Monday, June 15, 1896, a week shy of the longest day of the year, and Glasgow remained sunny and pleasantly warm well into the evening hours. Flowers and electric lighting (still something of a novelty) brightened the lecture rooms and hallways of the university buildings. Upwards of 2,000 distinguished visitors roamed the campus, spilling out onto the spacious lawns where they were serenaded by the pipers of the Gordon Highlanders. Scholars from around the country mingled with prominent Glaswegian businessmen and politicians. Stokes, now Sir George Gabriel Stokes, came from Cambridge. The astronomer Simon Newcomb was there, representing the National Academy of Sciences in Washington, D.C. From Princeton University came Professor Woodrow Wilson. The Prince of Wales, detained elsewhere by a prior engagement, sent his apologies. Almost every college and university in Great Britain sent one or more representatives, as did institutions from across Europe and North America.

In the library the visitors could marvel at an array of electric and mechanical devices, commercial and scientific instruments, all the product of one man’s inventive powers. Upstairs, courtesy of the Eastern, Anglo-American, and Commercial Cable companies, telegraph equip-

ment and siphon recorders stood ready. Congratulatory messages ticked in from around the world. One, sent from within the university, took seven minutes to travel via Newfoundland, New York, Chicago, San Francisco, Los Angeles, New Orleans, Florida, Washington, New York, and Newfoundland, arriving at the library, where it was presented to Lord Kelvin. He composed a short reply of thanks and sent it back around the same route. It looped around the western hemisphere in only four minutes.

Sir William Thomson had become Lord Kelvin (to be precise, Baron Kelvin of Largs) four and a half years earlier, in Queen Victoria’s New Year’s Honours list of 1892. He was the first British scientist to be raised to the peerage, but his ascent into the upper reaches of nobility did not spring from his purely scientific achievements. His commercial success and personal wealth exemplified Victorian entrepreneurial virtue and contributed to Britain’s economic and technological prowess. His telegraphic and marine navigation systems served in support of the empire. Lately he had made political forays on behalf of the Liberal Unionist party. A Scot of Irish origins, he vehemently opposed home rule for Ireland on the grounds (which his father would heartily have endorsed) that it would inevitably lead to religious quarrels and sectarian politics. He was not politically sophisticated, but he was plain spoken and direct, and his reputation guaranteed that his voice was heard.

Accepting the peerage, Thomson had to choose a title for himself. Lord Cable! Lord Compass! his nieces suggested. Lord Tom-Noddie would suit him, Thomson joked, in his simple way. His sister Elizabeth, more soberly, came up with “Kelvin” a couple of days later, only to find that Fanny and William Thomson had already had the same thought. Kelvin is the name of the small river that runs beside the university into the Clyde; it connects the academic world with the open sea.

The 1896 Glasgow celebration marked another milestone. William Thomson, later Sir William, now Lord Kelvin, had been a Glasgow professor for 50 years since taking up his post at the age of 22. The only position that might have drawn him away was the Cavendish chair at Cambridge, which he had in the end refused three times: at the outset, when Maxwell was appointed; again when Maxwell died in 1879, and the chair eventually went to Lord Rayleigh; and once more when Rayleigh

resigned after five years to return to his estate at Terling, in Essex, in order to set up his own laboratory and work in peace. Approached then about leaving Glasgow for Cambridge, Thomson, then 60 years old and just returned from giving the Baltimore lectures, had written: “I am afraid it cannot be—alas, alas—The wrench would be too great. I began taking root here in 1831 [when his father came to Glasgow with his young family], and have been becoming more and more fixedly moored ever since…. To make a new departure … would be a life’s work again.”

The Cavendish professorship went to a much younger man. Joseph John Thomson, invariably known as J. J., was a 28-year-old physicist from Manchester, second wrangler in 1880, to whom William Thomson’s old friend and colleague James Joule was a distinguished but by then frail and impoverished man, supported by a government pension after he had lost money through failed investments. Introducing his young son to Joule one day, J. J.’s father had said: “Some day you will be proud to be able to say you have met that gentleman.” Late in 1884, “to my great surprise and I think to that of everyone else,” J. J. became Cavendish professor. He remained there for 35 years and built the Cavendish into the world’s preeminent institution for experiments in the new physics of the late 19th and early 20th centuries. He discovered the electron in 1897. His colleagues and students pioneered the investigation of radioactivity and atomic and nuclear physics. This lay in the future. But William Thomson’s final refusal of the Cavendish chair and J. J. Thomson’s appointment marked the end of one kind of physics and the beginning of another.

At his jubilee Kelvin was lauded over three days with banquets and speeches testifying to his “pre-eminent service in promoting arts, manufactures, and science,” his contributions to “the improvement of natural knowledge,” his “triumphs … in the advance of scientific theory and experiment,” his “splendid discoveries … and valuable scientific inventions, which have … conferred signal benefits on the whole civilized world,” and more, much more, in the same vein. In reply, Kelvin began conventionally enough, thanking the city and university for their long loyalty to him, thanking his numerous colleagues—“friends and comrades, day-labourers in science”—for their congratulations and for the work they had all done over the years. But then, echoing Newton’s fa-

mous phrase about the small boy playing on the seashore, he went on: “When I think how infinitely little is all that I have done I cannot feel pride; I only see the great kindness of my scientific comrades, and of all my friends in crediting me for so much. One word characterizes the most strenuous of the efforts for the advancement of science that I have made perseveringly during fifty-five years; that word is failure. I know no more of electric and magnetic force, or of the relation between ether, electricity, and ponderable matter, or of chemical affinity, than I knew and tried to teach to my students … fifty years ago.”

It was a startling moment in an emotional evening. A great-niece of Kelvin’s, granddaughter of his sister Elizabeth, wrote that the word failure “seemed to ring through the hall with half-sad, half-yearning emphasis. Some of the people tried to laugh incredulously, but he was too much in earnest for that.” Kelvin moved swiftly on, to talk of the joy of experimental discovery, of the innumerable inventions and marvelous devices that scientific study had brought into being in the second half of the 19th century. This was more than adequate compensation, he told his audience, for the “philosophical failures” he spoke of. As people rose in turn to offer their own words of praise, Kelvin “seemed nearly to break down for a moment, but got through, and everybody said he never spoke better,” his great-niece reported. “There was something pathetic about it all—a sort of wonder that people should be so kind to him, and a wish that he had done more to deserve it all.”

Then they all sang “Auld Lang Syne.”

***

What Kelvin called failure is, in the standard histories of science, a progression of remarkable triumphs. By 1896 thermodynamics was largely settled, and Maxwell’s theory of electromagnetism had gained experimental support and widespread acceptance. These, with Newtonian mechanics, formed the core of classical physics, a body of knowledge that held center stage for just a decade or two before the unexpected discoveries of the 20th century began to push it to the background. From 1895 to 1897, the years bracketing Kelvin’s jubilee, the first of those new discoveries had put in an appearance: X rays, radioactivity, and J. J. Thomson’s identification of the electron. Physics, far from being wrapped up, still

had the capacity to surprise and perplex. Even so, physicists would have called this a time to take satisfaction in what had so recently been achieved. In 1846, when William Thomson took up his Glasgow position, neither heat nor energy, nor light nor electricity or magnetism, were understood except in a rudimentary way. Fifty years on, profound mathematical theories encompassed all these phenomena. Yet Kelvin talked of failure.

Natural philosophy had not gone as Kelvin had hoped. It turned into physics, for one thing, a title he disliked. During an 1862 lecture he had quoted Johnson’s definition—“Naturalist. A person well versed in Natural Philosophy”—and had said that “armed with this authority, chemists, electricians, astronomers, and mathematicians may surely claim to be admitted along with merely descriptive investigators of nature to the honourable and convenient title of Naturalist, and refuse to accept so un-English, unpleasing, and meaningless a variation from old usage as ‘physicist.’” Certainly he would rather be a student of natural philosophy than of physics, a subject he believed was becoming too abstract, too mathematical, and too isolated from the rest of science. Of mathematics itself, Kelvin had no fear; he had been a mathematical prodigy. But in the closing years of the century mathematical formalism was driving out, as Kelvin saw it, physical realism. He had still not reconciled himself to the elegant but spartan electromagnetic field theory of Maxwell. In his Baltimore lectures a dozen years earlier he had promoted his endlessly intricate attempts to construct mechanical models of the ether, a tangible physical medium that would carry electromagnetic influences. In 1896, Kelvin still pursued this increasingly lonely quest.

Kelvin also, and in similar isolation from the mainstream, cultivated his own view of atoms and molecules. As long ago as January 1867, only a few months after the successful conclusion of the Atlantic cable venture, the newly minted Sir William Thomson had presented to the Royal Society of Edinburgh a long account of what he called “vortex atoms.” His ideas, as always, combined novelties gleaned from other sources. In particular he referred to the “magnificent display of smoke-rings, which he recently had the pleasure of witnessing in Professor Tait’s lecture-room” and to a theoretical analysis of fluid motion from his old friend Helmholtz.

Tait had taken a wooden packing box, cut a circular hole in one end, and replaced the opposite end with a taut cloth. He filled the box with smoke from a piece of smoldering phosphorus, and by striking the cloth sharply with the flat of his hand, he could produce smoke rings up to a foot across and an inch in thickness. These rings, sailing gracefully across the room, were “pungent and disagreeable,” Thomson said, but wonderfully suggestive. He watched as two rings grazed up against each other: They met, quivered, then bounced away intact, like rubber rings. This put him in mind of “the clash of atoms” implied by the new kinetic theory of gases, in which the motion and collision of atomic entities were presumed to account for the overall properties of a gas.

Kinetic theory was then beginning its long and eventually triumphal ascent. The idea that matter consisted of small, hard atoms had ancient roots, but the modern theory, arising in the middle of the 19th century, owed most to the efforts of Clausius, Maxwell, and Ludwig Boltzmann in Vienna. If a gas consisted of tiny atoms speeding about and colliding constantly with each other, as kinetic theory held, then the overall properties of the gas ought to follow directly from consideration of the behavior of the atoms, as dictated by simple Newtonian mechanics. This was simple in principle but enormously complicated in practice, since there were trillions upon trillions of atoms in an ordinary volume of gas. Perhaps the greatest triumph of kinetic theory was Boltzmann’s derivation of a statistical formulation of entropy from the collective motions of atoms.

Thomson did not altogether object to kinetic theory, but he found it inadequate and restrictive, as indeed in a number of ways it was. An atom must clearly be more than an inert lump, with no qualities except mass and velocity. Atoms absorbed and emitted light at characteristic frequencies, not uniformly across the spectrum. This was the foundation of spectroscopy. Why was one material transparent and another opaque? Kinetic theory did not address such matters. Its defenders would argue that they were using an idealized model to tackle a specific issue—the derivation of the large-scale thermodynamics of gases from the microscopic dynamics of atoms. But Thomson never liked to deal with idealizations and limitations. If a model didn’t explain everything he wanted to explain, he would add to it somehow. In this case, what he needed was a model in which atoms had some sort of structure, some array of intrinsic properties, by

which he could try to understand the interaction of atoms with light and other electromagnetic phenomena. The vortex atom looked like a good bet.

