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## The 2018 George Sarton Lecture

Bruce J. Hunt (University of Texas) delivered the 2018 George Sarton Memorial Lecture in the History and Philosophy of Science at the annual meeting of the American Association for the Advancement of Science (AAAS) in February. The theme of the meeting was “Advancing Science: Discovery to Application,” focusing on how fundamental scientific research makes its way into practical use. Hunt set out to flip that over, or perhaps complete the cycle, by looking at how technological applications can sometimes stimulate and shape even the most fundamental science.

Consider one of the great scientific achievements of the 19th century: the formulation of “Maxwell’s equations” of the electromagnetic field. These four vector equations are now among the most highly regarded in all of physics; they govern everything from the propagation of light and radio waves to the workings of the electric power system, and they grace not just textbooks but t-shirts and are inscribed on the base of the statue of James Clerk Maxwell that stands in his native Edinburgh (see picture). How did these equations come to look the way they do? Why were they formulated in Britain, and why in the late 19th century? In particular, why were they cast into their canonical form not by Maxwell himself, but by Oliver Heaviside? The answers, Hunt argued, lie in submarine cable telegraphy, one of the characteristic technologies of the British Empire in the Victorian era.

From the time the first undersea line was laid across the English Channel in 1851 until the industry began to decline after the First World War, the global cable network was dominated by British firms and British expertise. As a maritime trading nation and the leading commercial, industrial, and imperial power of the day, Britain had both the greatest need for cables and the greatest capacity for making and operating them. In turn, cable telegraphy deeply shaped British work in electrical science. In particular, the peculiarities of signalling along cables led British physicists and engineers to pay far more attention to electromagnetic propagation phenomena than was required of their counterparts in Germany, France, or the United States, whose overhead landlines were electrically much simpler. Cable telegraphy played an especially important part in Heaviside’s thinking, including his formulation of “Maxwell’s equations.”

Heaviside was an unusual man; his best friend once described him as “a first-rate oddity” but “never... a mental invalid.” After growing up poor in London, he left school at age 16 and went to work assisting his brother Arthur, a telegraph engineer at Newcastle. Oliver soon shifted to a job on a newly-laid cable across the North Sea, where he was frustrated by the way electrical distortion limited the rate at which signals could be sent along the cable. Hoping to solve this problem, he took up the study of electrical theory and, at age 24, “retired” from the cable company. Returning to London to live with his parents, he devoted all of his time and considerable talents to the mathematical analysis of telegraphic problems.

Heaviside read Maxwell’s *Treatise on Electricity and Magnetism* soon after it appeared in 1873. Like many readers, he found it rich but not always elegantly expressed. In particular, Maxwell’s chapter on the “Fundamental Equations of the Electromagnetic Field” did not give the set of four vector equations now known as “Maxwell’s,” but instead a list of thirteen main equations involving the vector and scalar potentials and other quantities that do not appear at all in the famous four equations. As he dug into what he called that “mine of wealth, Maxwell,” Heaviside worked out many implications of the theory that Maxwell himself had not recognized, and also strove to cast it into a clearer and more readily usable form.

Maxwell had given formulas for how energy is distributed in the field around a charge or current but had not discussed how that energy might move around when the fields changed. Heaviside tackled this question in 1884 in hopes of shedding light on how energy gets from one end of a cable to the other. After a series of roundabout mathematical transformations, he hit upon a striking result: the energy flow at any point in the field is simply the vector product of the electric and magnetic intensities at that point. This had some surprising consequences, including that the energy conveyed by an electric current does not flow along within the wire, as everyone had always assumed, but instead flows through the space outside it, the wire serving only as a guide, not a pipeline. Convinced that such an important result should follow indirectly from the fundamental electromagnetic equations, Heaviside worked back from his energy flow formula and recast Maxwell’s list of thirteen equations into the compact set of four we now know as “Maxwell’s.” (As it turned out, the Cambridge-trained physicist J. H. Poynting had worked out the energy flow theorem a few months earlier; that is why it is now called the “Poynting flux” rather than the “Heaviside flux.” But Poynting was not as close as Heaviside to the problems of telegraphy and electromagnetic waves, and the flow formula did not lead him to the kind of deep restructuring of electrical theory that Heaviside undertook.)

Heaviside published his new equations early in 1885 in *The Electrician*, a London trade journal owned by cable interests. Calling them “Maxwell redressed,” he used them almost exclusively in his own work from then on. His papers on the subject attracted little notice at first, but in 1888, experimental work by Oliver Lodge and Heinrich Hertz drew physicists’ attention to electromagnetic waves, and they were delighted to find that Heaviside had already worked out the theory of such waves in great detail—in connection with telegraph problems. His work was soon taken up avidly by other “Maxwellians,” his papers were collected and republished in two thick volumes, he was elected a Fellow of the Royal Society, and by the mid-1890s his set of “Maxwell’s equations” was taking its place in textbooks. Einstein learned Maxwell’s theory from a textbook based quite directly on Heaviside’s work, and physics students ever since have studied essentially the equations Heaviside laid down in 1885. Few of them have had any idea how deeply rooted those equations were in the cable industry of late Victorian Britain.

This case study of Heaviside, cables, and “Maxwell’s equations” illustrates the value of examining scientific work in the broadest possible context. It might not seem on the surface that in order to understand why Maxwell’s equations look the way they do, or why they were formulated when and where they were, that we should first look to the role telegraph cables played in the British Empire—only when we put the equations in this context, however, can we see how deeply problems of telegraphic propagation and energy flow shaped their evolution, and so gain more insight into the reciprocal relationship between science and technology, between discovery and application.