Pursuing Power and Light: Technology and Physics from James Watt to Albert Einstein (Johns Hopkins Introductory Studies in the History of Science)

pu r su i ng power a n d light

j o h n s h o pki ns i n t ro d u c tory stu di es i n t h e h i story of science Mott T. Greene and Sharon Kingsland, Series Editors

Pursuing Power and Light

Technology and Physics from James Watt to Albert Einstein

Bruce J. Hunt

t h e j o h n s h opki ns u ni ver si t y pre ss ba lt i m o re

© 2010 The Johns Hopkins University Press All rights reserved. Published 2010 Printed in the United States of America on acid-free paper 9 8 7 6 5 4 3 2 1 The Johns Hopkins University Press 2715 North Charles Street Baltimore, Maryland 21218-4363 www.press.jhu.edu Library of Congress Cataloging-in-Publication Data Hunt, Bruce J. Pursuing power and light : technology and physics from James Watt to Albert Einstein / Bruce J. Hunt. p. cm. — (Johns Hopkins introductory studies in the history of science) Includes bibliographical references and index. ISBN-13: 978-0-8018-9358-2 (hardcover : alk. paper) ISBN-10: 0-8018-9358-5 (hardcover : alk. paper) ISBN-13: 978-0-8018-9359-9 (pbk. : alk. paper) ISBN-10: 0-8018-9359-3 (pbk. : alk. paper) 1. Technological innovations—History—19th century. 2. Technological innovations—History—20th century. 3. Research—History—19th century. 4. Research—History—20th century. 5. Physical sciences—Research— History—19th century. 6. Physical sciences—Research—History—20th century. I. Title. T173.8.H92 2010 609.034—dc22 2009020235 A catalog record for this book is available from the British Library. Special discounts are available for bulk purchases of this book. For more information, please contact Special Sales at 410-516-6936 or [email protected]. The Johns Hopkins University Press uses environmentally friendly book materials, including recycled text paper that is composed of at least 30 percent postconsumer waste, whenever possible. All of our book papers are acid-free, and our jackets and covers are printed on paper with recycled content.

Contents

Acknowledgments

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Introduction: A World Transformed

1

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Steam and Work

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Energy and Entropy

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The Kinetic Theory: Chaos and Order

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Electricity: Currents and Networks

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Electromagnetism: Ether and Field

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Electric Power and Light

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Into a New Century

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Epilogue: Einstein at the Patent Office Suggested Further Reading Index

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Acknowledgments

This book has had a long gestation, and I have incurred many debts along the way. I would like to start by thanking the teachers who introduced me to the history of science: Tom Hankins, Bob Kargon, Russell McCormmach, and the late Owen Hannaway. My thanks also go to good friends from my days in Baltimore, especially Bob Rosenberg, Bruce Hevly, and Robert Smith, and in Britain, especially Simon Schaffer, Andy Warwick, Crosbie Smith, Graeme Gooday, and Richard Noakes. I am also grateful for the friendship and support of my colleagues at the University of Texas, particularly Abigail Lustig and Al Martínez, and my graduate students Greg Cushman, Scott Knowles, Rubén Martínez, Frank Benn, Brett Bennett, and Angela Smith. All historians rely on libraries and archives, and I have been fortunate to be able to draw not only on the excellent resources at the University of Texas, but on archives at Trinity College Dublin, the Royal Dublin Society, the Royal Society of London, University College London, the Institution of Engineering and Technology, the Cambridge University Library, and the Porthcurno Telegraph Museum. I am also grateful to the University of Texas College of Liberal Arts and to my department chair, Alan Tully, for affording me the leave I needed to complete work on this book. It has been more years than I care to remember since Mott Greene, Sharon Kingsland, and Bob Brugger first invited me to embark on this project, and I thank them for their patience. I also thank Carolyn Moser for her careful copyediting. I owe special thanks to Ian Henry for turning my crude sketches into the four crisply drawn figures in Chapter 3 and the first figure in Chapter 5, and to Bill Burns for supplying the world cable map that appears in Chapter 4. My deepest thanks of course go to Beth, Peter, and Emma.

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pu r su i ng power a n d light

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Introduction

A World Transformed

The nineteenth century marked one of the great watersheds in human beings’ power over the world around them. In many basic ways, daily life in the eighteenth century differed little from that in ancient times. People still relied on their own muscles or on those of horses or oxen to carry their loads and pull their plows; on the wind to drive the sails of their ships; and on falling water to turn their mill wheels and grind their grain. Some first efforts had been made to harness the power of steam, but before 1780 it was used for little more than pumping water out of mines in England. Communications, too, had changed little for centuries: a message could still travel no faster than the person who carried it, and a traveler in 1780 typically took two months to cover the 900 miles from Rome to London, and anywhere from three weeks to three months to cross the Atlantic. Jump forward a little more than a century, say to 1910, and we find a very different world. Steam engines now drive giant factories, and networks of electrical lines spread power and light throughout the world’s cities. Railroads and steamships have turned crossing a continent or an ocean from a perilous journey of weeks or months into a routine trip of a few days. The first automobiles have begun to appear on the roads and the first airplanes in the skies. Communication has not just been sped up but has become almost instantaneous: a vast web of telegraph cables circles the globe, and telephone lines carry the sound of distant voices right into people’s homes. Wireless telegraphy has begun to emerge from its infancy, and the advent of radio broadcasting is already in sight. Along with these sweeping changes in the technologies of daily life, the nineteenth century also witnessed striking advances in scientific understanding. Charles Darwin’s theory of evolution is the best known of these, but the physical sciences made great strides as well, particularly in the study of energy, atoms, and electromagnetism. The scale and organization of the scientific enterprise also changed dramatically, as science came to be recognized as a profession and was increasingly pursued by legions of specialists working in great

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research laboratories and university departments. By the opening decades of the twentieth century, science and technology had become in many ways the defining features of modern life. One of the most persistent and important questions in the study of both science and technology is that of the relationship between the two. Is technology simply “applied science,” with scientists making all of the original discoveries and inventors and engineers then straightforwardly applying them to practical purposes? Or are scientific discoveries themselves largely by-products of the demands and opportunities presented by advancing technologies? Is the course of technological development determined chiefly by the course of previous scientific discovery, or is it the other way around? Many people have tried to define “science” and “technology” and to mark out the exact differences between them. None of these attempts have proven entirely satisfactory, and we should be wary of trying to define our way to an answer; however precise and carefully drawn our definitions, it will remain an open question whether they really capture what people mean when they use the words science and technology. It is nonetheless useful to draw a general distinction between the two, and perhaps the best is one of the simplest: broadly speaking, science is about knowing, while technology is about doing. Of course we often need to do a lot (with experiments and apparatus) to be able to know much, and we often need to know a lot (in the sense both of specific facts and of skills or “know-how”) to be able to do much, but this still leaves us with a broad distinction in aims and focus. The remaining overlap between knowing and doing reflects what seems to be a real overlap between science and technology. The English philosopher and statesman Sir Francis Bacon (1561–1626) famously declared that “knowledge is power.” He also said that researchers ought to pursue “experiments of light, as well as of fruit,” that is, experiments aimed at producing disinterested knowledge or enlightenment, as well as ones aimed at producing direct profit or benefit.¹ Modern science is partly about the pursuit of “light” in this sense, but as Bacon suggested, it is also about the pursuit of practical power, particularly through technology. The interaction between the pursuit of knowledge and the pursuit of power comes across especially clearly in two cases drawn from nineteenth-century technology and physics: the relationship between the development of the steam engine and the study of heat and energy, and the relationship between the development of the tele1. Bacon’s remarks on experiments of “light” and “fruit” are quoted in Thomas Sprat, History of the Royal Society (1667; repr., St. Louis: Washington University Press, 1958), p. 245.

Introduction

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graph and the study of electrical currents and waves. The first of these culminated in the formulation of the laws of thermodynamics—particularly the grand principles of the conservation of energy and the increase of entropy— and in the development and improvement of new power technologies. The second culminated in the formulation of field theory and the electromagnetic theory of light, and in the discovery of radio waves and their use in wireless communications. Steam and electrical technologies have transformed daily life over the last two centuries; they also transformed much of science. By examining their history, we will be able to cast light not only on some of the most important points in the history of modern physics, but also on fundamental questions about the evolving relationship between science and technology.

1 Steam and Work

The nineteenth century was powered by steam. Most of the textile mills that launched the first wave of the Industrial Revolution in the eighteenth century were driven by falling water, but it was steam that would eventually transform the industrial landscape, fostering the growth of smoky factory cities and powering the locomotives, riverboats, and ocean-going ships that revolutionized transportation. The harnessing of steam was principally the work of engineers (literally, people who built and ran engines) and only secondarily of scientists. Historians of science and technology have often and quite rightly observed that the steam engine did much more for science than science ever did for the steam engine. Many of the builders of the first steam engines were inspired by a scientific view of the world as something to be grasped and controlled, and several of them made excellent use of scientific methods of analysis and measurement. Their achievements owed little, however, to any existing stock of scientific knowledge about the connection between heat and work, for little such knowledge yet existed; in the eighteenth century, most scientific thinkers regarded heat and work as quite separate subjects. Real scientific knowledge of the relationship between the two—what came to be known as thermodynamics—was attained only several decades into the nineteenth century, as scientists and scientifically minded engineers sought to understand and improve the workings of the steam engines they saw proliferating around them. The story of the steam engine and the birth of thermodynamics provides a clear illustration of the chief theme of this book: that technology is not simply “applied science” but has often taken the lead and shaped the development of scientific knowledge. Power from Steam The expansive power of steam was known in ancient times, and as long ago as the first century AD, Hero of Alexandria described how jets of steam escaping from a small boiler could be used to spin a pinwheel. Steam power was not put

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to much practical use until the late seventeenth century, however, when it came to be linked both to new ideas about air pressure and the vacuum and to economic demands for a better way to clear water from deep mines. As coal mines, and particularly the copper and tin mines of Cornwall in southwestern England, were carried further below the water table, the difficulty and expense of pumping them out with human or animal power became overwhelming. Miners had the sense that riches lay just beneath the waters that were continually flooding their shafts and tunnels. In the late seventeenth century several people toyed with ways to use the pressure of steam to pump out the water, and in the 1690s Thomas Savery, a prolific English inventor and “projector” of speculative schemes, secured a patent on what he called “an engine to raise water by fire.”¹ It was an innovative and important device, though it never quite lived up to Savery’s claims for it. Savery’s engine consisted of a boiler (a sort of glorified tea kettle), a metal “receiver” that could hold 10 or 15 gallons of water, a few connecting tubes and valves, and two pipes, one running down into the water to be pumped out and the other pointing up to where it was to be discharged. The only moving parts were the valves used to control the flow of steam and water. After filling the receiver with steam from the boiler, the operator closed the connecting valve and poured cold water over the receiver. This condensed the steam within it and produced a partial vacuum. The pressure of the surrounding atmosphere (about 15 pounds per square inch) then pushed water up the lower pipe and into the partially evacuated receiver, much as when a person sucks water up a straw. In principle, water could be sucked up as much as 30 feet in this way, but since the vacuum in the receiver was never perfect, the practical limit was about 20 feet. Once the receiver was nearly full of water, the operator closed the valve on the lower pipe, opened one on the upper pipe, and reopened the valve from the boiler, letting in high-pressure steam that blew the water in the receiver out through the upper pipe. The operator had to complete the entire cycle about four times per minute while also tending the fire under the boiler and maintaining a supply of cooling water. Savery’s claim in his 1702 book The Miner’s Friend that a boy of 13 could learn to work the engine in half an hour should perhaps be taken with a grain of salt. Small versions of Savery’s steam pump could be made to spurt water very impressively, and he erected demonstration engines in London that could raise 50 gallons per minute to a height of nearly 60 feet, the first 16 feet by suction 1. Thomas Savery, The Miner’s Friend; or, An Engine to Raise Water by Fire (1702; repr., London: W. Clawes, 1827).

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and the rest by pressure. He found it hard to sustain such performance, however, for the boiler and receiver leaked steam and even threatened to explode when subjected to the high temperatures and pressures required to blow the water out the upper pipe. Although he managed to persuade Parliament to extend his patent until 1733, Savery was never able to make his engines work well in a practical setting. Most later Savery engines dispensed with the blowout stage and worked purely by suction. This made them much simpler and safer to operate but meant they could raise water no more than 15 or 20 feet, making them almost useless for their original purpose of clearing water from deep mines. The first really practical steam engine was developed between 1700 and 1712 by Thomas Newcomen (1663–1729), a maker of iron goods in southwestern England who was acutely aware of the Cornish miners’ need for effective pumps. How much Newcomen knew about recent scientific ideas about air pressure and the condensation of steam is unclear; indeed, he apparently began his work without even knowing of Savery’s recent invention. He soon showed himself, however, to be an astute designer and builder of workable machines. In place of Savery’s simple but troublesome receiver, Newcomen built his engine around a brass cylinder fitted with a sliding piston, much like that in an ordinary force pump. When the steam in the cylinder was condensed, the resulting partial vacuum did not suck water up directly, but instead pulled down on the piston (or rather, allowed the pressure of the atmosphere to push down on it), providing enough force to pivot a beam that could then work a pump or other machinery. By using steam only at low pressures, barely above that of the surrounding air, Newcomen avoided the danger of bursting boilers that had bedeviled Savery. Indeed, because the actual work in Newcomen’s engines was done by the pressure of the atmosphere, his machines were often called “atmospheric engines”; the steam was used only to produce a partial vacuum when it was condensed. The cylinder of a typical early Newcomen engine was about two feet across and eight feet long; after condensation, the pressure within it fell to seven or eight pounds per square inch, or about half that of the surrounding atmosphere. With only this reduced internal pressure now opposing the full weight of the atmosphere that was bearing down on the piston’s surface area of more than three square feet, each stroke delivered a force of nearly two tons, which could be repeated 15–20 times per minute. The first Newcomen engines could put out about five horsepower; by the 1780s, the largest could produce nearly 20 times that. By eighteenth-century standards, a Newcomen engine was a very powerful machine.

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Savery Steam Pump The English inventor Thomas Savery patented a steam pump in the 1690s that worked by a combination of suction and steam pressure. The operator started by opening a valve and letting steam from a boiler (F) fill a large oval receiver (A). (The version shown here had two receivers.) The operator then sprayed the receiver with cold water, condensing the steam within it and creating a partial vacuum that sucked water up a pipe (C) and through a oneway valve (D) until it filled the receiver. A fresh blast of high-pressure steam from the boiler then blew the water out of the receiver, through another valve (B), and out an upward-pointing pipe. The cycle was then set to repeat—if the highpressure steam had not blown out the joints on the receiver, as it often did.

 J. A. Ewing, The Steam-Engine and

Other Heat-Engines (Cambridge: Cambridge University Press, 1894), p. 6.

To make his engine a practical success, Newcomen had to solve a thousand small problems, from sealing the piston against seeping air to clearing the cylinder of air and water after each cycle. He also devised clever valve gear that made the whole thing run almost automatically. He was apparently led to one of his most important improvements by accident: having surrounded the cylinder with a jacket full of cooling water to help condense the steam, he was surprised one day when the piston suddenly slammed down with unusual force and speed, breaking the connecting machinery. It seems a small leak had allowed cold water from the surrounding jacket to spray directly into the cylinder, condensing the steam within it far more fully and abruptly than the old method of applying water to the outer surface ever could. Once Newcomen deliberately adopted it, such cold water injection became one of the keys to the effective operation of his engines. By later standards, Newcomen engines were terribly inefficient. In the 1770s the English engineer John Smeaton (1724–92) carefully measured the “duty” of various engines—that is, how much work they could perform per bushel of fuel burned. He had earlier done similar tests of the efficiency of dif-

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Newcomen Steam Engine Thomas Newcomen began building piston-driven steam engines in the early 1700s. The operator started one of Newcomen’s engines by opening a valve and letting steam at low pressure pass from a boiler into a large cylinder fitted with a sliding piston; in the version shown here, the cylinder sat directly above the boiler. A counterweight attached to a rocking beam was then able to raise the piston. Once the piston reached the top of the cylinder, the operator sprayed cold water into the cylinder, rapidly condensing the steam inside it. The resulting partial vacuum allowed the pressure of the surrounding atmosphere to push down on the upper surface of the piston. The powerful downward stroke of the piston worked the rocking beam, which

was in turn used to drive a pump or other machinery.  J. A. Ewing, The Steam-Engine and

Other Heat-Engines (Cambridge: Cambridge University Press, 1894), p. 10.

ferent types of water wheels, and such engineering measurements helped lay the groundwork for ideas that later became important in physics, particularly the concept of energy. Smeaton found that for each bushel of coal burned, a typical Newcomen engine could do work equivalent to raising between 4 and 5 million pounds of water a distance of one foot. By making systematic tests and modifications, he was able to build an engine whose duty approached 10 million pound-feet. This seemed to be about the limit, however, and it meant it paid to use a Newcomen engine only where it helped produce something of unusual value, as at a Cornish copper or tin mine, or where its fuel was practically free, as at a coal mine. Of about 700 Newcomen engines known to have been built in Britain before 1780, over 80 percent were used to pump water from mines, the great majority being coal mines.² A number of Newcomen engines were also erected on the European continent, and a few in the American colonies, again mainly to pump out mines. The Newcomen engine did not revolutionize the world economy; indeed, 2. John Kanefsky and John Robey, “Steam Engines in 18th-Century Britain: A Quantitative Assessment,” Technology and Culture 21 (1980): 169.

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it had little immediate impact outside the British mining industry. Newcomen himself won little acclaim during his lifetime, and few recognized the real significance of what he had begun. In hindsight, however, it is clear that by harnessing the power of steam and putting it to practical use, Thomas Newcomen had taken one of the first big steps toward building the modern technological world, based on burning fossil fuels, with all of the consequences for both good and ill that have followed in its train. James Watt James Watt (1736–1819) came along much too late in the development of the steam engine to deserve the credit he is often given as its “inventor.” Once he took it up, however, he did more than anyone else to turn the steam engine into a practical and efficient source of industrial power. Born into a Scottish family of surveyors and mathematics teachers, Watt had a strong interest in machines from an early age. In his twenties he set up shop as a maker of scientific instruments for Glasgow University, and early in 1764 he was asked to repair a model Newcomen engine used in lecture demonstrations. Though it had been carefully built to scale, the model burned a disproportionate amount of fuel and could scarcely be made to run for more than a few strokes at a time. While tinkering with the little engine, Watt became intent not just on repairing it, but on understanding its workings and improving its design. He made careful measurements to track down the cause of its high fuel consumption and consulted with Joseph Black, the Glasgow professor of medicine and chemistry, about his recent work on the “latent heat” that seemed to be absorbed when water was vaporized and then released when steam was condensed. Black helped Watt clarify his thinking about heat and temperature, but it is clear that Watt’s main findings grew out of his own experiments. It had long been known that much of the fuel burned in a Newcomen engine went simply to heat up its brass cylinder, which was then immediately cooled by the jet of cold water used to condense the steam. If the cylinder could somehow be kept hot through a full cycle, the fuel required to heat it back up after each condensation would be saved. But how could this be done? To produce a working stroke, Watt needed to produce a partial vacuum in the cylinder, and the only way he could see to do this was to cool the cylinder enough to condense the steam within it. Yet to start the next cycle, he had to fill the cylinder again with steam, which quickly used up much of its heat simply bringing the cold brass walls back up to the boiling point. There seemed to be no way to avoid the wasteful cycle of heating and cooling. Then one day in May 1765, as Watt was walking across the Glasgow Green,

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he hit on the solution: simply condense the steam somewhere else. Instead of injecting cold water directly into the hot cylinder, why not let the steam pass into an adjoining chamber that was kept immersed in a bath of cold water? As the first flow of steam entered this chamber and began to condense, the resulting partial vacuum would suck the rest of the steam out of the cylinder and begin the power stroke. A small pump would then remove the resulting water and any residual air from the condenser chamber, and the cycle could be repeated. Watt could thus keep the cylinder hot and the condenser cold, saving an enormous amount of fuel. Once he had hit on the idea for the separate condenser, Watt faced the long work of development and refinement needed to put it into practical form. Fortified with a loan from Black (as valuable in its own way as any earlier advice about latent heat), Watt experimented with various configurations and in 1769 secured a patent “for a method of lessening the consumption of steam and fuel in fire-engines.” A few years later he moved to Birmingham in the English Midlands and formed a partnership with Matthew Boulton, an ambitious local maker of metal goods. There they built a substantial enginemaking works and began designing and building hundreds of engines for buyers throughout Britain. As Boulton famously told a visitor, “I sell here, sir, what all the world desires to have,—power.”³ Boulton and Watt found a ready market among those seeking more efficient pumping engines. In 1778 Smeaton tested one of the new Watt engines and found that, for each bushel of coal burned, it could raise nearly 19 million pounds of water a distance of one foot—nearly four times the duty of an ordinary Newcomen engine and twice that achieved even by Smeaton’s own improved version. With improved workmanship, particularly in the accurate boring of cylinders, Watt soon raised the duty of his engines to over 25 million. By charging a royalty amounting to one-third the cost of the fuel saved by switching to their more efficient engine, Boulton and Watt were able to save their customers money while turning an excellent profit for themselves. Boulton saw that the market for pumping engines was inherently limited—as he observed, “there is no other Cornwall to be found”—and he began to push Watt to design engines that could be used to drive textile mills and other factories.⁴ Such applications required steady rotative motion of the kind that had long been supplied by water wheels. In fact, some desperate mill own3. James Boswell, Life of Johnson (1791; repr., Oxford: Oxford University Press, 1980), p. 704. 4. Matthew Boulton, quoted in Richard Hills, Power from Steam: A History of the Stationary Steam Engine (Cambridge: Cambridge University Press, 1989), p. 62.

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Watt Steam Engine with a Separate Condenser In the 1760s, James Watt hit on a way to improve the Newcomen engine by adding a separate condenser. Instead of being forced to cool the entire cylinder in order to condense the steam within it, one could now condense the steam in a separate chamber (C) that was kept constantly cool by a bath of cold water. Watt made many other improvements to the steam engine, including adding a steam jacket to keep the cylinder constantly hot and a small pump (A) to remove water and residual air from the chamber.  J. A. Ewing, The Steam-Engine and

Other Heat-Engines (Cambridge: Cambridge University Press, 1894), p. 14.

ers, beset by low water or diverted streams, had already begun to use Savery and Newcomen engines to pump water back up to turn their wheels. The obvious inefficiencies of this “water-returning” technique led various millwrights to try to couple their old engines directly to mill machinery, but the jerky stroke of the Newcomen engine made this difficult. In the early 1780s Watt introduced improved valves and linkages that smoothed out the stroke of his engines and enabled them to deliver steady rotative motion. This soon set off a boom in the use of steam engines to power mill machinery. Nearly two-thirds of the steam engines built in the eighteenth century went up in the 1780s and 1790s, and more than half of these new engines were used to drive textile mills or other factories. Watt ran his boilers at pressures only a little above that of the atmosphere, so that in his engines, as in Newcomen’s, the work was done not by the expansive force of the steam but by atmospheric pressure pushing on the piston after the steam had been condensed. Watt knew that steam at higher pressures could be used to drive the piston directly, but his deep fear of boiler explosions kept him from pursuing this course. Others were not always so cautious, and by the 1790s engineers around Britain were beginning to experiment with high-

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pressure steam. Richard Trevithick, a Cornish builder of pumps and engines, began producing steam at several times atmospheric pressure and using it to drive a piston directly. He dispensed with the separate condenser and simply vented the spent steam into the air, leading to his engines being called “puffers.” Such engines were compact and powerful, and between 1801 and 1804 Trevithick used them to drive his first experimental steam carriages and locomotives. Even without condensers, the little puffer engines were surprisingly efficient, often achieving duties greater than those of much larger Watt engines. Unfortunately, working at such high pressures posed real dangers, and when the boiler of one of Trevithick’s engines exploded near London in 1803, killing four, Boulton and Watt spread the word that using high-pressure steam was not worth the risk. Safety fears kept high-pressure engines from coming into wide use in Britain until years later, and when they were eventually adopted to power steamboats and railway locomotives, the death toll from bursting boilers turned out to be almost as high as Watt had warned. Trevithick knew his high-pressure engines were efficient, but he was not sure why. One of the keys was expansive working, a principle Watt himself had hit upon some years earlier. If we let high-pressure steam into a cylinder and then cut off the flow before the piston has completed its upward stroke, the steam will continue for a time to expand on its own, pushing against the piston with gradually diminishing force until the pressure within the cylinder drops to that of the atmosphere. An engine worked expansively puts out a little less power than one in which steam is admitted throughout the full stroke, but it uses far less fuel, since more of the expansive force in the steam is put to work before it is sucked into the condenser or vented into the air. The advantages of expansive working come into play, however, only when the pressure of the steam entering the cylinder is substantially greater than that of the atmosphere, and Watt did not pursue the idea in his own low-pressure engines. Trevithick practiced expansive working in some of his high-pressure engines, though initially more by accident than design. Other engineers, particularly Arthur Woolf, made more deliberate use of the principle in two-stage engines that used the exhaust steam from a small high-pressure cylinder to supply a larger low-pressure cylinder fitted with a condenser. Such compound engines could wring even more work from a given quantity of steam, but they were expensive to build and tricky to operate. In England, where coal was abundant, it was usually cheaper to build a simple single-stage engine and pay for the extra fuel it burned than to invest in a more efficient compound engine. British engineers found a better market for their fuel-efficient designs in coun-

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tries where coal was more expensive, and after 1815 compound engines came into wide use in France. Smeaton, Watt, and a number of other early steam engine makers borrowed methods and techniques from science, particularly to analyze the workings of their engines and test their performance. Smeaton’s measurements of duty provide a clear example of such scientific engineering, as do his systematic efforts to improve the design and operation of the Newcomen engine. Watt, too, made careful measurements, fitting his cylinders with pressure gauges that enabled him to check that the condensation was complete and the valve settings were optimal. In the 1790s, he and his assistants devised an “indicator diagram” that tracked how the internal pressure changed as the piston moved along the cylinder. By simultaneously marking on a single sheet both the pressure on the piston and the distance through which it acted, the indicator diagram gave a graphic depiction of the output of the engine: the area enclosed by the curve measured the work delivered by each stroke. By carefully studying such diagrams, an experienced engineer could see how to adjust an engine for maximum efficiency, or even how to improve its design. Not surprisingly, Boulton and Watt considered the indicator diagram one of their most valuable trade secrets, and it did not become public knowledge until the 1820s. While engineers such as Smeaton and Watt drew on scientific methods and techniques, they made little use of scientific knowledge about the relationship between heat and work, for little such knowledge yet existed. The mechanics of force and work were well understood in the eighteenth century, and phenomena of heat and temperature were becoming the focus of close scientific study by both chemists and physicists, particularly toward the end of the century. Within the main Newtonian tradition, however, heat was thought to have little to do with work. Although the physical sciences made rapid advances in the decades around 1800, they did so mainly along lines unrelated to the power revolution that was gathering steam in those same years. Laplacian Physics Isaac Newton (1642–1727) once said that if he had seen further than others, it was because he stood on the shoulders of giants. In the eighteenth century no giant loomed larger than Newton himself, and for more than a century after the publication of his Principia (1687), scientists and natural philosophers viewed the physical world largely in the light cast by his achievements. Building on the work of Nicholas Copernicus and Johannes Kepler on the structure of the planetary system and of Galileo Galilei on the motion of bodies, New-

