The Maxwellians

Excerpt from The Maxwellians by Bruce J. Hunt (1991)

Foreword by L. Pearce Williams

In 1873, James Clerk Maxwell published a rambling and difficult two-volume Treatise on Electricity and Magnetism that was destined to change the orthodox picture of reality. This treatise did for electromagnetism what Newton‘s Principia had done for classical mechanics. It not only provided the mathematical tools for the investigation and representation of the whole of electromagnetic theory, but it altered the very framework of both theoretical and experimental physics. Although the process had been going on throughout the nineteenth century, it was this work that finally displaced action-at-a-distance physics and substituted the physics of the field.

Like Newton’s Principia, Maxwell’s Treatise did not immediately convince the scientific community. The concepts in it were strange and the mathematics was clumsy and involved. Most of the experimental basis was drawn from the researches of Michael Faraday, whose results were undeniable, but whose ideas seemed bizarre to the orthodox physicist. The British had, more or less, become accustomed to Faraday’s “vision,” but continental physicists, while accepting the new facts that poured from his laboratory, rejected his conceptual structures. One of Maxwell’s purposes in writing his treatise was to put Faraday’s ideas into the language of mathematical physics precisely so that orthodox physicists would be persuaded of their importance.

Maxwell died in 1879, midway through preparing a second edition of the Treatise. At that time, he had convinced only a very few of his fellow countrymen and none of his continental colleagues. That task now fell to his disciples.

The story that Bruce Hunt tells in this volume is the story of the ways in which Maxwell’s ideas were picked up in Great Britain, modified, organized, and reworked mathematically so that the Treatise as a whole and Maxwell’s concepts were clarified and made palatable, indeed irresistible, to the physicists of the late nineteenth century. The men who accomplished this, G. F. FitzGerald, Oliver Heaviside, Oliver Lodge, and others, make up the group that Hunt calls the “Maxwellians.” Their relations with one another and with Maxwell’s work make for a fascinating study of the ways in which new and revolutionary scientific ideas move from the periphery of the scientific thought to the very center. In the process, Professor Hunt also, by extensive use of manuscript sources, examines the genesis of some of the more important ideas that fed into and led to the scientific revolution of the twentieth century.

L. PEARCE WILLIAMS. – Ithaca, New York

“Maxwell’s equations”


James Clerk Maxwell’s theory of the electromagnetic field is generally acknowledged as one of the outstanding intellectual achievements of the nineteenth century—indeed, of any century. The late Richard Feynman once remarked, with perhaps only a little hyperbole, that “from a long view of the history of mankind […] there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics”. Even the American Civil War, Feynman said, “will pale into provincial insignificance” besides this more profound event of the 1860s.[1] By the mid-1890s the four “Maxwell’s equations” were recognized as the foundation of one of the strongest and most successful theories in all of physics; they had taken their place as companions, even rivals, to Newton’s laws of mechanics. The equations were by then also being put into practical use, most dramatically in the emerging new technology of radio communications, but also in the telegraph, telephone, and electric power industries. Maxwell’s theory passed to the twentieth century with an enormous reputation it has retained ever since.

It is thus perhaps surprising to find that the fullest statement Maxwell gave of his theory, his 1873 Treatise on Electricity and Magnetism, does not contain the four famous “Maxwell’s equations,” nor does it even hint at how electromagnetic waves might be produced or detected. These and many other aspects of the theory were quite thoroughly hidden in the version of it given by Maxwell himself; in the words of Oliver Heaviside, they were “latent” in the theory, but hardly “patent.”[2]

Maxwell was only forty-eight when he died of cancer in November 1879. He was only a quarter of the way through revising his Treatise for a second edition, and the task of digging out the “latent” aspects of his theory and of exploring its wider implications was thus left to a group of younger physicists, most of them British. Between roughly 1879 and 1894, these “Maxwellians,” led by George Francis FitzGerald (1851-1901), Oliver Lodge (1851-1940), and Oliver Heaviside (1850-1925), with a key contribution from the German physicist Heinrich Hertz (1857-1894), transformed the rich but confusing raw material of the Treatise into a solid, concise, and well-confirmed theory—essentially, at least for free space, the “Maxwell’s theory” we know today. It was they who first explored the possibility of generating electromagnetic waves and then actually demonstrated their existence; it was they, along with J. H. Poynting (1852-1914), who first delineated the paths of energy flow in the electromagnetic field and then followed out the far-reaching implications of this discovery; it was they who recast the long list of equations Maxwell had given in his Treatise into the compact set now universally known as “Maxwell’s”; and it was they who began to apply this revised theory to problems of electrical communications, with results that have transformed modern life. It was mainly the Maxwellians who gave Maxwell’s theory the form it has since retained, and it was largely through their work that it first acquired its great reputation and breadth of application.