Tait’s experiments with smoke rings arose from his translation of an 1858 paper by Helmholtz that discussed rotatory motion in fluids. Helmholtz had defined, for a fluid with some arbitrary set of internal motions, a quantity he called the Wirbelbewegung, or vortex motion, which he showed was conserved. That is, the collective rotational motions of an idealized frictionless fluid might behave in a hugely complicated way, the fluid stirring about this way or that, but their total magnitude measured by Helmholtz’s prescription would remain constant. (A cup of tea, stirred with a spoon and then left alone, will of course come to a standstill after a time. This is mainly because of friction between tea and cup.)

In particular Helmholtz had shown that a “vortex ring”—a toroidal or doughnut-shaped volume of spinning fluid—was stable. Vortex rings could not appear out of nowhere, nor could they vanish. Thomson seized on this mathematical theorem and built on it a tentative atomic theory. Permanent existence was a basic criterion for any structure that might qualify as an atom, but vortex rings had much more going for them than that. Like the atoms of kinetic theory, they would interact with each other in ways determined purely by dynamics, although in a far more complicated fashion. The collision of two rings was a difficult though “perfectly solvable mathematical problem,” Thomson wrote. “Its solution will be the foundation of the proposed new kinetic theory of gases.”

Beyond that, the vibrations and oscillations of vortex rings, which Thomson had amused himself with in Tait’s laboratory by poking at a smoke ring with his finger, had the capacity to explain spectroscopy. Each atom, pictured as a ring with some set of possible oscillations determined by its structure, would interact with light at a characteristic set of frequencies. Finally, if a vortex ring was a stable rotatory motion of the light-transmitting ether itself, then the physical attributes of the ether should completely determine the interaction of a vortex atom with light.

Here in principle, Thomson asserted, was the foundation of what we might now call a grand unified theory of light and matter. “Helmholtz’s rings are the only true atoms,” Thomson confidently declared. Working

out a full theory would not be easy: “Even for a simple Helmholtz ring, the analytical difficulties which it presents are of a very formidable character, but certainly far from insuperable in the present state of mathematical science.” This sort of exercise, like his Baltimore models of the ether, suited Thomson perfectly. Underlying it all was simple Newtonian mechanics, applied to a certain medium. Vortex atoms were purely dynamical constructions, and consequently all their properties followed from dynamical laws alone. Matter was a dynamical phenomenon. Light was a dynamical phenomenon. The laws of electricity and magnetism, formulated by Maxwell in what Thomson regarded as a suspiciously abstract style, would turn out to be the dynamics of the ether. Maxwell himself, speaking at the British Association meeting in 1870, endorsed Thomson’s proposal as a project worthy of serious investigation and said that if it succeeded the constitution of the physical world would be “nothing but matter and motion.”

Thomson latched onto this marvelous, intoxicating vision without reservation. The striking spectroscopic properties of sodium—the bright double line that gives sodium lights their lurid yellow hue—had caught Thomson’s interest years ago, and he was quick to suggest that “the sodium atom … may very probably consist of two approximately equal vortex rings passing through one another like two links of a chain. It is … quite certain that a vapour consisting of such atoms, with proper volumes and angular velocities in the two rings of each atom, would act precisely as incandescent sodium-vapour acts—that is to say, would fulfil the ‘spectrum test’ for sodium.” In the space of two sentences Thomson’s enthusiasm for vortex atoms took him from “very probably” to “quite certain” without a second thought. Thermodynamics was already a branch of mechanics. Now light and electromagnetism and the properties of atoms would all likewise reduce to dynamical theorems and proofs. This would be a theory of everything, for its day. There was nothing else to explain.

***

Even by the standards of the 19th century, before the mills and factories of the burgeoning academic industry had processed scholarly and scientific prose into the passive-voiced porridge it has mainly become

today, it took an odd author indeed to begin a work of mathematical physics thus:

The paper then discussed some propositions concerning wave motion in electromagnetic theory. Its author, Oliver Heaviside, was certainly different from other people, but he made no pretence of being wooden headed. Born in 1850 in the London slums (around the corner, he would say, from the blacking factory where the young Charles Dickens spent a harshly formative period), Heaviside escaped his origins by becoming a telegraph engineer—the same route Edison took with such great success. But Heaviside was at heart a mathematician and a theorist, and he singularly lacked the personal skills by which men get on in business.

He applied for membership in the new Society of Telegraph Engineers, but was informed that mere telegraph clerks did not qualify. “What would Edison say if he were here now?” Heaviside later remarked. “I was riled. I had already had one of my inventions tried in a rough experimental way by the [Post Office] with success…. So I went to Prof. W. Thomson and asked him to propose me. He was a real gentleman and agreed at once…. So I got in, in spite of the P.O. snobs.” Having proved his point by obtaining membership, he attended no meetings and never paid his dues, with the result that he was kicked out some years later.

Beginning in the mid-1870s, he began a lengthy project to formulate a comprehensive theory of signal transmission by the electric telegraph

according to the full Maxwellian theory of electromagnetism. This was the subject Thomson had begun, 20 years earlier, with only a limited understanding of electric phenomena at his disposal. Heaviside’s treatment was mathematically sophisticated, but practical too, and led to new principles for the design of long telegraph cables, whether overland or undersea. The appearance of the telephone at this same time made new demands of electrical theory. It was no longer enough to get indeterminate but recognizable blips down a cable. Telephony over any distance demanded an output that faithfully reproduced the input. Heaviside’s theoretical analysis supplied a sound basis to the new technology, but his ideas were at first firmly resisted by the British Post Office. Heaviside’s invariable response to opposition was sarcasm of a creative and eccentric flavor, which won him no allies.

As the scope of electrical technology blossomed, the Society of Telegraph Engineers transformed itself in 1888 into the Institution of Electrical Engineers. As well the telephone, industrial and domestic electricity were on the rise. Systems for wiring, insulation, and connection were tried out and patented. Thomson himself devised and then marketed through his instrument company one of the first electricity meters.

In his address as inaugural president of the IEE, Thomson made special mention of Heaviside’s new treatment of telegraphy. But his praise came on the back of a hesitant and grudging nod toward Maxwell: “Maxwell’s ‘electro-magnetic theory of light’ marks a stage of enormous importance in electro-magnetic doctrine, and I cannot doubt but that in electro-magnetic practice we shall derive great benefit from a pursuing of the theoretical ideas suggested by such considerations. In fact, Heaviside’s way of looking at the submarine cable problem is just one instance of how the highest mathematical power of working and of judging as to physical applications, helps on the doctrine, and directs it into a practical channel.”

Heaviside had used Maxwell’s theory to help him understand the telegraph better. Thomson saw this achievement exactly backward. He believed Heaviside’s investigation of the telegraph would illuminate Maxwell’s theory and remedy what he regarded as its flaws.

By this time Heaviside had abandoned with disgust his connection to the unappreciative telegraph industry and had gone to live with his

parents in Devon, barely surviving on their meager resources. He had a brother living nearby but hardly ever visited “because he thought the cart-men shouted abuse at him.” Around this time he was put up for membership in the Royal Society, a process that resembled entry into the baseball hall of fame. Names were proposed and seconded, a secret ballot was taken, some succeeded, others did not, and those who failed could campaign again the next year, until they got in or got the message.

Heaviside was proposed by Oliver Lodge, another young physicist making a name for his work in electromagnetism, and seconded by Thomson. As he explained to Thomson, his attitude was awkward: “I have to give you my best thanks for your consideration in offering to second Oliver Lodge’s F.R.S. proposal. As he has probably told you, I am somewhat cranky on the subject; rather than be passed over, I would prefer never to be nominated; so he has suggested postponement.” To Lodge he wrote enigmatically: “You may judge of the intensity of my feelings as to possible rejection by the fact that I have so good a man as you for my proposer and no less than Sir W. T. for seconder, and still I am not happy. (I had a wicked mammy, a more than brutal pappy; they kicked me, strapped me, flogged me, whacked me. Still I was not happy!)” Such was Heaviside’s strange, pugnacious humor; he was living with his parents (nursing them, so he claimed) when he wrote this.

An arrangement was made. Lodge, Thomson, and others worked behind the scenes, apparently, to rig the balloting in 1890 and guarantee Heaviside a place, and so he became F.R.S., with or without his full compliance. He never traveled up from Devon to go to meetings in London.

Crankiness apart, Heaviside was now working hard in his isolation, going from a specific treatment of telegraphy to a more general and theoretical reworking of Maxwell’s electromagnetism. The Nobel laureate Leon Lederman has joked that the essential criterion for an acceptable “theory of everything” in modern physics is that the necessary equations should fit on a T-shirt. Science and engineering students may occasionally be seen wearing T-shirts with Maxwell’s equations on them, these being, until about the 1970s, the nearest thing to a theory of everything that physicists had thus far devised. In Maxwell’s own time, however, no one would have worn a T-shirt bearing his equations, and not just because Victorian gentlemen didn’t wear T-shirts. What we now regard as

Maxwell’s equations in their standard form—four concise laws, cryptic to the uninitiated, encapsulating the links between electricity and magnetism—are due to Oliver Heaviside.

This is not to say that Heaviside deserves credit for the conception of electromagnetic theory. Using the standard mathematics available to him, Maxwell expressed his theory in Cartesian coordinates, separately denoting the x, y, and z components of the electric and magnetic fields and writing down complicated differential equations, occupying many pages, to capture the variation of these three components with respect to each of the three coordinates. Heaviside, in the 1880s, was a pioneer of what is now called vector calculus. A vector is a quantity with magnitude and direction, such as a velocity. A scalar is simply a magnitude. In electromagnetism, electric charge is a scalar, and the electric field is a vector—because it has orientation. Moreover, it is a vector field, in other words a vector quantity that varies from place to place. So too the magnetic field. Maxwell’s theory connects the amplitude and geometrical pattern of electric and magnetic fields to the spatial distribution of electric charge² and also to the time variation of the fields.

The three basic operations of vector calculus are grad (for gradient), div (for divergence), and curl (for twist or rotation), which roughly indicate the geometrical property of a vector or scalar field that the operations elucidate. Pages of repetitious equations turn into single condensed statements.

Heaviside did not invent this kind of mathematics, but he made innovative use of it in electromagnetism. Not only do the equations become simpler, but their meaning becomes more transparent. Using this compact and elegant notation, Heaviside was able to provide a more rigorous statement of the mathematical properties of the electromagnetic field than Maxwell had been able to do, and this in turn led to a more

precise statement of the physical significance of certain aspects of the theory. Notably, Heaviside (and independently J. H. Poynting) proved that the electromagnetic field carried energy. It had been generally assumed that when electricity moved about, all the energy was carried by electric currents. This certainly was Thomson’s view. But with vector notation instead of the old mess of Cartesian components, it became possible to find a mathematical definition of energy that could be followed with relative ease through complex algebraic manipulations. It became apparent that electromagnetic energy, like the fields, pervaded space and was not concentrated only in charges and currents.

These and other insights were the work, in the 1880s and 1890s, of a young group of mathematical physicists who became known as the Maxwellians. Heaviside and Lodge, along with the Irishman George Francis FitzGerald, were the leaders of this informal movement. In essence, it was the Maxwellians who not only produced Maxwell’s equations as they are taught (and printed on T-shirts) today, but also illuminated and enlarged Maxwell’s theory by using the new methods to apply it in much more general ways and to trace in detail the physics of electromagnetism when regarded as a form of energy.