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ton had formulated a set of mathematical laws of force and motion that could account for everything from the orbit of a planet to the fall of an apple. His law of universal gravitation, which states that every particle in the universe attracts every other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them, came to be seen as the model of what a good scientific theory ought to be. Many natural philosophers in the eighteenth century hoped they would eventually be able to explain the phenomena of heat, light, electricity, and magnetism in the same way, as consequences of mathematically definable forces acting across the short distances between microscopic particles. Most engineers of the day followed a different course, for while they found Newton’s laws of motion useful for analyzing the workings of their machinery, they saw little practical advantage in attempting to reduce macroscopic phenomena to the action of molecular forces. Among the strongest and most ambitious proponents of the Newtonian or “astronomical” approach to physics were the French mathematician PierreSimon Laplace (1749–1827) and his circle of followers, known as the Laplacians. Laplace had shown great mathematical talent at an early age and rose rapidly in the scientific establishment of prerevolutionary France, winning election to the Royal Academy of Sciences when he was just 24. He refined and extended Newton’s work on the motions of the planetary system, developing powerful new mathematical techniques that he eventually codified in his monumental Mécanique céleste (Celestial Mechanics), published in five volumes between 1799 and 1825. Laplace came to be known as “the Newton of his age,” a title that appealed to his considerable vanity. The mathematician J. L. Lagrange (1736–1813) supposedly once said that Newton was the happiest man who could ever live, for there was only one system of the world and he had found it. If true, that left Laplace in an awkward position: he might be the Newton of his age, but Newton had apparently left him with no more worlds to conquer. Perhaps in response, Laplace turned to what was in effect a new world: that of the minute particles that he and many other scientists of his day believed were responsible for the phenomena of heat, light, electricity, and magnetism. Newton had sometimes speculated about such things; now Laplace would bring Newton’s own methods and standards to bear on this microworld, measuring and calculating the forces acting between tiny molecular particles just as Newton had found those acting between the sun and planets. Laplace’s friend Claude Louis Berthollet (1748– 1822) sought to do the same for chemistry, explaining the whole range of chem-

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ical properties and reactions by attractive and repulsive forces between particles of matter. Laplace began his move from celestial mechanics to terrestrial physics in the early 1780s when the chemist Antoine Lavoisier (1743–94) asked him to help with some experiments on heat. Together they developed the ice calorimeter, a device that used the melting of measured amounts of ice to gauge the heat released in various reactions. Lavoisier and Laplace looked on heat as a fluid made up of tiny weightless particles of “caloric.” By using their calorimeter to measure how heat passed between different states and substances, they hoped to be able to find quantitative laws governing how particles of caloric acted on one another and on ordinary matter. Laplace was also intrigued by work the French engineer Charles Coulomb (1736–1806) published in 1785 on electrical forces. It had long been known that electrically charged bits of chaff or paper attract or repel one another, but Coulomb was the first to measure these minuscule forces quantitatively, using a sensitive torsion balance he had devised. He found that electrostatic forces followed an inverse square law, just like Newton’s law of gravitation: double the distance between two charged particles and the force between them falls by a factor of four. This discovery opened a wide new field to which Laplace and his followers could transfer the powerful mathematical tools he had developed for celestial mechanics, enabling them to solve electrical problems with great precision and rigor. Laplace wanted to do the same thing across the board, and by the 1790s he had formulated a comprehensive explanatory program. As he declared in his 1796 System of the World, by discovering the laws of molecular force, “we shall be able to raise the physics of terrestrial bodies to the state of perfection to which celestial physics has been brought by the discovery of universal gravitation.”⁵ Laplace sought to explain all physical and chemical phenomena, and ultimately the workings of the entire universe, by attractive and repulsive forces acting between invisibly small particles. Moreover, he would base his claims not on loose speculation and guesswork but on rigorous mathematical theory coupled to precise experimental measurement. In its sweep and ambition, the Laplacian program was truly Napoleonic. Laplacian science was Napoleonic in a more direct sense as well: it relied on the patronage of Napoleon Bonaparte himself. Napoleon had been trained 5. P. S. Laplace, quoted in Robert Fox, “The Rise and Fall of Laplacian Physics,” Historical Studies in the Physical Sciences 4 (1974): 95.

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as an artillery officer and was proud of his scientific and mathematical abilities. As a rising young general in 1797, he had won election to the scientific section of the Institute of France, the successor to the old Royal Academy of Sciences and the pinnacle of the French scientific world. His chief sponsors had been Laplace and Berthollet. Both before and after he seized control of the French state in 1799, Napoleon liked to surround himself with scientists, both to draw on their expertise and to use their intellectual prestige to bolster his own claims to legitimacy as the proper heir to the ideals of the Enlightenment. He brought Berthollet and many other scientists along on his 1798 expedition to Egypt and later appointed several to high posts in his government, including Laplace, who served briefly as minister of the interior before it became clear he was temperamentally unsuited to such an administrative position. Napoleon subsequently named both Laplace and Berthollet to the French Senate, positions that brought them great prestige and substantial incomes. The depth of Napoleon’s real commitment to reason and science is questionable; his main concern was to strengthen his own grip on power, and he was quite willing to pull back from the ideals of the Enlightenment when it suited his political purposes. Whatever his true motives, however, Napoleon’s rule provided fertile ground for French science and particularly for the ambitious efforts of Laplace and Berthollet. In 1801, Berthollet bought a large country house at Arcueil, just outside Paris; in 1806 Laplace moved in next door. Berthollet built an excellent laboratory there, and in 1807 he and Laplace launched the Society of Arcueil, a private scientific club that met at Berthollet’s house. Although it never had more than about 15 members and lasted only until 1814, this little society did much to shape the course of French physics and chemistry. Laplace and Berthollet would invite bright young students to its meetings, befriend them, draw them into working on the Laplacian program, and then pull strings to advance their scientific careers. The Ecole Polytechnique provided their chief recruiting ground. An elite school founded by the revolutionary government in 1794, it offered a hand-picked group of a few hundred “cadets” intensive instruction in science and mathematics intended to prepare them for later specialized engineering training and eventual military or government service. Both Laplace and Berthollet taught at the Ecole Polytechnique at various times, and almost all of the younger Laplacians, including Jean-Baptiste Biot, Siméon-Denis Poisson, Joseph Gay-Lussac, and François Arago, had been students there. From their base at Arcueil, Laplace and Berthollet used their combination of scientific eminence and political power to run much of the business of the

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scientific section of the institute, and thus much of the French scientific world. They made active use of the system of prize competitions, in which the institute would set a research topic, solicit anonymous entries, and then choose a winner, who received a cash award and a big boost to his or her career. By selecting an appropriate topic, recruiting entrants, and then helping judge the results, Laplace and Berthollet were able to steer research in directions they desired while also cementing the loyalty of their Laplacian recruits. This strategy worked especially well in the competition announced in 1808, when entrants were asked to explain double refraction, the puzzling ability of certain crystals to split a beam of light into two beams with oddly different properties. Etienne Malus won the prize in 1810 with a brilliant paper that bolstered the Laplacians’ favored particle theory of light by showing how short-range molecular forces could produce the splitting. In the course of his experiments, Malus also discovered that light reflected off glass at a glancing angle becomes “polarized,” so that it can pass through a double-refracting crystal or other filter only if the crystal or the filter is oriented in a particular way. It was as if the beam of light had acquired left and right “sides.” Malus’s discovery opened a new realm of optical research, and his death in 1812 deprived the Laplacian group of one of its rising stars. The Laplacians scored successes in other prize competitions, notably one in 1811 on the specific heats of gases, but they ran into increasing troubles after the initial fall of Napoleon in 1814 and his final defeat at Waterloo in 1815 deprived them of their most powerful political backing. When the French monarchy was restored, Laplace quickly swore allegiance to the new king and in 1817 was rewarded by being made a marquis, but his willingness to turn with the political winds led many to deride him as “the weathercock.” The Arcueil circle was by then clearly in decline. Laplace and Berthollet were in their late 60s, and though Biot and Poisson remained loyal, several of the younger members, especially Arago, chafed at being mere followers. The Laplacians’ grip on prize competitions began to slip. One on the vibrations of elastic surfaces, set in 1809 with the expectation it would be solved in Laplacian fashion, remained open until 1816, when Sophie Germain (1776–1831), who as a woman had been excluded from the Arcueil circle, won it with a brilliant mathematical analysis that ignored the Laplacians’ model of particles and forces. The Laplacians faced another setback two years later when they used a prize competition to try to head off a feared resurgence of the wave theory of light. The outcome of the latter episode reveals much about both the strengths and weaknesses of the Laplacian program. The chief French proponent of the wave theory of light was a young grad-

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uate of the Ecole Polytechnique, Augustin-Jean Fresnel (1788–1827). He had not been drawn into the Laplacian circle and had instead begun work as a government engineer, building roads and bridges in the provinces. In his spare time he took up optics, performing delicate experiments and becoming convinced that light consists not of streams of bullet-like particles but of waves in a jelly-like “ether” that fills all space. Thomas Young (1773–1829) had been developing similar ideas in England, but he attracted little support, and Fresnel seems initially to have been unaware of his work. Amid the political turmoil of 1815, Fresnel returned to Paris and soon attracted the attention of Arago, by then a sort of renegade Laplacian. Together they launched an anti-Laplacian insurgency that was partly a political struggle for control of French scientific institutions and partly an intellectual struggle over the true nature of light: particles or waves. The main evidence in favor of the wave theory was the appearance of dark, light, and colored bands around the edges of otherwise crisp shadows. According to wave theorists, these diffraction bands, and the even more striking patterns of parallel lines produced when light was allowed to pass through two closely spaced slits, could result only from the interference of waves of light, as the crests and troughs of waves coming from different points either reinforced each other or canceled each other out. The Laplacians wanted to blunt this argument by finding an alternative explanation based on molecular forces acting on streaming particles of light, and in hopes of eliciting such a theory they set diffraction as the topic of the 1818 prize competition, now under the auspices of the resurrected Royal Academy of Sciences. Arago was named to the committee of judges, but the rest of its members were Laplacian loyalists: Biot, Poisson, Gay-Lussac, and Laplace himself. Fresnel submitted a very strong entry in which he showed not only how to measure the wavelengths of the different colors of light, but also how to calculate the positions and even the intensities of the diffraction bands they produced. With its close fit between precise experimental measurements and elaborate mathematical theory, Fresnel’s entry met all of the Laplacians’ criteria except one: it was not based on particles and forces. Would the committee nonetheless award Fresnel the prize? In 1819 it did just that, with Laplace himself apparently casting the deciding vote. In the end, the Laplacians’ standards of mathematical theory and quantitative experiment were evidently more important to them (or at least to Laplace himself ) than was their model of particles and forces. By the mid-1820s the Laplacian group was rapidly passing from the scene, but it had already left a permanent mark on how science is done. By uniting

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precise quantitative experiment with mathematical theory, the Laplacians had helped bring Newtonian physics down to earth. They had important successes, but their grand ambitions soon led them to push physics into areas in which their own model of particles and forces did not work well, and it was eventually forced to give way to approaches that recognized other mechanisms and modes of action. The new experimental and mathematical physics the Laplacians had forged lived on, however, and the high standards they had set soon came to pervade the physical sciences. By the 1820s, and more fully and definitively in the decades that followed, physicists were ready to bring those rigorous standards to bear on a question of growing practical importance: the relationship between heat and work. Sadi Carnot and the Birth of Thermodynamics In the summer of 1824, one of the most remarkable books in the history of physics first appeared in the bookstalls of Paris. A slim volume of just over 100 pages, Reflexions on the Motive Power of Fire, and on Machines Fitted to Develop That Power offered a pathbreaking analysis of the steam engine and a clear statement of the general principles governing how the flow of heat can be harnessed to produce work. Its author, a young army engineer named Sadi Carnot (1796–1832), is now acclaimed as the founder of the science of thermodynamics. At the time, however, his ideas raised hardly a ripple in the scientific world. Sadi Carnot was the son of Lazare Carnot (1753–1823), himself an eminent army engineer and mathematician. The elder Carnot was also a leading figure in the French Revolution, known as “the Organizer of Victory” for his role in raising and directing the armies that defended revolutionary France in the 1790s. Napoleon later appointed him minister of war, but Carnot soon resigned to pursue his scientific interests. His writings helped found the French tradition of engineering mechanics, in which general scientific and mathematical principles are used to analyze the workings of machines. In his most important result, Lazare Carnot showed that any percussion in a series of gears or turbulence in a hydraulic system reduces the efficiency with which the machine or system can transmit power. This “principle of continuity” foreshadowed later ideas about the conservation of energy. After graduating from the Ecole Polytechnique in 1814, Sadi Carnot followed his father into the army engineering corps. With the restoration of the monarchy in 1815, however, Lazare Carnot was forced into political exile and his son’s military career languished. In 1820 Sadi Carnot took a leave of absence,

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essentially entering the army reserves, and devoted himself to private study in Paris of scientific, engineering, and economic questions. Although he shared the Laplacians’ commitment to quantitative experiment and their belief in the caloric theory of heat, Carnot was not invited to join their fading circle at Arcueil, nor did he pursue their goal of explaining phenomena by forces acting between microscopic particles. Although he sometimes speculated about such molecular interactions, he preferred, like most engineers, to focus on macroscopic quantities he could measure and manipulate, such as pressure, volume, and temperature. Carnot’s interest in engineering and economic development soon drew him to the steam engine. Like many others, he was convinced that the preeminence Britain enjoyed in the 1820s was based on the power of steam. “To take away today from England her steam-engines,” he declared, “would be to dry up all her sources of wealth, to ruin all on which her prosperity depends, in short, to annihilate that colossal power.”⁶ Hoping to achieve wealth and power of their own, French industrialists erected hundreds of steam engines in the decade after 1815, many of them compound engines built by enterprising British engineers. The high duty such engines could achieve when run at high pressures was a great selling point in France, where coal was expensive, and enthusiasts began to suggest that by running at even higher pressures, and perhaps using air or alcohol as the working substance in place of steam, there might be no limit to how much work could be extracted from a bushel of coal. This was just the sort of question that appealed to Carnot, both as a keen student of industrial economics and as heir to his father’s work on the efficiency of machines and to the broader French tradition of scientific engineering. Selftaught British engineers might excel at actually making steam engines, but it was a French engineer, trained at the Ecole Polytechnique, who took up the task of working out their underlying principles. Carnot began by noting a crucial point that Watt’s invention of the separate condenser had helped bring to the fore: steam engines work by exploiting the flow of heat from a hot place to a colder one, that is, from the boiler to the condenser. A source of heat alone is not enough; without a reservoir of cooling water, the steam could not be condensed and the engine would not work. Even the high-pressure puffer engines that vented their steam into the open air were in fact using the atmosphere itself as a giant low-temperature reservoir and exploiting the flow of heat into it. Enclose the whole system in an insulated 6. Sadi Carnot, Reflexions on the Motive Power of Fire (1824), ed. and trans. Robert Fox (Manchester: Manchester University Press, 1986), p. 4.

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box, so that heat could not continually flow away from it, and any steam engine would soon stop running. A steam engine, Carnot said, works much like a water wheel. Just as a water wheel produces useful work by harnessing the flow of water from a higher elevation to a lower one, so a steam engine harnesses the flow of heat or “caloric” from a higher temperature to a lower one. Caloric was not used up in the process, Carnot said, any more than water is used up when it passes through a water wheel. He regarded caloric as a real substance and argued that it simply passed from a more concentrated state in the boiler to a more diffuse one in the condenser water; all of the caloric was still there, he said, just as all of the water was still there in the lower pool after it passed through a water wheel. Carnot drew an important lesson from this analysis: for maximum efficiency, every flow of heat, every “fall” of caloric from a high temperature to a lower one, should be put to work, just as every inch of the fall of water in a well-designed water wheel is harnessed to turn the wheel. Any heat that is allowed to pass from the boiler of a steam engine to its cooling reservoir without working the piston along the way is wasted just as surely as is water that spills over the top of a dam. A hot object should never be allowed to touch a cold one, Carnot said, for the heat that inevitably flows between them by conduction could, with proper design, have been harnessed to do useful work. Indeed, in the world around us heat is continually passing from hotter objects to cooler ones, tending eventually to reduce everything to a state of lukewarm uniformity. The task of the engineer, as Carnot saw it, is to find the best way to capture that flow and turn it to human use. In an argument of striking originality, Carnot showed that there is an absolute limit to the amount of work any heat engine can produce from the fall of a given quantity of heat. Imagine, he said, the simplest possible heat engine: two bodies, one hot and one cold, and a box of air fitted with a piston. Start by putting the box in contact with the hot body; as the air absorbs heat, it will expand and push the piston upward, doing work. If we now insulate the box, the air within it will continue to expand for a time, doing further work as it gradually cools; this corresponds to the expansive working of a steam engine. When the temperature of the box of air has fallen to that of the cold body, Carnot said, put the two in contact and slowly compress the air at a constant temperature until all of the heat it had earlier absorbed from the hot body has passed into the cold one. Most analysts would have stopped at this point, for Carnot had laid out a uniquely efficient way to generate work by the transfer of heat without ever letting two bodies at appreciably different temperatures come into contact. Carnot went on, however, to add a crucial final step: remove

Clapeyron’s Form of the Carnot Cycle In 1824, Sadi Carnot worked out the most efficient possible cycle of operations for any heat engine; in 1834, Emile Clapeyron cast it into the graphical form shown here, which closely resembles one of James Watt’s indicator diagrams. The Carnot cycle has four stages: (1) Isothermal expansion (from a to b on the graph): We begin by placing a cylinder filled with air in contact with a hot body, A (at temperature 1). As heat flows from A into the cylinder, the air within the cylinder expands and does work by pushing the piston outward. (2) Adiabatic expansion (from b to c): We next put the cylinder in contact with an insulating body, B, thus blocking any further flow of heat. The air in the cylinder continues to expand on its own, pushing the piston further outward and doing additional work as the air cools, its temperature dropping from 1 to 2. (3) Isothermal compression (from c to d ): We now put the cylinder in contact with a cooler body, C (at 2), and push the piston inward. As we do work by compressing the air in the cylinder, heat flows from the cylinder into C. (4) Adiabatic compression (from d back to a): Finally, we put the cylinder back in contact with the insulating body, B, and push the piston further inward. As we do additional work by com-

pressing the air in the cylinder, its temperature rises back up to 1. Because the expansions take place at higher temperatures and pressures than the compressions, the air does more work as it pushes the piston outward during stages (1) and (2) than we must do to restore the system to its original state by pushing the piston back inward during stages (3) and (4). The Carnot cycle is fully reversible and has two net effects: a quantity of heat flows via the cylinder from the hot body, A, to the cooler one, C ; and the engine performs an amount of work proportional to the area enclosed by the curve abcd. The closer we can come to producing a curve of that shape, the more efficient our engine will be.  J. A. Ewing, The Steam-Engine and

Other Heat-Engines (Cambridge: Cambridge University Press, 1894), p. 50.

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the box from contact with the cold body, he said, and continue to compress the air until its temperature rises back to that of the hot body. This will return the system to its original state so that the whole process can be repeated. The key to what became known as the “Carnot cycle” was its reversibility: since heat was allowed to flow only between bodies that were at virtually the same temperature, the whole sequence could be run backwards. By compressing the air at the higher temperature and forcing it to expand at the lower one, we could, by doing work, pump heat from the cold body to the hotter one, just as we can pump water uphill by running a water wheel backwards. As Carnot pointed out, this meant that no engine, however complex and whatever its working substance, could ever produce more work from a given fall of heat than would a simple box of air run in his reversible cycle. If such a super-efficient engine existed, we could simply hook it to one running the Carnot cycle in reverse and use the latter to pump all of the heat back up to the higher temperature to be run through again, like a pair of water wheels that were somehow rigged to feed each other while still producing useful work. We would be getting something for nothing, and on the grounds that such a perpetual motion machine is impossible, Carnot concluded that no heat engine could be more efficient than his ideal reversible one. Carnot went on to show that the limit on the amount of work an engine can generate is set by the high and low temperatures between which it operates: the further the caloric falls, the more work it can do. That is why engines that were run at high temperatures and pressures, such as Trevithick’s puffers, were able to achieve such high duties. Even the best high-pressure compound engines fell far short of the theoretical maximum, however; using measurements of the expansion of steam, Carnot showed that in practice such engines harnessed no more than about 5 percent of the motive power that burning a bushel of coal could in principle produce. Although Carnot had shown there was an upper limit on the efficiency of any heat engine, there was still great room for improvement, and his little book gave pointers on how this might be achieved. It would be nearly 30 years before Carnot’s advice was taken. When his Reflexions appeared in 1824 it attracted a few favorable notices, but no one took up its ideas in a serious way. Both physicists and engineers of the day seem to have found Carnot’s approach too foreign to their own ways of thinking. After Carnot died of cholera in 1832, most of his papers were burned; his book had already been largely forgotten. His ideas might have been lost sight of altogether had not another French engineer, Emile Clapeyron (1799–1864), published a paper in 1834 in which he cast Carnot’s mainly verbal arguments into

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mathematical and graphical form. Clapeyron had worked for a time in Russia and may have seen indicator diagrams being used by Boulton and Watt engineers erecting steam engines there. By plotting Carnot’s sequence of expansions and compressions on the axes of an indicator diagram, showing how the volume changed along with the temperature and pressure, he was able to make the meaning of the Carnot cycle much clearer; for instance, the work produced in each cycle appeared simply as the area enclosed by the resulting curve. He also made more explicit the assumption that caloric is conserved during its flow from a higher temperature to a lower one. Although Clapeyron’s paper did not stir up much interest when it was first published, it was translated into English in 1837 and German in 1843. These publications helped keep Carnot’s ideas alive until a new generation of physicists began to take them up and extend them in the later 1840s. Carnot’s efforts had been inspired by the rapidly advancing development of the steam engine and by his desire to find the principles behind what engineers had so far accomplished largely through trial and error. His analysis gave deep insights into how the flow of heat can best be harnessed to produce useful work and into the limits on this process; had engineers made full use of his teachings, they could have substantially improved the efficiency of their engines. Carnot had based his arguments on the caloric theory, which held that heat is a physical substance that can neither be created nor destroyed. We know from his few surviving manuscript notes that after publishing his book he became convinced that caloric does not exist and that heat is simply a mode of motion, the bouncing around of ordinary molecules. Perhaps that is why Carnot did not publish any further analyses of heat and work after his 1824 Reflexions: he may have realized that dropping the caloric theory would force him to recast much of his earlier argument, and it was not easy to see how this might be done. Certainly, questions about the status of caloric complicated the reception of Carnot’s theory of heat engines, for by the time other scientists began to take it up in the late 1840s, they, like him, had begun to think not in terms of caloric but of a broad new concept: energy.

2 Energy and Entropy

Nowadays, people blithely talk about energy as if they know exactly what it is. Companies buy and sell it, public officials make policy about it, and consumers try (we hope) to use it wisely. For all its ubiquity, however, “energy” is a slippery concept and more recent in origin than one might expect. The idea that all of the forces and powers of nature are manifestations of a single pervasive but impalpable quantity emerged in its modern form only in the 1840s; by 1860, it had come to be widely accepted as a fundamental scientific truth. Yet the inner nature of energy has remained elusive; as we shall see, its usual definition, “capacity to do work,” breaks down in some important cases. The main law governing its transformations is, however, simple enough: although energy can change from one form into another—say, from chemical to thermal to mechanical to electrical to radiant, as it does when energy from a coal-fired power plant passes along the wires to light up your home—it can neither be created nor destroyed. Whatever else happens, the total amount of energy in any closed system remains the same. The law of the conservation of energy, also known as the first law of thermodynamics, is perhaps the most sweeping generalization in all of science, uniting everything in the universe, from atoms to humans to stars, under a single overarching principle. Its companion, the second law of thermodynamics, is more subtle but no less consequential. It too was first formulated around 1850, although its key term, entropy, has never entered popular language in quite the way energy has. The second law was foreshadowed by Sadi Carnot’s observation that as heat flows from hot to cold, it tends toward a lukewarm equilibrium from which no further useful work can be derived. The total amount of energy in the world may never change, but as time goes on, less and less of it is available for our use. According to the second law, the universe is slowly but inevitably running down. With its grim forecast of inescapable “heat death,” the second law sounded a pessimistic counterpoint to the faith in progress that otherwise marked the nineteenth century. The laws of energy and entropy had many roots. Some lay within physics

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itself, or in neighboring sciences such as chemistry and physiology; others could be found in religious or philosophical beliefs. The new science of thermodynamics grew most directly, however, from the study of power technologies, particularly steam engines, hot air engines, electrical motors, and other means for converting one form of energy into another. As such devices proliferated in the first decades of the nineteenth century, the science of energy began to take shape. Converting Forces In her widely read 1834 book On the Connexion of the Physical Sciences, the English mathematician and popular writer Mary Somerville (1780–1872) observed that “the progress of modern science, especially within the last five years, has been remarkable for a tendency to simplify the laws of nature, and to unite detached branches by general principles.”¹ Close connections had recently been discovered between electricity and magnetism, and there were growing indications that heat and light were, in some of their forms, almost identical. More and more ways were being found to convert one kind of force into another, and by the 1840s several scientists and natural philosophers were beginning to suggest that behind the multiplicity of physical phenomena lay a single unifying reality: energy. The formulation of the law of the conservation of energy is a classic case of multiple independent discovery in the history of science. It is not hard to come up with a list of 10 or 15 people who, between the late 1830s and early 1850s, put forward ideas that could later be seen as having foreshadowed one or another aspect of the law of the conservation of energy. Theories about the interconvertibility of forces, the indestructibility of “motive power,” and the equivalence of heat and mechanical work all contributed to the formulation of what became the first law of thermodynamics. The idea of the conservation of energy was not quite “in the air” in the 1840s, but its ingredients certainly lay close to the surface. A series of electrical discoveries in the first decades of the nineteenth century played an important part in the evolution of ideas about the conversion of forces and the conservation of energy. We will examine these discoveries more closely in Chapter 4 but for now will focus briefly on how they contributed to the emergence of the concept of energy. In 1800 the Italian physicist 1. Mary Somerville, On the Connexion of the Physical Sciences (London: John Murray, 1834), preface.

