household words, belongs in great measure to Thomson and Tait,” Maxwell wrote in his idiosyncratic way. “The two northern wizards⁶ were the first who,

without compunction or dread, uttered in their mother tongue the true and proper names of those dynamical concepts which the magicians of old were wont to invoke only by the aid of muttered symbols and inarticulate equations.”

As late as the 1870s, in other words, Maxwell found it necessary to remark on the gap between practical physics and mathematical reasoning. Thomson and Tait provided the means to bridge that gap. That the book appeared at all was entirely due to Tait, but the philosophy behind it was Thomson’s. Tait at heart was a formalist. He invested many years of effort in promoting a novel kind of mathematics called “quaternions,” a cousin to modern vector analysis. Quaternions, Tait claimed, offered a marvelous degree of compactness in writing down complex mathematical equations. He proudly explained to the Cambridge mathematician Arthur Cayley how he had transformed one of Thomson’s mathematical arguments: “Three pages of formulae can easily, and with immense increase of comprehensibility, be put in as many lines of quaternions.”

This quixotic enthusiasm drew few converts, however, least of all Thomson. Tait compared quaternions to a pocket map, containing a prodigious amount of information in compact form. To this Cayley dryly replied that, as with a pocket map, the thing had to be unfolded again to be of any use. Maxwell, in a characteristically backhanded remark about one of Tait’s quaternionic papers, noted the “remarkable condensation not to say coagulation of style, which has rendered it impenetrable to all but the piercing intellect of the author in his best moments.” Tait strove to introduce quaternionic notation into T and T′, but Thomson breezily paid no attention. “We have had a thirty-eight year war over quaternions,” he explained long afterward to a colleague. “Times without number I offered to let quaternions into Thomson and Tait if he could only show that in any case our work would be helped by their use. You will see that from beginning to end they were never introduced.”

Thomson never approved of mathematical formalism for its own sake. Although Cayley disdained quaternions, he was still too rarefied a mathematician for Thomson’s taste. Writing to Helmholtz in order to convey his compliments to another German scientist who had succeeded in working out a long, difficult, but practical problem, Thomson remarked: “Oh! That the Cayleys would devote what skill they have to

such things instead of to pieces of algebra which possibly interest four people in the world, certainly not more.” More bluntly, he told Glasgow students that “the art of reading mathematical books is judicious skipping.” For scientists, in other words, the point of mathematics was to solve physical problems. Remarkably, Thomson and Tait’s 1867 Treatise on Natural Philosophy was the first textbook to bring to undergraduates a comprehensive summary, mathematical but at the same time practical, of physics in all its scope and variety.

***

While goading Thomson toward completion of their joint textbook, Tait had also managed to write a book of his own, prompted by the controversy with Tyndall over the origins of the law of conservation of energy. His Sketch of Thermodynamics appeared in 1868. Ostensibly, Tait aimed to provide a thorough and rational account not simply of the two laws of thermodynamics but also of their genesis. He praised Joule as the originator of the first law and made light of Mayer’s claims. But he also had a second agenda, relating to the second law. Clausius, in 1865, had come up with the name “entropy” and phrased the second law of thermodynamics as the rule that entropy never decreases. In what were called reversible processes, entropy stayed the same; in irreversible processes (the working of real engines, friction, conduction of heat without production of work, and so on), entropy grew. The notion of reversibility goes back to Carnot. Thomson, in 1852, had made a start on understanding the thermodynamics of irreversibility. Two years later Clausius had written down the modern definition of entropy but didn’t yet extend its utility to all processes, reversible and irreversible. When he finally came up with the name entropy, Clausius recognized a physical concept that had emerged, in a tangled and difficult way, during the intervening years. Tait set himself to untangle this history, and he came to the new and remarkable conclusion that his friend Thomson had actually done all the hard work in 1852 and that Clausius’s subsequent contributions were at best minor clarifications.

At least that is what his published Sketch declared. His correspondence with Thomson reveals a different story. In his 1852 paper, Thomson had imagined a series of steps constituting a reversible cycle,

and for each step he calculated the heat going in or out of the system, divided by the temperature at which the exchange took place. The sum of these increments, he showed, was zero. This is the germ of a formal definition of entropy. However, Thomson did not draw any special attention to this quantity but only used it in the course of obtaining other results.

In letters to Thomson in January 1868, Tait castigated him for providing an inadequate proof of the fact that the sum of the heat transfers divided by temperature was zero around a reversible cycle. It “is no proof at all—not even a chain of reasoning, merely a set of detached links! How you let it be printed in such a state I can’t imagine. Everybody sees you had the proof in your eye, but whether you or the printers omitted a leading step I can’t of course tell.”