To all this Thomson remained cool. It is not altogether easy to see why. The Maxwellians put great emphasis on the primacy of energy, a philosophy Thomson had long endorsed. Their use of a compact mathematical notation ought to have pleased him, as he could have taken it as part of his lifelong battle against “aphasia,” the unaccountable inability of otherwise intelligent people to understand mathematical arguments. Yet he did not like grad, div, and curl, and preferred to stick with the cumbersome Cartesian notation of old. Perhaps he, if no one else, could discern physical meaning in arrays of equations laboriously written out component by component. Heaviside wrote to him once that the new style “save[s] letters, and eases the memory, an important matter when there are a great many vectors.” But the point, he said, “is not just to save space, it is to simplify ideas and language, and harmonise our symbolization with Faraday’s way of viewing things; components never come in them, in general investigations, and I am sure Faraday never thought of components.”

To no avail. In Baltimore Thomson had declared that Faraday “did

the most” to cure the “mathematical disease of aphasia from which we suffered so long…. The old mathematicians used neither diagrams to help people understand their work, nor words to express their ideas. It was formulas, and formulas alone. Faraday was a great reformer in that respect with his language of ‘lines of force.’” Maxwell had carried through Faraday’s project to completion, and Heaviside transformed it into a more accessible language. Along the way Thomson fell behind. He favored mathematical theories based on physical pictures, but the physical pictures had to be of a certain kind. Wheels and springs and pulleys he could countenance, but not an intangible vector field stretching and flexing unseen through space. Above all, the notion that these abstract entities purported to carry energy distressed him.

Perhaps too Thomson was influenced in part by his long-running battle against the quaternionic notation his friend Tait so heartily espoused. Tait himself objected with typical vehemence to the new vector notation because he regarded it as a watered-down version of his cherished quaternions. A quaternion was a particular combination of a vector and scalar, constructed so that quaternion operations always produced other quaternions. This appealed to Tait’s sense of mathematical tidiness, but it went against nature. The vector electric field and the scalar electric charge have distinct and separate physical identities. The corresponding quaternion, a combination of the two, does not. Heaviside remarked in one paper that “if we put aside practical application to Physics, and look upon Quaternions entirely from the quaternionic point of view, then Prof. Tait is right, thoroughly right, and Quaternions furnishes a uniquely simple and natural way of treating quaternions.”

At one point the dispute boiled over into the pages of Nature, with Tait attacking the growing number of adherents to the vectorial doctrine. But Heaviside was no Tyndall, responding with the measured distaste and veiled disdain of a Victorian gentleman. He went in for outright mockery, delivered with transparent glee: “Passing to Prof. Tait’s letter, it seems to be very significant. The quaternionic calm and peace have been disturbed. There is confusion in the quaternionic citadel; alarms and excursions, and hurling of stones and pouring of boiling water upon the invading host…. It would appear that Prof. Tait, being unable to bring his massive intellect to understand my vectors … has delegated to Prof.

Knott the task of examining them, apparently just upon the remote chance that there might possibly be something in them that was not utterly despicable.”

Thomson disliked both quaternions and vectors, mainly for the same reason: To him they obscured rather than illuminated physics. He referred to “Heaviside’s nihilism,” and this opinion extended to the philosophy of the Maxwellians in general. He thought they embraced a kind of mathematical formalism that distanced itself further from true physics the more formal it became. He hankered still after mechanical models of the ether, as he had in Baltimore. Heaviside, many years later, commented: “Lord Kelvin used to call me a nihilist. That was a great mistake, (though I did throw a bomb occasionally, to stimulate an official humbug to say something about electricity and how to apply it). He was most intensely mechanical, and could not accept any ether unless he could make a model of it. Without the model he did not consider electromagnetics to be dynamical. But I regard electrodynamics as being fully dynamical.”³

This was the essence of Kelvin’s difficulty over Maxwell. When he said he wanted a mechanical model of the ether, he meant something he could construct out of wheels and pulleys and springs and gyrostats, all embedded in some suitable jelly or wax. These were the mechanical ingredients he permitted in his theorizing. Heaviside and the other Maxwellians believed equally strongly in the existence of an ether—that is, a medium in which electromagnetic waves traveled. They believed, however, that the electric and magnetic fields that their new treatment of Maxwell revealed so clearly were, in themselves, dynamical entities with genuine physical significance. But they were sui generis, not reducible to jellies and pulleys.

FitzGerald had criticized Thomson’s ideas as early as 1884. The Baltimore lectures had been reported in summary fashion in Nature, with reference to shoemaker’s wax and various kinds of pitch as analogs to the

sort of ether Thomson imagined. FitzGerald found this highly unsatisfactory. He objected strongly to “Sir Wm. Thomson’s speaking of the ether as like a jelly. It is in some respects analogous to one, but we certainly know a great deal too little about it to say that it is like one. May be Maxwell’s conceptions as to its structure are not very definite, but neither are any body’s as to the actual structure of a jelly…. It seems very unlikely that any jelly is at all like the ether that Maxwell supposes. … I also think that Sir Wm. Thomson, notwithstanding his guarded statements on the subject, is lending his overwhelming authority to a view of the ether which is not justified by our present knowledge and which may lead to the same unfortunate results in delaying the progress of science as arose from Sir Isaac Newton’s equally guarded advocacy of the corpuscular theory of optics.” The last phrase refers to Newton’s insistence that light consisted of particles, not waves, an opinion that had its merits at the time but retarded the later acceptance of wave theory in England.

Coming from a man just 33 years old, this was sharp criticism of his renowned elder. But Thomson never took personal offense in scientific debate; indeed he embraced a blunt exchange of views. According to Rayleigh, in fact, Kelvin admitted late in his life that “a certain amount of opposition was good for him.” He and FitzGerald embarked on a substantial though frankly useless correspondence. Thomson could never accept certain aspects of Maxwell’s theory, simply because he could find no familiar physical analog to them. FitzGerald tried to persuade him that these parts of the theory corresponded to real physical phenomena, but no reconciliation came.

Rather remarkably, Thomson’s views on Maxwell merited occasional mention in the newspapers, in the way that momentous meaning was teased out of official pronouncements from the Kremlin in the last days of the Soviet Union. At the 1888 British Association meeting in Bath, the correspondent from the Times reported with extreme circumspection that “Sir William Thomson in one paper cautiously made what must be regarded as a somewhat noteworthy admission with reference to Clerk-Maxwell’s fundamental theory…. He considered Maxwell’s fundamental assumption ‘not wholly tenable.’ In all his previous utterances on the subject, Sir William has described Maxwell’s views on this point as com-

pletely untenable, so that the change in his position is of great importance to all interested in electro-magnetic theory.” Thomson wrote to the paper to explain that he had slightly softened his wording after talking to FitzGerald, among others. But this was the full extent of FitzGerald’s influence. In 1896 he was still making the same point he had tried to make after Baltimore. Responding to a letter from Kelvin, FitzGerald wrote: “You say … ‘The luminiferous ether we must imagine to be a substance which so far as luminiferous vibrations are concerned moves as if it were an elastic solid.’ Now this ‘we must’ is entirely unjustifiable. We need do nothing of the kind…. I cannot see how you are justified in concluding that ‘we must’ deal with the ether as if it were an elastic jelly. The electromagnetic properties of the ether are a much better key to its properties than light waves, and I cannot see, nor apparently can you, how it can be both electric and magnetic and at the same time an elastic solid.”

The ether had by this time come under experimental as well as theoretical attack. In 1887, at the Case Research Institute (now Case Western Reserve University) in Cleveland, Ohio, Albert Michelson and Edward Morley performed the celebrated experiment in which they tried, and failed, to find a difference between the speed of two light beams running at right angles. This addressed an old and unresolved issue. If light propagated through an ether that filled space, and if the earth is also moving through that ether, should not light beams have slightly different velocities depending on their direction relative to the motion of the earth? From the theoretical standpoint, other issues presented themselves. How could the earth pass through a solid ether? Or, in fact, would the ether (because of friction) move with the earth in the vicinity of the planet but revert to a cosmically stationary state at great distances? Whatever the answer, there would be consequences for the way light traveled near the earth’s surface.

Michelson and Morley showed, to a high degree of precision, that light moved at precisely the same speed near the earth, regardless of its direction. Kelvin took this to mean that the earth dragged the ether along with it (his old friend Stokes had made a similar proposal decades ago), and that in turn meant further complication for his models of the ether. FitzGerald, along with the Dutch physicist Hendrik Lorentz, made a

more radical suggestion: Perhaps the physical dimensions of moving objects shrank slightly when they moved relative to the ether. In that case, light would move a little more slowly when it had to go upwind, so to speak, but any measuring stick would shrink by the same amount, so the apparent velocity of light would remain unchanged.

Still, there was the assumption in either case that the ether existed and that some complex interaction between ether, light, and matter would explain the result of the Michelson-Morley experiment. FitzGerald was closer to the truth than Kelvin, but he died in 1901, at the same age as Maxwell had died and apparently of a similar cause. Not until 1905 did Albert Einstein propose his special theory of relativity, which said that light always moved at the same speed and that moving objects apparently got shorter. This was not, in Einstein’s proposal, an absolute effect—it depended on who was doing the measuring and was a consequence of the “relativity” of measurement for observers moving at different velocities. There was no genuine FitzGerald-Lorentz contraction of moving objects. Einstein made no mention of an ether. In his theory the ether simply vanished, and so came to an end half a century of strenuous and increasingly baroque efforts to construct mechanical models of the ether, none of which ever proved satisfactory.

***

At the British Association meeting of 1892 in Edinburgh, the presidential address was delivered by Archibald Geikie, a Scottish geologist and friend of Kelvin. He began by reminiscing about the early influence of arguments from physics restricting the lifetime of the earth, coming as they did at a time when geologists had given the matter no thought at all: “It is not a pleasant experience to discover that a fortune which one has unconcernedly believed to be ample has somehow taken to itself wings and disappeared. When the geologist was suddenly awakened by the energetic warning of the physicist, who assured him that he had enormously overdrawn his account with past time, it was but natural under the circumstances that he should think the accountant to be mistaken, who thus returned to him dishonoured the large drafts he had made on eternity.”

The geologists, grumbling and uncomfortable, had nevertheless ac-

cepted the limitations imposed by physics, and with a salutary effect on their reasoning. But the physicists, Geikie complained, had still not been satisfied. “The geologist found himself in the plight of Lear, when his bodyguard of one hundred knights was cut down. ‘What need you five-and-twenty, ten, or five?’ demands the inexorable physicist, as he remorselessly strikes slice after slice from his allowance of geological time. Lord Kelvin is willing, I believe, to grant us some twenty millions of years, but Professor Tait would have us content with less than ten millions.”

Geologists were becoming more confident of their science, however, particularly in their ability to reason quantitatively about the formation and erosion of terrestrial rocks. They now had their own calculations about age, which they were willing to put up against the numbers coming from the physicists’ camp. Geikie went so far as to suggest that the physicists might not know as much as they thought they knew. “Some assumption, it seems to me, has been made, or some consideration has been left out of sight, which will eventually be seen to vitiate the conclusions,” he told his audience. “After careful reflection on the subject, I affirm that the geological record furnishes a mass of evidence which no arguments drawn from other departments of Nature can explain away, and which, it seems to me, cannot be satisfactorily interpreted save with an allowance of time much beyond the narrow limits which recent physical speculation would concede.”