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Alessandro Volta (1745–1827) found that by stacking discs of copper and zinc on bits of pasteboard dampened with a weak acid, he could produce a steady electric current. The current from such a “pile,” or battery, could generate sparks, heat a wire until it glowed, decompose water into its constituent hydrogen and oxygen, and produce other striking effects. What ultimately drove the current was not immediately clear, but by the 1820s most scientists believed it to be a chemical reaction between the metals and the acid in the pasteboard. The battery and circuit thus showed that chemical affinity could produce electrical force, which could in turn produce heat and light or, by decomposing water or another compound, regenerate the force of chemical affinity. In 1820 the Danish physicist Hans Christian Oersted (1777–1851) found that an electric current flowing in a wire could deflect a magnetized needle. This demonstrated that electric force could produce magnetic force, which could in turn generate motion, and inventors soon devised simple motors that used electric currents to turn wheels and do other mechanical work. In 1831 the English experimenter Michael Faraday (1791–1867) brought the relationship between electricity, magnetism, and motion full circle when he discovered electromagnetic induction: when a magnet is moved or spun near a coil of wire, an electric current appears in the wire. By turning a crank and doing mechanical work, Faraday could now generate an electric current, lead it down a wire, and use it to drive a distant motor. The combination of electrical generator, wire, and motor provided a way to take work done at one place and transmit it for use at another—the basis for the huge electric power systems we rely on today. Faraday was deeply religious and saw “force” as something only God could create or destroy. Absent divine intervention, he said, the amount of force in the world remains constant, and human efforts and natural processes can do no more than move it from place to place or change it from one form into another. Belief in the convertibility of forces was reinforced in the 1820s when physicists found they could generate an electric current by joining wires made of two different metals into a loop and heating one junction while keeping the other cool. Such “thermocouples” seemed to produce electrical force directly from heat. They also provided a sensitive way to measure small changes in temperature, and in the 1830s several physicists used thermocouples to show that radiant heat could be reflected, refracted, and polarized just like visible light. A.-J. Fresnel (1788–1827) had shown more than a decade before that light consists of waves rather than particles; now it appeared that radiant heat, too, must consist of such waves. The heat of the sun thus comes to us not as streams

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of caloric, but as waves in the ether. Such waves must either be heat itself or be able to generate heat when they strike matter. Either way, it was becoming harder to believe that heat was a material substance. The caloric theory was in trouble by the mid-1830s, but it had survived a strong attack more than 30 years before. Benjamin Thompson (1753–1814) was a colorful soldier of fortune and sometime inventor from Massachusetts who had fought on the British side in the American Revolution. He later served as an adviser to a variety of European rulers, and in Munich in the 1790s acquired the title by which he became best known: Count Rumford. In 1797 he did experiments on heat while supervising the boring of brass cannon barrels for the Bavarian army. That friction produces heat had long been known, but caloric theorists said this was simply because, as two objects are ground against each other, caloric is squeezed out by pressure or released by abrasion. By using horses to drive a drill with a dull bit, Rumford showed that continued friction could generate enormous amounts of heat—far more, he argued, than could plausibly have been squeezed out by the modest pressure of his drill or released from the tiny chips of brass it threw off. This proved, he said, that caloric could not be a real substance and that heat must instead be a form of motion. Adherents of the caloric theory brushed off these claims, declaring that the experiments proved only that ordinary matter contains more caloric than Rumford had supposed and that pressure and abrasion can release it in abundance. In focusing on the heat produced by friction, Rumford had put his finger on a weak point in the caloric theory, but the evidence he presented was not as airtight as he liked to claim. It was only decades later, after belief in the interconvertibility of forces had won acceptance on other grounds, that Rumford’s experiments came to be seen as having decisively refuted the caloric theory. By the early 1840s the idea that forces are never really destroyed but simply change from one form into another had many proponents, including Faraday in England, the chemist Justus von Liebig in Germany, and the engineer Ludvig Colding in Denmark. Among its most influential advocates was the British lawyer and amateur scientist William Robert Grove (1811–96). Grove had done extensive work on electrical batteries, which he came to see as essentially devices for converting chemical force into other forms. In a series of lectures in 1842–43 and a book, On the Correlation of Physical Forces (1846 and many later editions), Grove cited many such conversion processes and argued that they held the key to understanding the full range of physical phenomena. The great remaining problem, he said, was to determine the “exchange rate” governing the conversion of one kind of force into another. If this could be quan-

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tified, we would be able to trace the passage of force from one form into another and back again, with none of it ultimately being lost. Grove did not know it, but a value for the most important such exchange rate, that between mechanical work and heat, had already been published, though not in a form calculated to inspire confidence. Robert Mayer (1814–78) was a young German physician who in 1840 had set off as a ship’s doctor on a year-long voyage to the East Indies. Off Java, several crewmen came down with fever, and following the usual practice of the day, Mayer opened their veins to let blood. He was struck by its color, a much brighter red than he was used to in Germany, and at first worried he had hit an artery. On the long voyage home he brooded over what he had seen and traced out its implications. He accepted Lavoisier’s theory that we generate body heat by oxidizing our food. Since in a hot climate we do not need to burn as much food to keep ourselves warm, we should expect venous blood to retain more of its oxygen in the tropics than it does in a cold climate; indeed, as Mayer had observed, it might remain almost as brightly red as arterial blood. But if the oxidation of food is the source of our internal body heat, Mayer asked, what about the heat we can generate externally, by doing work and, like Rumford’s horses, producing friction? All of the heat we produce must, he said, be charged to the same account; it must all derive ultimately from the oxidation of our food, whether the heat appears internally in our bodies or externally in objects on which we perform work. From this, Mayer drew a sweeping conclusion: there must be a universal equivalence between heat and work. Mayer became obsessed with the idea that work can be converted into heat according to a fixed ratio. On his return to Germany, he pestered his friends about it and called on local physics professors to explain his theory. Most had trouble taking him entirely seriously, especially when he told them he could raise the temperature of a bottle of water simply by shaking it. Mayer felt sure his idea of the indestructibility of “force” held the key to the deepest secrets of the universe, ranging from the efficiency of steam engines to the immortality of the soul. He tried to bolster his case with mathematical arguments, but his grasp of the subject was weak; in a letter to a friend, he once ended up trying to prove that 2  0. It is perhaps not surprising that when Mayer sent his first paper on force and heat to the leading German physics journal, the Annalen der Physik, it was rejected. Was Mayer a crank? Perhaps, but if so, he was that rare thing, a crank who was right. After his first paper was turned down, Mayer tried to make his ideas more palatable by emphasizing measurable facts. With remarkable insight, he

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found a way to use existing data on the compression and heating of gases to derive a value for the conversion of work into heat—what later came to be called the mechanical equivalent of heat. If we let a mass of one kilogram fall from a height of 365 meters and then convert all of the resulting work into heat, it would, Mayer said, be enough to raise the temperature of a kilogram of water by 1°C (that is, to produce one kilocalorie of heat). He sent a short paper with this result to Liebig’s Annalen der Chemie in 1842; it was promptly published and later provided the foundation for Mayer’s claim to be counted as the discoverer of the law of the conservation of energy. He had high hopes that his paper would be recognized as a great contribution to science and was bitterly disappointed when it attracted little notice. Mayer and his work would probably have been completely forgotten had not others independently hit on similar results a few years later. One of these was Hermann von Helmholtz (1821–94), a young German scientist who followed a path in some ways quite similar to Mayer’s and in others very different. Like Mayer, Helmholtz was trained as a physician and had a deep interest in questions of bodily heat and work. He was, however, far more adept at mathematics than Mayer and better equipped to relate his ideas about force (in German, Kraft) to existing scientific theories. According to a well-known theorem in Newtonian mechanics, the total “living force,” or vis viva, of a system of bodies does not change when those bodies undergo elastic collisions. The vis viva of a particle is defined as its mass times the square of its velocity (mv 2), and the theorem stated that while vis viva can pass from one body to another in such collisions, the total for all of the bodies involved remains constant. Helmholtz also argued that what he called “tensional force” (Spannkraft) can be converted into vis viva and back again. In the most familiar case, the weight of a body multiplied by its height above the ground defines its gravitational Spannkraft (in later terms, its potential energy); as the body falls and acquires speed, this turns into vis viva. When it hits and bounces back up, slowing as it rises, its vis viva turns back into Spannkraft. This much was already familiar, but in his 1847 essay “The Conservation of Force” (“Die Erhaltung der Kraft”), Helmholtz showed that if the world consists solely of particles acting on each other through forces of attraction and repulsion, as in the Laplacian model, then the sum of all forces, both living and tensional, must always be constant. Force, as Helmholtz defined it, was not only convertible but rigidly conserved. One problem remained, however: what about friction and inelastic collisions? If we drop a ball made of soft clay, it does not bounce back up but just goes splat; the Spannkraft it had at the top turns into vis viva on the way down

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but then seems to be lost completely when the ball hits the ground and stops. Helmholtz replied that the vis viva of the ball is not really lost but is simply redistributed as invisible motion of its molecules, which, he said, constitutes heat. He found a mathematically precise way to express the previously vague idea that forces can be converted from one form into another and proceeded to use his conservation law to elucidate a wide range of physical phenomena. Although the older generation of German physicists regarded Helmholtz’s essay as overly speculative—like Mayer’s first paper, it was rejected by the Annalen der Physik, and Helmholtz instead had it published as a pamphlet—within a few years younger scientists in both Germany and Britain came to regard it as a founding statement of the principle of the conservation of energy. Helmholtz’s essay lacked one thing, however: solid empirical data on the conversion of work into heat. Helmholtz was unaware of Mayer’s 1842 paper, and though he cited more recent experiments by the young Englishman James Joule, he seems not to have grasped the real magnitude of what Joule had achieved. James Joule and the Mechanical Equivalent of Heat James Prescott Joule (1818–89) did more than anyone else to establish the principle of the conservation of energy and to determine the mechanical equivalent of heat. His family owned a large brewery near Manchester, England, and he shared the direct and practical orientation for which the inhabitants of that great industrial center were known. Joule helped run the brewery for many years and drew on its resources, particularly for precise temperature control, in many of his experiments. His chief interest, however, lay not in making beer but in discovering scientific truths. Joule was one of the last great scientific amateurs; he never held a professional or academic scientific position and pursued his researches chiefly out of personal curiosity and commitment to the advancement of knowledge. While still in his teens, Joule was caught up in the widespread “electrical euphoria” of the 1830s. The invention of the first electric motors had stoked hopes that electricity might soon provide a clean and efficient source of power that would supplant the steam engine and revolutionize the economy. Electromagnetic theory, as then understood, even led some enthusiasts to suggest there might be no limit to the “duty” an electric motor might achieve; by running the motor at higher and higher speeds, they said, we could squeeze as much work as we wished from even a small battery. Joule shared these hopes and began building motors of his own in the late 1830s. “I can hardly doubt,” he declared in 1839, “that electro-magnetism will ultimately be substituted for steam to propel machinery,” and he cited theoretical grounds for believing that

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“the cost of working [an electric motor] may be reduced ad infinitum.”² Electricity seemed to offer a realistic prospect of getting something for nothing. Joule was too practical minded to rely solely on theory, however, and in 1840–41 he carefully tested the actual efficiency of his motors. His bright hopes were soon dashed as it became clear that even the best electric motors could achieve only a miserably low duty. The batteries powering Joule’s motors burned through five pounds of zinc to do as much work as a good steam engine could produce by burning a single pound of coal—and pound for pound, zinc cost 70 times as much as coal. More efficient electric motors would no doubt be made in the future, but Joule found it hard to believe they could ever be improved by the factor of 350 needed to compete with steam engines. Battery-powered motors had no real prospect of supplanting steam engines for anything beyond a few specialized uses, and Joule’s dreams of cheap electric power faded rapidly in the 1840s. Joule continued to study the performance of his electric motors, batteries, and generators, focusing in particular on the heat that appeared in their coils and connecting wires. By the end of 1840 he had established what later became known as “Joule’s law”: an electric current generates heat at a rate proportional to the square of its strength multiplied by the resistance of the conductor (I 2 •R ). He then noticed that when the battery or generator drove a motor that did mechanical work, less heat appeared in the wires—and the more work, the less heat. Like many other scientists of the time, Joule became convinced that heat was not a substance but simply invisible motions of the molecules that make up ordinary matter. Moreover, he claimed, work and heat are interconvertible: not only can work be turned into heat, either by mechanical friction or electrical resistance, but under some circumstances, such as in a steam engine, heat can be converted into work. This was his first glimmer of the principle of the conservation of energy, and to put it on a quantitative basis, he set out in 1843 to measure the ratio between work and heat, or what he initially called “the mechanical value of heat.” His first method was indirect: using a hand crank or falling weights to spin a magnet and coil between the jaws of a powerful electromagnet, he generated electric currents whose heat he captured in a cylinder filled with water. His initial results were rough, but they indicated that letting a weight of about 800 pounds fall a distance of one foot would suffice to raise the temperature of a pound of water by 1°F—in other words, 800 foot-pounds of work was 2. Quoted in Donald Cardwell, James Joule: A Biography (Manchester: Manchester University Press, 1989), pp. 31–32.

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about equal to one British thermal unit, or “Btu,” of heat. (In metric terms, the fall of about 440 kilograms through one meter would raise the temperature of a kilogram of water by 1°C, or generate one kilocalorie of heat.) Convinced he was on the track of a fundamental result, Joule strove to improve the accuracy and persuasiveness of his measurements. First, he eliminated the electrical middleman: instead of relying on a complicated apparatus involving wires, magnets, and the mysterious intermediary of electricity, he found ways to convert mechanical work directly into measurable heat. He compressed air using a pump immersed in water and showed that the total heat generated again pointed toward a mechanical equivalent of about 800 footpounds per Btu. He forced water through small holes in a piston, measured the heat generated by friction, and again found a value of 800 foot-pounds per Btu, or perhaps a little less. Finally, in 1845, Joule embarked on his famous series of paddle wheel experiments, in which he showed he could raise the temperature of water by a measurable amount simply by stirring it. The idea behind Joule’s paddle wheel experiments was simple: expend a measured amount of work agitating a known quantity of water and, once the water has stopped swirling around, measure any change in its temperature. Actually doing it was difficult, however, for the expected rise in temperature was very small and there were many possible sources of error—even the heat radiating from the experimenter’s own body could throw off the measurement. Aided by a talented instrument maker, J. B. Dancer, Joule fitted a small brass vessel with a set of paddles driven by cords attached to falling weights. The descent of the weights gave a direct measure of the work expended, and Dancer’s exquisitely sensitive thermometer—readable to within a hundredth of a degree—showed the increase in temperature. Working in a large cellar at his family brewery, aided by workmen to raise the weights, and drawing on brewers’ techniques for the careful regulation and measurement of temperature, Joule arrived by summer 1847 at a consistent value for the mechanical equivalent of heat: 782 foot-pounds of work raised the temperature of a pound of water by 1°F. Using whale oil or mercury in place of water gave the same value to within less than 1 percent. (Joule repeated the measurement under even more exacting conditions in 1849 and arrived at a figure of 772 foot-pounds per Btu; the currently accepted value is 778.) In retrospect, Joule’s work in the 1840s stands as one of the great achievements of nineteenth-century physics. It was not seen that way at the time. His first paper on the mechanical equivalent of heat, presented at the 1843 meeting of the British Association for the Advancement of Science, was ignored. The Royal Society of London rejected his 1844 paper on the heating of air by com-

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Joule’s Paddle Wheel Experiment Convinced by experiments with electric motors that work could be converted into heat, James Joule devised his paddle wheel apparatus in 1845 as a way to demonstrate and measure such conversion directly. He attached a weight to a string in such a way that the slow descent of the weight made a set of paddle wheels turn within a closed tub of water. The work done as the weight fell through a given distance would, he said, all be converted into heat by the friction of the paddles against the water. Joule used a delicate thermometer to measure

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the resulting slight increase in the temperature of the water and showed that there was a constant ratio between the work the falling weight expended in turning the paddles and the heat the paddles generated within the water. Put into standard units, he found that the fall of 782 pounds through one foot would raise the temperature of one pound of water by 1°F. Joule’s measurement of the “mechanical value of heat” became one of the experimental foundations of the law of the conservation of energy.  Balfour Stewart, Lessons in Elementary

Physics (London: Macmillan, 1870), p. 206.

pression. When he delivered a lecture entitled “Matter, Living Force, and Heat” at a Manchester church reading room in April 1847, a local newspaper published the text, but the broader scientific community paid no attention. Joule did what he could to bring out the wider significance of his work. Like Faraday, he related the conservation of force to God’s role as creator, saying it was “manifestly absurd to suppose that the powers with which God has endowed matter can be destroyed any more than that they can be created by man’s agency.”³ He also stressed the practical value his findings could have for 3. James Joule, “On Matter, Living Force, and Heat” (April 1847), in Scientific Papers of James Prescott Joule, 2 vols. (London: Taylor and Francis, 1884), 1:269.

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understanding and improving steam engines. Carnot and Clapeyron had been wrong, he said, to claim that steam engines derive their work simply from the fall of heat from a high temperature to a lower one, the heat (or caloric) itself being conserved. Joule was confident that careful measurements would show that less heat passes out of the cylinder of a steam engine into its cooling water and surroundings than enters it from the boiler, and that the difference would be found to equal the work done by the engine. Moreover, his figures indicated that even the best existing engines converted no more than a tenth of the heat content of their fuel into useful work. If Joule was right, there was evidently great scope for improvement. The turning point in Joule’s quest to be heard came on 24 June 1847 at the annual meeting of the British Association for the Advancement of Science, held that year at Oxford. Joule was given only a few minutes to describe his paddle wheel experiments, but that was enough to catch the attention of a young Scottish scientist in the audience. Still two days shy of his twenty-third birthday, William Thomson (1824–1907) had already been professor of natural philosophy at Glasgow University for nearly a year and was widely (and, as we shall see, rightly) regarded as a rising star of British science. He was deeply imbued with Carnot and Clapeyron’s doctrine of the conservation of heat, but as he listened, he became convinced that Joule had in fact turned work into heat. After Joule’s talk, the two men struck up a conversation that soon matured into a lasting friendship. Thomson drew other physicists’ attention to Joule’s results, and within a few years the equivalence of work and heat was widely accepted as an established fact. Thomson was left, however, with a troubling puzzle: how could Carnot and Joule both be right? If heat was in fact not conserved, what became of Carnot’s beautiful theory of the steam engine? Thomson, Clausius, and the Second Law Joule had shown directly that a little under 800 foot-pounds of work could be turned into 1 Btu of heat, and he was firmly convinced that heat could be converted into work by the same ratio. Steam engines turn heat into work every day, he said, though with a miserably low efficiency that he hoped to improve. If Joule was right, however, there seemed to be no reason to stop at improving the fuel efficiency of steam engines. If lowering the temperature of a bucket of water by a few degrees could release thousands of foot-pounds of useful work, why could we not drive our engines by simply tapping the abundant heat energy of our surroundings? What keeps us from building a ship that would take in seawater at the front, turn some of its heat into work, toss ice

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cubes out the back, and propel itself across the ocean without burning any fuel at all? Carnot had no doubt been right when he said it was impossible to get something for nothing in this way, but he had based his argument on the assumption that heat is conserved—an assumption Joule’s experiments had refuted. If Joule was right, must Carnot be wrong? William Thomson wrestled with this dilemma through the late 1840s. The German physicist Rudolf Clausius took it up as well, and in the early 1850s he and Thomson found slightly different but ultimately equivalent ways to resolve it. Their solution, soon dubbed the second law of thermodynamics, had far-reaching implications not just for the operation of engines but for the fate of the universe. Thomson (known after 1892 as Lord Kelvin) was born in Belfast but grew up mainly in Scotland, where his father taught mathematics at Glasgow University. William was clearly a clever lad, and his ambitious father groomed him for greatness, starting him in college courses when he was only 10. Thomson also read widely on his own and published significant papers on the mathematical theory of heat flow while still in his teens. In the early decades of the nineteenth century, Glasgow was emerging as a great industrial center, filled with cotton mills and shipyards—along with slums and smoke. The local industrialists shared a characteristic Scottish concern with thrift, economy, and the avoidance of waste. For many, this was a matter not just of good business but of good morals, reflecting their adherence to Presbyterian doctrines of man’s responsibility to use God’s gifts wisely and well. Thomson absorbed these attitudes from an early age, particularly from his father and his older brother James, who was beginning a career as an engineer deeply concerned with the efficiency of water mills and steam engines. When he was 17, Thomson was sent south to study mathematics at Cambridge. He spent the next three and a half years preparing for the Mathematical Tripos, a grueling five-day examination widely regarded as the top test of British brainpower. Although his teachers considered him the most talented young mathematician of his generation, he came in second on the examination in January 1845; the winner excelled at writing out answers quickly, while Thomson reportedly spent his time exploring the nuances of the questions posed, some in fact based on his own published work. The longtime professor of natural philosophy at Glasgow was by then in failing health, and Thomson’s father hoped to land the job for his son. To bolster his credentials as an experimentalist, William headed to Paris and spent the spring of 1845 working in the laboratory of Victor Regnault (1810–78), the leading French experimental physicist of the day. In hopes of improving the

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efficiency of the country’s steam engines, the French government had commissioned Regnault to perform extensive experiments on the properties of steam, and Thomson learned much from him about the physics of heat and the art of precision measurement. In 1846 Thomson was elected professor of natural philosophy at Glasgow at the age of 22. In sorting through his predecessor’s set of disused demonstration apparatus, he came across a model of a Stirling engine, a clever device that generated work by passing air back and forth between a hot cylinder and a cold one. The Stirling engine provided perhaps the closest practical embodiment of Carnot’s ideal cycle, and Thomson’s encounter with the model, and with a group of Glasgow enthusiasts for similar hot air engines, helped focus his attention on problems of work and heat. He had studied Clapeyron’s essay while in Paris and searched without success for a copy of Carnot’s Reflexions, by then already rare. Thomson was convinced by Clapeyron’s account of Carnot’s theory and accepted the principle of the conservation of heat, though he was open to the growing evidence that caloric might not be a real substance. In 1848 he used Carnot’s theory to construct a new temperature scale based not on the expansion of mercury or any other substance, but on the principle that the fall of a given quantity of heat through each degree should produce an equal amount of work. The resulting “Kelvin scale,” as it was later known, set absolute zero at 273°C, at which point a body would contain no heat at all. Thomson’s belief in Carnot’s theory was reinforced when his brother James pointed out a surprising consequence: since water expands on freezing, applying pressure to a block of ice must lower its melting point, or we could build a perpetual motion machine driven by the expansion of ice at a constant temperature. When William Thomson did the experiment late in 1849, he found that pressure indeed lowered the melting point of ice by a fraction of a degree, brilliantly confirming Carnot’s theory. By then, however, his encounter with Joule had already led Thomson to rethink some basic issues. Although willing from the first to grant that Joule had turned work into heat, he was not convinced the process could run the other way; as he pointed out, the conversion of heat into work had not yet been directly demonstrated, and it would contradict Carnot’s theory. Joule had proved, however, that heat could not be a substance, and he insisted that the only way to make sense of many experiments on electrical heating, the compression of gases, and other phenomena was to admit that heat actually disappears when work is generated. Thomson began to waver; in an 1848 paper he still cited what he called “Carnot’s fundamental axiom” of the conservation of

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heat, but added a footnote calling attention to Joule’s “remarkable discoveries” and confessing that “as yet much is involved in mystery” concerning the relationship between heat and work.⁴ Late in 1848 Thomson finally obtained a copy of Carnot’s Reflexions from his friend Lewis Gordon, professor of engineering at Glasgow and a proponent of hot air engines. Thomson studied the little book closely and soon published a detailed account of Carnot’s theory. His objection to accepting the conversion of heat into work crystallized around a crucial point: if we grant that a steam engine turns some of the heat from its boiler into work, what are we to say becomes of the “mechanical effect” that is evidently lost whenever heat flows from a hot body to a colder one without passing through such an engine? If we were to pipe the steam straight into the condenser, so that it bypassed the cylinder and did nothing but heat up the cooling water, what would become of the work that, with more care, we could have extracted from the steam? Like Faraday and Joule, Thomson believed the powers God had created must be permanent, and in one of his first uses of the word energy in its modern sense, he declared that “nothing can be lost in the operations of nature—no energy can be destroyed.”⁵ Yet if heat and work were truly equivalent, the ordinary conduction of heat from hot objects to cold ones was destroying motive power all around us all the time. Thomson was at an impasse. Thomson’s paper caught the eye of Rudolf Clausius (1822–88), then a teacher at a Berlin secondary school and soon to emerge as one of the leading theoretical physicists in Germany. Clausius had already begun to think deeply about how heat is related to work and motion; as we will see in the next chapter, he was a pioneer in developing the kinetic theory of gases, which traces heat phenomena to the invisible motions of molecules. He accepted Joule’s demonstration that work can be converted into heat and opened his 1850 paper “On the Motive Power of Heat” by noting that the advent of the steam engine had made it natural to ask how much heat it takes to produce a corresponding amount of work. He also accepted Carnot’s proof that the amount of work that can be derived from a given flow of heat depends on the difference of temperatures through which it falls. Clausius did not accept the conservation of heat, however, and said Thomson had been wrong to identify it as the foundation of Carnot’s theory. The real heart of the theory, Clausius argued, lay in Carnot’s assertion that 4. William Thomson, “On an Absolute Thermometric Scale” (1848), in Mathematical and Physical Papers, 6 vols. (Cambridge: Cambridge University Press, 1882–1911), 1:102n. 5. William Thomson, “An Account of Carnot’s Theory” (1849), in Mathematical and Physical Papers, 1:118.

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to extract work, we must harness a flow of heat from a higher temperature to a lower one. Indeed, the key point in Clausius’s statement of the second law of thermodynamics, initially tossed off almost as an aside, was the seemingly banal observation that, left to itself, heat flows only from hotter bodies to colder ones. We can make heat flow in the opposite direction, from cold to hot, only by a compensating expenditure of work (as is now done in the compressor of a refrigerator or air conditioner). Once we recognize this, Clausius said, we can readily reconcile Joule with Carnot and put the laws of heat and work on a sound and comprehensive basis. In particular, we see that there is no contradiction between Joule’s claim that as a quantity of heat flows from hot to cold we can convert part of it into work, and Carnot’s statement that we must inevitably dump the rest at the lower temperature. All of the energy we started with will still be there at the end, but the portion that remains as heat at the lower temperature cannot be turned into work unless we can find a still colder body for it to flow into. Thus, as heat flows from hot to cold, less and less of it remains available to be converted into useful work. Thomson responded to Clausius by publishing a long paper in 1851 in which he clarified several important points and explored their implications. He now accepted wholeheartedly that heat can be converted into work and formulated two overarching principles, later codified as the first and second laws of thermodynamics: (1) heat and work, or what Thomson called “mechanical effect,” are interconvertible according to a set ratio, their sum remaining constant; and (2) it is impossible to generate work by cooling a body below the temperature of the coldest body around it. The first of these must be true or we could make what is called a perpetual motion machine of the first kind, in which work is produced out of nothing. The second (which, as Thomson noted, is logically equivalent to Clausius’s principle concerning heat flow) must be true or we could make a perpetual motion machine of the second kind, like the ship described earlier that sucks heat out of seawater and turns it into work, tossing out ice cubes along the way. As Thomson noted, if this second principle were not true, “a self-acting machine might be set to work and produce mechanical effect by cooling the sea or earth, with no limit but the total loss of heat from the earth and sea, or, in reality, from the whole material world.”⁶ Indeed, if the machine expended its work on friction, as a ship does in plowing through the sea, it would reheat it surroundings, from which it could again draw energy. The machine could run on forever, doing useful work while endlessly recycling 6. William Thomson, “On the Dynamical Theory of Heat” (1851), in Mathematical and Physical Papers, 1:179n.