The evolution of “Maxwell’s theory” in the years after Maxwell’s death provides a striking example of a process quite common in science, as in other fields of intellectual endeavor. Scientific theories rarely spring fully formed from the mind of one person; a theory is likely to be so refined and reinterpreted by later thinkers that by the time it is codified and passes into general circulation, it often bears little resemblance to the form in which it was first propounded. The practice in science of naming theories after their originators often obscures the historical process by which scientific syntheses are achieved. One is tempted to seek all of “Newtonianism” in Newton, or all of “Darwinism” in Darwin. One of the main aims in the pages that follow is to trace the formation of such a theoretical synthesis in some detail and to show that “Maxwellianism,” though undeniably built on Maxwell’s ideas, was in many ways the work of his successors. “Maxwell was only 1/2 Maxwellian,” Heavisde declared in 1895; I examine here what it meant to be a Maxwellian and trace the transformation of ideas that lay behind Heaviside’s remark.[3]

Another of my aims is to trace the evolution of the Maxwellians as a scientific group and to show how they stimulated and helped one another, both in their strictly scientific work and in more practical affairs. Science is a more social and cooperative process than is sometimes appreciated, and one of the most effective ways to capture its richness is to examine in detail the workings of a small group. The key to such a study of the Maxwellians is their surviving letters and notebooks, through which one can follow the course of their thoughts and actions almost day by day and see how strongly they influenced one another. In the work of FitzGerald and Lodge on ether models and electromagnetic waves; in Lodge and Heaviside’s joint battles with W. H. Preece of the Post Office Telegraph Department; in Heaviside and FitzGerald’s long collaboration on the problem of moving charges and on the puzzle of the ultimate nature of the electromagnetic field—in all of these, the cooperative nature of the Maxwellian’s work can be clearly seen in their correspondence. Heaviside in particular virtually lived his life on paper; he was something of a recluse, and his letters and published writings were his main contact with the outside world. FitzGerald and Lodge, too, left very full records of their activities. Although all three were pioneers of electrical communications, they lived before telephones were common, and since they were physically separated—Heaviside in London and later Devon, Lodge in Liverpool, and FitzGerald in Dublin—they kept in touch mostly via letters, hundreds of which have been preserved. These enable us to reconstruct not only their work but something of their personalities and to see them engaged in the 1880s and 1890s in the lively business of remaking Maxwell’s theory and of probing, as they thought, into the ultimate foundations of the physical universe.

Maxwell himself is only a minor character in this story; he died before the Maxwellians’ work was well begun. But his ideas pervade the book, as they pervaded the Maxwellians’ own work. Though greatly reinterpreted and recast, Maxwell’s ideas always formed the core of the Maxwellian synthesis. In one of the most interesting of his unpublished writings, Heaviside reflected on the doctrine of the immortality of the soul. In its old religious sense, the idea had, he believed, been thoroughly discredited. But there was, he said, another “and far nobler sense” in which the soul truly was immortal. In living our lives, each of us “makes some impression on the world, good or bad, and then dies”; this impression goes on to affect future events for all time, so that “a part of us lives after us, diffused through all humanity, more or less, and all of Nature. This is the immortality of the soul,” Heaviside said. “There are large and there are small souls,” he went on.

The immortal soul of John Ploughman of Buckinghamshire is a small affair, scarcely visible. That of a Shakespeare or a Newton is stupendous. Such men live the best parts of their lives after they shuffle off the mortal coil and fall into the grave. Maxwell was one of those men. His soul will live and grow for long to come, and, thousands of years hence, it will shine as one of the bright stars of the past, whose light takes ages to reach us, amongst the crowd of others, not the least bright.[4]

This light from Maxwell has come down to us mainly through the Maxwellians; it was they who developed the most important implications of his theory and cast it into the form in which it has become most widely known. In the pages that follow, we trace how this light was refracted and refocused by the Maxwellians and how it was passed along to the next generation, to be transformed and reinterpreted again.

[1] Feynman 1964, 2:1.11

[2] Heaviside 1892, 2:393 [1888]

[3] Heaviside to FitzGerald, [Mar. 1895], FG-RDS; internal evidence places this undated fragment between FitzGerald’s letters to Heaviside of 8 and 15 Mar., OH-IEE.

[4] Heaviside notebook 8, OH-IEE; a slightly different version is quoted in Appleyard 1930: 257. It was probably written in 1886; cf. Heaviside 1892, 2:77 [1886].

Featured Image Source: Arrayás, M., Bouwmeester, D., & Trueba, J. L. (2017). Knots in electromagnetism. Physics Reports, 667, 1–61. doi:10.1016/j.physrep.2016.11.001 [link]. (cf. QRI’s topological solution to the phenomenal binding problem).

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