A wary impasse reigned. Kelvin, in truth, was more inclined to allow 100 million years as a reasonable maximum, while Tait’s assertion that the age could hardly exceed 10 million years was strident but lonely. If physicists’ numbers rested on a handful of assumptions, however, geological arguments seemed full of guesses and speculations about weathering and erosion and sedimentation and deposition, none of which seemed to have the fundamental certitude that physical law offered.

But that certitude began to show cracks. One of the weaker arguments limiting the earth’s age came from consideration of the effect of tides in slowing the planet’s rotation, coupled with measurements of the departure of the planet’s shape from a perfect sphere, which indicated its rotation at the time it solidified. This line of analysis had always been rife with physical uncertainties and mathematical difficulties.

By odd coincidence, the man who refined these arguments enough

to extract reliable results was George Howard Darwin, the fifth child of Charles and Emma Darwin and the third to grow to adulthood. Often in poor health, he struggled to get into Trinity College, Cambridge, but then surprised himself and delighted his father by becoming second wrangler in 1868. As a fellow at Trinity he subsequently dabbled for a while in various mathematical ventures, including a sophisticated attempt to statistically analyze ill health among the offspring of marriages between first cousins. In 1877, having seen some earlier work by Thomson, he wrote a paper, “On the Influence of Geological Changes in the Earth’s Axis of Rotation,” in which he addressed the “wandering” of the poles due to slow viscous stirring of the earth’s interior. The paper was sent to Thomson for review. Thomson, as was his habit when he saw something that struck him as possessing insight and originality, made contact with the author directly to discuss not only the work at hand but possible ramifications of it. Thus George Darwin encountered the difficult problem of analyzing tidal effects on the earth’s rotation, to which he added the further complication of regarding the planet’s interior as a stiff semi-liquid rather than an absolutely rigid solid.

Darwin was not an original mathematician or an especially imaginative physicist, but he was a prodigious calculator. The problems he tackled would today be programmed into a computer, but solving them “by hand” had some advantages. The success of some approximate methods and the failure of others often indicates which physical effects are important and which negligible. Darwin, said a colleague, “never hesitated to embark on the most complicated computations if he saw a chance of attaining his end,” and he disparaged displays of elegant mathematics “which are in fact mere conjuring tricks with symbols.” In short, he was a man after William Thomson’s heart, and he had moreover the patience or perhaps monomania to mount an almost lifelong investigation of a problem Thomson could never quite find the time to properly address.

Charles Darwin was overjoyed that his son made such an impression on a matter that had so agitated him over the years. “My dear old George,” he wrote, “All of us are delighted, for considering what a man Sir William Thomson is, it is most grand that you should have staggered him so quickly, and that he should speak of your ‘discovery, etc.’ … Hurrah for the bowels of the earth and their viscosity and for the moon and for the Heavenly bodies and for my son George.”

Through lengthy and laborious calculation, and using the best empirical knowledge he could find of the properties of rocks making up the earth’s mantle, Darwin proved (what seems not at all surprising today) that the body of the planet is amenable to small, slow changes in shape, as external forces and internal conditions vary. His work laid the foundations for understanding many aspects of tidal friction (including both ocean tides and the much smaller but still significant tidally induced flexure of the crust and mantle). He showed how variations in the rotation and figure of the earth could diagnose inaccessible physical parameters such as the viscosity of the planet’s interior. Darwin also analyzed the orbit of the moon, which recedes as the earth spins slower, in order to maintain overall conservation of angular momentum. This led to models in which the moon broke off originally as a fragment of the spinning earth, and so led to another estimate of the age of the system from the time the moon would take to achieve its present orbit. The coupling of the earth-moon system with the sun’s gravity induces changes in the tilt of the earth’s axi….

And so on. As far as Thomson’s particular interest went, the main conclusion of Darwin’s lifelong work was a negative one. Because the earth is not perfectly rigid, it can adapt its shape slowly as its rotation slows. There is no credible way to determine the planet’s age from its present rotation period and current measures of tidal friction. Darwin could at best only establish limits. In papers published in 1879 he estimated that tidal friction operated on a timescale of perhaps 700 million years. This alone meant that tidal arguments had no ability to limit the earth’s lifetime to the kind of number that Thomson had long talked about. In any case, Darwin freely admitted that there were too many uncertainties in the properties of the earth’s interior to be sure even of the estimates he gave. “Under these circumstances, I cannot think that any estimate having any pretension to accuracy can be made as to the present rate of tidal friction,” he concluded.

Of course, this simply meant that the tidal argument was of no use in Thomson’s battle with the geologists and biologists. Heat loss from the earth continued to provide a stricter limit and a smaller allowable age. But the fact that one of the restrictions Thomson had long insisted on had now been lifted from their shoulders, and by Charles Darwin’s son,

gave geologists, biologists, and their sympathizers reason to think the other restrictions might turn out to have concealed flaws. In 1895 John Perry, a physicist and former student of Kelvin, went back to the original calculation of heat loss and claimed to have found just such a loophole.

Thomson, in order to obtain an answer, had assumed the earth to be uniform throughout in its thermal properties—the same conductivity and heat capacity everywhere. Perry offered a simple modification. He imagined the earth as a crust surrounding an interior and allowed the two components to have different properties. The thermal attributes of the crust, he observed, were known from direct measurement, but as to the interior there was only guesswork or assumption. By solving this more complex mathematical problem, in which he had assistance from Oliver Heaviside, Perry showed that with a not excessively outrageous choice of thermal properties for the interior, he could obtain strikingly different conclusions about the age of the earth. The starting point (a uniformly molten sphere) and endpoint (a solid earth with measured surface temperature gradient of 1°F per 50 feet of depth) were the same, but because the interior distribution and flow of heat were significantly different in the two-component model, the time from start to finish could be much longer. Perry claimed that an age as much as a few hundred times the original estimate of 100 million years was possible. Ten billion years was surely enough for any geologist or biologist.

Perry sent a draft of his paper to Kelvin but got no immediate response and was reluctant to pursue his criticism. As he explained, with excessive melodrama, “I was Lord Kelvin’s pupil, and am still his affectionate pupil…. He has been uniformly kind to me, and there have been times when he must have found this difficult. One thing has not yet happened; I have not yet received the thirty pieces of silver.”

Unwisely, Perry then approached Tait, who responded with barely coherent scorn. He wrote dismissively of his “entire failure to catch the object of your paper. For I seem to gather that you don’t object to Lord Kelvin’s mathematics. Why then drag in mathematics at all… ?” Tait told Perry that it was “absolutely obvious” that changing the thermal properties of the interior would alter the result: “I don’t suppose Lord Kelvin would care to be troubled with a demonstration of that.” As to what the interior properties of the earth might be, Tait simply declared, “I don’t

suppose anyone will ever be in a position to judge,” as if that settled the matter.

Perry reiterated that his point was not to establish definitively a greater age for the earth, only to show that a greater age was distinctly possible and that Tait and Kelvin, if they disagreed, ought to supply some counterargument. “What troubles me,” he told Tait, “is that I cannot see one bit that you have reason on your side, and yet I have been so accustomed to look up to you and Lord Kelvin, that I think I must be more or less of an idiot to doubt when you and he were so ‘cocksure.’”⁴ Tait responded by asking Perry again why he thought the interior was different from the crust and, with startling irrelevance, added, “do you fancy that any of the advanced geologists would thank you for 10 billion years instead of 100 million? Their least demand is for one trillion.”

Kelvin, when he finally weighed in, was by contrast eminently reasonable. Perry’s argument was “clearly right” but neither new nor surprising to him. His original analysis of 1862 referred explicitly to the possibility of a difference in conductivity between crust and interior, and this was one of the reasons he had allowed a range of 20 million to 400 million years for the earth’s age. He observed, slyly or more likely obliviously, that “100 millions …. is all Geikie wants,” this being the figure the geologists had reluctantly accepted because it was as much as Kelvin would give them.

More pertinently, Kelvin questioned whether the difference between crust and interior could be as great as Perry suggested. He adduced some relevant bits of laboratory data to argue otherwise. He admitted “it is quite possible I should have put the superior limit a good deal higher, perhaps 4,000 instead of 400.”

No solid conclusion emerged. Perry had pointed out a difficulty, but neither he nor Kelvin (and certainly not Tait) was able to come up with any sound estimate of what the heat loss argument now said about the age of the earth. It could be bigger than 100 million years, but not nearly as big as Perry imagined, unless the interior of the earth was wildly strange

and different from its crust. Still, geologists and biologists took heart from the confusion. Another of the supposedly restrictive calculations that Kelvin had so long promulgated had turned out be much shakier than he had let on.

The shackles were loosening. At the 1896 British Association meeting, E. B. Poulton of Oxford explained to his fellow biologists the uncertainties that had recently been demonstrated in the physicists’ calculations. He told them Tait’s oft-repeated views were “entirely indefensible…. The obligation is all on the other side, and rests with those who have pressed their conclusions hard and carried them far,” and concluded roundly that “Natural Selection will never be stifled in the Procrustean bed of insufficient geological time.”

At the same meeting George Darwin began his lecture to the physicists by saying “amongst the many transcendent services rendered to science by Sir William Thomson, it is not the least that he has turned the searching light of the theory of energy on to the science of geology,” but then he went on to enumerate the mounting difficulties. The tidal argument had proved empty. “Professor Tait cuts the limit down to 10,000,000 years; he may be right, but the uncertainties of the case are far too great to justify us in accepting such a narrowing of the conclusion.”

All in all, Darwin concluded, there were so many uncertainties “that we should do wrong to summarily reject any theories which appear to demand longer periods of time than those which now appear allowable. … It should be borne in mind that many views have been utterly condemned when later knowledge has only shown us that we were in them only seeing the truth from another side.” (Privately, Darwin had said the same thing to Thomson 10 years earlier: “I do not wish to combat the fundamental proposition at all, & only wish to speak against such dogmatism as I find in Tait’s writings & not in yours. It appears to me that we know far too little as yet to be sure that we may not have overlooked some important point.”)

Wise words, but Kelvin did not like to heed them. The following year, in his last formal pronouncement on the subject, he fulfilled a long-standing promise to Stokes by delivering a lecture, “The Age of the Earth as an Abode Fitted for Life,” to the Victoria Institute in London. He

repeated his by now tired old disparagement of the geological uniformitarians, who really no longer existed. He admitted the tidal argument was probably not helpful but restated his figure of 100 million years for the age of both the sun and the earth. No real progress had been made in understanding the heat of the sun, but as the century drew to an end, radioactivity had entered the world’s laboratories as a mysterious physical phenomenon awaiting experimental scrutiny and theoretical explanation. What it was no one then knew. But clearly there were things in the world of physics that went beyond the limits of established knowledge. Kelvin mentioned none of this and repeated his offer of 100 million years, no more.

He sent a copy of his lecture to Archibald Geikie, who sent thanks for this “latest blast of the anti-geological trumpet.” But he was no longer willing simply to cave in to Kelvin’s strictures. “The geological & biological arguments for a longer period than you would allow seem to me so strong that I do not see how they are to be reconciled with the physical demands.” Geikie did not know how to get around the physics, but he was sure there must be a way.