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the same store of energy. Clausius and Thomson did not so much prove that such a wonderful device could not be built as take its impossibility for granted and proceed to trace out the consequences. The laws of thermodynamics, as formulated by Clausius and Thomson, are in effect very precise and general statements of the principle that there is no free lunch. Entropy, Dissipation, and Heat Death The formulation of the second law of thermodynamics was rooted in the analysis of heat engines, but its ramifications extended far more widely. When the law was applied to the processes of nature as well as the workings of machines, it pointed to a grim future in which the active energies of the universe must inevitably run down. The Scottish geologist James Hutton (1726–97), the father of uniformitarianism, had declared at the end of the eighteenth century that the surface of the earth reveals “no vestige of a beginning, no prospect of an end”; the processes of erosion, sedimentation, and mountain-building had, he said, been cycling along for unimaginable ages and would continue on into the indefinite future, wearing down the landscape only to build it up again. The developmental evolutionists of the nineteenth century went further, foreseeing an endless upward progression of living things toward perfection. To these happy prospects the second law said no, they could not be true. While it did not rule out local progress that might last millions of years, the second law decreed that in the end the sun and stars must all burn out, the earth must cool, and the entire universe must head toward eternal “heat death.” An important step in consolidating the new science of thermodynamics was the introduction of appropriate terminology. Although Thomson had occasionally used the word energy as early as 1849, it was another Scotsman, W. J. Macquorn Rankine (1820–72), who in the 1850s brought it into general use in place of mechanical effect and related expressions. An active engineer and the author of a widely used textbook on steam engines, Rankine also coined the term potential energy to distinguish energy that is stored, as in a compressed spring or a raised weight, from what he called “actual energy,” such as that of a moving body. Although some critics derided potential energy as little more than a name for something that had, at least temporarily, passed out of real existence, Thomson and Joule endorsed the term and it soon came into wide use. In the 1860s energy of motion came to be known as kinetic energy. The status of heat as a form of energy remained problematic. Although there was good reason to think that heat was the kinetic energy of molecules, the second law put strict limits on its convertibility into other forms of energy. Indeed, in the absence of a colder body into which some of the heat could flow,

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there was no way to convert any of the heat in a body into work or anything else, making it hard to apply to it the usual definition of energy as “capacity to do work.” Joule fell back on defining energy as anything that could be converted into an equivalent amount of heat. In practice, physicists simply became familiar enough with energy that most of them no longer felt a need to define it in terms of anything they regarded as more fundamental. As Clausius cast the laws of thermodynamics into mathematical form in the early 1850s, he identified an important new quantity to which he initially gave a rather awkward name: “the equivalence value of a transformation.” In 1865 he renamed it entropy, from the Greek word for “turn” or “transform.” Consider a quantity of heat passing at a constant temperature from one body to another, as from the heat reservoir to the cylinder of a Carnot engine. Clausius defined the change in the entropy (S) of a body as the amount of heat (Q) passing into it divided by the temperature T (measured on the absolute, or Kelvin, scale): S  Q /T. When a quantity of heat enters or leaves a hot body, the change in the entropy of the body is relatively small; when the same quantity of heat enters or leaves a cold body, the change in its entropy is relatively large, simply because the same quantity of heat is being divided by a smaller temperature. For a reversible Carnot engine, the change in entropy sums to zero over a full cycle; a little less heat leaves the cylinder at the lower temperature than entered it at the higher temperature, and the difference in quantities of heat, which the engine converts into work, is just enough to make the changes in entropy at the two temperatures cancel out. In any other process, the net entropy increases; in particular, when heat passes directly from a hot body (at temperature TH) to a colder one (at temperature TC ), the cold body always gains more entropy (Q /TC ) than the hot one loses (Q/TH ), simply because TH is greater than TC . As heat flows from hot to cold and the entropy of a system increases, differences of temperature even out, and less and less heat energy is available to be converted into useful work. The system moves toward a state of lukewarm equilibrium in which heat can no longer flow and activity comes to a stop. As Clausius put it in his most concise and striking formulation of the laws of thermodynamics: (1) the energy of the universe is constant; (2) the entropy of the universe tends toward a maximum. The cosmic consequences of the inexorable increase in entropy were recognized well before the word itself was coined. In 1852 Thomson published a short paper with an ominous title: “On a Universal Tendency in Nature to the Dissipation of Mechanical Energy.” Whenever heat flows from a hot body to a colder one by any means except through a perfect reversible engine—and

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such perfection can never be achieved in any real engine—there is, he said, an “absolute waste of mechanical energy available to man.” No energy is actually destroyed, but friction and conduction continually dissipate available energy into lukewarm heat, from which less and less useful work can be extracted. This fact obligates us, Thomson believed, to strive at all times to minimize waste and dissipation, while recognizing that we can never eliminate them altogether. It also implies that the world as a whole is running down and so must have had a beginning and must have an end. As Thomson put it, “Within a finite period of time past, the earth must have been, and within a finite period of time to come the earth must again be, unfit for the habitation of man as at present constituted.”⁷ Thomson’s conclusion fit well with his larger view of history, which was deeply Christian and thus inescapably linear: time, he believed, runs in one direction from the creation of the world to the incarnation of Christ and on to the final judgment. This conflicted directly with the cyclic, or uniformitarian, view espoused by the geologists James Hutton and Charles Lyell (1797– 1875); indeed, when numbers were put to it, Thomson’s position conflicted even with the milder form of uniformitarianism that did not regard the earth as truly eternal but held that it had remained essentially unchanged for many billions of years. As Thomson pointed out, since the earth is warmer than the surrounding space, it must continually radiate heat in all directions, and measurements of the temperature of rocks in deep mines gave a rough indication of the rate at which heat flows up from the interior to replace that lost into space. In an 1865 paper, “The ‘Doctrine of Uniformity’ in Geology Briefly Refuted,” Thomson took only a few lines to show that the earth could not have been in its present state for as long as, say, 20 billion years, since at current rates of flow enough heat would have passed outward in that time to have melted the entire globe many times over. Thomson went on to argue that the earth can have been cool enough to have a solid crust for no more than a few hundred million years, a figure he later shaved down to less than 30 million years. Assuming that the sun derives its energy from gravitational contraction, he also concluded that it can have been shining at its present rate for no more than about 20 million years and can go on doing so for only a few million more. Presenting his conclusions as straightforward consequences of the sec7. William Thomson, “On a Universal Tendency in Nature to the Dissipation of Mechanical Energy” (1852), in Mathematical and Physical Papers, 1:514.

Energy and Entropy

Artist’s Conception of Death by Cold In 1894, the French astronomer and popular writer Camille Flammarion published a science fiction novel, La Fin Du Monde, in which he imagined different ways in which the world might end. One, pictured here, appeared to be guaranteed by the second

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law of thermodynamics: the gradual death of the sun would eventually plunge the earth into eternal cold and darkness.  Camille Flammarion, Omega: The Last

Days of the World (New York: Cosmopolitan, 1894), p. 105; originally published as La Fin Du Monde (Paris: Flammarion, 1894).

ond law of thermodynamics, Thomson declared in 1862 that “the inhabitants of the earth cannot continue to enjoy the heat and light essential for their life, for many million years longer, unless sources now unknown to us are prepared in the great storehouse of nature.”⁸ Thomson’s target was clear: Charles Darwin (1809–82) and his theory of evolution. Natural selection was clearly a very slow process, and Darwin had followed Lyell in assuming the earth to be immensely old. In his Origin of Species (1859), Darwin had ventured an estimate of 300 million years just for the visible erosion of the Weald, a valley in southern England, while suggest8. William Thomson, “On the Age of the Sun’s Heat” (1862), in Popular Lectures and Addresses, 3 vols. (London: Macmillan, 1891–94), 1:375.

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ing that other geological features had been completely worn away, and new ones had risen on their ruins, unimaginably long before. Thomson objected strongly to Darwin’s suggestion that living things are the products of a blind process of natural selection rather than divine design, and he saw the age of the earth as the Darwinians’ weak point. If he could show the earth to be only a few tens of millions of years old, he thought it would be hard for anyone to believe that the slow process of natural selection had had enough time to produce all of the complex forms of life, including humans, we see in the world today. The superior prestige of Thomson’s seemingly solid physics overawed most geologists and biologists of the day, and though Darwin himself felt sure there must be some flaw in Thomson’s reasoning, most other evolutionists accepted the shorter time scale and simply said, somewhat implausibly, that evolution must have proceeded much more quickly than they had first thought. Thomson’s short limit on the age of the earth was a major problem for Darwinians in the last decades of the nineteenth century and contributed to a growing sense at the time that the theory of evolution by natural selection was in serious trouble. A few physicists and geologists managed to pick holes in Thomson’s assumptions and stretch the age of the earth to perhaps a few hundred million years, but it was only after the discovery of radioactivity in 1896 that the cooling rate argument really fell apart. As it became clear that disintegrating atoms of radium, uranium, and other elements are continually releasing vast amounts of energy within the earth, and as techniques were developed to use rates of radioactive decay to determine the age of rocks, Thomson (now the elderly and very distinguished Lord Kelvin) saw his claims decisively refuted. It became evident that the earth is several billion years old, and astrophysicists later determined that the sun, powered by nuclear reactions in its core, has been pouring out light and heat for billions of years and is likely to continue on for billions more. Ernest Rutherford (1871–1937), a pioneer in the study of radioactivity, later told how in 1904 he spotted Lord Kelvin in the audience at one of his public lectures. He realized, he said, “that I was in for trouble at the last part of my speech dealing with the age of the earth, where my views conflicted with his. 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

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upon me.”⁹ Kelvin himself never accepted evolution by natural selection, but after Rutherford’s work, objections to it based on a lack of sufficient time faded away. Even the discovery of radioactivity only stretched the cosmic time scale, however; it did not defeat the second law of thermodynamics or erase the chilling prospect of universal decline. Even if powered by nuclear reactions, the sun and stars must eventually exhaust their fuel and fade to darkness. Until then, living things, including humans, could continue to harness part of the enormous flow of energy from the hot sun to the cooler earth (and the portion of that flow from previous ages that had been captured by plants and locked up in deposits of coal and oil), but this must finally run out and the world settle into lukewarm stasis. As Clausius had put it in 1867, as heat flows from hot to cold and entropy rises toward a maximum, “the occasions of further changes diminish; and supposing this condition to be at last completely attained, no further change could evermore take place, and the universe would be in a state of unchanging death.”¹⁰ Thomson cheerily said this should not lead to “dispiriting views” about the fate of humanity, since “an overruling creative power” would no doubt act to avert eternal heat death, but short of such divine intervention, there seemed to be no escape from the dire consequences of the second law of thermodynamics.¹¹ All of this raised a basic question, however: what really lay behind the second law? Why was entropy seemingly fated always to increase? As formulated by Clausius and Thomson, the second law was simply a generalization from experience; it asserted that heat never flows on its own from a cold body to a hotter one but did not explain in terms of any underlying theory of heat why this must be so. Joule and others had provided good grounds for thinking that heat was the invisible motion of the smallest parts of matter, but this did not in itself account for the second law or shed much light on why heat flows in the way it does. The move from formulating the empirical laws of energy and entropy to working out the detailed mechanisms behind them required the development of a new branch of physics: kinetic theory. 9. A. S. Eve, Rutherford (Cambridge: Cambridge University Press, 1939), p. 107. 10. Rudolf Clausius, quoted in S. G. Brush, The Temperature of History: Phases of Science and Culture in the Nineteenth Century (New York: B. Franklin, 1978), p. 61. 11. William Thomson, “On the Age of the Sun’s Heat” (1862), in Popular Lectures and Addresses, 1:357.

3 The Kinetic Theory

Chaos and Order

The formulation of the laws of thermodynamics gave new urgency to an old question: What is heat? The caloric theory was already in sharp decline by the late 1840s, and the idea that heat is a manifestation of invisible molecular motions was on the rise. No one was yet sure just what form such motions might take, however, nor how they might account for known thermal phenomena or such things as the properties of gases. Why, if heat is simply the motion of molecules, does it always tend to flow from hot to cold, and why are there such strict limits on the amount that can be converted into other forms of energy? What, at a molecular level, lies behind the second law of thermodynamics and the seemingly inexorable running down of the world into a sea of lukewarm heat? The known laws of thermodynamics were essentially just generalizations from experience; by penetrating to the underlying causal mechanisms, physicists hoped to gain deeper insights into what heat really is and why it behaves as it does. Some even hoped that if they could somehow grasp the detailed mechanism of heat, they might be able to find a way around the grim dictates of the second law and so elude the prospect of universal heat death that otherwise awaits us. The question of the nature of heat prompted some of the most searching physical inquiries of the second half of the nineteenth century, culminating in the formulation of the kinetic theory of gases. The success of the kinetic theory helped in turn to resurrect one of the oldest and most ambitious programs of modern science: the effort to explain everything in the physical world in purely mechanical terms, as consequences simply of the motion of matter. After some earlier false starts, the kinetic theory of gases made rapid strides in the 1850s and 1860s. Its fundamental hypothesis was simple: a gas, the theory proposed, consists of an enormous number of tiny particles flying around at random, their impacts exerting pressure on any surrounding surfaces and their motions constituting heat. Although the theory turned out to contain subtleties that would occupy physicists for decades to come, its main outlines

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were worked out fairly quickly, chiefly by Rudolf Clausius and James Clerk Maxwell. By the late 1860s they had shown that a simple kinetic model could account for the main phenomena of heat and most of the known properties of gases and had pointed the way toward more detailed investigations later made by Ludwig Boltzmann and others. These theoretical investigations, and the experiments that went with them, bolstered the growing belief in the physical reality of atoms. They also cast the second law of thermodynamics into a new and revealing light, in which the law appeared as a matter of statistical probability rather than as an absolute physical truth. Perhaps most tellingly of all, the kinetic theory of gases showed that, when examined closely, even seemingly solid and precise laws of nature might turn out to be founded not on the workings of a neat and orderly underlying clockwork, but on molecular chaos. The Gas Laws and Early Kinetic Theories Scientific study of the physical properties of air and gases got its start in the seventeenth century. Experiments with barometers and air pumps established that air can be compressed and rarefied, and pointed toward a mathematical relationship between pressure and volume. In 1662 the English natural philosopher Robert Boyle (1627–91) published results that were later codified as “Boyle’s law”: as the pressure on a quantity of air is increased, its volume decreases proportionally, so that if, for instance, the pressure is doubled, the volume is cut in half. Expressed algebraically, the law states that P • V  a constant. Boyle hedged his initial statement with qualifications, presenting it not as an exact and universal law but as a tentative and limited empirical generalization. The law nonetheless fit the actual behavior of gases very well and later proved of great practical value, not least to James Watt in his work on the steam engine. Strictly speaking, Boyle’s law holds only for constant temperatures, for it had long been known that air expands when heated and contracts when cooled. Indeed, some of the first thermometers devised in the seventeenth century used the expansion and contraction of a column of air to indicate changes in temperature, though these soon gave way to the more convenient and now more familiar glass tube filled with mercury. In 1802 a young Laplacian chemist, Joseph Gay-Lussac (1778–1850), carefully measured the thermal expansion of gases and showed that the pressure of a gas held at a constant volume increases in proportion to the rise in temperature. Combining Boyle’s law with Gay-Lussac’s yielded P • V  r (T  C ), where r is a constant, T is the temperature, and C is a constant that depends on the scale used, about 273° for the Celsius scale or 460° on the Fahrenheit scale. If Gay-Lussac’s law held true all

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the way down, one would thus expect the pressure of a gas to fall to zero at around 273°C or 460°F, the “absolute zero” of the later Kelvin scale. Gay-Lussac emphasized the practical value of his law for measuring the heat released or absorbed in chemical reactions, gauging variations in the density of the atmosphere, and analyzing the workings of steam engines. Like other Laplacians, he viewed heat phenomena through the lens of the caloric theory and so saw the thermal expansion of gases as a very simple process: each of the stationary particles of a gas is surrounded, the theory said, by a repulsive cushion of caloric, and as more caloric is added, these cushions grow fatter, pushing the particles of gas farther apart. Conversely, when the gas is compressed, excess caloric is almost literally squeezed out and flows away as heat. The caloric theory could explain a wide range of phenomena with considerable precision, and it dominated most thinking about heat and gases in the late eighteenth and early nineteenth centuries. The alternative view of heat as a form of motion never entirely disappeared, however. Francis Bacon and John Locke had been among its advocates in the seventeenth century, and it remained a respectable minority view even when the caloric theory was at its height during the Laplacian decades of the late eighteenth and early nineteenth centuries. The motional theory was, however, generally regarded as poorly suited to mathematical treatment and as too speculative to be accepted as true. The kinetic theory of gases was initially pursued independently of theories of heat, most notably by the Swiss mathematician Daniel Bernoulli (1700– 1782). In 1738, Bernoulli suggested that a volume of air could be pictured as a box filled with tiny particles bouncing around at random. He easily derived Boyle’s law, showing that if we reduce the volume of the box, the pressure will increase proportionally, simply because, with a shorter distance to travel, the particles will strike the walls more often. He also showed that the pressure would increase with temperature and would be proportional to the mass of the particles and the square of their velocity. To later eyes, this might suggest a connection between vis viva and heat, but Bernoulli did not pursue the point. Bernoulli’s theory attracted little support in the eighteenth century, perhaps because scientific tastes were shifting away from devising hypothetical mechanisms and toward formulating descriptive mathematical laws. The discovery at mid-century that “latent heat” is apparently stored and released during changes of phase, as when steam condenses or water vaporizes, also seemed difficult to explain on the kinetic theory, while it fit well with the image of caloric being stored by molecules. The kinetic theory of gases began its halting reemergence in the early de-

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cades of the nineteenth century, initially through the efforts of John Herapath (1790–1868), an English mathematics teacher. Self-taught, pugnacious, and eccentric, Herapath knew little of earlier work on kinetic theory, but in the 1810s he independently rederived Bernoulli’s results on the relationship between pressure and volume in a gas consisting of hard particles in random motion. He went beyond Bernoulli by explicitly identifying the motion of these particles as heat and deriving various consequences for the thermal properties of gases, but the value of this work was undercut by Herapath’s erroneous definition of temperature as proportional to the speed of the particles rather than its square. In 1820 he sent a long account of his theory to the Royal Society of London, which rejected it as too speculative. Although he managed to get the paper published elsewhere, Herapath long nursed a grudge against the society, whose rejection he rightly believed had damaged his scientific reputation. After becoming editor of a railway trade journal in the 1830s, he used its pages to air his grievances and disseminate more of his theoretical results. By then, however, he was widely regarded as a crank, and his massive Mathematical Physics, published in 1847, attracted little favorable scientific notice. James Joule, himself something of a scientific outsider in those days, was one of the few to take it up, in 1848 publishing a calculation of the speed of a gas molecule (about 6,225 feet per second for hydrogen at 60°F) that drew heavily on Herapath’s ideas. The next important proponent of the kinetic theory had even worse luck than Herapath. J. J. Waterston (1811–83) was a Scottish engineer and mathematics teacher; from 1839 to 1857 he taught at an East India Company school in Bombay. There, he not only independently retraced most of Bernoulli and Herapath’s steps but carried kinetic theory substantially further, particularly by linking temperature to the square of the velocity of the particles and deriving many of the known thermal properties of gases. Waterston’s results first appeared as an appendix to a book on the workings of the central nervous system that he published anonymously in 1843; not surprisingly, this attracted no notice from physicists. Two years later, he sent a long paper on kinetic theory to the Royal Society, but the mathematicians who examined it recommended against publication, one declaring it to be “nothing but nonsense, unfit even for reading before the Society.”¹ Under the rules then in force, rejected papers were relegated to the archives of the society, and Waterston, who had not retained a full copy of his paper, was unable even to get it returned. 1. Stephen G. Brush, The Kind of Motion We Call Heat, 2 vols. (Amsterdam: North Holland, 1976), 1:145.

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Kinetic Model of a Box of Air As initially conceived by Daniel Bernoulli and others in the eighteenth century, the kinetic theory pictured the molecules in a box of air bouncing around at random, their collisions with the walls being felt as

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the pressure of the air. If we were to reduce the volume of the box, the molecules would have a shorter distance to go and so would hit the walls more often, increasing the pressure proportionately. The theory could thus readily account for Boyle’s law and other simple gas laws.

Such treatment left Waterston understandably bitter, and though he published several shorter accounts of his ideas over the next few years, he eventually turned his attention to other issues. There is reason to think that some of Waterston’s ideas seeped into the thinking of other scientists, but his main work on kinetic theory remained almost wholly unknown until 1891, when the physicist Lord Rayleigh, then serving as secretary of the Royal Society, came across the rejected 1845 paper in the archives, recognized its merit, and ordered it published in the Philosophical Transactions of the society. The scientific world finally recognized that Waterston had been more than a decade ahead of subsequent work on the kinetic theory of gases. This acclaim came too late for Waterston himself, however; he had died in 1883, apparently washed off a breakwater while walking near his home in Scotland. The Kinetic Theory of Gases: Clausius and Maxwell Herapath and Waterston aside, modern kinetic theory got its lasting start in the late 1850s at the hands of Rudolf Clausius and James Clerk Maxwell. Over the next decade, they showed that a simple model of particles flying around at random not only could account for most of the known properties of heat and gases but also led to new results that could be confirmed experimentally. Clausius and Maxwell also took the first steps toward treating molecular motions

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statistically, showing that many of the measurable properties of gases result from averaging together the varying attributes of enormous numbers of individual particles. By the mid-1860s the kinetic theory of gases no longer lay at the speculative fringe of science but had become a respected and rapidly developing area of research. In an ironic twist, the development of modern kinetic theory was sparked not by Herapath and Waterston’s impressive writings but by a much less substantial paper by a German chemist, August Krönig, that appeared in 1856. Like Bernoulli, Krönig began by deriving Boyle’s law from a simple model of particles in motion, though he garbled the numerical factors so badly that he ended up claiming that the pressure a quantity of air exerts on the ground amounts to only half its weight. He also derived Gay-Lussac’s law and several other results, but he seems to have had a poor grasp of his own theory, and there is reason to think that he may have drawn much of it from a muddled reading of a paper of Waterston’s he had come across in his role as editor of a German journal that published accounts of foreign scientific publications. Flawed as it was, Krönig’s paper appeared at a time when physicists were increasingly convinced that heat must be a form of motion and were casting around for ideas about what form that motion might take. His paper helped bring kinetic theory back into scientific discussion; most importantly, it prompted Clausius to publish ideas he had been pursuing privately for years. Clausius said later that even before he published his first paper on thermodynamics in 1850, he believed that heat was a form of motion and had begun to explore the workings of kinetic models of gases. He kept these early investigations to himself, in part because he did not think they were yet conclusive enough to publish, and in part because he wanted to keep his strict reasoning about the general principles of thermodynamics separate from any speculative hypotheses about the unseen motions of molecules. Krönig’s paper finally pushed him into print, and early in 1857 Clausius brought out a paper bearing the intriguing title “The Kind of Motion We Call Heat.” As this phrase suggests, and as one might expect from a founder of thermodynamics, Clausius focused on what kinetic theory could say about heat phenomena and the thermal properties of gases. He corrected various of Krönig’s mathematical errors and emphasized that while the temperature and pressure of a gas arise from the linear motions of its molecules, their rotations and internal vibrations account for a significant part of their total kinetic energy and so of the total heat. By measuring how much the temperature of a quantity of gas rises when a given amount of heat is added to it at constant volume and then under constant pressure, we can deduce, Clausius said, that linear motion accounts for just

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under two-thirds of the kinetic energy of a typical gas molecule, the remainder being split between rotational and perhaps vibrational motions. Here, Clausius was treading on what would become a persistent problem for the kinetic theory of gases: as we will see, the theory predicted a value for the “ratio of specific heats” that differed significantly from that found by experiment. The discrepancy would not be fully resolved until the advent of quantum theory in the twentieth century. Clausius approached most problems in kinetic theory by trying to find the average value of a quantity and then treating all particles as if they shared that value. This greatly simplified the mathematics and allowed him to calculate such things as the speed of a typical molecule—which, by reasoning much like Joule’s, he found to range from about 470 meters per second (1550 feet per second) for an oxygen molecule at room temperature to about 1900 meters per second (6200 feet per second) for a much lighter hydrogen molecule. Clausius knew that the actual speed of any individual molecule might well be significantly more or less than this average value, but he put this fact to use only once, in his theory of evaporation. The molecules in a liquid jostle one another, he said, but unlike those in a gas, they generally lack the speed needed to break free and travel any appreciable distance on their own. Occasionally, however, a molecule near the surface of a liquid may chance to acquire just enough speed to overcome the attraction of its neighbors and fly off into space, carrying its kinetic energy with it and thus cooling the liquid by evaporation. Clausius explained latent heats of vaporization and condensation in a similar way and so answered what had been a nagging objection to the kinetic theory. When heat is added to a liquid near its boiling point, he said, the energy does not immediately raise the temperature but instead goes into overcoming the attractive forces between the molecules. As molecules fly off to form a vapor, part of their kinetic energy is stored, or becomes “latent,” as the potential energy of these attractive forces. This latent heat is recovered when the vapor condenses and the molecules “fall” back toward each other, converting the potential energy of their attractive forces into the kinetic energy, or heat, of the molecules in the liquid. Clausius’s paper was generally well received, but a critic soon raised a telling objection: why, if molecules in the air are traveling at hundreds of meters per second, does it take a minute or more for the odor from, say, an open bottle of ammonia to diffuse across a room? One would think the ammonia molecules would fly to every corner of the room in a fraction of a second. Clausius answered that before any molecule can go very far it will inevitably collide with another and ricochet off in a new direction. He introduced the

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concept of “mean free path,” the average distance a molecule travels between collisions, and though unable to put a firm number on it, he showed that it must be a tiny fraction of a millimeter. A molecule of ammonia will thus collide with a neighbor and completely change its direction billions of times each second; even banging around at hundreds of meters per second, it will thus take some time to make its way across a room. The next major step in the development of kinetic theory was taken by James Clerk Maxwell (1832–79), now widely regarded as the greatest physicist of the nineteenth century. His father was a Scottish landowner who dabbled in science, and his mother, who died when Maxwell was only eight, came from an intellectually distinguished Edinburgh family. Maxwell was educated first at Edinburgh and then at Cambridge; like William Thomson, later his good friend, he finished second on the Mathematical Tripos examination. He became known as a talented though sometimes sloppy mathematician and as the possessor of an extraordinary insight into physical processes. In 1859 Maxwell was a young professor at Aberdeen in northern Scotland when he read Clausius’s paper on the mean free path of molecules and decided to tackle the kinetic theory as what he called “an exercise in mechanics.”² He began by assuming gas molecules to be small, hard, perfectly elastic spheres— not because he thought they were likely really to be such simple “billiard balls,” acting on each other only by contact, but because the model was definite and he could readily investigate its consequences. He had no trouble showing, as others had before him, that a gas made up of such particles would obey Boyle’s and Gay-Lussac’s laws and that, as chemical evidence suggested, equal volumes of two different gases held at the same temperature and pressure would contain equal numbers of molecules. From viscosity measurements, he was able to estimate the mean free path of a molecule in air to be about 1⁄447,000 of an inch, or less than a ten-thousandth of a millimeter. Maxwell next took a step that put kinetic theory on the path it has followed ever since: abandoning all hope of tracking the paths of individual gas particles, he turned to statistical methods to characterize how they would behave in groups. In this he was influenced by recent work in the social sciences, particularly that of the Belgian astronomer-turned-sociologist Adolphe Quetelet (1796–1874). Drawing on techniques developed to average out errors in astronomical observations, Quetelet had devoted great efforts to delineating the characteristics of the “average man” as revealed by government statistics. 2. James Clerk Maxwell to G. G. Stokes, 30 May 1859, in P. M. Harman, ed., Scientific Letters and Papers of James Clerk Maxwell, 3 vols. (Cambridge: Cambridge University Press, 1990–2002), 1:610.