When he came to write his Sketch, though, Tait suppressed his private reservations and declared blithely that the general definition of what became entropy was, after all, clearly stated in Thomson’s 1852 paper. He sent drafts of the relevant sections to both Clausius and Helmholtz. Clausius evidently responded, and critically, because Tait later wrote to Helmholtz professing no wicked intent: “Is it fair to ask you whether you think with Clausius that my little pamphlet will only do me harm? … I wish to avoid strife and to produce a useful little text-book; but, if Clausius is right, I had better burn it at once.” The letter from Clausius to Tait apparently does not survive, but there is a fragment from Tait to Thomson, of the right date, referring to an angry missive from an unnamed German: “I enclose a letter just rec’d from him, which rather startles me—you having told me how meek and mild he appeared to you. Dummheit [stupidity] and Hinterlist [cunning, trickery] are pretty strong—and I don’t at all like his application of ‘auffällig’ [egregious] to myself.”

This may well have been from Clausius. Helmholtz tried in a more gentlemanly way to dissuade Tait: “For my part I must say that I have a great aversion to all priority quarrels…. If then you divest your writing of its polemical garb it will in my opinion be thankfully received and will have more influence than with this polemic.”

Calm consideration not being Tait’s cup of tea, he went ahead and published his Sketch of Thermodynamics “in all its individuality,” as his biographer put it. In writing the book, Tait had corresponded a good deal

with Maxwell, who absorbed Tait’s views on Clausius and Thomson and the second law and promoted them in his own Theory of Heat, published in 1871. Clausius now protested in the pages of the Philosophical Magazine that Tait and Maxwell had managed to bestow all the credit for working out the concept of entropy on Thomson, leaving him only with the honor of providing the name. He argued, cogently, that Thomson did not make the important step of extending his analysis to irreversible as well as reversible processes. Another tedious dispute followed. Tait responded by ignoring the main point and making some nitpicking remarks about Clausius’s original definition of entropy.

Under this provocation Clausius then embarked on his own book about thermodynamics, which predictably met with Tait’s disapproval. Thomson’s response to this was indirect and curious. He arranged for the publication in the Philosophical Magazine of a supposedly personal letter, beginning “My dear Thomson,” in which Tait evaded Clausius’s arguments and reinstalled Thomson as the inventor of entropy. Thomson then added a short note of his own to say, without elaboration, that he agreed with Tait’s assessment. Thus he allowed the idea to get into print that he had come up with the concept of entropy, without ever quite saying so explicitly. Tait’s method was to take every statement by Clausius strictly at face value, whereas in scanning carefully Thomson’s published works on thermodynamics he allowed himself to infer what Thomson really meant to say, although he hadn’t quite managed to say it clearly at the time. By going along with Tait, Thomson was colluding in a significant reinterpretation of history. Perhaps, Tait being so persuasive and insistent, Thomson really came to believe his friend’s rereading of his own papers. Perhaps, with hindsight, when the laws of thermodynamics had become more or less obvious, he imagined that he had known the truth all along.

Many years earlier, in his dispute with Whitehouse over the Atlantic cable, Thomson had remarked that his theory of the telegraph was “like any theory, merely a combination of established truths.” This, if he really believed it, marked his great flaw as a scientist. To ponder the wider significance of the quantity that eventually became entropy would to him, perhaps, have been going beyond the established truths. Thomson was content to fit empirical knowledge into a system of elementary theo-

retical rules. Clausius (and also Rankine, in his obscure way) went further and perceived a universal second law of thermodynamics and a general conception of entropy. Tait, with Thomson’s implicit agreement, scorned Clausius and Mayer and others because they made large statements on insufficient evidence. So they did, and that is precisely why they deserve credit for seeing where the truth lay even though their evidence was incomplete and their reasoning loose. It must have been galling to Thomson to understand, looking back, that he could have gone further. Tait, who came on the scene after the early confusion had been swept away, could see this even more clearly. Unable to understand why his brilliant friend Thomson had not taken his ideas to their seemingly obvious conclusion, Tait decided that in fact he must have but simply hadn’t bothered to write it all down explicitly. But brilliance and imagination are not the same thing.

***

In 1871 the British Association convened in Edinburgh for its annual meeting. Thomson accepted the invitation to serve as president and delivered the meeting’s keynote address. In keeping with tradition, he paused to mark the passing of a number of notable scientists that year and summarized recent progress in his own field, physics. But presidency of the BA was a forum from which he could address all of science, and Thomson did not shy away from pronouncing on a number of other issues. He restated his restrictive views on the age of the earth and the sun, scolded the geologists again for not paying enough attention, and then moved on to biology.

The inanimate sciences, Thomson maintained, offered a model for scientific inquiry in general. “The essence of science, as is well illustrated by astronomy and cosmical physics, consists in inferring antecedent conditions, and anticipating future evolutions, from phenomena which have actually come under observation. In biology the difficulties of successfully acting up to this ideal are prodigious. The earnest naturalists of the present day are, however, not appalled or paralyzed by them, and are struggling boldly and laboriously to pass out of the mere ‘Natural History stage’ of their study, and bring zoology within the range of Natural Philosophy.”