***

Meanwhile the early promise of the vortex atom began to fade in the light of both mathematical and physical problems. Maxwell had written to Tait in 1867 endorsing what he called “worbles” (a play on the German Wirbel, presumably, not some obscure Scotticism), and he wrote approvingly of them in 1872, in a review for Nature of Thomson’s collected papers on electromagnetism. He particularly noted that the billiard-ball atoms of simple kinetic theory could not explain spectroscopy: “It would puzzle one of the old-fashioned little round hard molecules to execute vibrations at all. There was no music in those spheres.” He praised Thomson as well as Helmholtz for developing the theory of vortex atoms. Even so, he had some concern it was a difficult road that might lead nowhere. “But why does no one else work in the same field? Has the multiplication of symbols put a stop to the development of ideas?”

Equally, however, Maxwell saw the virtues of the coming methods for dealing with electromagnetism. At the 1870 British Association meeting he spoke favorably of helpful mathematical innovations that “can

often transform a perplexing expression into another which explains its meaning in more intelligible language,” and he cited vectors as a specific example. When he died in 1879 his guiding intelligence was lost. Had he lived, though, it is clear Maxwell would have been a Maxwellian, alongside FitzGerald, Heaviside, and the rest.

In 1882 the subject of the Adams Prize at Cambridge University (named for the mathematician John Couch Adams, who in 1843 had predicted the existence of Neptune from its perturbing influence on other planets) was the interaction of two vortex rings. J. J. Thomson won the prize. “Like most problems in vortex motion,” he recalled in his dry but oddly humorous way, it “involved long and complicated mathematical analysis, and took a long time.” Few besides William Thomson saw in the increasing complexity and difficulty of vortex analysis the prospect of a universal theory. Most, like the Maxwellians, sought to pare and simplify.

Thomson, on the other hand, continued to develop vortex models despite evident shortcomings. He had realized that the original assumption of vortex ring stability was not quite watertight: “After many years of failure to prove that the motion in the ordinary Helmholtz circular ring is stable, I came to the conclusion that it is essentially unstable, and that its fate must be to become dissipated.” The total amount of rotation, as Helmholtz had proved, remains constant, but the rotating fraction of the fluid spins out into ever finer and more filigreed threads, so that the rotating and nonrotating parts of a fluid become ever more minutely intermixed.

That was the end of the vortex atom, but Thomson turned this disappointment into a new model of the ether, which he called the vortex sponge. It consisted of a fine-grained admixture of rotating and nonrotating elements. Regarded as a fluid, it could support waves with a form analogous to electromagnetic waves in Maxwell’s theory—or approximately so. The vortex sponge was so difficult to analyze that even Thomson could only come up with inexact solutions that he hoped captured the essential physics. Undeterred, he pushed ahead, trying to pin down the exact nature of the little rotating elements in his sponge ether. He took off into realms of fluid behavior that were permissible, under Newtonian mechanics, but so far removed from the world of tangible phenomena that to most of his colleagues it seemed he had lost sight of

his goal of constructing an ether model that was comprehensible because it was “mechanical.” Rayleigh wrote to a physicist friend: “Sir W. is full of a froth theory of the ether! This will lend itself to sarcasm even better than the jelly theory.”

In 1889, when Thomson spoke to the Institution of Electrical Engineers in praise of Heaviside’s improved theory of telegraphy and practical electromagnetism, he spoke plainly of his unhappiness with the state of affairs as it then stood. “I may add that I have been considering the subject for forty-two years—night and day for forty-two years. I do not mean all of every day and all of every night; I do not mean some of each day and some of each night; but the subject has been on my mind all these years. I have been trying, many days and many nights, to find an explanation, but have not found it.” Seven years later, writing again to FitzGerald, nothing much had changed. He could not find a satisfactory ether model, but neither would he accept the bare mathematical formalism of the Maxwellians. “It is mere nihilism, having no part or lot in Natural Philosophy, to be contented with two formulas for energy, electromagnetic and electrostatic, and to be happy with a vector and delighted with a page of symmetrical formulas…. I have not had a moment’s peace or happiness in respect to electromagnetic theory since Nov. 28 1846 [his early works on analogies between electric fields and elasticity]. All this time I have been liable to fits of ether dipsomania, kept away at intervals only by rigorous abstention of thought on the subject.”

Five years later Lord Kelvin took to a desperate assertion: “It has occurred to me that, without contravening anything we know from observation of nature, we may simply deny the scholastic axiom that two portions of matter cannot jointly occupy the same space, and may assert, as an admissible hypothesis, that ether does occupy the same space as ponderable matter.” It had always been the goal to find an ether model that explained electromagnetic phenomena in their own right and also explained their interaction with matter. Now Kelvin was saying ether and matter could occupy the same portion of space and know nothing of each other. This was not a suggestion embraced by other physicists.

***

As the end of the century approached, Kelvin’s growing isolation was not only intellectual. His brother James, who had been beside him at Glasgow as professor of engineering since the death of Rankine in 1872, died in 1892 at the age of 70. His sister Elizabeth died in 1896, having reached 77 years of age. Of his siblings only his brother Robert in Australia still lived, but they had not seen each other since Robert left Scotland in 1850 and would never do so again. Robert died in 1905. Kelvin had a collection of nieces and nephews. James Thomson Bottomley, son of his long-dead sister Anna, was his assistant in Glasgow, generally lived with him there or at Netherhall, performed experiments for him, and lectured frequently when Kelvin was away on business. Elizabeth had three surviving children, her daughters Elizabeth and Agnes, to whom Kelvin remained close, and a son George who figures little in family tales. (Another son, David Thomson King, had gone into the cabling business and died in a shipwreck in 1875.) Elizabeth edited her mother’s memoir of Kelvin and added her own recollections. Agnes wrote her own personal reminiscence.

Friends and colleagues were beginning to disappear too. In 1885 Fleeming Jenkin died at the age of 52 after what should have been minor surgery. Their collaboration on telegraph matters had subsided over the years, but having been professor of engineering at Edinburgh since 1868 Jenkin saw Thomson from time to time and made the acquaintance of the Blackburns at their lonely, lovely house on the Moidart Peninsula, where he took up highland dancing with enthusiasm. More affecting for Kelvin was the death in 1894 of Hermann von Helmholtz, whom he had known and admired since their first meeting in the Rhine valley almost 40 years earlier. Helmholtz, at the age of 72, had decided to visit the 1893 World’s Fair in Chicago. His wife, already concerned about his health, went with him, and on their tour they got as far west as Denver, which they found dull and unsophisticated. They preferred the East Coast, Boston in particular, which was “quite English…. Some intellectual interest attaches to this city, unlike that awful Chicago,” Anna von Helmholtz reported home.

On the steamer returning to Europe, Helmholtz fell badly down a narrow stairway, lost consciousness, and never fully recovered his physical or mental strength. He suffered a stroke the following summer and

died a few months later. Scientifically, Helmholtz and Kelvin had much in common. Whereas Kelvin had started as a mathematician and moved toward physics and engineering, Helmholtz had trained as a physician, moved to physics, and taught himself mathematics. Both were versatile and ingenious, makers of instruments and solvers of problems more than philosophers. Both became public figures in their own countries, though Helmholtz was an able administrator while Kelvin remained a free spirit in matters of bureaucracy and organizations. Helmholtz had served as first director of the Physikalische-Technische Reichsanstalt in Berlin—the world’s first government-funded laboratory for applied science and technology, a project that Werner Siemens had both pushed for politically and underwritten financially. Kelvin saw the need for such an institute in his own country but, perhaps wearied by his old battles with the Admiralty, had exerted no great effort to bring it about. Not until 1900, due largely to the efforts of Lord Rayleigh, did the British government inaugurate the National Physical Laboratory in the London suburbs.

In Germany Helmholtz was regarded by many younger researchers as a fearsome man of stiff formality. In fact he was rather shy. Kelvin was oblivious to matters of etiquette. (Fanny once had to shush him at dinner with Queen Victoria, when he was about to correct in front of distinguished guests Her Majesty’s misstatement on some nautical question.) In Kelvin’s unconstrained company it was impossible to indulge in formalities, and Helmholtz gladly let go the attempt. At the Edinburgh British Association meeting in 1892, “Helmholtz and Uncle William were inseparable, and both spoke a good deal in the sections,” a niece reported.⁵ Helmholtz, who was not as powerful a mathematician as Kelvin, had a stronger and simpler sense of physics. He made great contributions to the physical understanding of hearing and sound, for example, and he never once tried to make an ether model. His death took away one of the few people whose opinions Kelvin could occasionally bring himself to attend to. More characteristic is a tale recounted by Lord Rayleigh’s son. Kelvin

was visiting the Terling estate “full of indignation” at some new electrolytic theory he had recently heard about. He pounced on a textbook from Rayleigh’s library to learn more about this theory but came across some smallish error after a couple of pages and immediately put the book aside: “It is Mayer’s old mistake of 1842, and here it is again in 1895!” Then he was persuaded to keep reading anyway and started to see there was something to the idea after all. “He will think before long that he discovered it himself,” observed Rayleigh to his son, after Kelvin had left. Rayleigh also remarked on the difficulty of getting Kelvin to concentrate on some argument, even to the extent of reading a page of a paper: “The first line would send him off on some train of thought of his own, and his eye would wander from the printed page.”

Throughout his long travails over ether theories Kelvin had corresponded with Stokes on the finer points of fluid mechanics. He remarked in passing during the Baltimore lectures how “I always consulted my great authority, Stokes, whenever I got a chance.” Even so, it often took repetitious explanations from Stokes, a patient and long-suffering man, to bring a point finally to Kelvin’s full attention. When they talked in person at Cambridge, J. J. Thomson recalled, “Stokes would remain silent until Kelvin seemed at any rate to pause. On the other hand, when Stokes was speaking, Kelvin would butt in after almost every sentence with some idea which had just occurred to him, and which he could not suppress.” On just one occasion, when Kelvin was talking wildly about atoms, Stokes got his dander up enough to resist: “He was so much in earnest that Kelvin for once could not get a word in edgeways: as soon as he started to speak, Stokes raised his hand in a solemn way and, as it were, pushed Kelvin back into his seat.”

***

If physics, or rather natural philosophy, represented by this time a source of frustration and even failure to Kelvin, he enjoyed compensations in the form of his reputation and public demand for his pronouncements. In 1897 the British Association met again in Canada, this time in Toronto. The visit of the noted savants, Kelvin prominent among them, was greeted by banner headlines and extravagant prose on the front page of the local newspaper. “The Men of Science Arriving,” the Toronto Globe

informed its readers on Monday, August 16, assuring them on Wednesday that the city was “Ready for the Men of Science.” When, the next day, the Men of Science arrived, they saw news of their meeting blazoned across the entire front page of the Globe, with woodcuts depicting the university buildings and the emblems of the British Association, along with reports of cordial welcoming speeches from the mayor and others, which drew hearty thanks from the distinguished visitors.