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The word statistics, in fact, comes from that for “state”; it originally referred only to the collection and tabulation of population and trade figures about a country, and only gradually came to be applied to the analysis of quantitative data of other kinds. Nineteenth-century statisticians emphasized that even when we do not have detailed information about individuals in a population, we can still make useful statements about averages. For large groups, such averages are often remarkably stable even when the causes of individual events are unknown and highly variable; as statisticians liked to point out, the number of letters posted without an address changes little from week to week, even though the reasons that someone might forget, in any particular case, to address a letter before mailing it are completely capricious. The orderly patterns that statisticians were able to extract from collections of random events—in particular, the “bell curve,” or normal distribution of values around a mean—gave Maxwell a powerful tool he could bring to bear on gas theory: many observable properties such as temperature and pressure are, he said, simply stable averages arising from chaotic underlying processes. Clausius had gone as far as to calculate the average values, such as the mean free path and the mean molecular speed, that result from random collisions. Maxwell went further, shifting the focus from the average to the deviations from it and working out how molecular velocities are distributed around the mean. As the particles in a box of gas collide with each other and with the surrounding walls, they change their speeds and directions in ways that, though strictly determined by Newton’s laws of motion, are effectively random, since they depend on slight and unknown differences in the initial positions and motions of the particles. By assuming the motions along each of the three directional axes to be completely random and independent, Maxwell was able in 1859 to derive the curve describing how the speeds of the particles in a gas will be distributed; essentially, he simply combined the normal bell curves for velocities along each of the axes. The overall shape of the curve was given by a general formula, but its steepness and the location of its peak depended on the temperature: the higher the temperature, and thus the higher the average speed of the particles, the further out the peak lay along the curve. Maxwell’s distribution curve clearly showed that the speeds of particles are spread on either side of the mean and that even a fairly cold gas contains some molecules that are moving faster than most of those in a gas at a higher temperature. This fact had some remarkable consequences, as we shall see. Maxwell’s first attempts to use his billiard ball model and speed distribution curve to analyze the diffusion of gases and the conduction of heat were

The Kinetic Theory

The Maxwell Distribution of Speeds in Gas In 1859, James Clerk Maxwell used statistical principles and the laws of probability to work out a formula that showed how, in a given volume of gas, the number of molecules traveling at a specified speed would

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vary with temperature. Here, we see the resulting curves for a low temperature, T1, and a higher temperature, T2. The spread of speeds for each temperature shows us that even a relatively cold gas must contain a significant number of molecules that are moving faster than some of the molecules in a hotter gas.

marred by several mathematical mistakes, as Clausius soon pointed out; at one point, for instance, Maxwell forgot to convert from hours to seconds when he was calculating rates of heat flow. Maxwell had better luck with viscosity, or gaseous friction, correctly showing that in a gas made up of billiard ball particles the viscosity would increase with the square root of the temperature (measured from absolute zero) and, surprisingly, would be independent of the density. That a very thin gas would produce as much frictional resistance as a dense one was, as Maxwell admitted, “certainly very unexpected,” but it followed in the theory from the way the longer mean free path of molecules at low density acted to spread the friction over more of the surrounding space. When Maxwell published his first paper on kinetic theory early in 1860, he thought it likely that experiments would contradict his predictions about viscosity and so prove the billiard ball model to be wrong. Indeed, he already knew that the model could not be quite right, since it required the kinetic energy of the molecules of most gases to be equally divided between linear and rotational motions and so led to a figure for the ratio of specific heats that did not fit measured values. Existing measurements said little about how the viscosity of air might vary with temperature and density, so Maxwell decided to do the experiments himself. In 1860 Maxwell lost his position at Aberdeen when the two colleges there

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were merged. He soon landed a new professorship at King’s College in London, where, as we will see in Chapter 5, he collaborated on an important series of experiments to determine the value of the ohm, the unit of electrical resistance. During this work, Maxwell noticed how air resistance slowly damped the oscillations of a swinging needle, and he realized that this could provide an accurate way to measure the viscosity of air: he could simply time the decaying swings of a set of discs twisting back and forth at the end of a long wire. In the mid-1860s, assisted by his wife, Katherine, and working mainly in the attic of their London home, Maxwell made the measurements and found that the viscosity of air increases directly with the temperature rather than with its square root, contradicting the first prediction of his billiard ball model. When he varied the density, however, he found that his second and more surprising prediction was brilliantly confirmed: dense air turned out to offer no more frictional resistance than did thin air. This result was hard to explain except on some version of the kinetic theory, and while Maxwell’s experiments made it clear that molecules could not be simple billiard ball particles, they greatly bolstered the case for accepting the broader kinetic theory. In 1866 Maxwell returned to kinetic theory in an important paper “On the Dynamical Theory of Gases.” Responding to Clausius’s earlier criticisms, he now tackled diffusion, heat conduction, and other phenomena with mathematical tools far more general and powerful than those he had used in 1859. As we shall see in later chapters, Maxwell followed a similar pattern in his work on electromagnetic theory: as he turned a problem over and over in his mind, he systematically moved back and forth between highly specific mechanical models, like his 1859 billiard ball model of a gas, and more general theories based on broad dynamical principles, as in his 1866 paper. He never gave up his goal of finding a complete mechanical explanation, but he continually strove to see how far he could go in formulating the general laws governing phenomena without invoking any detailed hypothesis. In his “Dynamical Theory of Gases,” Maxwell showed that almost any theory of how molecules might act on each other led to the viscosity of a gas being independent of its density. The observed direct dependence of viscosity on temperature, by contrast, followed only if one assumed that, instead of colliding like billiard balls, the molecules repel each other at very short distances with a force that falls off with the fifth power of the distance between them. (Clausius had already shown that molecules evidently exert a weak attractive force on each other over somewhat greater distances.) Maxwell left for later the question of exactly how, in mechanical terms, these short-range forces might be produced, but he showed that assuming an inverse fifth-power repulsion made complicated terms in the

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equations cancel each other out, greatly simplifying the mathematics and allowing viscosity and heat conduction results to be calculated exactly. In his 1866 paper, Maxwell also returned to the question of how molecular speeds are distributed. Instead of relying on his earlier and admittedly precarious assumption that speeds along different axes are completely independent, he now offered a more rigorous derivation based on analyzing the results of collisions. He arrived at the same distribution he had found before and showed that it would be stable, in that further collisions between the particles would not change the overall spread of their speeds. He also argued that no matter how the speeds of the particles in a box of gas are initially distributed— if those in one part are moving very quickly, for instance, while those in another are moving more slowly—they will, as they collide and exchange energy, move toward the standard distribution. Here was a hint of a kinetic explanation of the second law of thermodynamics: the tendency of heat to flow from hot to cold, and the resulting rise in entropy, might be simply a consequence of the way collisions tend to average out the differing speeds of particles, bringing them into the stable distribution that corresponds to a lukewarm intermediate temperature. Mix fast-moving particles with slow-moving ones and you get a lot of particles moving at middling speeds; it seemed simple enough. As Maxwell soon discovered, however, the real connection between the kinetic theory and the second law is far more subtle and complex than that. Maxwell’s Demon By the late 1860s, the kinetic theory of gases appeared to be on a solid footing. The gas laws and many of the known thermal and mechanical properties of gases had been shown to follow from a simple model of particles in random motion, and since the kinetic theory treated heat as simply the mechanical energy of these particles, the theory was clearly compatible with the first law of thermodynamics: no matter how the particles might collide with one another, their total energy would be conserved. Maxwell’s discussion of how any mix of molecular speeds would quickly converge toward his standard distribution suggested that the second law, too, might follow fairly readily from the kinetic model. As physicists looked more closely, however, they began to see problems. In Thomson’s formulation, the second law decrees that it is impossible to produce work by cooling a body below the temperature of the coldest body near it. If heat is simply molecular motion, however, there is no obvious reason why we should not be able to lay hold of each molecule and, in the process of bringing it to rest, convert all of its motion—that is, all of its heat energy—into

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useful work. If the kinetic theory is right, it seems we should be able to build an engine that would take in seawater, extract its heat, throw out ice cubes, and drive a ship across the ocean without consuming any fuel at all. Something about “the kind of motion we call heat” evidently makes this impossible—but what? How can the second law and the kinetic theory both be true? The first step toward solving this puzzle lay with one of the most intriguing characters in nineteenth-century physics, a tiny imaginary being who came to be known as “Maxwell’s demon.” To better understand the tensions between kinetic theory and the second law, we should first look more closely at how the kinetic theory explains the ordinary flow of heat. Picture a box of air divided by a partition into a cool side (A) and a hot side (B). If we were to connect the two sides through a heat engine we could, by a cycle of operations like Carnot’s, extract useful work from the flow of heat from B to A. Now imagine that instead of hooking up such an engine we simply poke a hole through the partition and let the air on the two sides mix together. Fast-moving molecules from B will pass into A and, as they collide, impart some of their kinetic energy to the slower molecules there; similarly, slow-moving molecules from A will pass into B and absorb energy as they are struck by the faster molecules on that side. Initially, the curves describing how molecular speeds are distributed on the two sides will have distinct peaks corresponding to their different temperatures, but as the mixing continues these will coalesce into a single curve with a peak about midway between the initial values. In other words, A will heat up and B will cool down until both sides end up at a single intermediate temperature. The total kinetic energy, or heat, of the air in the box will not change, but its entropy will increase, and the work we could have extracted by hooking up a heat engine will no longer be available to us. Heat conduction is, in thermodynamic terms, a one-way process; in kinetic theory, it results from a mixing that evidently cannot be undone. Or can it? The laws of impact are all time-reversible; any collision that can happen in one direction could just as well happen in the other. What if, after the mixing is complete, we were suddenly and accurately to reverse the motion of every particle in the box? (We can imagine placing innumerable tiny elastic barriers within the box so that all of the particles simultaneously hit them and bounce straight back.) Everything would now run backward: molecules from B that had lost energy through collisions would regain it, while those from A would lose all they had gained; heat would flow spontaneously from A back toward B, making it hotter and violating the second law. In short, the whole scene would look like a movie run in reverse. As William Thomson remarked in an 1874 article, “The Kinetic Theory of the Dissipation of Energy,” if we

The Kinetic Theory

Mixing Hot and Cold Air If we let a box of hot air mix with a box of cold air, we get a box of lukewarm air. According to the kinetic theory, this occurs because collisions between the molecules average out their speeds; the previously distinct curves showing how speeds are distributed in each box merge to form a single intermediate curve. No energy has been

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lost, but the opportunity to extract useful work from the flow of heat from hot to cold has slipped away; energy has been conserved, but entropy has increased. Moreover, this averaging out of temperatures is evidently a one-way process; left to itself, a box of lukewarm air will not spontaneously separate itself into a hot side and a cold side.

could somehow reverse all molecular motions, some very odd things would occur: “The bursting bubble of foam at the foot of a waterfall would reunite and descend into the water; the thermal motions would reconcentrate their energy, and throw the mass up the fall in drops re-forming into a close column of ascending water.”³ Life itself would run backwards: as Maxwell noted in a December 1870 letter to J. W. Strutt (later Lord Rayleigh), we would “see all [our] friends passing from the grave to the cradle till we ourselves become the reverse of born, whatever that is.”⁴ None of this would violate the laws of mechanics, but it would completely contradict the second law of thermodynamics, as well as our ordinary experience. Maxwell drily told Strutt that “the possibility of executing this experiment 3. William Thomson, "The Kinetic Theory of the Dissipation of Energy" (1874), in Thomson, Mathematical and Physical Papers, 6 vols. (Cambridge: Cambridge University Press, 1882– 1911), 5:11–12. 4. James Clerk Maxwell to J. W. Strutt, 6 Dec. 1870, in Harman, Scientific Letters and Papers of Maxwell, 2:582–83.

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is doubtful,” but added that much less than full reversal would suffice “to upset the 2nd law of Thermodynamics.” He then gave a very clear account of a thought experiment he had first proposed in a letter to his friend P. G. Tait three years before, and of the imaginary being Thomson was soon to dub “Maxwell’s demon.” Consider again our box of air. Once it has been thoroughly mixed, the temperature and thus the average speed of the molecules will be the same on both sides, though as we have seen, some will be moving faster than the average and some more slowly. Now equip the connecting hole with a door and a tiny doorkeeper—Maxwell never liked the term “demon,” for the creature need not possess any supernatural powers, just keen eyesight and quick reactions; nonetheless, the name stuck and we will use it here. When the demon sees a molecule approaching from side A that is going faster than the average, he lets it through into B; when he sees one going more slowly, he closes the door and keeps it on side A. Conversely, when he sees a slower-than-average molecule approaching from side B, he lets it through into A, while keeping any faster ones bottled up in B. With time, most of the faster molecules will end up in B and the slower ones in A. Without doing any work on the molecules, but simply by opening and closing a tiny door, the demon has been able to sort the lukewarm air in the box into a hot side and a cold side, reducing the entropy and violating the second law of thermodynamics. If we were now to let the heat reconcentrated in B flow through a heat engine into A, we could extract useful work; with help from our little doorkeeper, we could thus turn an ordinary box of air into a perpetual motion machine of the second kind. At about the same time Maxwell was inventing his demon, the Austrian physicist Josef Loschmidt (1821–95) was pursuing his own doubts about the universal validity of the second law. Instead of positing an intelligent doorkeeper, Loschmidt noted that if at any moment we knew the exact motion of every molecule in a box of air, we could predict all of their future motions and, by opening and closing a door at just the right times, could separate the faster molecules from the slower ones and so cause heat to flow from a cooler place to a hotter one. He concluded that there must be a loophole in the second law and that fears of universal heat death were thus misplaced. Though he could not say quite how to do it in practice, Loschmidt was convinced there must be a way to reverse the dissipation of energy, and that we would thus have “an inexhaustible supply of transformable heat at hand in all ages.”⁵ If we could 5. Josef Loschmidt, quoted in Edward Daub, “Maxwell’s Demon,” Studies in History and Philosophy of Science 1 (1970): 221.

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Maxwell’s Demon In 1867, James Clerk Maxwell introduced an imaginary “demon” as a way to illustrate the statistical nature of the second law of thermodynamics. Imagine a box of air divided into two parts, with a tiny “demon” standing guard at a small door between them. The demon, gifted with nothing more than keen vision and quick reaction times, is able to detect how fast individual molecules are going and can open and close the door as needed. Beginning with the entire box at a uniform lukewarm temperature, he sets out to separate the faster-moving “hot” molecules from the slower-moving “cold” ones. When he sees a fast-moving molecule heading toward the left, he opens the door and lets it through; when he sees a slower molecule heading that way, he keeps the door closed.

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Conversely, when he sees a slow-moving molecule heading toward the right, he lets it through, while closing the door on any faster molecules and keeping them confined to the left side. Over time, the demon is thus able to gather all of the faster “hot” molecules on the left side of the box and all of the slower “cold” ones on the right, simply by opening and closing the door at the right times. Such a separation of hot from cold without any net expenditure of work would violate the second law. Moreover, once the demon had separated the hot and cold portions of air for us, we could connect the two sides through a heat engine and proceed to extract useful work as the heat flowed on its own from the hot side to the cold side. We would thus, in thermodynamic terms, have been able to get something for nothing.

just figure out the trick, we need never again burn coal or any other fuel but could continually draw useful work from the ambient heat around us. Maxwell held out no such cheery hopes. He knew that we have no sharpeyed, quick-fingered demons to call upon and no prospect of gaining detailed knowledge of the motions of all of the molecules in even a small box of gas. His aim was not to evade the second law but to shed light on its true meaning.

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His demon argument showed, he believed, that the second law is fundamentally statistical and reflects not so much the intrinsic nature of the physical world as the limits on our knowledge of molecular motions. The second law would have no meaning for a being who was unable to harness any of the energies of the world around it, Maxwell said, nor would it apply to one who, like his demon, “could trace the motion of every molecule and seize it at the right moment.” The second law is, in a sense, a very human law, appropriate to our middling place in the scale of things: “It is only to a being in the intermediate stage,” Maxwell said, “who can lay hold of some forms of energy while others elude his grasp, that energy appears to be passing inevitably from the available to the dissipated state.”⁶ It is only for us that heat appears as a distinct form of dissipated energy, into which all others are continually and irreversibly slipping. Boltzmann, Gibbs, and Statistical Mechanics Although Maxwell had made a persuasive case for regarding the second law as ultimately statistical rather than absolute, he left the detailed proof of this claim to others. Ludwig Boltzmann and later J. Willard Gibbs were among those who took up what proved to be the challenging task of showing exactly how and why molecular motions lead to increases in entropy. Between the 1870s and the turn of the century, they developed what came to be known as statistical mechanics, a sophisticated set of mathematical techniques that greatly illuminated the molecular foundations of thermodynamics and the relationship between disorder and entropy. Along the way they encountered controversies over not just the validity of kinetic theory, but the reality of atoms themselves. Ludwig Boltzmann (1844–1906) was born and educated in Vienna and spent most of his career teaching at universities there and in Graz, Austria. High-strung and emotionally volatile, he would probably now be regarded as manic depressive or bipolar. He attempted suicide more than once and eventually hanged himself when he was 62. Before his bouts of depression became too debilitating, however, he led an active career as a teacher, experimenter, and theorist. He worked in many areas of physics, including optics and electromagnetism, but following the lead of his friend and teacher Josef Loschmidt, he devoted his greatest efforts to kinetic theory and related areas of molecular science. 6. James Clerk Maxwell, “Diffusion” (1877), in W. D. Niven, ed., Scientific Papers of James Clerk Maxwell, 2 vols. (Cambridge: Cambridge University Press, 1890), 2:646.

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Boltzmann’s first significant work, published when he was just 22, was an attempt to derive the second law of thermodynamics directly from the laws of mechanics, as Helmholtz had done for the first law nearly 20 years before. Although he brought out some intriguing mechanical analogies to entropy in systems that run in repetitive cycles, like orbiting planets or swinging pendulums, such cases were not central to thermodynamics. The real interest in thermodynamics lay in irreversible processes, particularly the flow of heat from hot to cold, and Boltzmann gradually came to see that explaining such changes would require something beyond just the laws of mechanics. Although he never met or even corresponded with Maxwell, Boltzmann greatly admired the Scottish physicist’s writings on kinetic theory. In 1868, he generalized Maxwell’s formula for molecular velocities to take into account external forces such as gravitation and so was led to what physicists still call the “Maxwell-Boltzmann distribution.” Four years later, he followed this achievement with a paper in which he fleshed out Maxwell’s originally rather sketchy argument that the distribution formula represented an equilibrium toward which any other state of molecular motion would evolve over time. Boltzmann defined a new quantity, later known as H, that gave a measure of how far a given set of speeds deviated from the Maxwell-Boltzmann distribution; he then showed that as particles collide and exchange energy, the value of H will fall until, at zero, the particles reach their stable distribution. In fact, Boltzmann argued, H is just another name for the entropy, S (with a change of sign, so that H  S), and a falling value of H represents the flow of heat toward thermal equilibrium. By combining mechanics with statistics, he had at last succeeded in deriving the second law from more fundamental principles. Boltzmann’s “H–theorem” of 1872 is now recognized as one of the great achievements of kinetic theory. Boltzmann initially believed his theorem proved that H must always decrease, just as entropy always increases. Loschmidt, however, raised a telling objection, essentially the one Maxwell and Thomson had raised earlier by invoking their imaginary demon. If we were suddenly to reverse the velocities of every particle in a box of air, Loschmidt said, would not H then begin to increase and entropy to decrease? How could Boltzmann claim that every possible state of molecular motion must evolve toward the Maxwell-Boltzmann distribution, when here was a case that clearly ran in exactly the opposite direction? Boltzmann conceded Loschmidt’s point, but insisted that such states of increasing H are extremely unlikely. Consider a deck of cards, initially neatly stacked from ace of spades to two of clubs. As we shuffle them together, the cards become less ordered until after a few shuffles their sequence is, to all ap-

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pearances, completely random and further shuffling has no evident effect. This state of equilibrium corresponds to H falling to zero and the entropy rising to a maximum. If we keep shuffling, however, the cards may, simply by chance, fall back into their original order. It could happen—but don’t bet on it. The likelihood of the cards spontaneously falling into any particular order can be calculated: for a deck of 52 cards, the probability that they will line up on their own from highest to lowest is about one in 8  1067. (For comparison, the universe is only about 4  1017 seconds old.) Similarly, as the particles in a box of air randomly bounce around, all of the faster ones might, simply by chance, end up on one side and all of the slower ones on the other. That is, if the kinetic theory is true, a lukewarm box of air might spontaneously separate into a hot side and a cold side, with no help from Maxwell’s demon. This would clearly violate the second law of thermodynamics, but it would not violate any of the laws of mechanics or of probability. In principle it could happen, but again, don’t bet on it. Given the enormous number of particles involved (as Loschmidt himself had been among the first to show, a single cubic centimeter of air contains about 1019 molecules), the likelihood of such a spontaneous separation actually occurring is, as Boltzmann showed, vanishingly small. In an 1877 response to Loschmidt, Boltzmann explicitly cast his argument in terms of molecular order and chaos. We can, he said, treat the problem simply as one of parceling out a large number of particles over an array of possible energy states. This was the key step toward formulating what became known as statistical mechanics, and it had the great advantage of freeing Boltzmann’s results from any dependence on the unknown details of how molecules interact. By simply counting up the different ways the particles could be distributed across the array of possible states, he could calculate the probability that any particular case would occur. Consider again a deck of cards. Of the 8  1067 different sequences into which the 52 cards can fall, the overwhelming majority will show no evident pattern or order. Since each individual sequence is equally likely to occur, any particular shuffle is thus almost certain to produce a sequence that appears completely jumbled. Similarly, the most probable distribution of molecular speeds in a box of air is the one corresponding to the largest number of distinct ways the total energy can be divided among the particles. This, Boltzmann showed, is simply the familiar Maxwell-Boltzmann distribution. Moreover, he showed, the entropy of any given state of the system is proportional to the number of different ways the energy can be parceled out to produce that state (or more precisely, to the logarithm of that number). Expressed mathematically, S  k • logW, where S is the entropy, W is the probability of the corresponding distribution, and k is what is now known as Boltz-

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mann’s constant. With its striking connection between entropy and probability, this formula encapsulated Boltzmann’s greatest contribution to physics. Appropriately, it now stands inscribed on his tomb in Vienna. With his entropy formula, Boltzmann had seemingly nailed down a proof that the second law of thermodynamics is ultimately statistical rather than absolute. His struggles were not over, however. In the 1880s and 1890s several chemists and physicists, led by Wilhelm Ostwald (1853–1932) and Ernst Mach (1838–1916), objected that Boltzmann had demoted the second law to a second-class status. The second law states that, left to itself, heat always flows from hot to cold and entropy always tends to increase. Now Boltzmann was claiming, on the basis of an admittedly hypothetical theory about unseen molecules, that heat might occasionally flow from cold to hot and entropy might sometimes spontaneously decrease. The second law had been empirically confirmed innumerable times; in a sense, it was reconfirmed every time a steam engine did its work. Boltzmann’s supposed violations of the law, by contrast, had never once been observed. (In fairness, Boltzmann’s critics had to admit that on his theory, such violations would be so unlikely that one would not expect ever to observe them—though this raised the question of what weight one should give to such a seemingly vacuous prediction.) If the kinetic theory conflicted with the absolute and universal validity of the second law, Ostwald and Mach said, so much the worse for the kinetic theory and the whole underlying claim that the world is made up of discrete atoms. Boltzmann’s entire theoretical structure was, they said, nothing more than a house of cards founded on empty speculations. Boltzmann found these criticisms exasperating and beside the point. He had answers for most of the objections raised against kinetic theory, but as the years wore on he felt increasingly embattled. The first volume of his Lectures on Gas Theory appeared in 1896; by the time the second volume was ready two years later, the attacks had, he said, greatly increased, and he saw himself as “only an individual struggling weakly against the stream of time.” Nonetheless, he resolved to lay out his theory as clearly and fully as he could, so that when in some future era “the theory of gases is again revived, not too much will have to be rediscovered.”⁷ Boltzmann no doubt took the attacks on kinetic theory too much to heart; its opponents were never all that numerous, though Mach and Ostwald were for a time influential in Austria and Germany. What role, if any, the fight over kinetic theory and the reality of atoms played in 7. Ludwig Boltzmann, Lectures on Gas Theory (1896–98), trans. Stephen G. Brush (Berkeley: University of California Press, 1964), p. 216.

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precipitating Boltzmann’s fatal depression is still debated. The irony is that by the time of his death in 1906, final victory was already in view: statistical mechanics had begun to score a series of triumphs, experimental evidence in favor of kinetic theory was accumulating rapidly, and the case for believing in the reality of atoms was becoming unassailable. The chief advance in statistical mechanics came from an unexpected quarter. J. Willard Gibbs (1839–1903) was a professor at Yale; trained initially as an engineer, he had long been the most notable, and almost the only, theoretical physicist in America. He was best known for his work in pure thermodynamics, particularly a long paper, “On the Equilibrium of Heterogeneous Substances” (1876–78), in which he had shown how the laws of energy and entropy could be applied to a wide range of processes involving chemical reactions and phase changes. Gibbs wrote in an austere style, eschewing speculative hypotheses and founding his reasoning as much as possible on ascertainable facts. This gave his work great power and generality, and his writings later provided much of the theoretical foundation for the emerging field of physical chemistry as well as for many branches of chemical engineering. Gibbs’s approach differed widely from Maxwell and Boltzmann’s frequent reliance on hypothetical mechanisms, and it is not surprising that Ostwald, who translated Gibbs’s writings into German, cited him as an opponent of attempts to reduce thermodynamics to a theory of molecular motions. By the 1890s, however, Gibbs was already hard at work doing just that. His landmark Elementary Principles in Statistical Mechanics appeared in 1902. Gibbs’s book was “elementary” only in the sense of being fundamental; it was anything but easy reading. Building on Boltzmann’s work, Gibbs focused on the statistics of what he called “ensembles,” enormous collections of mechanical systems that differ only in the positions and velocities of their component particles. He then worked out the relative probabilities of different configurations within an ensemble and showed how such configurations and their probabilities could be correlated with temperature, entropy, and other macroscopic properties. Gibbs’s derivation of the entropy law was more general and less open to objection on mathematical grounds than Boltzmann’s had been, and his methods gradually came to be recognized as definitive. In 1905 Albert Einstein (1879–1955), then an obscure young patent examiner in Switzerland, worked out his own form of statistical mechanics and used it to explain the “Brownian motion” seen when pollen grains and other small particles immersed in liquids are viewed under a microscope. Einstein showed that this jittery motion results from random fluctuations in the number of molecules striking different sides of the particles; it is, in a sense, molecular

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chaos made visible. Einstein’s theory led to quantitative predictions that the French experimentalist Jean Perrin (1870–1942) was soon able to confirm with great precision. Coming on top of evidence from the study of radioactivity and related phenomena, Perrin’s measurements clinched the case for the real existence of atoms. Although the obstinate Ernst Mach went to his grave still declaring atoms to be no more than convenient fictions, by 1910 Ostwald and most of Boltzmann’s other old opponents had accepted both the reality of atoms and the validity of the kinetic theory. Heat, they belatedly agreed, really was just the invisible motion of molecules. The second law of thermodynamics started as a rule governing the operation of steam engines and other machines that harnessed “the motive power of fire.” From Carnot, it passed to Clausius and Thomson, who turned it into a general law about the flow of heat and the limitations on its conversion into work. Maxwell and Boltzmann then transformed this universal law of nature into a theorem in molecular probability, having the same sort of truth as the statement that you will never be able to flip “heads” a million times in a row. The development of kinetic theory was not driven by overtly technological concerns; no one tried to find the mean free path of a molecule or the shape of the Maxwell-Boltzmann distribution in an effort to improve the efficiency of steam engines or develop new industrial processes, though insights drawn from kinetic theory in fact later led to new methods for liquefying gases and separating chemical substances. The driving force behind the development of kinetic theory was simply the desire to understand physical phenomena and explain them in the simplest possible mechanical terms. Once set upon this task, Clausius, Maxwell, Boltzmann, and other scientists were relentless in its pursuit. That heat and the second law became the focus of scientists’ interest at all in the nineteenth century reflects, however, the broad technological context that had generated both the scientific problem and the means to solve it.