Having praised biologists for taking at least baby steps on the way to becoming real scientists, Thomson moved on to criticisms of Darwinian theory. In a nutshell, he would admit the possibility of natural selection but would not go so far as to endorse evolution in its full scope. By natural selection he conceived of the idea that creatures with slightly different qualities might be more or less well suited to their conditions. Some would prosper, others would suffer. This had a nice mechanistic ring to it, which appealed to Thomson. But if evolution meant the appearance of wholly new kinds of creatures from those already existing, or even more radically the appearance of life when none had existed before, then he would not go down that road.

Criticism of this sort he had perhaps learned from his friend Fleeming Jenkin, whose 1867 review of the Origin of Species had made a number of intelligent observations hampered by a crabbed vision of what evolution involved. In essence, Jenkin had conceived of a fixed population within which a limited number of genetic elements (as we would now call them) shuffled about from one generation to the next. He offered an example illustrative of his time. Jenkin imagined a white man shipwrecked on an island inhabited by savages. The unquestionably superior qualities of this Crusoe would lead to him being acclaimed king, acquiring many wives, and so on. But by virtue of his very desirability, his innate advantages would then be diluted and dissipated among his numerous offspring. Such would be the fate of any superior individual within a larger population, Jenkin argued; better-adapted individuals would always be overwhelmed by the common herd. Thus he believed advantage, in Darwin’s theory, would always be squelched by what statisticians call regression to the mean.

Thomson took a similar line. He and Jenkin apparently believed that genetic elements would be randomly reassigned at each generation, and so failed to grasp the idea that a small genetic advantage, if it is passed down from one generation to the next, can gradually come to dominate a population. They therefore balked at the idea of new permanent traits, still less new species, arising. He quoted with approval Darwin’s famous sentence about the “grandeur in this view of life” as the result of selection acting upon and enlarging some original stock. But then he deliberately omitted Darwin’s mention of the “origin of species by natural selection”

because, as he said, “I have always felt that this hypothesis does contain the true theory of evolution, if evolution there has been, in biology.” On a related point Thomson was adamant: “Dead matter cannot become living without coming under the influence of matter previously alive. This seems to me as sure a teaching of science as the law of gravitation.”

No clear argument emerges from Thomson’s summary. He would not accept that life can come into being from inanimate matter without the agency of some higher power, but neither would he say that the Creator assembled life on earth directly in its present form. He accepted that natural selection can work in creating some of the variety of life, but he leaned toward the view that human origins are a question apart. He would not relinquish the role of a Creator and suggested that Bishop Paley’s old argument from design had been too lightly abandoned. In short, he wanted to have a scientific account of life, but only up to a point. In Thomson’s view the evidence of creation and design was all around us. And yet he did not want to say that there is only creation and design, because Darwin’s theory of variation and selection appealed to him as a rational mechanism acting on living organisms.

In the end he finessed the difficult question of where creation ends and natural selection takes over. He noted that material from elsewhere rains constantly on to the earth in the form of meteors. He observed that when a barren lava flow, after not too many years, becomes covered with vegetation, we take it for granted that life has blown in from elsewhere, rather than spontaneously originating on the cooling rocks. Thus he introduced his new suggestion: “Hence and because we all confidently believe that there are at present, and have been from time immemorial, many worlds of life besides our own, we must regard it as probable in the highest degree that there are countless seed-bearing meteoritic stones moving about through space. If at the present instant no life existed upon this earth, one such stone falling upon it might, by what we blindly call natural causes, lead to its becoming covered with vegetation…. The hypothesis that life originated on this earth through moss-grown fragments from the ruins of another world may seem wild and visionary; all I maintain is that it is not unscientific.”

The notion that life originated elsewhere in the universe didn’t solve the problem of its origin, only pushed the question offstage and allowed

Thomson to imagine that whatever happened subsequently on earth adhered to his mechanistic view of science. His audience reacted with a mixture of puzzlement and amusement. Huxley commented that unless Thomson believed that life came to earth in the form of elephants and acorns and crocodiles and coconuts, a largely evolutionary explanation for the present array of species remained necessary. Churchmen were disappointed that Thomson didn’t denounce Darwin altogether. Biologists and geologists were skeptical of the idea of viable germs of life flying about through the empty reaches of space.

Nevertheless this proposal by Thomson is characteristic of his thinking. He believed in the universal and encompassing power of scientific reasoning and felt no hesitation in applying the certain rules of mathematical physics in areas beyond the realms in which he had made his reputation. Mathematical physics, indeed, was his model for science in general. Yet when powers of scientific analysis led him inexorably toward a fundamental question—inanimate origin of life or creator?—he abruptly became timid, and drew a veil over the hard dilemmas that his firm belief in science threw up before him.