Kelvin featured strongly in reports from the Friday sessions, for which the Globe’s valiant but struggling headline writer came up with the banner “A Day of Good Things: Extremely Interesting Proceedings at the Meeting of the British Association.” The question of large-scale power production and consumption had only lately impinged on public consciousness, as the coal-based economy went from strength to strength and, crucially, electricity generation and distribution began to blossom, bringing what had been industrial matters into the domestic realm. Kelvin spoke about the world’s supply of coal and, more provocatively, about the supply of oxygen in the atmosphere, which the burning of coal used up. He offered an ingenious calculation: If all atmospheric oxygen came up originally from the respiration of plants, and if all ancient plants decayed and turned into fuel of one sort or another, then he could show that the ultimate limit on terrestrial power would come not from running out of coal but from running out of oxygen to combust it with. This is not at all true, in fact, since only a tiny fraction of vegetation turns into coal, but his fearlessness in tackling enormous questions by means of a few simple scientific assumptions showed he had lost none of his bravado.

Kelvin had come to Toronto after visiting Niagara, where he had official business as a consultant on continuing efforts to generate electricity from the power of the falls. In 1890 he had been invited by an American consortium to serve as chairman of an international commission to study the feasibility of electricity generation from Niagara Falls, an idea first seriously proposed by William Siemens in 1887. As early as 1879, however, Kelvin had spoken to a British parliamentary committee on the advantages of electricity over gas for lighting and industrial purposes and said then that he “believed the Falls of Niagara would in the future be used for the production of light and mechanical power over a large area of North America.” By 1893 the international commission had chosen a

design offered by Westinghouse, and two years later the first power plant came into operation. When Kelvin visited in 1897, two generators were running, the nearby town of Niagara Falls was lit by electricity, and a number of industries, notably Union Carbide and American Cyanamide, had set up plants to take advantage of the newly abundant electric power.

Impressed by the scale of activity, Kelvin looked grandiosely ahead. In interviews with local reporters he talked of a time “when the whole water from Lake Erie will find its way to the lower level of Lake Ontario through machinery, doing more good for the world than even that great scene which we now possess in contemplation of the splendid scene which we have before us in the waterfall of Niagara…. I do not hope that our children’s children will ever see the Niagara cataract.” He repeated his prediction to a Toronto reporter: “As the demand goes on increasing, so the amount of horse-power developed will increase, until the whole water power of Niagara will be used for doing mechanical work.”

Kelvin’s attitude toward nature was a little inconsistent. He may have been happy to see Niagara Falls vanish, but he loathed motor cars and voted in the House of Lords for a bill restricting the use of cars because he didn’t want to see the pristine Scottish landscape ruined. In London on one occasion his niece Agnes took him to an art exhibition and showed him a romantic painting of Glen Sannox, with mist adorning the mountains. Kelvin, she reported, was annoyed that the artist had not waited until the mist cleared because it obscured a notable geological feature.

Kelvin envisaged a time when electricity from Niagara would travel farther afield, but the transmission of electric power was a controversial scientific question. Any wire, even the best copper, had some resistance to an electric current, which generated heat and wasted power. As Joule had first shown more than half a century ago, that power loss went in proportion to the resistance times the square of the current. Higher voltages and lower currents meant more efficient transmission of power, but high voltages presented dangers and practical difficulties. Speaking to the British Parliament two decades earlier, Kelvin had talked of thick copper conductors in the form of tubes, with cooling water running down them, able to transmit power for hundreds of miles. Since then, however, he had thought more closely about the economics of power loss and formulated what has sometimes been called Kelvin’s law of power transmission:

The “most economical size of the copper conductor for the electric transmission of energy … would be found by comparing the annual interest on the money value of the copper with the money value of the energy lost in it annually in the heat generated in it by the electric current.” Guided by this principle he now estimated that electricity could travel up to 300 miles with acceptable power loss, if 20,000 volts were used, but he recoiled from such large potentials. “I would not advise manufacturers to settle farther than ten miles from Niagara Falls,” he told a reporter for the Buffalo Express. Speaking just the next day to a Toronto reporter, he was a little more generous: He thought power might usefully travel 20 or even 30 miles from the falls.

Kelvin gave out his opinions freely during his visit and spoke easily to journalists. “A gentleman of exceedingly pleasant manners” with an “amiability of disposition,” wrote one. “He is a remarkable example of a great man whose native character has remained unchanged despite … the elevation to a lofty social position.” The Buffalo reporter reported with dry humor the contrast between this member of the British nobility and “a plain American citizen,” the chief Niagara engineer Coleman Sellers. “The man with the title looks and acts like a plain citizen. The plain citizen looks and acts as if he were the autocrat of all the Russias. Lord Kelvin is approachable and affable.” During the interview Sellers kept interrupting to say that Lord Kelvin was hungry and wished to go to dinner. Kelvin at first smiled indulgently and carried on talking. On the second occasion he “looked annoyed. He looked at Coleman Sellers for a moment, then turned to the reporter again.” Finally Sellers dragged him away by the arm.

“Lord Kelvin is short and thin and gray and plain,” the Buffalo reporter told his readers. “He is very lame, but there is something in his appearance that does not belie his youthful record as an athlete, when he won the Silver Sculls at Cambridge…. His head is large and his gray beard is thin and straggling. His baldness runs to the crown and his immense forehead is smooth and polished as a roc’s egg…. His small blue eyes are kindly and genial in their expression. His clothes fit badly, after the English fashion.”

Kelvin had some years earlier allied himself with the losing side of the peculiarly fierce controversy that raged, around 1890, over the rela-

tive merits of direct current and alternating current systems for power transmission. The debate took off when the eccentric Serbian engineer Nikola Tesla, brought over from the Edison laboratories in Paris to work with Thomas Edison himself at Menlo Park, had given a presentation in 1888 describing the virtues and promise of his “polyphase generator” for producing alternating currents at high voltage. George Westinghouse, a railway entrepreneur, heard the talk and promptly hired Tesla away from Edison to design power transmission systems using the new technology. Edison, a devout direct current man, started a campaign assailing the dangers of alternating current, the height of which involved proposing that a man sent to the electric chair should be said to have been “westinghoused” or “consigned to the westinghouse.”

The suggestion that alternating current is fearsomely dangerous while direct current is pleasantly safe seems absurd, when a few thousand volts of either will satisfactorily kill anyone. There is a smidgen of reason at the bottom of the argument. A given alternating voltage will transmit less power down a wire than the same direct voltage, because the alternating current oscillates from some peak value, through zero, to the same peak value in the opposite direction, and so on. The numerical factor of importance here is the square root of 2, approximately 1.414. A somewhat higher voltage is needed for an alternating current system to achieve the same efficiency in transmission as a direct current system. And higher voltage means greater danger.

Although the Niagara commission that Kelvin chaired endorsed Westinghouse’s alternating current system for the falls, Kelvin himself never abandoned his preference for direct current. It fit in with his idealized law about the economics of power transmission. Having calculated costs and efficiencies, he insisted it made sense to choose the better solution. This argument, however, neglected utterly the relative ease (and therefore lower cost) of producing large alternating voltages and reducing them to safe values for domestic use. The transformer—two coils of wire wrapped around a common iron core, the same device Faraday had used in 1831 to demonstrate simple electromagnetic induction—could step alternating voltages up and down with no fuss. A changing electromagnetic field induces a current in a wire; a static one does not, and this is why direct current transformers do not exist. For efficient power trans-

mission, high voltages are essential, and direct current systems cannot do the job.

Kelvin understood all these matters perfectly well, yet insisted that the quantitative efficiency argument ought to trump all other concerns. It is an extreme example of the kind of tunnel vision he increasingly showed on technological as well as scientific matters. Having once grasped a certain point of view and justified it with an appropriately quantitative analysis, he seemed impervious to all other considerations. It was the nearest thing he possessed to a philosophy of science. In one of his most famous and memorable remarks about the power of the scientific method, he declared: “I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.”

This was the wellspring of his attitude in all departments of science—indeed in all useful kinds of rational thought. It was why he favored the precise arguments of physics limiting the lifetimes of the earth and the sun over the woolly speculations of geologists and biologists. It was why, in a broader sense, he insisted on literally mechanical models of ether and atoms and would not succumb to the nihilism of the Maxwellians, who were willing to accept a mathematical structure based on no tangible model. Where in that were physical notions he could touch, assess, and quantify?

Kelvin valued mathematics not for any formal elegance or alleged esthetic qualities but because it enabled him to think and reason with confidence. Mathematics “is merely the etherealisation of common sense,” he told the citizens of Birmingham in an address at the town hall there in 1883. In a similar vein he praised empirical science, bolstered by mathematical argument, over abstract theorizing. Opening new laboratories at University College in Bangor, Wales, in 1885, he said forcefully: “There is one thing I feel strongly in respect to investigation in physical or chemical laboratories—it leaves no room for shady, doubtful distinctions between truth, half-truth, whole falsehood. In the laboratory everything is found either true or not true. Every result is true. Nothing not

proved true is a result;—there is no such thing as doubtfulness.” And further, if merely measuring things seemed like dull work, he declared that when investigation is done with a purpose, “measurement itself becomes an object to inspire the worker with interested ardour. Dulness [sic] does not exist in science.”

Reason flowing from quantitative knowledge suffused Kelvin’s attitude toward life in general. When he visited Stokes in Cambridge, the two elderly men used any opportunity to engage in playfully intense scientific analysis. “For instance, the eggs were always boiled in an eggboiler on the table, and Lord Kelvin would wish to boil them by mathematical rule and economy of fuel, with preliminary measurements by the millimetre scale, and so on,” the physicist Joseph Larmor recalled. In more serious matters, Kelvin’s insistence on simplicity of thought came across as naivete. At an 1887 dinner commemorating the jubilee of Britain’s first telegraph line (from Euston to Camden, in London), he confidently informed the assembled guests that instant telegraphic communication between London and Dublin demonstrated “the utter scientific absurdity of any sentimental need for a separate parliament in Ireland. [This] seems to me a great contribution of science to the political welfare of the world.” Oceanic telegraphy, despite the expectations of editorial writers for the Times of London and New York, had not banished international tension and war; it was hardly likely to quell the ancient disagreements between Ireland and England. But these disputes were, to Kelvin, irrational to begin with; they ought not, therefore, to exist in the first place, and so he imagined it would be an easy matter to dispose of them, if only people would talk plainly and stick to the facts.

***

Plain talk had not dissipated Kelvin’s scientific disagreements. Some of the novel discoveries of the 1890s were more revolutionary than others. When Wilhelm Röntgen announced in 1895 the discovery of a penetrating kind of radiation that could pass through flesh and create an image of bones, Kelvin hoped at first it would bear out an aspect of his mechanical conception of the ether. In Maxwell’s theory, electromagnetic radiation consisted strictly of transverse waves, or side-to-side oscillations, as of a violin string. But if the ether bearing electromagnetic radiation

were some kind of solid-liquid-jelly-sponge affair, then in general it would be expected to support longitudinal waves, or alternations of compression and rarefaction along the direction of radiation, rather than perpendicular to it. Perhaps the Röntgen waves were longitudinal ether oscillations. Kelvin had held out ever since the Baltimore lectures that such waves, absent from Maxwell’s theory, could not be ruled out and ought to be sought experimentally.

Quickly, though, it became apparent that X rays, as the new radiation became known, were ordinary electromagnetic waves beyond the ultraviolet, with higher energy and shorter wavelength than had been encountered before. Kelvin (whose confidence in his numerous ether models was wavering anyway) accepted this conclusion with little hesitation.