4 Electricity

Currents and Networks

Today, most of us are surrounded by and dependent on a whole array of electrical technologies: lights, air conditioners, telephones, elevators, computers, and the list goes on. A major power blackout is big news; the failure of our electrical communications networks would be even bigger news—if anyone still had a way to get the word out. The growth of these technologies, and of people’s dependence on them, dates from the middle decades of the nineteenth century; before about 1830, almost the only electrical devices on the market were lightning rods, a few medical implements, and various scientific toys and instruments. The development of electrical technologies, first for communications and later for power and light, was closely tied to the rise of electrical science, culminating in the formulation of Maxwellian field theory and the discovery of the electron. This was not a simple story of scientific discoveries leading to technological applications, however, nor did it exactly parallel the case of the steam engine and thermodynamics, in which the development of a new technology clearly preceded and stimulated the creation of a new branch of science. The links between electrical science and technology ran both ways in the nineteenth century; each fed off the other. The first electrical technology to have a broad social and economic impact was the telegraph, which first appeared in the late 1830s. Its origins were closely tied to earlier scientific discoveries; just as importantly, the subsequent development of electrical science was deeply shaped by the demands and opportunities presented by the growing web of telegraph wires and cables. New Currents Before the nineteenth century, electricity was a science of sparks and shocks. Most early electrical experiments were intended to display this mysterious power of nature in the most spectacular fashion possible or to bring out the strange subtleties of its action. It had been known since ancient times that a piece of amber, when rubbed, will attract bits of chaff; our word electric, in

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fact, comes from the Greek for “amber,” elektron. In the eighteenth century, experimenters found they could produce great quantities of electricity by rubbing a glass globe or plate and could convey its effects to a distance along damp threads, wires, or other conductors. They also found they could store a substantial charge of electricity in a “Leyden jar,” a simple glass jar partially covered inside and out with metal foil and fitted with a conducting rod running down to its inner surface. By connecting the rod to a frictional generator, an experimenter could, in effect, “pour” electricity into the jar; since the electricity could not pass through the glass, a charge built up on the inner metallic surface, while an equal and opposite charge accumulated on the outer surface. When the two surfaces were connected through a wire or other conductor—a human hand did nicely—the opposing charges abruptly recombined, producing a crackling jolt that, with a large jar, could be strong enough to knock a person down. Aside from such transient flows, eighteenth-century experimenters dealt with electricity only in its static form; they studied charges, not currents. They had long known that opposite charges attract each other, while like charges repel, but the exact law governing electrical forces remained unclear until the French engineer Charles Coulomb tackled the problem in 1785. As we saw in Chapter 1, Coulomb used a delicate torsion balance to show that the force one electric charge exerts on another falls off with the square of the distance between them, just as the attraction between masses does in Newton’s law of gravitation. Coulomb used a similar apparatus to show that the force between magnetic poles also follows an inverse square law, but he did not believe this indicated any real connection between electricity and magnetism; they were, he said, wholly separate subtle fluids that simply happened to obey the same force law. Coulomb’s results fit well with the rising Laplacian program, which sought to reduce all physical phenomena to forces of attraction and repulsion acting between invisibly small particles. On this view, the scientific study of electricity was simply a matter of measuring the attraction or repulsion between charged bodies and then working out, in a mathematically rigorous way, the underlying law of force. As the eighteenth century drew to a close, electricity appeared to be settling in as a fairly well understood, though hardly central, branch of physics. In fact, discoveries made in Italy were about to take electrical science in new and surprising directions. In 1791 Luigi Galvani (1737–98), a medical professor in Bologna, published an account of observations he had made while dissecting frogs. He had noticed that when he touched a scalpel to an exposed

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nerve in a dead frog’s leg while an electrical machine was sparking nearby, the attached muscle suddenly contracted, making the leg kick. Frog legs turned out to be exquisitely sensitive electrical detectors, and Galvani soon found he could make one twitch without using a spark at all, simply by running a brass hook through the nerve tissue and then touching both it and the attached muscle with a piece of iron wire. He concluded that the nerves of living things, and even recently dead ones, contain “animal electricity” that can be discharged, just like the electricity in a Leyden jar, by a properly placed conducting wire. Alessandro Volta (1745–1827), a physics professor at Pavia, took up Galvani’s discovery but denied it had anything to do with “animal electricity”; the frog’s leg was no more than a detector, Volta said, and the electrical force that made it kick arose simply from the contact of dissimilar metals, such as the brass hooks and iron wires Galvani had used to form his circuits. In 1800 Volta showed that he could produce sparks and other electrical effects from a simple stack of copper and zinc discs interleaved with bits of dampened pasteboard, without using frog legs or any other animal parts. Volta’s electrical “pile,” or battery, seemed to act like a small Leyden jar that was somehow able continually to recharge itself. It provided experimenters for the first time with a continuous source of electric current and so opened a vast new realm for scientific research and technological use. Much of the subsequent history of electrical science and technology can be read as a series of attempts to come to grips with the puzzles and possibilities presented by currents like those from Volta’s battery. Initially, most researchers focused on the battery itself, piling up evidence that it was not driven by the simple contact of dissimilar metals, as Volta had argued, but by chemical reactions in the moistened pasteboard. The current in the conducting wire did not attract much attention until 1820, when the Danish physicist Hans Christian Oersted (1777–1851) made a surprising discovery. Influenced by German Naturphilosophie, Oersted believed that all physical forces share an underlying unity. Rejecting the view that electric and magnetic forces are entirely separate, he also questioned the usual assumption that the current from a voltaic battery is a simple flow of electric fluid, picturing it instead as a complex “electric conflict” involving the continual separation and recombination of positive and negative electricities within the wire. Oersted thought this electric conflict might also produce magnetic forces, but his efforts to demonstrate such an effect all ended in failure. Finally, while delivering a lecture early in 1820, Oersted tried a deceptively simple experiment. Connecting a wire across the poles of a battery, he held it

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Oersted’s Magnetic Needle Deflected by an Electric Current In 1820, the Danish physicist H. C. Oersted discovered that when he placed a magnetized needle near a wire carrying an electric current, the needle turned to point at right angles to the direction of the current. The effect was not a simple attraction or repulsion but appeared to show that electric currents somehow exerted a more complex directive force on magnets. Earlier physicists had often noted parallels between electrical and magnetic phenomena, but Oersted was the first to demonstrate

that electric currents could act directly on magnetized objects.  Adolphe Ganot, Elementary Treatise on

Physics, trans. E. Atkinson, 14th ed. (New York: W. Wood, 1893), p. 809.

lengthwise above a magnetized compass needle—and watched as the needle swung until it pointed across the wire. When he held the wire below it, the needle swung to point in the opposite direction. The electric conflict was evidently not confined to the conducting wire, Oersted said, but set up a swirling vortex in the surrounding space that made the magnetized needle point like a weather vane in the wind. Most other physicists dismissed Oersted’s theories as muddled and mistaken, but they were quick to take up his experimental discovery. In Germany, J. S. C. Schweigger found he could strengthen the effect by suspending the magnetized needle within an upright coil of several turns of wire, producing a “galvanometer” that quickly became the most widely used detector of electric currents. In England, William Sturgeon wrapped a current-carrying wire around a horseshoe made of soft iron, producing an electromagnet more powerful than any natural magnet, while Michael Faraday showed in 1821 that a wire carrying a current can be made to rotate continuously around a magnetic pole. In France, the Laplacian physicists J. B. Biot and Felix Savart used techniques much like Coulomb’s to measure the force that currents exert on magnetic poles and went on to formulate the mathematical law governing such forces. The first comprehensive theory of electromagnetic forces was worked out in the early 1820s by André-Marie Ampère (1775–1836), an eccentric, largely self-taught French mathematician. Although he had previously paid little attention to electricity and magnetism, word of Oersted’s discovery set him off

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on a flurry of experimentation and theorizing. Within days, Ampère had demonstrated that wires carrying electric currents flowing in parallel directions attract each other, while those carrying currents flowing in opposite directions repel. He also showed that a current-carrying coil behaves much like a bar magnet, aligning itself with the earth’s poles and attracting or repelling other nearby coils or magnets. Ampère went on to suggest that all permanent magnets are really electromagnets, composed not of Coulomb’s imaginary magnetic fluids but of tiny molecular rings of electric current that, when aligned, combine to exert magnetic forces. Ampère was never a member of the Laplacian circle; a friend of A.-J. Fresnel and François Arago, he instead supported their anti-Laplacian insurgency. Fresnel’s work on the wave theory of light had convinced Ampère that space is filled with an elastic ether, and he believed that electromagnetic forces would ultimately be found to result from the invisible motions of this ether. In his mathematical work, however, Ampère generally followed the Laplacians’ practice of formulating force laws that were independent of any speculative hypotheses, and in a series of papers published in the early 1820s he showed how known electromagnetic phenomena could be explained by forces of attraction and repulsion acting between short segments of electric current. By 1826 Ampère had cast the mathematical theory of the forces between steady currents into essentially the form it has retained ever since. Ampère’s characteristic way of working was to propose a law of force, devise a piece of apparatus with which to test some aspect of it, and have the apparatus built by a skilled instrument maker. (Ampère was reportedly too clumsy to build or operate anything himself.) He often used a “null” method in which the force in question would be exactly balanced by a contrary one, so that when the current was switched on and the experiment began, nothing actually moved. This gave his arguments an aura of great precision and rigor, since he did not need to rely on difficult and uncertain measurements of the strength of small forces, but it tied his experimental results very closely to his specific theories and left little room for novel discoveries to turn up in the laboratory. Ampère in fact later confessed that he never performed some of the experiments described in his papers, though he argued with some justice that the results of other experiments made it clear how these imaginary ones would have turned out. James Clerk Maxwell once called Ampère “the Newton of electricity,” and in the sense that he reduced a mass of complicated phenomena to a few simple laws of force, Ampère certainly deserved the title. His work left important questions unanswered, however, particularly about the way currents might be-

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have when they were changing rather than steady, and his methods gave little guidance as to how one might address such questions. As it turned out, the next great steps in the study of electromagnetism came along lines very different from Ampère’s formulation of laws of force between currents, and were taken by a man, Michael Faraday, to whom the mathematics behind such laws remained a closed book. Faraday’s Lines of Force Michael Faraday (1791–1867) was among the most admired scientists of his day. Celebrated during his lifetime as a great experimental discoverer, an eloquent public lecturer, and a figure of unimpeachable personal integrity, he was later lauded for originating the concept of the electromagnetic field, now regarded as one of the great theoretical advances of the nineteenth century. It took Faraday many years to draw together the threads that would eventually form his field theory, and other scientists even longer to accept his contention that we should look to the surrounding space, rather than to charges, currents, and magnets themselves, for the real key to electromagnetic phenomena. Faraday kept himself aloof from commercial pursuits, but he had a strong interest in technology and was happy to see many of his experimental discoveries and theoretical ideas taken up in connection with telegraphy and other electrical technologies. The son of a London blacksmith, Faraday worked his way up from extremely modest beginnings. His family were members of what he later called “a very small and despised sect of Christians known, if known at all, as Sandemanians,” and his devotion to this simple but demanding faith deeply shaped his life and thought.¹ In particular, the characteristic Sandemanian emphasis on the unadorned word of God led Faraday to try to grasp and express the workings of the physical world in the most direct way possible, without recourse to elaborate mathematical theories. He received only the most basic schooling, and at age fourteen, after working for a time as an errand boy, he was apprenticed to a bookbinder. As he read the books that passed through his hands, Faraday developed a passion for science and for self-improvement and soon began a single-minded effort to educate himself and make his way in the scientific world. In 1812, Faraday chanced to attend a series of lectures on chemistry at the Royal Institution, a privately endowed scientific center in London. The lec1. Michael Faraday to Augusta Ada Lovelace, 24 Oct. 1844, in F. A. J. L. James, ed., Correspondence of Michael Faraday (London: IEE/IET, 1991–), 3:266.

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tures were delivered by Sir Humphry Davy (1778–1829), the leading British chemist of the day, and in hopes of making an impression, Faraday wrote out an elaborate set of notes, bound them, and presented them to Davy. The gambit paid off: Davy soon helped Faraday land a job as a laboratory assistant at the Royal Institution and in 1813 brought him along as his personal assistant on extended tour of continental Europe. A special invitation from Napoleon enabled Davy and his party to travel freely even though France and Britain were still at war. Faraday had never before been more than a few miles from his London home, and the trip broadened his horizons enormously. It also strengthened his aspirations to become a scientist himself, and he chafed as Sir Humphry and Lady Davy often treated him as little more than their servant. On returning to London in 1815, Faraday took up a permanent post at the Royal Institution. He moved into rooms in the building, and it would remain his home until his retirement nearly 50 years later. The Royal Institution had been founded in 1799 by Benjamin Thompson (Count Rumford) and a group of wealthy Englishmen to promote economic improvement through scientific research and education. Davy, a dashing figure who counted William Wordsworth and other Romantic poets among his circle of friends, was hired as the professor of chemistry. He soon turned the institution into a venue for fashionable lectures at which the cream of London society was shown the latest scientific wonders. Faraday assisted Davy in his chemical researches and had charge of the apparatus in the institution laboratory. He also strove to make his own mark in science, notably with his 1821 discovery of electromagnetic rotation, but Davy seems to have resented Faraday’s rise from subordinate to potential rival. Although Faraday’s reputation as a researcher and public lecturer grew steadily through the 1820s, he did not fully emerge into his own until after Davy’s death in 1829. In August 1831, Faraday discovered electromagnetic induction. Oersted had shown that electric currents produce magnetic forces; now Faraday, after many attempts, found a way to make magnetic forces produce electric currents. The discovery, made in the basement laboratory of the Royal Institution, exemplified Faraday’s skill at coaxing new phenomena from simple apparatus. He began by winding two coils of insulated wire around an iron ring. A steady battery current in the first coil had no effect on the second, but when Faraday threw a switch and suddenly started or stopped the current in the first coil, the needle of a galvanometer connected to the second coil jumped. No current actually passed between the coils, but the change in the current flowing in the first coil somehow induced a momentary surge of current in the second one. Faraday soon showed that the effect was essentially magnetic: the current

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flowing in the first coil turned the iron ring into an electromagnet, and when the current was started or stopped, the resulting change in the magnetism of the ring produced a fleeting current in the second coil. The ring and coils formed a primitive transformer, a device that would later play a crucial role in alternating current power systems. Faraday found that he could also induce a current by plunging a bar magnet into a coil of wire; as the magnet entered the coil, it generated a brief pulse of current, and then a second in the opposite direction when it was pulled out. Within a few months after Faraday announced his discovery, instrument makers were putting spinning coils and magnets together to build the first magneto-electric generators. One could now produce an electric current by simply turning a crank, without using a battery at all. Inventors also devised arrangements of electromagnets that, when fed with a current, turned round and round—the first electric motors. By turning the crank of one of the new magneto generators, an experimenter could turn mechanical work into electrical energy, convey it along a wire, and then use it to drive a distant motor, where the electrical energy would reappear as mechanical work. These early combinations of magnetos and motors were balky and inefficient, and it would be several decades before Thomas Edison and others would build the first practical electrical power systems, but Faraday’s discoveries helped lay the foundations while also bringing out important points about the conservation and transformation of energy. Most other physicists would have tried to explain electromagnetic induction mathematically by forces acting between electrical particles or segments of current; indeed, the German physicists Wilhelm Weber (1804–91) and Franz Neumann (1798–1895) later did just that, with considerable success. Faraday, however, was no mathematician, and at a time when Ampère and others were applying sophisticated mathematical methods to electromagnetic phenomena, Faraday’s papers lacked even the simplest equations. This was no doubt chiefly because his own aptitude and training lay in chemistry rather than mathematics, but it also reflected a principled objection, perhaps deriving from his literalist religious views, to dressing the direct truths of the laboratory in what he regarded as the artificial costume of mathematical symbols. Faraday sought instead to depict electric and magnetic phenomena in visual and physical terms, particularly through what he called “lines of force.” If we sprinkle iron filings around a bar magnet, they arrange themselves into beautiful patterns of curving lines, converging on the magnetic poles and spreading out through the intervening space. Most mathematically trained physicists, and certainly those who followed Coulomb and the Laplacians,

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looked on such lines as simply the geometrical result of the forces the poles of the magnet exerted on the tiny bits of iron. They believed these forces acted directly at a distance and saw no reason to think that, absent the filings, anything significant was going on in the space around a magnet. Faraday, in contrast, looked on this space not as an inert void but as a site teeming with activity; the sprinkled filings did not create the lines of force, he said, but simply revealed tensions that were already there. As he studied the patterns made by iron filings, Faraday came to picture each line of force as an “axis of power” running between the opposing poles and straining, like a stretched rubber band, to draw them together. Every part of the surrounding medium was polarized, he said, and magnetic forces did not act directly across space but by “contiguous action” from one particle of the medium to the next. According to Faraday, electromagnetic induction results from the cutting of lines of force. Each time a line of magnetic force cuts a wire, he said, it gives the wire a kick of electromotive force, producing an impulse of current. When the coil and magnet are both motionless and the magnetic force is steady, no lines are cut and there is thus no kick and no current. If, however, the coil moves past the magnet or the magnet past the coil, or if the lines of magnetic force either grow or shrink (as when an electromagnet is switched on or off), the magnetic lines will cut the turns of the coil and thus generate a current in the wire. Faraday could not yet say exactly how or why this cutting produced an electric current, but the image of moving lines of force gave him a vivid and almost tactile feel for the process. In his notebooks, Faraday began to sketch a three-way relationship linking electric current, magnetism, and motion. Oersted had shown that an electric current can move a magnetized needle, and Faraday himself had shown in 1821 that a magnet can move a wire that is carrying an electric current. With his discovery of electromagnetic induction, Faraday completed the cycle by showing that a magnet moving near a coil of wire can produce an electric current. This was a great unification, but it raised subtle issues about the relationship between force and motion, and about the real meaning of motion itself, that were to lurk in the background of electrical theory for the rest of the century. Many of these questions were not fully resolved until the advent of relativity theory; it was no accident that Albert Einstein opened his famous 1905 paper “On the Electrodynamics of Moving Bodies” with an analysis of Faraday’s classic experiment with a moving magnet and a coil of wire. Influenced more by chemical ideas about powers and polarities than by the orthodox Newtonian concept of forces acting directly at a distance, Faraday began to question the usual view that electricity consists of positive and nega-

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Faraday’s Lines of Force around a Magnet If we sprinkle iron filings around a bar magnet, they spontaneously arrange themselves into curving patterns like the one shown here. To Michael Faraday, such “lines of force” were not just a pretty curiosity but the key to a fundamental truth of nature. The space around a magnet is not

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an inert void, he said, but is instead filled with the force and activity revealed by the sprinkled filings. Faraday’s conception of lines of force held the seeds of what would become the field theory of electromagnetism.  Michael Faraday, Experimental

Researches in Electricity, vol. 3 (London: Quaritch, 1855), plate IV, fig. 3.

tive particles whose motion constitutes an electric current. He focused instead on the lines of electric force that, on analogy to magnetic lines, he pictured spreading out from electrified bodies and running through the surrounding insulating medium, or “dielectric,” such as air or glass. Faraday regarded these lines of force as the true foundation of all electrical phenomena; charges, he said, are quite secondary, merely superficial effects that arise when a line of force passes from an insulator (such as glass or air) that is able to sustain electrical tension into a conductor (such as copper) in which it breaks down. Thus, rather than seeing a Leyden jar as a bottle filled with electric fluid, he saw it as a bundle of powerful electrical tensions that were located, not in the inner and outer metal coatings, but within the insulating dielectric—in this case, glass— that separated them. Faraday’s reconceptualization of the function of wires was similarly radical, for he pictured an electric current not as the flow of a fluid but as the continual breaking down of tension within a conducting wire. When a battery is hooked up in a circuit, he said, it quickly sets up a state of electrical strain within the connecting wire and throughout the space around it. The metal of the wire is unable to sustain this strain, which immediately begins to break down, leaving

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a charge on its surface and a “current” of continually decaying strain that keeps churning along inside the wire as long as the battery continues to supply fresh electric force. In 1837, Faraday’s rethinking of the nature of charge and current led him to perform a series of experiments that culminated in his discovery of specific inductive capacity. If the glass within a Leyden jar is the real seat of electric tensions, Faraday reasoned, then if we were to use a different insulating dielectric, the jar ought to store a different amount of charge. He proceeded to build a special Leyden jar from which he could, in effect, remove the glass and replace it with pieces of shellac, sulfur, or other insulators. Holding the tension (in later terms, the voltage) between the inner and outer metal surfaces of the jar constant, he found that the total charge stored by the jar changed by a measurable amount as he inserted each new substance. While this did not prove all of Faraday’s ideas about the nature of charge and current to be correct, it clearly showed that the dielectric was not just an inert separator but instead played an active part in electrical phenomena. By the late 1830s, Faraday felt he was on the verge of a major breakthrough in understanding electromagnetism, but he had trouble pulling it all together. He pictured lines of force hopping from molecule to molecule through the dielectric, but while this worked well enough for material media such as glass or air, it failed for the vacuum, where he had to fall back on the old picture of electric and magnetic forces acting directly at a distance. Nor did magnetism seem to be universal in the same way electrical forces were; although he could produce either electrical polarization or conduction, or both, in any substance, iron and nickel (and, as he later showed, cobalt) were the only materials that showed any signs of being magnetic. Faraday’s efforts to push further were stymied, and at the end of 1839 he was brought to a dead stop by ill health. He was troubled by headaches and vertigo; his memory, never strong, worsened to the point that he often lost his train of thought. Whether brought on by overwork, mercury poisoning, or a minor stroke, these problems left Faraday unable to do much scientific work for several years. His memory remained poor for the rest of his life, but by about 1843 his health had recovered enough for him to return to the laboratory. Over the next 10 years he made important new experimental discoveries and also took the final steps toward framing the field theory that had been just beyond his reach in the 1830s. Other scientists of the day respected Faraday’s skill as an experimenter and public lecturer, but most dismissed his theoretical ideas as confused and childish. Several patronizingly said that while Faraday’s ideas about lines of force seemed to help him think up useful experiments, they were really no more than

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a mental crutch suited to someone who could not handle a proper mathematical theory. As late as 1855, G. B. Airy, the head of the Greenwich Observatory and himself both a distinguished mathematical physicist and Faraday’s good friend, declared that Coulomb’s inverse square law gave a complete mathematical account of magnetic forces, and said no one who really understood the situation would “hesitate an instant in the choice between this simple and precise action, on the one hand, and anything so vague and varying as lines of force, on the other hand.”² By then, however, a few cracks were opening up in the wall of indifference to Faraday’s theories. As we will see in the next chapter, William Thomson and James Clerk Maxwell had begun to cast Faraday’s field ideas into mathematical form, with consequences that were to transform electromagnetic theory. Just as importantly, Faraday’s ideas about induction and conduction were being taken up and given wide circulation in connection with a revolutionary new technology: telegraphy. Lightning Wires Once scientists had established that an electric current can pass along a substantial length of wire and deflect a needle or trip a lever at the far end, it did not take long for inventors and entrepreneurs to find ways to use batteries, wires, and magnets to convey telegraphic signals. By the mid-1840s several workable telegraph systems were in use and networks of wires were spreading rapidly across Europe and America, with wide-ranging effects on the dissemination of news and the workings of commercial markets. With time, science too was affected, as the growing telegraph industry created both a new demand for electrical knowledge and new opportunities for acquiring it. Before the introduction of the electric telegraph, a message could generally travel no faster than the messenger who carried it. Almost the only exceptions were the small number of dispatches that passed along the networks of optical telegraphs erected in France and a few other countries after 1793. The French system, devised by Claude Chappe and adopted by the revolutionary government as a wartime measure, consisted of a chain of towers erected on hilltops a few miles apart, each topped by a crossbar with two swiveling arms. An operator set the arms to indicate the signs of a code; his counterpart at the next station watched through a telescope, noted down the signs, and set the arms of his own apparatus to relay the message along its way. Repeated from station to station, this process could pass a message hundreds of miles in less than an 2. G. B. Airy to John Barlow, 7 Feb. 1855, in Henry Bence Jones, Life and Letters of Faraday, 2 vols. (London: Longmans, Green, 1870), 2:352.

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hour. In the 1790s the British Admiralty built its own chain of optical telegraphs from London to the naval base at Portsmouth, and similar systems were erected elsewhere. Although they provided a valuable service, optical telegraphs were expensive to maintain and failed in darkness or fog. They are now nearly forgotten, a few scattered spots bearing the name “Telegraph Hill” standing as almost the only reminders that they ever existed. That electricity might be used to transmit messages was first suggested in the 1750s. The earliest proposals called for using frictionally generated static electricity to produce sparks or repel pith balls at the far end of a wire. This worked over distances up to a few miles, but frictional electricity was produced at such high tension that it was hard to keep the wires adequately insulated. The best of the electrostatic systems was one built in 1816 by a young Englishman, Francis Ronalds (1788–1873), which he demonstrated working through eight miles of wire. When Ronalds tried to interest the Admiralty in his system, however, they told him they were happy with their optical telegraph, and he soon gave up his efforts. After Volta and Oersted’s discoveries, inventors turned from electrostatic systems to ones that used currents to produce electromagnetic effects. In 1820 Ampère proposed a telegraph having separate wires and needles for each letter of the alphabet, with words being spelled out by sending a current along the wire corresponding to each letter. Ampère never built the device, but Pavel Schilling, a Russian diplomat working in Munich, devised a similar system that used several wires and a set of coded signals. Schilling later simplified his telegraph to work with a single wire and showed it widely in the early 1830s but was unable to bring it into practical use before his death in 1836. In America, Joseph Henry (1797–1878) rigged an electromagnet to ring a bell with a current that had passed through more than a mile of wire but went no further than to demonstrate the feat to his classes at the Albany Academy in 1831. Indeed, except for a line the German physicist Wilhelm Weber and the mathematician C. F. Gauss (1777–1855) strung up in 1833 to exchange signals between their laboratory and observatory in Göttingen, none of the earliest electromagnetic telegraphs amounted to much more than lecture demonstrations. Early in 1836 W. F. Cooke (1806–1879), a young Englishman who had been studying in Germany, saw a demonstration of Schilling’s telegraph and decided to make it his ticket to wealth and fame. He quickly patched together a telegraph of his own based on the gearing of a music box, the only kind of mechanism he knew much about, but his knowledge of electromagnetism was so meager he could barely get it to work across a room, much less across the hundreds of miles he envisioned. On returning to London, he sought out Faraday,

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who told him the basic principle of his telegraph was sound but expressed doubts about its commercial prospects. In November 1836 Cooke turned to Charles Wheatstone (1802–75), a young physics professor at King’s College London who was studying the transmission of electric currents. It turned out Wheatstone had already been thinking about telegraphs himself, and the two men soon decided to pool their efforts. Wheatstone came from a family of musical instrument makers, and his first scientific studies focused on how sound travels along stretched strings and wooden rods. He then took up electricity and in 1834 used a clever rotating mirror device to show that electric currents run along wires at about the speed of light. He also began to work out ideas for an electric telegraph, though more as a scientific puzzle than a commercial enterprise. When Cooke came to him, Wheatstone saw an opportunity to combine his own scientific expertise with Cooke’s entrepreneurial drive, but while the two men became partners, they continued to circle each other warily, each eager not only to make the telegraph a practical success but also to secure as much credit and reward as possible for himself. Rejecting Cooke’s music box device as unworkable, Wheatstone drew on his knowledge of currents and magnetism to devise an improved needle telegraph. He and Cooke filed for a patent in June 1837 and installed their first short line at a London railway station a month later. They laid a more permanent 13-mile line along a railway west of London in 1839, running the cottoncovered wires through iron tubes buried beside the tracks. Their first telegraphs had six wires and five needles, but they soon found that by using a simple code, they could send messages just as readily with only two needles, or even one. They also gave up burying their wires in the ground, finding it cheaper and easier to string them from overhead poles. At first Cooke and Wheatstone’s system was used mainly for simple railway signaling, but after the new Electric Telegraph Company acquired their patent rights in 1845, more lines were built for public use. Wheatstone’s work on the telegraph fed back into his scientific research, notably in a paper on methods of electrical measurement that he presented to the Royal Society in 1843. Although he devised these methods to help improve telegraphic signaling, he noted that they were “not limited to this especial object” and would prove useful “in all inquiries relating to the laws of electric currents.”³ Most of the paper focused on Ohm’s law, which had attracted 3. Charles Wheatstone, “An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit,” Philosophical Transactions 133 (1843): 303.

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little attention when first published in 1827. G. S. Ohm (1789–1854) was a German mathematics teacher who had shown that the current in an electric circuit is proportional to the electromotive force (voltage) divided by the resistance of the conductor, expressed algebraically as I  V/R. Wheatstone read Ohm’s paper, recognized its value, and arranged to have it published in English translation in 1841. In his own paper, Wheatstone described a clever way to measure resistances by balancing them against each other; although he made clear that the method was based on an arrangement devised a few years before by S. H. Christie, it has been known ever since as the “Wheatstone bridge.” Wheatstone’s techniques later came to be widely used by both physicists and electrical engineers, but at first few telegraphers saw much need for such accurate electrical measurements. If a usable current got through, that was enough for them, and many were content to use their fingers or tongues to detect it. Effective demand for precision electrical measurements, or even for standard units of current and resistance, did not emerge until the late 1850s, largely in connection with the new technology of submarine cable telegraphy. In the United States, the electric telegraph is usually credited to Samuel F. B. Morse (1791–1872), though he is perhaps more accurately seen as its promoter than as its inventor. Romantic images of the lone genius notwithstanding, it would be a mistake to ascribe the invention of the telegraph to a single person; like many technologies, it was the product of the combined efforts of many hands and minds. A talented painter who became the first professor of art at New York University, Morse knew little about electricity until, on a voyage home from Europe in 1832, a fellow passenger told him about recent discoveries in electromagnetism. It struck Morse that if a pulse of current could make itself felt instantaneously across a room, it might be made to do so across a continent and so provide a way to send messages to any distance. Knowing almost nothing of what others had already done, he seems to have imagined he was the first ever to conceive of electrical signaling. Over the next few years Morse cobbled together a remarkably cumbersome telegraph. Starting with a wooden frame originally used to stretch canvases, he hung from it a wooden pendulum with a pencil on its end. When a pulse of current entered from the connecting wire, an electromagnet mounted on the frame pulled the pendulum to one side and then released it; as it swung, the pencil marked a V on a paper tape that was pulled along by clockwork. Morse read off the resulting series of marks as numbers and translated them into words by referring to a special code book. To send a message, he would set a row of metal teeth into a grooved stick and pull it along beneath an electrical

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contact to produce a coded sequence of pulses in the connecting wire. At first he could send signals no more than about 40 feet before the current became too weak to work the electromagnet, but Leonard Gale, a chemistry professor at New York University who was familiar with Henry’s work, showed Morse how to produce more intense currents by rearranging his batteries and winding more turns of wire around his magnet. By September 1837, Morse could send signals through about a thousand feet of wire. Lacking both the money and the mechanical skill to develop his device further, Morse turned to a former student, Alfred Vail (1807–59). Vail’s father owned an ironworks in New Jersey and was willing to invest in the project; moreover, Vail himself was a skilled mechanician. Seeing great potential in electric telegraphy, he signed on as Morse’s junior partner and over the winter of 1837–38 began to turn the clumsy canvas-stretcher device into the simple and robust system later familiar as the “Morse telegraph.” In Vail’s hands, the swinging pendulum gave way to a compact steel stylus that clicked up and down to mark the moving paper tape. (Operators later stopped using the tape after finding they could read messages by the clicking sound alone.) According to some accounts, Vail even devised the famous “Morse code” of dots and dashes to represent letters; in any case, this soon supplanted Morse’s original system based on numbers and a code book. Vail also replaced Morse’s cumbersome sending apparatus with a simple finger-key—later known as a “Morse key”—with which operators could tap out messages directly. Under the terms of their partnership agreement, however, all of Vail’s contributions, and Gale’s as well, were folded into Morse’s patent. Morse initially filed for the patent in October 1837, and it was finally granted in 1840; from the first, all public credit went to Morse alone. Morse and Vail demonstrated their improved telegraph in New Jersey, New York, and Washington, D.C., early in 1838, and Morse showed it off on a European tour in 1838–39. Although the device attracted some favorable notice, Morse’s application for an English patent was rejected on the grounds that the invention was not really new. The whole project made little headway until 1843, when careful lobbying helped Morse win a congressional grant to build an experimental line from Washington to Baltimore. The first lengths of line were insulated with cotton and laid underground in lead pipes, but shady contracting and high costs soon brought the work to a halt. Shifting to the cheaper expedient of stringing their wires from overhead poles, Morse and his partners successfully completed the 40-mile line in May 1844. It soon drew attention by carrying the first reports of the presidential nominating conven-

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tions being held in Baltimore, but Congress decided not to extend the line further, and thereafter the development of the telegraph in the United States was left to private enterprise. Telegraph lines spread rapidly—perhaps too rapidly—in the United States in the late 1840s. By 1850 dozens of competing companies had strung over 12,000 miles of wire, but many lines were so badly built that they barely worked. In some areas, companies did not even bother with poles, instead simply hanging their wires from brackets nailed to trees. Not surprisingly, both the quality of service and the reputation of the new technology suffered badly. In other countries, the telegraph advanced more slowly but somewhat more surely. By 1850 the Electric Telegraph Company had built over 2,000 miles of lines along British railways, and government-owned lines soon went up in various parts of continental Europe and British India. The American telegraph industry went through a brutal shakeout in the late 1850s, and by 1866 the Western Union Company had established a virtual monopoly throughout the country. In Britain, the government bought out the private companies in 1868 and made the telegraph network part of the postal system, as it had been from the first in most other countries. From its earliest days, telegraphy was the subject of expansive and utopian rhetoric. The electric wires were often described as the “nervous system” of the nation, binding it together and vivifying its parts; comparing its effects to those of railways and steamships, innumerable editorial writers declared that the telegraph had “annihilated time and space” and defeated the tyranny of distance. The effects of the telegraph were felt first and most strongly in the commercial world, as the availability of up-to-date price information helped consolidate fragmented local markets in grain, cotton, and other commodities. Commercial messages and market reports accounted for over two-thirds of the traffic on American telegraph lines in the 1850s; and in the 1860s the glassdomed “stock ticker” became a familiar sight, spewing out minute-by-minute price fluctuations on seemingly endless streams of paper tape. The telegraph also reshaped the news business. As early as 1846, six New York newspapers joined together to pool the gathering of telegraphic news reports, thus launching the Associated Press, the first and still the largest of the “wire services.” Newspapers began to carry same-day accounts of distant events, and though early telegraphic bulletins were usually brief and fragmentary, news reporting quickly acquired a reach and immediacy it had never before possessed. Telegraphs were also put to many other uses, including distributing accurate time signals, gathering weather information to track storms, and connecting fire alarm boxes in cities. Not all of the effects of the telegraph were

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positive, however. In the early days, the lines were so faulty and operators so inexperienced that messages, if they arrived at all, were often garbled and useless; when the lines were working, swindlers all too often used them to manipulate markets and cheat the unwary. In 1854, Henry David Thoreau declared that the telegraph offered no more than “improved means to an unimproved end,” a quicker way to convey what need not have been said at all. “We are in great haste to construct a magnetic telegraph from Maine to Texas,” he noted, “but Maine and Texas, it may be, have nothing important to communicate.”⁴ More typical, however, were the sentiments that Edward Copleston, a Welsh bishop, recorded in his diary after visiting Wheatstone in 1840. “Last night I was hardly able to sleep,” he wrote, as he pondered the implications of the telegraph. “Gas and steam have done much,” he said, but electricity “is destined to do much more, and to work an incalculable change in human affairs. It far exceeds even the feats of pretended magic, and the wildest fictions of the East.”⁵ The Cable Empire The first telegraph lines all ran overland, but as the web of wires spread, there was a growing demand for lines that could cross rivers, seas, and even oceans. The first successful submarine cable was laid across the English Channel in 1851; more soon followed, most famously the failed Atlantic cable of 1858 and the two successful ones of 1866. By 1880, submarine cables stretched to almost every corner of the globe and were rapidly transforming international communications. Significantly, almost all of these cables were built, laid, and operated by British firms. There is no great mystery why this should be so: Britannia ruled the waves in the nineteenth century, and it was only natural that she should seek to extend that rule beneath the waves as well. As a maritime trading nation and as easily the leading commercial, industrial, and imperial power of the day, Britain had both the greatest need for submarine cables and the greatest capacity for laying them. British dominance of the global cable industry had important consequences for science as well as for commerce. As British physicists and engineers confronted the problems peculiar to building and operating long submarine cables, their scientific work was led in distinctive directions. Some of the leading features of British electrical science in the Victorian period, including its emphasis on precision measurement and its focus on the electromagnetic field, had deep roots in cable telegraphy. 4. Henry David Thoreau, Walden (1854; repr., New York: Norton, 1966), p. 67. 5. Quoted in Brian Bowers, Sir Charles Wheatstone, FRS, 2nd ed. (London: IEE, 2001), p. 66.

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Morse, Wheatstone, and others had experimented in the 1840s with underwater wires covered with tarred rope, but they soon realized that effective submarine telegraphy would require a better insulating material. One soon came to hand in the form of gutta-percha, a rubber-like natural plastic derived from the sap of Malayan gutta trees. Malayans had long used this pliable, waterproof material to fashion whips, hats, and other objects; and soon after the first samples appeared in England in 1843, Faraday and others pointed out that gutta-percha was a good electrical insulator and well suited to covering wires. In Germany, Werner von Siemens (1816–92) used it to insulate an underground telegraph line laid from Berlin to Frankfurt in 1849, and similar underground lines were laid in Britain as well. Gutta-percha proved even more useful on underwater lines, beginning with the 27-mile-long cable J. W. Brett and his Submarine Telegraph Company laid across the English Channel in 1851. Brett’s cable earned handsome profits carrying market reports and other news between London and Paris, and entrepreneurs looking to cash in soon set about laying cables to Ireland, Holland, and across the Mediterranean. Many of these early attempts failed, and those that succeeded owed more to luck than to any real understanding of the problems involved. Proponents of the new technology were undaunted, however, and as they bent over their maps and globes, they began to visualize cables spanning all the oceans of the world. The great prize, of course, would be the Atlantic. Even the fastest steamships in the 1850s took more than a week to cross from Liverpool to New York, and the demand for quicker transmission of transatlantic news, particularly grain and cotton prices, was intense. One scheme called for laying a short cable from Nova Scotia to Newfoundland, intercepting steamers as they passed that easternmost outpost of North America, and telegraphing their news ahead to New York, beating the arrival of the ship itself by two or three days. When Cyrus Field (1819–92), a wealthy young New York merchant, learned of the project in 1854, he hatched a plan for something far more ambitious: a cable directly from Newfoundland to Ireland, with connections at either end to New York and London. To lay a cable across nearly 2,000 miles of open ocean would be an audacious enterprise, far beyond anything previously attempted, but Field foresaw great advantages—and profits—if it could be done, and he set about securing landing rights and organizing a company. He soon recognized, however, that the capital and expertise needed to make the cable a reality could be found only in Britain. Backed by Brett and other British investors, Field formed the Atlantic Telegraph Company in London in October 1856 and optimistically promised to lay the cable the following summer. Whatever the enthusiasm of Field and his partners, others had serious

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doubts that an Atlantic cable could ever be made to work. Many of their concerns centered on “retardation,” a troubling phenomenon telegraphers had first encountered on underground lines and submarine cables a few years before. Faraday brought it to wider notice in January 1854, when, in a lecture at the Royal Institution, he described experiments the telegraph engineer Latimer Clark (1822–98) had shown him in which short, sharp signals sent into one end of a cable or long underground line emerged at the other greatly stretched out and noticeably delayed. This posed a serious problem for telegraphers, for it meant that if they tried to send too many words per minute along their cables, the successive pulses of current would run together into an indecipherable blur. The effect worsened with length, calling into question whether a cable across the Atlantic would be able to carry enough messages per day to pay for itself. Retardation might be bad news for telegraphers, but Faraday welcomed its discovery as providing “remarkable illustrations of some fundamental principles of electricity, and strong confirmation of the truthfulness of the view which I put forth sixteen years ago” on the relationship between induction and conduction.⁶ Since the late 1830s, Faraday had been arguing that a wire cannot carry a steady current until the insulating dielectric around it has been thrown into a state of electrical strain, with the consequent storage of a certain amount of charge on the surface of the wire. The inductive capacity (or “capacitance”) of most ordinary circuits, including overhead telegraph wires, is so low and the stored charge thus so small that the whole process occurs almost instantaneously; indeed, since they saw no delay in the flow of current, most scientists of the time regarded Faraday’s idea that induction precedes conduction as a needless complication. On submarine cables and underground lines, however, the seawater or damp earth surrounding the insulated wire acts like the outer coating of a Leyden jar, greatly increasing the capacitance of the line and enabling it to hold much more charge. This slowed down the process of induction and produced the retardation Clark and others had observed; it also made Faraday’s ideas seem less like fanciful theorizing and more like a possible key to solving one of telegraph engineers’ most vexing practical problems. Werner von Siemens had noticed retardation effects on his own underground lines as early as 1849, leading him, he later said, to take Faraday’s ideas on dielectrics and electrical conduction more seriously than others in Germany did at the time. Siemens’s buried lines failed after just a year or two, 6. Michael Faraday, “On Electric Induction—Associated Cases of Current and Static Effects” (1854), in Experimental Researches in Electricity, 3 vols. (London: Quaritch, 1839–55), 3:508.

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Atlantic Telegraph Cable aboard the U.S.S. Niagara in 1857 When Cyrus Field and his partners were laying plans for the first Atlantic telegraph cable, they realized that even though the cable would be only ⅝ inch in diameter— scarcely as thick as a person’s finger—the more than 2,000 miles of it needed to span the ocean would be too bulky to fit into any single ship then afloat. They therefore split the cable between the U.S.S. Niagara,

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on loan from the U.S. Navy, and H.M.S. Agamemnon of the British Royal Navy, with the two lengths to be spliced together in mid-ocean. The project drew lavish coverage in the press, including this full page engraving from the Illustrated Times of London showing the cable being paid out from the deck of the Niagara during the first, failed attempt in August 1857.  Illustrated Times, 15 Aug. 1857; courtesy

of Naval Historical Foundation.

however, as their insulation succumbed to the combined effects of hurried construction, mistakes in handling materials, and the depredations of rats with a taste for gutta-percha. The Prussian telegraph authorities soon replaced them with overhead wires, bringing the German encounter with retardation phenomena to an early end. The British, too, pulled up most of their underground lines in the mid-1850s, but by then their growing network of undersea cables meant they could not escape from retardation problems so easily. Among those intrigued by the discovery of retardation was William Thomson, who late in 1854 combined Faraday’s ideas about induction with equations drawn from the theory of heat flow to produce a mathematical theory of how pulses of current travel along wires. Thomson’s theory marked a crucial advance; Oliver Heaviside, later a great expert on telegraphic propagation, called

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it “the first step towards getting out of the wire into the dielectric.”⁷ Thomson showed that the retardation on a cable is proportional to both its resistance and its capacitance, and so would be lowest on a fat copper wire covered by a thick layer of gutta-percha. This was bad news for proponents of the Atlantic project, who hoped to use a thin, cheap cable rather than a thick, expensive one. Worse, Thomson’s theory said that retardation would increase with the square of the length of a cable. Extrapolating from the slow signaling—just a few words per minute—achieved on a 300-mile cable recently laid in the Black Sea, Thomson concluded in 1855 that a cable of the same thickness across the Atlantic, six times as far, would suffer 36 times as much retardation and would thus be too slow to pay for itself. E. O. Wildman Whitehouse (1816–90), a English surgeon turned electrical experimenter, tried to blunt Thomson’s criticisms, announcing in 1856 that tests on actual cables showed the “law of squares” to be no more than “a fiction of the schools.”⁸ Field was delighted to hear this and quickly brought Whitehouse into the Atlantic Telegraph Company as its “electrician,” in charge of all electrical arrangements. Thomson stood by his theory, declaring that Whitehouse had misinterpreted his own experiments, but conceded that he had been hasty in blaming the slow signaling on the Black Sea cable principally on retardation (poorly adjusted instruments were apparently the main culprit); he concluded that with careful handling, an Atlantic cable of ordinary thickness should be able to carry signals at a slow but usable rate. In December 1856, Glasgow investors elected Thomson to the board of directors of the Atlantic Telegraph Company, and thereafter he worked closely on the project. Rushing to meet the ambitious schedule he had promised his investors, Field ordered over 2,000 miles of relatively thin cable, only ⅝ inch in diameter—about as thick as a man’s thumb. Whitehouse performed some simple electrical tests, declared the cable fit for service, and watched from shore as a small group of ships set out in August 1857 to lay it across the Atlantic. Just over 300 miles out from Ireland, however, the cable snapped. Dejected, the flotilla’s crew turned back to unload the remaining coils while Field and his backers regrouped to try again the next year. Over the winter Field’s engineers devised and built improved laying machinery, but they left the cable itself to sit for months in the open air, its gutta-percha insulation steadily deteriorat7. Oliver Heaviside, “Electromagnetic Induction and Its Propagation” (1886), in Oliver Heaviside, Electrical Papers, 2 vols. (London: Macmillan, 1892), 2:79. 8. E. O. Wildman Whitehouse, “The Law of Squares—Is It Applicable or Not to the Transmission of Signals in Submarine Circuits?” Athenaeum, 30 Aug. 1856, 1092.

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World Cable Map, 1901 By the end of the nineteenth century, the network of submarine telegraph cables reached into almost every part of the globe. A short-lived cable had first been laid across the Atlantic in 1858, and two more permanent ones in 1866; in the 1870s, cables were laid to India, Australia, and Japan and along the coasts of Africa and South America. The first cable across the Pacific, shown here as a dashed line running from Canada to Australia and New Zealand, was completed in 1902; a second, starting from San Francisco,

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reached Hawaii later that year and was extended to Guam and the Philippines in 1903. The great majority of the cables laid between 1850 and World War I were built, owned, and operated by British firms. The demands and opportunities presented by the cable industry did much to shape British work in electrical physics in the second half of the nineteenth century.  “Eastern Telegraph Co.’s System and Its

General Connections,” unpaginated foldout in W. Clauson-Thue, A.B.C. Telegraphic Code, 5th ed. (London: Eden Fisher & Co., 1901); courtesy of Bill Burns.

ing. After three more failed attempts in June 1858, the flotilla set out in July to make one last try. This time everything finally went right, and on 5 August 1858 the word went out from Ireland and Newfoundland that the Atlantic cable had been successfully completed. It was immediately hailed in speeches, sermons, and editorials as the great wonder of the age; a celebration in New York became so exuberant that City Hall caught fire and nearly burned down. There was a troubling delay, however, before the cable delivered up its first messages. During the laying, the operators had received signals aboard ship on

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Thomson’s “mirror galvanometer,” a sensitive instrument that used a beam of reflected light in place of the usual heavy pointer and so was able to show the passage of even the weakest currents. Once the ends of the cable had been landed, however, Whitehouse hooked up his own much heavier relays, which proved unable to receive readable signals. In desperation, he began sending jolts of current from a five-foot induction coil rippling down the cable, further damaging its already fragile insulation, but even then could not get his relays to respond. After about a week, the exasperated board of directors dismissed Whitehouse and turned the Irish end of the cable over to Thomson. Using batteries and his mirror galvanometer, he managed to send and receive a substantial number of messages over the next few weeks, but the condition of the cable steadily deteriorated. By early September it was dead. The Atlantic cable had aroused enormous pride and enthusiasm on both sides of the ocean, making its demise doubly discouraging. The public came to look upon oceanic cable telegraphy as a great failed technology, an impression that was reinforced in 1860 by the collapse, at enormous cost to the British government, of a cable laid down the Red Sea and on to India. In 1859 the badly battered Atlantic Telegraph Company joined with the British government to form a committee to investigate and advise on the whole subject of submarine telegraphy. What had gone wrong, and was there any way to put it right? The “Joint Committee” took testimony from experts, commissioned experiments, and drew up a massive report, published in 1861, that became the bible of cable telegraphy. It identified serious mistakes in the design, manufacture, and handling of the Atlantic and Red Sea cables and declared that it was these, rather than anything intrinsic to oceanic telegraphy, that had led to their failure. Cable telegraphy presented “no difficulties . . . which skill and prudence cannot and will not overcome”; with due care, the report concluded, “this class of enterprise may prove as successful as it has hitherto been disastrous.”⁹ The committee particularly stressed the importance of making accurate electrical measurements and exercising careful quality control during manufacture and laying. The committee laid much of the blame for the failure of the 1858 cable on Whitehouse’s shoulders (perhaps even more than the large share he deserved), declaring his methods to be slipshod and unscientific. In contrast, it pointed to Thomson’s work as proof of how much science, properly pursued, could contribute to the success of cable telegraphy. 9. Report of the Joint Committee on the Construction of Submarine Telegraph Cables (London: HMSO, 1861), pp. xii, xxxvi.

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The report of the Joint Committee stimulated important scientific work, particularly the formation in September 1861 of the British Association Committee on Electrical Standards. As we will see in the next chapter, this committee, led by Thomson, Maxwell, and the cable engineer Fleeming Jenkin, went on to develop essentially the system of electrical units—the ohms, volts, and amperes—still used today, while also laying the foundations for major advances in both electrical theory and practice. Encouraged by the report of the Joint Committee, Field and the Atlantic Telegraph Company decided to try again and settled on a design for a new and thicker cable, in line with Thomson’s advice. Investors, however, were understandably leery at the prospect of sinking another £500,000 (the equivalent of about $50 million today) at the bottom of the sea. The project was on the verge of stalling completely when John Pender’s newly formed Telegraph Construction and Maintenance Company offered to build and lay the cable largely at its own risk. The cable was duly made and tested, and the Great Eastern, the only ship afloat big enough to carry the full length, was chartered to lay it. The great ship set out from Ireland in July 1865 and was nearly two-thirds of the way across when once again the cable snapped and sank. The project seemed cursed, but Field and Pender held firm and set about raising the money to try again the next year. This time all went smoothly, and on 27 July 1866 the cable was landed at Heart’s Content, Newfoundland. The Great Eastern then returned to the spot where the 1865 cable had broken, grappled it up from the bottom of the sea, spliced on a length of new cable, and completed it to Newfoundland. By September the Atlantic was spanned by two working cables, and Europe and North America have been in direct telegraphic contact ever since. The success of the Atlantic cables sparked a global boom in cable laying. Additional lines were laid across the Atlantic, and new ones were laid to India (1870), Hong Kong (1871), and Australia (1871) and along the coasts of South America (1873–76) and Africa (1879). By 1880 the oceans of the world were spanned by nearly 90,000 miles of cables; by 1900, that total had more than doubled. The overwhelming majority of these cables were built, laid, and run by British companies—indeed, most were controlled by one man, “cable king” John Pender (1816–96). Throughout the late nineteenth and early twentieth centuries, London’s position at the center of the sprawling web of submarine cables enabled it to control much of the global flow of information, greatly bolstering British imperial and commercial power. Many factors, including British control of the gutta-percha market in Singapore, made it hard for other countries to crack the British cable monopoly. The most important single fac-

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tor, however, was British dominance of the relevant technical expertise. Cable telegraphy was the most advanced “high-tech” industry of its day, and the store of specialized knowledge and skills that British scientists and engineers had been building up since the 1850s gave them an almost insurmountable advantage over later entrants into the field. William Thomson stands as a fitting symbol of the intertwining of British electrical science and cable technology in the nineteenth century. From 1854 until his death in 1907, he combined pioneering theoretical and experimental work on electricity and magnetism with close involvement in the practicalities of submarine telegraphy, including sailing on many of the early cable-laying expeditions. He was knighted in 1866 for his work on the Atlantic cables and earned a fortune from his patents on telegraphic instruments and apparatus. When he was raised to the peerage in January 1892, Thomson had to choose a new name to go with his new title. He soon settled on “Kelvin,” after a small river that flows near the University of Glasgow, but only after friends and family had half-jokingly suggested he instead call himself “Lord Cable.”¹⁰ It would have been an apt choice, reflecting not only the main source of his public fame but also the stimulus for some of his most important scientific work. 10. Agnes Gardner King, Kelvin the Man: A Biographical Sketch by His Niece (London: Hodder and Stoughton, 1925), pp. 105–6.