Electrons, J. J. Thomson’s discovery of 1897, also fitted in at first with Kelvin’s view of the physical world. That there might exist tiny objects carrying electric charge was no great surprise. What exactly they were remained mysterious. Inevitably, Kelvin’s thoughts took him in his own direction. In a 1902 essay eccentrically entitled “Aepinus Atomized,” he tried to revive, in modern clothing, a mid-18th-century theory of electricity due to Franz Ulrich Theodor Aepinus of Rostock, in what is now northern Germany. Aepinus proposed that there was a single kind of electric substance, of which an excess represented a positive charge and a deficit a negative charge. Kelvin proposed that “Aepinus’ fluid consists of exceedingly minute equal and similar atoms, which I call electrions, much smaller than the atoms of ponderable matter.” These electrions were not simply free particles reacting to electric forces alone. They interacted with atoms of ordinary matter through a complicated force law. A neutral atom contained a certain number of electrions; with too few or too many, an atom acquired an overall electric charge. The forces controlling the loss and reacquisition of electrions by atoms were meant, Kelvin explained, to account for the variety of chemical properties displayed by the atoms of the (newly formulated) periodic table. And he hoped too he could explain the geometry of crystal lattices and the regular arrangement of atoms in solids through this single force law.

This proposal, complex yet sketchy, was entirely characteristic of Kelvin’s thinking. Beginning with a handful of simple assumptions

(electrions, atoms, a force law between them), it quickly piled up mathematical complications, without yielding specific predictions. It was, to use another historical term, a Boscovichian theory, harking back to the ideas of Roger Boscovich, an 18th-century Serbo-Croat priest who had proposed a model in which both attractive and repulsive forces operated between atoms, depending on the distance between them. By adjusting the force appropriately, Boscovich hoped to explain chemical reactions, absorption, adhesion, and so on. Not too many years earlier Kelvin had hoped his vortex atoms, in which the only ingredients were a suitable ether and Newtonian mechanics, would provide a universal explanation of matter. But that project had failed, and Kelvin reached back to the 18th century for ideas that had been proposed as philosophical speculations but never developed into mathematical theory. The weakness of Boscovichian atomic theory, from the modern perspective, is that the force law between atoms is assumed into existence and made as complicated as it needed to be in order to explain whatever the theory was meant to explain. But this was Kelvin’s way of thinking, taken to a final extreme. Forces and particles he was happy with, though the particles were of a mysterious nature and the forces complex and unproven. On the other hand, he still would not accept the disembodied field theory of the Maxwellians.

***

Kelvin celebrated his 75th birthday in 1899 and at last retired from his position as professor of natural philosophy⁶ at Glasgow University. Except for five years at Cambridge and a few months in Paris, he had belonged to the university, student and teacher, for 67 years, going back to the days when, as an eight-year-old boy, he sat in on his father’s math-

ematics lectures. He insisted on maintaining a connection and on his retirement was duly enrolled as a “research student” of the university. But he lectured no more and was free to spend his summer months in London, where he engaged in scientific or political or commercial business, or in the south of France for his own and his wife’s health, returning in the winter to Netherhall. In this peripatetic life he was never without a green notebook, in which he jotted ideas and worked out bits of theory and noted experimental suggestions and corresponded with his fellow natural philosophers as furiously as ever.

Health problems occasionally slowed him down. Late in 1895 his bad leg troubled him, becoming swollen and keeping him in the house well into the following year. Forced into physical inactivity, he redoubled his demands of everyone else. Propped up in bed, wearing a bright red jacket draped over with a blue and white quilt, and with papers and notebooks scattered all about him, he issued notes and instructions and urgent demands. His recovery was interrupted by a bout of pleurisy, but he was well again by the time of his jubilee that summer. Toward the end of that year he suffered for the first time an acute attack of facial pain, diagnosed as inflammation of the fifth nerve. Such attacks, lasting a few days and disappearing as abruptly as they came, troubled him for the rest of his life. “A horrid demon of the No. 5 nerve,” he sometimes called it, and it caused him to cancel lectures and miss dinner engagements. But he rebelled at being cooped up, and when the pain departed he resumed his robust and enthusiastic habits and traveled and lectured and socialized as much as ever.

In 1902 he and Lady Kelvin embarked on another trip to the United States, his fourth and last. It was a triumphal tour. Arriving in New York on April 19, he immediately went to Columbia University to attend the installation of a new president. He mingled with a distinguished crowd, including President Roosevelt and Andrew Carnegie. Kelvin, “looking very venerable, limping, and wearing a large monocle,” came in on the arm of the governor of New York. He spoke to a reporter for the New York Times, full of enthusiasm for Marconi’s wireless telegraph but dismissive of heavier-than-air flight by dirigible. Two evenings later the American Institute of Electrical Engineers gave a reception for him, where he met Edison, Tesla, Westinghouse, and many other luminaries of the

burgeoning U.S. electrical industry. Traveling down to Washington, D.C., he stayed with Mr. and Mrs. George Westinghouse, who gave the noble couple a grand dinner, with numerous distinguished guests, both political and academic. On April 24 Kelvin testified before a congressional committee in favor of a metrication bill. He wished his own country would take the initiative, he said, but added that he would be glad to see the United States in the vanguard, so long as the goal was accomplished.

Then it was on to Niagara, to observe the great progress there not only in the generation of electricity but in the accompanying rise of power-hungry industries. He saw a plant that made nitric acid from atmospheric nitrogen and inspected an electric furnace. “There is practically no limit to the temperature the electric furnace can get,” he mused out loud. “It ought to be easy to manufacture the diamond” from ordinary carbon. This was reported in both the Times of April 28 and the Rochester Democrat and Chronicle of April 29, but when a Rochester reporter asked him about it the following day he responded with a smile, “Oh, there is nothing practical in that.”

In Rochester his host was George Eastman, founder of Kodak, of which Kelvin had been named a director (he was also vice-chairman of the Kodak Company of London). He talked of the scientific basis of photography and also of its scientific potential, particularly in astronomy. The purpose of his visit to Rochester, indeed of this whole trip to the United States, was to inspect the new camera works and offer his technical advice on the many new processes and technologies operating there. But his opinion on science past, present, and future was always in demand. The Rochester reporter found him altogether down to earth. “Before Lord Kelvin has been conversing five minutes, the visitor is beguiled into thinking that he has known Lord Kelvin as long as he has known anybody. His courteous, unaffected manner puts one at ease at once.”

Kelvin held forth on electric power transmission (“a success … no longer an experiment”) and on wireless telegraphy (“I think Marconi has got it”), but soon the conversation turned to the possibility of power generation from Rochester’s river, the Genesee. Now Kelvin began to pepper his interviewer with questions about the size and course of the river, the falls running to the lake, and the numerous tributary streams. A detailed map and an engineer’s survey were fetched. Before long Kelvin

had picked out a plausible location for a hydroelectric plant and assured the reporter that power could satisfactorily be carried from there to the city itself, but he cautioned that these were preliminary ideas. His combination of unfettered thinking with insistence on precision impressed the reporter. “He is too exact in his methods to announce a conclusion prematurely, although he is wonderfully quick to grasp details and is as keen for information on the subject like the water power of the Genesee as a newspaper reporter.”

Though the Rochester journalist could not know it, this was his attitude to ether models and atomic theories too. Once the concept was set down, it was a matter of working out all the details, and unless all the details could be got right at once, no solution was yet acceptable.

There followed Kelvin’s raucous reception at the university, where an attack of the number five demon kept his remarks briefer than he had intended, except that once he warmed up to his task he carried on anyway. He described to the students his own fortunate life, as the child and product of universities, who had spent his whole existence in or around colleges. “Both as a student and as a professor, I love the college atmosphere.” He urged his listeners to “acquire knowledge, and make use of every hour. As we grow to advanced age, we can look back upon the pictures formed in the college days. Fill your minds with these pictures. They are pleasant to bring to your recollection as you grow to age.”

Mellow thoughts such as these were probably lost on his youthful audience, but Kelvin’s nostalgia was, typically, of a pleasurable kind. Fond recollection, not regret—but then he was a man who had never wasted a moment, so that even what he came to regard as failure might seem time well spent, in a worthy endeavor.

On a tour of the university Kelvin eagerly looked over the physics and chemistry laboratories but insisted also on seeing the boiler rooms and the heating and ventilation systems, which he “commended … in high terms.” A day or two later he left Rochester for a reception at Cornell, then continued on to Yale to take an honorary degree.

Lord and Lady Kelvin traveled by private railroad carriage, furnished by George Eastman and filled by his wife with orchids and violets from their conservatory. The eager reporter from the Rochester Democrat and

Chronicle joined the train for the first part of the journey, anxious to hear more about Kelvin’s ideas for electricity generation from the Genesee River. They were grand plans indeed, if the newspaper account is to be believed. This “greatest of living scientists, whose simple dictum is law in matters electrical, whose achievements on physical lines have deservedly carried him to the highest rank of England’s nobility … presented Rochester with the formula by which its greatness is to be achieved and its dream of practically unlimited power for industrial purposes realized.”

The reporter noted that Kelvin went against standard practice by proposing direct rather than alternating currents for transmission. He explained that with the multiphase system pioneered by Tesla and Westinghouse, voltages on neighboring high-tension cables could differ enormously if their currents were out of phase. “A cat may make a connection across the wires, and in its death disable the system,” he said. Kelvin proposed instead a system of 20 direct current generators at 2,000 volts each, connected in series to produce 40,000 volts, which would satisfactorily transmit power up to 100 miles with acceptable losses. As Kelvin elaborated on his plan, the reporter “covertly pinched himself, to make sure that he was not dreaming.”

After an hour of these thrilling revelations, Kelvin talked briefly of his fascination with the camera works he had seen in Rochester. As the reporter made to leave, Kelvin immediately took up page proofs that needed his urgent attention. They represented a version, to be published finally in book form, of the Baltimore lectures he had given almost 20 years earlier. “I work on these proofs whenever I get even fifteen minutes’ time,” Kelvin told the starry-eyed reporter.

Two days later the Rochester newspaper ran another story, with careful comments from “one gentleman, who is in a position to speak with authority,” scotching rumors that a company had already been formed to put Kelvin’s plan into effect. Discussions would take place, it was said, but a good deal of preliminary investigation would be needed. It hardly needs saying that Kelvin’s extravagant plan for a system of direct current generators and transmission lines spreading across the Genesee valley to Rochester never came to pass.

***

In March 1903 Pierre Curie and Albert Laborde announced that the radioactive decay of a radium salt released heat. This was seven years after Becquerel’s discovery of radioactivity, and the transmutation of an atom of one element into an atom of another was an established fact. The nature of the transmutation was baffling, however, not least because the nature of atoms remained mysterious.

Curie and Laborde’s finding caused a stir in the physics world. At the British Association meeting in September of that year there was a demonstration of a little piece of radium making the mercury rise in an ordinary thermometer. One scientist commented that this phenomenon “can barely be distinguished from the discovery of perpetual motion, which it is an axiom of science to call impossible, [and] has left every chemist and physicist in a state of bewilderment.” It seemed like energy from nowhere, appearing out of an otherwise inert mineral.

Whatever the explanation, this new source of energy had implications for the age of the earth and the sun. In a very short note published in Nature on July 9, 1903, an amateur astronomer by the name of William Wilson calculated that the entire output of energy by the sun could be accounted for if the sun contained 3.6 grams of radium in every cubic meter. This simplistic but telling bit of arithmetic attracted little notice. But at the end of September, shortly after the BA meeting, George Darwin weighed in. He cited recent measurements by the young New Zealand physicist Ernest Rutherford, then at McGill University in Montreal, of the heat released by radium, and reckoned that if the sun as a whole were made of some such material, its age could be many times greater than the age calculated long ago by Kelvin. This was all speculative, he admitted, but “knowing, as we now do, that an atom of matter is capable of containing an enormous store of energy in itself, I think we have no right to assume that the sun is incapable of liberating atomic energy, to a degree at least comparable to that which it would do if made of radium.” Unlike the commentator at the BA meeting, Darwin did not hesitate to conclude that any energy released by radioactive atoms must have been stored up somehow beforehand. Whatever an atom might be, it could not create energy from nothing.

A week later J. Joly of Dublin applied the same thinking to the age of the earth. Kelvin had always assumed that the planet was a passively cool-

ing body, slowly losing whatever original heat it had possessed. But if radioactive minerals constantly generated interior heat, the old argument fell apart. Joly concluded confusedly that “the hundred million years which the doctrine of uniformity requires may, in fact, yet be gladly accepted by the physicist.” The uniformitarians, of course, had originally assumed unlimited time; it was the physicists who had beaten the geologists down to 100 million years.

Kelvin responded at the 1903 BA meeting with off-the-cuff remarks, later written up in more elaborate form, to the effect that he thought radioactive heat must come not from within the decaying atoms but ultimately from the surrounding ether. Atoms took in energy, stored it up temporarily, and released it when they decayed. The heat, he said, comes “from without the atoms, where it exists in a form we have not yet found the means of detecting.” In papers published in the next couple of years, and in presentations at succeeding BA meetings, he reached back again to the old ideas of Aepinus and Boscovich to devise mechanical models of the atoms, with components held in place by forces whose form he concocted for the purpose. These atoms could be, so to speak, spring loaded by absorbing energy from the ether. Then they would burst apart, shooting “electrions” and other fragments into space, possibly at speeds exceeding the speed of light. These models were inventive and ingenious, as ever, but increasingly detached from the developing ideas about atoms. Rutherford, along with other young men such as Frederick Soddy, were measuring precisely the heat released in radioactive transformations and determining the identity of the particles released. Lord Rayleigh’s son, Robert Strutt, who became the fourth Lord Rayleigh in 1919 when his father died, was among those who established the possibility of dating rocks by assaying the radioactive decay products they contained. Soon, ages of hundreds of millions of years were spoken of for perfectly ordinary minerals in the earth’s crusts.

One old combatant who did not speak in this final round of the debate over the age of the earth was P. G. Tait, who had died in 1901. His last year was miserable. His third son, Freddie, had taken up golf as soon as he could walk and became one of the great players of his day. He won the British amateur championship twice, in 1896 and 1898. Tait took fierce pride in his son’s achievements. One of Tait’s lasting contributions

to physics was his 1891 proof that backspin on a golf ball, via the agency of a fluid mechanical phenomenon called the Magnus effect, imparts lift and thus allows the ball to fly much farther than if it were not spinning. Tait’s ferocity in debates over physics was matched by an equally intense patriotism. When the Boer War erupted in 1899 between British forces and rebellious Afrikaaners, Tait rejoiced that his son signed up and went to South Africa to fight. Young Tait was brave in a way that tends to excite mockery today—a good-hearted, good-looking, cheery sporting fellow, by no means an intellectual, sailing out eagerly and unquestioningly to the fringe of the empire to defend British pride and power. His father doted on him. Freddie Tait, a lieutenant in the Black Watch, shipped out on October 24, 1899. On December 11 he was wounded by a bullet in his leg at the Battle of Magersfontein. By the end of the month he had recovered. Early in February he was sent to Koodoosberg and on the seventh he was hit by a bullet to the chest and died where he fell.

Tait, who had lost never an atom of self-confidence in all his long-running scientific controversies, was vanquished utterly by the death of his beloved son. He continued to teach, but listlessly, with none of his former vigor. He went to St. Andrews as usual in the summer of 1900, but the golf course now held only painful memories. He retired from teaching that winter, simply leaving one day and never coming back to the lecture room. John Low, a golfing friend who published a life of Freddie Tait in 1900, recorded that “the Professor seemed very depressed as though afraid to enter into any conversation which might become reminiscent of the golf which had Freddie for its central figure…. I do not think that he ever got back into his true gait after Freddie’s death; the light seemed to have left the eyes which in repose often wore an expression of weariness.”

The following summer he had the use of a friend’s house and sat in the garden clutching his copy of Low’s book, reading over and over again the accounts of Freddie’s tournaments and victories. He died on July 4 at the age of 70. In his obituary Kelvin recalled Tait’s “rough gaiety … cheerful humour … this was a large factor in the success of our alliance for heavy work, in which we persevered for eighteen years…. We had keen differences (much more frequent agreements) on every conceivable subject,—quaternions, energy, the daily news, politics, quicquid agunt

homines, etc., etc. We never agreed to differ, always fought it out. But it was almost as great a pleasure to fight with Tait as to agree with him. His death is a loss to me which cannot, as long as I live, be replaced.”

Barely 18 months later, on February 1, 1903, Kelvin had to contend with the death of his oldest scientific friend and confidante, George Gabriel Stokes, his lifelong adviser and consultant in mathematical physics. Stokes was by then 83 years old and died quietly after a peaceful retirement. He had lived in Cambridge with his daughter’s family since the death of his wife in 1899. Stokes was a firm, taciturn man. He had served for some years in Parliament, under the old system by which Cambridge University nominated a member. Isaac Newton had been M. P. likewise in earlier times, and it is said he spoke only once, to ask for a window to be shut. Stokes surpassed Newton, dutifully attending every session and saying never a single word.

J. J. Thomson recalled that Stokes had great powers of analysis but was “exceedingly cautious about coming to a conclusion.” The voluminous correspondence between Kelvin and Stokes—some 650 letters spanning 55 years—is almost wholly technical. Occasionally there are personal remarks in the gruff style of Victorian men, such as when each announces to the other that he is about to be married. “My principal intelligence must belong to the non-scientific head which is that I am engaged to be married to Miss Robinson daughter of Dr Robinson,” Stokes informed William Thomson in 1856, in an unpunctuated rush.

In 1879 Stokes assembled a selection of his papers for publication in book form and consulted Thomson on many points he wished to revise or refine. In one letter, after describing some changes he proposed in order to make the allotment of credit for original ideas scrupulously fair and unambiguous, he signed off by remarking that “it is curious how these things bring back our work together in 1847.” In their entire correspondence, this small plangent sentence is the closest either Stokes or Thomson came to a confession of intimacy. Kelvin’s obituary notice of Stokes was conventional enough, describing his numerous original researches and the help he freely offered over the years to other researchers, including himself. But Arthur Schuster, a young physicist, saw a deeper response at Stokes’s funeral: “I shall always remember Lord Kelvin, as he stood at the open grave, almost overcome by his emotion, saying in a low voice: ‘Stokes is gone, and I shall never return to Cambridge again.’”

***

Exactly 20 years after he had delivered his celebrated series of lectures in Baltimore, Kelvin published in 1904 the version he had been tinkering with off and on ever since. In 1900 Max Planck’s first intimation of quantum theory had appeared; in 1905 Einstein’s four remarkable papers on quantum theory and relativity ushered in a new era of physics. The appearance, between those milestones, of Kelvin’s fantastically elaborated mechanical models of the ether, supplemented with new materials such as his curious essay “Aepinus Atomized,” was a bizarre anachronism. Details had changed to accommodate new discoveries, but the intellectual foundation of this project remained what it had been in Baltimore—a mechanical universe, in the old-fashioned Newtonian clockwork sense.

The lectures were politely received. Kelvin was the most publicly known scientist of the day, and everyone liked him, though they might mock his thinking. Commenting in Nature, the young physicist Joseph Larmor couched his reservations in carefully respectful terms. Kelvin’s “expression of distrust of ‘the so-called electro-magnetic theory of light’ stands as in the original…. In this chain of simple, yet brilliant and attractive ideas, Lord Kelvin has gradually forged a reconciliation between fact and theory that would probably have been received with universal acclaim thirty years ago. Nowadays, as regards most people, the need has ceased to be so strongly felt…. [Kelvin] would perhaps say that [Maxwell’s electromagnetism] is a successful description rather than an explanation, and he would probably desire to modify the terms of the description in order to bring it closer to the train of dynamical ideas in which he would search for the explanation. And here we are at the parting of the ways.”

Confusion over the nature of radioactivity rumbled on. In August 1906 Kelvin wrote to the London Times arguing against the idea, by then widely accepted, that radioactive decay involved the transmutation of one element into another. His line of thinking was as much semantic as physical. He proposed that heavier elements were compounds, in a molecular sense, of lighter ones, and split into their various components when they disintegrated. Radium, in other words, was a compound of helium and other lighter elements, not a true element in its own right. Nowadays, knowing that atomic nuclei are built from protons and neu-

trons, we say that the different elements are all combinations of the same ingredients. One might almost suggest that Kelvin was reaching in this direction, but since no one at that time had any clear idea of what atoms were made of, the debate had no real substance. Other physicists wrote in to disagree. The Times itself weighed in with an editorial asking for Kelvin’s views to be taken seriously, on account of his great reputation and experience.

But young scientists have little respect for seniority. Frederick Soddy wrote to the paper on August 31, putting the case against Kelvin, and concluding that “it would be a pity if the public were misled into supposing that those who have not worked with radio-active bodies are as entitled to as weighty an opinion as those who have…. Atomic disintegration is based on experimental evidence, which even its most hostile opponents are unable to shake or explain in any other way.”

Summarizing these inconclusive exchanges a few weeks later in Nature, Soddy’s veiled tribute to Kelvin came close to condescension. “Whatever opinion may be formed of the merits of the controversy, all must unite on admiration for the boldness with which Lord Kelvin initiated his campaign, and the intellectual keenness with which he conducted, almost single-handed, what appeared to many from the first almost a forlorn hope against the transmutational and evolutionary doctrines framed to account for the properties of radium. The weight of years and the almost unanimous opinion of his younger colleagues against him have not deterred him from leading a lost cause, if not to a victorious termination, at least to one from which no one will grudge him the honours of war.”

Even Ernest Rutherford, the great pioneer of radioactivity and atomic theory, who had written to his mother years ago of his admiration for Kelvin, could not help but think of the aging natural philosopher as a child. They had met at a scientific party at Terling, Lord Rayleigh’s estate. Rutherford described the proceedings to his wife: “Lord Kelvin has talked radium most of the day, and I admire his confidence in talking about a subject of which he has taken the trouble to learn so little. I showed him and the ladies some experiments this evening, and he was tremendously delighted and has gone to bed happy with a few small phosphorescent things I gave him.”

Long afterward, Rutherford recalled Kelvin with fond indulgence. In 1904 he had given a public lecture at the Royal Institution on radioactivity, in which he intended to touch on the question of the earth’s age. Kelvin was in the audience. In his much-retold account, Rutherford recalled that “to my relief, Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye, and cock a baleful glance at me! Then a sudden inspiration came, and I said Lord Kelvin had limited the age of the earth, provided no new source was discovered. That prophetic utterance refers to what we are now considering tonight, radium! Behold! the old boy beamed upon me.”