5 Electromagnetism

Ether and Field

Field theory turned the usual view of physical reality on its head. In place of the old image of isolated bits of matter acting directly on each other across empty space, field theory pictured space as filled with energy and activity, crisscrossed by lines of force that were in a sense more real than the charges and currents on which they converged. In field theory, the whole comes before its parts, with those parts drawing their significance, even in a sense their existence, from their place and role within the surrounding field. Michael Faraday planted the seeds of the field approach in the 1830s and cultivated it further in the 1840s, but field theory did not fully flower until the 1850s and 1860s, when William Thomson and James Clerk Maxwell cast Faraday’s ideas into mathematical form and tied them to the notion, drawn from the wave theory of light, that space is filled with an all-pervading ether. Maxwell and his successors went on to develop a comprehensive field theory of electricity and magnetism, including an electromagnetic theory of light, while striving also to explain it all by the workings of a mechanical ether. Field theory was a distinctively British pursuit in the nineteenth century; most physicists in other countries stuck with action-at-a-distance theories until the 1880s and 1890s. These national differences had many sources, but perhaps the most important was rooted in British dominance of cable telegraphy. The peculiarities of signaling through long submarine cables exposed British scientists and engineers to problems of electrical propagation that their counterparts in other countries did not encounter, and so led the British to pay special attention to field effects and the role the dielectric plays in electromagnetic phenomena. The British cable industry also spurred work in precision electrical measurement that bolstered Maxwell’s theory. There is an irony here, for in a way the British cable industry dug its own grave. By fostering the development of Maxwell’s field theory, cable telegraphy helped lead to the discovery of electromagnetic waves. This led in turn to the invention of wireless telegraphy, or radio—the technology that, in the twentieth century, finally

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gave other countries a way to break the monopoly on global communications that Britain had built on its network of submarine cables. Faraday in a New Light As his health improved in the early 1840s, Faraday returned to the laboratory and to his pursuit of a unified theory of electromagnetism. He took a major step in that direction in September 1845, when he discovered that magnetic forces can alter the polarization of a beam of light. The “Faraday effect” and a string of related discoveries clinched his belief that lines of force represent real physical states of the electromagnetic medium. When Thomson and Maxwell took up the Faraday effect in the 1850s, they used its evidence of a link between magnetism and light to open a new chapter in theorizing about the ether and electromagnetism. The orthodox view that electric and magnetic forces act directly between isolated particles had been laid down by Charles Coulomb in the 1780s and elaborated mathematically by the Laplacian physicist S.-D. Poisson. A.-M. Ampère’s work in the 1820s fit with this approach, and in the 1840s the German physicists Franz Neumann and Wilhelm Weber independently extended it to account for electromagnetic induction. Neumann and Weber combined mathematical skill with mastery of the art of precision measurement, and they constructed theories that fit the experimental data very well. Neumann’s theory was highly abstract, however, and his “electrodynamic potential” gave little insight into any underlying physical processes, while Weber’s theory, based on forces acting directly between streams of electric particles, relied on many untestable hypotheses. Weber’s basic law also required the force between two particles to vary with their velocity, leading to apparent violations of the conservation of energy and landing him in a long and heated dispute with Hermann von Helmholtz. Faraday paid little attention to these mathematical theories, preferring to work along his own more intuitive lines. Many physicists questioned, however, whether his ideas about lines of force and electric induction were consistent with the results Coulomb and Poisson had established. Faraday argued that his discoveries about specific inductive capacity and induction along curved lines proved that electric forces act contiguously, hopping from one molecule to the next across a medium, rather than acting directly at a distance, as Coulomb had claimed. Did this mean that Coulomb’s law was wrong? Or, as seemed more likely to most physicists of the day, did it simply mean that Faraday had misconstrued the meaning of his own experiments?

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Taking up the question in the early 1840s, Thomson showed that Faraday’s results did not contradict Coulomb’s and that, when applied to a medium whose parts could be electrically polarized, the two theories were mathematically equivalent. Thomson was not really endorsing Faraday’s approach—his papers could just as easily be read as defending Coulomb’s—but as he looked more closely, he began to see real strengths in Faraday’s way of treating electric and magnetic phenomena. He was particularly struck by Faraday’s idea that electric induction physically strains the dielectric across which it acts. Physicists had long known that subjecting a piece of glass to mechanical strain (bending or twisting it, for example) can affect the polarization of light passing through it, and in August 1845 Thomson wrote to ask Faraday if he had ever noticed a similar effect in a dielectric under electric induction, such as the glass in a Leyden jar. Faraday replied that he had not, but he set out to see if magnetic forces might produce a similar effect. He soon found that when he sent a beam of polarized light through a piece of glass placed across the poles of a strong electromagnet, or within a long coil of wire carrying a strong current, the plane of polarization was turned in the same direction as the flow of current in the coil. Faraday declared that he had directly “illuminated” a line of magnetic force, an achievement that made the lines seem more real to him than ever. Maxwell later remarked, somewhat prematurely, that the discovery of the magnetic rotation of light “did not lead to such important practical applications as some of Faraday’s earlier discoveries”; in fact, it now provides the basis for some types of rewritable optical disks and other technologies that combine optics with electronics. Maxwell was certainly right, however, when he said that Faraday’s discovery had proved “of the highest value to science” by providing what amounted to an inside look at the way magnetic forces affect both light and matter.¹ Faraday’s work on magneto-optic rotation and related discoveries about how lines of magnetic force pass through different kinds of matter strengthened his belief in what he now began to call the magnetic “field,” and he soon began to speculate more openly about it. In an 1846 lecture on “ray vibrations,” he suggested that particles of matter may be simply “centers of force” at which electric and magnetic lines converge, and that these lines of force might serve to explain light as well. Faraday accepted the wave theory of light but had doubts about the ether, suspecting it was just another imaginary subtle fluid. 1. James Clerk Maxwell, “Faraday” (1877), in W. D. Niven, ed., Scientific Papers of James Clerk Maxwell, 2 vols. (Cambridge: Cambridge University Press, 1890), 2:792.

Electromagnetism

The Faraday Effect on Polarized Light In 1845, Michael Faraday found that when he passed a polarized beam of light through a piece of glass that he had placed in a strong magnetic field, the plane of polarization of the light was turned through a measurable angle. This “Faraday effect” provided the first clear evidence connecting magnetism to light, and in the

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1850s it led William Thomson and James Clerk Maxwell to important insights about the structure of the ether, the workings of the electromagnetic field, and the nature of light. In particular, Faraday’s discovery convinced both Thomson and Maxwell that magnetic fields must be filled with “molecular vortices,” tiny bits of matter or ether that whirled around the lines of force.

But how could there be waves without something to carry them? Perhaps, Faraday suggested, light is simply vibrations of the lines of electric and magnetic force that stretch from particle to particle across space. He had already shown that magnetic forces can affect light, and it seemed plausible to him that light might ultimately be electromagnetic. The idea was not without problems; for one thing, it seemed hard to believe that individual lines of force stretch from the sun and each of the distant stars to the molecules in our eyeballs and that the light we see is just the twanging of these lines. Sketchy as it was, however, Faraday’s notion of “ray vibrations” contained a first hint of what, in the hands of Maxwell and his successors, would become the electromagnetic theory of light and later the technology of radio waves. Before Maxwell took up the task in the mid-1850s, almost the only attempts to express Faraday’s ideas in mathematical form had come in a few terse papers by Thomson. Maxwell had first studied electricity and magnetism at Edinburgh, but when he arrived at Cambridge in 1850, he found that the mathematical theory of those subjects, as well as of heat, had been dropped from the curriculum because their scientific foundations were regarded as not yet sufficiently secure. During his student days Maxwell focused on optics and mechanics, but after completing his degree in January 1854, he began to cast around

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for a new topic. This was just as Faraday’s lecture at the Royal Institution about retardation on telegraph cables was attracting attention, and whether stimulated by this or for reasons of his own, Maxwell decided to take up electricity. He knew Thomson through family connections and wrote to ask him what he ought to read. Maxwell soon dove into Faraday’s Experimental Researches in Electricity, absorbing his accounts of phenomena and his characteristic way of thinking about them. Maxwell was a strongly visual thinker and clearly preferred Faraday’s robust fields and lines of force to what he saw as the abstract attractions and repulsions of Weber’s theory, which he also read at this time. Most other theorists, however, would not take Faraday’s ideas seriously until they could be cast into rigorous mathematical form. Building on Thomson’s earlier work, Maxwell set out to do so. Over the winter of 1855–56, Maxwell wrote a long paper, “On Faraday’s Lines of Force,” in which he laid out what he called a “physical analogy” between Faraday’s lines of electric and magnetic force and the lines of flow of an imaginary fluid. Picture positive and negative charges, or the opposite poles of a magnet, as sources and sinks of a fluid that is generated at one pole and disappears into nothingness at the other. In a stable field, such a fluid would flow smoothly along the lines of force, as if confined within imaginary tubes. These tubes would grow fatter, and the flow within them slower, where the forces are weakest, and would be thinner and their flow more rapid where the forces are strongest. Maxwell showed that the mathematical rules governing the paths of such flows exactly match those governing Faraday’s lines of force, and that the known laws of attraction, repulsion, and inductive capacity could all be derived from this fluid model. Maxwell never meant for these tubes of fluid to be taken literally; he had introduced them, he said, solely to illustrate Faraday’s ideas about lines of force by relating them to the more familiar phenomenon of fluid flow. Maxwell’s ambitions went far beyond mere illustration, however, and he said he hoped his flow analogy might open the way toward “a mature theory, in which physical facts will be physically explained.”² Maxwell saw inklings of such a true physical theory in a paper Thomson published in 1856. By analyzing the Faraday effect, Thomson had shown that the magnetic rotation of light could occur only if something—either bits of ether or molecules of matter—was physically spinning around along the lines of magnetic force. The Atlantic telegraph project was then drawing Thomson more deeply into electrical topics, while his work with Joule had already con2. James Clerk Maxwell, “On Faraday’s Lines of Force” (1855), in Niven, Scientific Papers of Maxwell, 1:159.

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vinced him of the truth of the kinetic theory of heat. His Glasgow engineering colleague W. J. M. Rankine had recently published a theory of heat based on hypothetical “molecular vortices,” and now Thomson thought the Faraday effect might point the way toward a theory in which heat, light, electromagnetism, and perhaps even the structure of matter itself would be explained by the invisible motions of a mechanical ether. Thomson was laying out an ambitious program of mechanical explanation that would occupy him and many other leading physicists, especially in Britain, for the rest of the century. He did not immediately take up the task himself, however, and it was Maxwell who developed Thomson’s analysis of the Faraday effect into a remarkable new theory of the electromagnetic field. Maxwell’s Whirling Ether Writing in 1882, Maxwell’s friend Lewis Campbell said he wished he could “recall the date (1857?) of a drive down the Vale of Orr [near Maxwell’s home in Scotland], during which he described to me for the first time, with extraordinary volubility, the swift, invisible motions by which magnetic and galvanic phenomena were to be accounted for. It was like listening to a fairy-tale.”³ Maxwell published a detailed account of his theory in several installments in 1861–62 under the title “On Physical Lines of Force.”⁴ With its intricate array of whirling vortices and “idle wheel particles,” Maxwell’s model of the ether struck many readers at the time, and has struck many ever since, as a fairy tale, an example of the Victorian scientific imagination run wild. Complex and contrived as it was, however, Maxwell’s vortex model proved immensely fruitful, leading him to deep insights about the workings of the electromagnetic field and its relationship to light. Maxwell had already shown that magnetic forces can be explained by tensions acting along the lines of force and pressures pushing out laterally from them. Taking Thomson’s analysis of the Faraday effect as his starting point, he set out in “Physical Lines” to show that a spinning motion in the magnetic field could provide a mechanical cause for these tensions and pressures. Instead of picturing lines of force as tubes of flowing fluid, as he had in “Faraday’s Lines,” Maxwell now suggested that they were long vortices or whirlpools whose rapid spinning made them bulge out sideways and contract along their lengths. In Part I of his paper, he showed how bundles of such vortices, each much 3. Lewis Campbell and William Garnett, Life of James Clerk Maxwell (1882; repr., New York: Johnson, 1969), p. 199n. 4. James Clerk Maxwell, “On Physical Lines of Force,” Parts I–IV (1861–62), in Niven, Scientific Papers of Maxwell, 1:451–513.

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smaller than an ordinary molecule, could account mechanically for known magnetic forces. In particular, he showed that the kinetic energy of an array of such vortices, whether pictured as threads of whirling ether or strings of spinning spherical cells, would be spread across space in just the same way that, in Faraday’s theory, magnetic energy is distributed across the field. Maxwell admitted he did not yet have conclusive proof, but by 1861 he felt all but certain that magnetic fields are really filled with vortices of whirling ether. He even did an experiment to see if the vortices acted as tiny gyroscopes, as in principle they should, but his apparatus was not sensitive enough to give any definite result. So far so good—but as Maxwell noted, neighboring vortex cells would all be spinning in the same direction, forcing their adjoining edges to rub together and interfere. How could he avoid this problem and, if possible, enable the vortices to pass their motion smoothly from one to the next? Using a trick borrowed from mechanical engineering, Maxwell opened Part II of “Physical Lines” by adding a layer of small round particles between his vortex cells. Since these would spin in the opposite direction from the vortices, they would act as “idle wheels” to pass along rotational motion, as was often done in gearing for machinery. In a stable magnetic field, all of the vortices would turn together at a steady rate and the idle wheels would simply spin in place. Maxwell did not provide fixed axles for his idle wheels, however, and though he treated the wheels in electrical insulators as bound within a single molecule, those in a conductor would, he said, be free to move in any direction. Thus if some of the vortices in a conductor began to spin more quickly, corresponding to a changing magnetic field, the row of wheels caught between these faster vortices and the adjoining slower ones would be pushed along in the direction the faster ones were turning. This flow of idle wheel particles corresponded, Maxwell said, to an electric current produced by electromagnetic induction. As frictional forces brought the flow to a stop, and as the rapidly spinning wheels brought the slower vortices up to speed, everything would gradually settle down to a steady spinning in place, corresponding to the stable magnetic field left after the induced currents had died away. Conversely, if we could somehow push a row of idle wheels along, they would force the vortices on either side to turn in opposite directions, corresponding to an electric current setting up rings of magnetic force around itself. Maxwell sometimes referred to his idle wheel particles as “electricity,” but it is important to recognize that he did not regard them as carrying charge or being at all like Coulomb’s and Weber’s particles of electric fluid; Maxwell’s idle wheels were in no sense precursors of the electron. Maxwell’s ether was

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Maxwell’s Vortex Model of the Electromagnetic Ether In a long paper, “On Physical Lines of Force,” which appeared in installments in 1861 and 1862, James Clerk Maxwell laid out an intricate mechanical model of the ether, from which he derived the first version of his electromagnetic theory of light. The hexagonal cells shown here represent spinning vortices of ether, while the smaller circles represent “idle wheel particles” that serve to pass rotational motion from one layer of vortices to the next. The rotation of the vortices represents a magnetic field, Maxwell said, with the lines of magnetic force running along the axes of rotation (shown here as a plus sign for vortices spinning counterclockwise and as a minus for those spinning clockwise). If all of the vortices in a region are spinning at a steady rate, corresponding to an unchanging magnetic field, the idle wheel particles will simply rotate in place; if the rate of spin of the vortices changes, however, the idle wheel particles will be pushed along between the vortices until their rates of spin equalize. Conversely, if a line of idle wheel particles is forced along between two layers of vortices (as shown here from A to B), the vortices on either side will be

forced to turn in opposite directions, corresponding to the magnetic field set up around an electric current. In the last installments of his paper, Maxwell examined what would happen if the vortices were elastic, like pieces of rubber. He found that the medium would then be able to convey waves; moreover, measurements of electric and magnetic constants indicated that the waves would travel at the speed of light—strongly suggesting, he said, that light itself consists of waves in the same medium that exerts electric and magnetic forces.  James Clerk Maxwell, “On Physical

Lines of Force,” Philosophical Magazine 23 (1862): plate 1.

purely mechanical; the motion and pressure of his vortices and idle wheels produced what he identified as electric and magnetic forces, but they did so mechanically, not electromagnetically. Maxwell did not look on an electric current as a stream of charged particles flowing within a wire, but instead, as a field phenomenon defined primarily by the pattern of magnetic forces that appeared in the surrounding space. That in his model a row of idle wheel particles was pushed along in the direction of the current was, in Maxwell’s view, distinctly secondary.

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Toward the end of Part II, Maxwell admitted that the idea of idle wheels rolling along the rims of magnetic vortices might seem “somewhat awkward” and said he did not “bring it forward as a mode of connexion existing in nature, or even as that which I would willingly assent to as an electrical hypothesis.”⁵ This passage has often been cited by those who claim that Maxwell never meant for his vortex model to be taken seriously and only used it to explore a crude analogy between mechanical and electromagnetic systems. In fact, Maxwell made it clear that the idle wheels were the only part of his model that he considered “awkward,” and that he thought the evidence for the real existence of magnetic vortices remained strong. Contrived and clumsy as they were, Maxwell’s idle wheels had the merit in his eyes of showing that mechanical causes could in principle account for electromagnetic phenomena, and so of pointing the way toward a mature theory in which the true mechanism of the field would be revealed. Part II of “Physical Lines” appeared in April and May 1861, and Maxwell originally meant for that to be the end of it. Over the summer, however, he began looking for a way to make his model account for electrostatic forces. When he found one, he got an unexpected bonus: evidence that light itself might be waves in the same medium that produces electric and magnetic forces. He took up his paper again and added two new parts, published early in 1862, that proved even more important than the earlier installments. Maxwell already knew that to make his vortex cells spin properly and bulge in the middle in the way needed to produce magnetic forces, they had to be elastic solids—they must, like rubber balls, yield to pressure and then spring back when it was released. As we have seen, he also assumed that in conductors the idle wheels would be free to move in any direction while in insulators they would be bound within a single molecule. What happened, then, at the boundary between a conductor and an insulator—for instance, between the plates of a Leyden jar? The elasticity of the vortex cells gave the machinery some “give,” so that as the idle wheels moving through the conductor butted up against the insulating dielectric, they were not immediately brought to a stop. Instead, they strained and twisted the vortices within the dielectric until the distorted cells pushed back hard enough to make the whole system lock up. This corresponded to the charging of a Leyden jar, with energy being stored in the strained vortices just as it was in a dielectric subject to electric induction. Maxwell even used energy considerations to show that the patterns of elastic strain 5. Maxwell, “On Physical Lines of Force, Part I” (1861), in Niven, Scientific Papers of Maxwell, 1:486.

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in the vortices would produce attractive and repulsive forces just like those between electrostatic charges. Maxwell soon realized a deeper point: the process of straining the vortices would itself constitute a fleeting electric current. In the short time it took to twist the vortices until they locked up, the idle wheel particles around each vortex cell would be slightly displaced from their initial positions. This brief motion did not amount to a regular current, Maxwell said, but it was the beginnings of one, and it would occur even in nonconductors, including in seemingly empty space. The “displacement current” generated by a changing electric force became a crucial part of Maxwell’s field theory and later provided the keystone he needed to complete his system of electromagnetic equations. The next implication Maxwell drew from his model was even more notable. If the electromagnetic medium is an elastic solid, he reasoned, then it must be able to vibrate and carry transverse waves like those we see in a block of rubber or a bowl of jelly. We can find the speed of such waves in two different ways: by timing their passage directly, or by separately measuring the density and rigidity of the medium and then inserting those values into the appropriate wave equation. In the summer of 1861, Maxwell worked out a formula that expressed the speed at which waves would travel through his vortex medium in terms of known electric and magnetic constants. He had to make several simplifying assumptions, and some of his methods of calculation were later criticized, but his final result was certainly eye-catching: the waves in his vortex medium appeared to travel at almost exactly the speed of light. The key number in Maxwell’s theory was the ratio between the electrostatic and electromagnetic units of charge. Weber and Kohlrausch had measured this “ratio of units” in Germany in 1856 and found it to be a velocity equivalent to 310,740 kilometers per second, or 193,088 miles per second. The best figure Maxwell could find for the speed of light, from measurements the French physicist Hippolyte Fizeau had made using a rapidly spinning toothed wheel, was 193,188 miles per second. This was an astonishingly close match, and Maxwell initially regarded it as conclusive; in Part III of “Physical Lines,” published in January 1862, he declared that “we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”⁶ In fact, the match was a little too good to be true; Maxwell had seen a mistaken report of Fizeau’s result, which should have been 195,647 miles per second, and Weber and Kohlrausch’s measurement of 6. Maxwell, “On Physical Lines, Part III” (1862), in Niven, Scientific Papers of Maxwell, 1:500; the emphasis is Maxwell’s.

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the ratio of electrical units was open to considerable uncertainty. Nailing down those numbers and establishing just how close to each other they really were would prove to be a demanding task, as Maxwell himself soon found. When the last two parts of “Physical Lines” appeared in 1862, Maxwell did not yet have a fully formed electromagnetic theory of light. He had a mechanical theory of light as waves in an elastic solid, and a mechanical theory of electric and magnetic forces as the strain and motion of his vortices and idle wheels. He also had a numerical coincidence that suggested his vortices were made of the same elastic substance that carried the waves of light. He was not, however, able to describe these waves in purely electromagnetic terms, and when in the last part of his paper he tried to use his spinning vortices to explain Faraday’s magnetic rotation of light—the discovery that had started it all—he had only partial success. Maxwell felt sure he was on the trail of a deep truth about electromagnetism and light, but he was not there yet. When “Physical Lines” first appeared, most physicists regarded it as clever but not entirely convincing. As one of Maxwell’s friends told him, the coincidence between the speed of light and the ratio of units was “a brilliant result,” but it would take more than that to convince people that “every time an electric current is produced, a little file of particles is squeezed out between rows of wheels.”⁷ Maxwell’s model could account for most known electric and magnetic phenomena, but it did not fit the experimental evidence any better than Weber’s theory did, and it required more hypotheses about the structure of the ether than most physicists were willing to swallow. The main empirical point in Maxwell’s favor was the apparent match between the speed of light and the ratio of units, but it would take a lot of work, both theoretical and experimental, to make that coincidence scientifically persuasive. To bolster his case, Maxwell would need better electrical measurements. His pursuit of them over the coming years would have far-reaching consequences for both high theory and industrial technology. Cables, Ohms, and the Speed of Light As it happened, Maxwell’s desire in the early 1860s to pin down the value of the ratio of units coincided with a push by the cable industry to adopt a standard system of electrical units. The failure of the first Atlantic cable led to widespread calls for more accurate electrical testing and better quality control, and particularly for a reliable and uniform standard of electrical resistance. Before the 1860s, no such accepted standard existed, leaving cable engineers with 7. C. J. Monro to James Clerk Maxwell, 1861, in Campbell and Garnett, Maxwell, p. 329.

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no effective way to compare and combine their electrical measurements. Working closely with scientists, they eventually settled on a unit of resistance, the “ohm,” whose value was closely tied to the ratio of units and thus, on Maxwell’s theory, to the speed of light. Maxwell played a leading role in the laboratory work needed to settle the value of the ohm and in subsequent efforts to measure the ratio of units. He began this work in hopes it would strengthen the evidence supporting his theory of the electromagnetic field; what he perhaps did not anticipate was the important effect his encounter with the practicalities of electrical measurement would have on the way he thought about and formulated that theory. In its 1861 report, the Joint Committee on submarine telegraphy had put much of the blame for the failure of the first Atlantic cable on the inadequate methods of electrical testing used by Wildman Whitehouse, the company electrician. Echoing remarks Thomson and others had made in their testimony, the committee called for the adoption of standard measures of electrical resistance and capacity similar to the units of length and weight had that long been established by law. Without such standards, the committee warned, engineers could not ensure the quality of the copper and gutta-percha used in their cables, nor could they draw up accurate specifications or enforceable contracts. With proper standards, they would be able to measure and record the exact resistance of each mile of cable they laid and, by tests performed on the shore ends, could direct repair ships to the exact location of any breaks or faults in the insulation. In the summer of 1861, Thomson set out to enlist the British Association for the Advancement of Science to supply this need, and with the help of a young cable engineer named Fleeming Jenkin (1833–85), he soon secured the appointment of a committee of physicists, chemists, and telegraph engineers to devise an appropriate standard of electrical resistance. Thomson was not alone in pushing for the adoption of electrical standards. At the same 1861 meeting of the British Association, two leading cable engineers, Charles Bright (1832–88) and Latimer Clark (1822–98), issued their own call for a connected system of units for electrical resistance, tension (or voltage), current, and capacity. They laid out how the units would be related to one another, principally through Ohm’s law (voltage  current  resistance), and suggested the units be named for famous electrical researchers (“volt,” “ohma,” “farad,” and so on). They urged that the magnitudes of the units be chosen to suit the practical needs of telegraphers and worried at first that Thomson’s committee might focus too closely on purely scientific niceties. In fact, the interests of cable engineers were always strongly represented on the British Association committee, which both Bright and Clark later joined.

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The idea of defining a unit of electrical resistance was not new in the 1860s. In 1843 Wheatstone had proposed a unit based on the resistance of a copper wire a foot long, and in the early 1850s telegraph engineers introduced their own units based on the resistance of a mile or kilometer of wire of specified thickness. It soon became clear, however, that supposedly identical samples of copper often differed widely in their resistivity; in 1857, Thomson found that some lengths of wire intended for the first Atlantic cable conducted only about half as well as others. It turned out that very slight impurities could greatly affect the resistivity of copper, calling into question any unit defined by a specified length and thickness of wire. Mercury seemed to be free of this problem, and in 1860 the German industrialist Werner von Siemens proposed a unit based on the resistance of a tube of pure mercury one meter long and one square millimeter in cross section. A primary mercury standard could be very accurately made, Siemens said, and handier wire coils then calibrated against it. Siemens’s unit was not, however, part of any unified system of units for voltage, current, and other electrical quantities. Such a unified system already existed in 1861, but almost no one used it. Building on Gauss’s earlier work on magnetism, in 1851 Weber had devised a system of “absolute” electrical units based not on the resistance of a coil of wire, but on the mechanical unit of force, and so ultimately on the fundamental units of length, mass, and time—in the metric system, the meter, the gram, and the second. He defined a unit of charge as one that (by Coulomb’s law) would exert a unit of force on an identical charge a unit distance away, and a unit of current as one that (by Ampère’s law) would exert a unit of force on a parallel current a unit distance away. As we have seen, the ratio between the resulting electrostatic and electromagnetic units of charge came out as a velocity; according to Weber, who pictured currents as streams of electrical particles, it was essentially the speed at which the electromagnetic repulsion between two moving charges of opposite sign exactly balanced their electrostatic attraction. He noted that this speed was very great, comparable to that of light, but gave no particular significance to this fact. Using Ohm’s law to define the electromagnetic unit of resistance, Weber showed that it, too, came out as a velocity, but with a magnitude that was far too small to be of much practical use: a piece of ordinary copper wire with a resistance of 1 meter per second would be less than a thousandth of an inch long. Not surprisingly, most telegraph engineers who knew of Weber’s system regarded it as little more than a scientific curiosity. Thomson, who had one foot among the cable engineers and one among the physicists, saw great merits in Weber’s system and pushed the British Asso-

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ciation committee to adopt a version of it. He had a simple answer to those who objected that Weber’s resistance unit was too small: just use a convenient decimal multiple. If the practical unit of resistance, the “British Association unit” or ohm, were set equal to 10 million meters per second in Weber’s system, it would have a value close to that of Siemens’s mercury unit and about equal to the resistance of 200 feet of ordinary copper wire. For Thomson, the great attraction of Weber’s system was the way it tied the units for resistance, tension, and current together through the unit for work, or energy, “the great connecting link between all physical measurements.”⁸ In particular, the product of electrical tension and current is power (in modern terms, volts  amps  watts), so that simple multiplication gives the rate at which a current performs work or, as Joule had shown in the 1840s, generates heat in a resistor. Weber’s focus on forces acting between particles reflected his essentially Laplacian approach to electrical phenomena. Thomson, himself a pioneer of the new science of thermodynamics, saw an emphasis on energy relations as a way to bring electrical measurements into line with the great unifying theme of nineteenth-century physics. When the British Association committee began its work in 1861, Maxwell was a young physics professor at King’s College London. He had little experience with electrical measurements, but his vortex model had convinced him that such measurements held the key to confirming his electromagnetic theory of light. Toward that end, he joined the British Association committee in 1862 and soon became one of its most active members. He and Fleeming Jenkin coauthored an important paper “On the Elementary Relations between Electrical Measurements” and, with the physicist Balfour Stewart and the cable engineer Charles Hockin, began the painstaking laboratory work required to turn the ohm from an abstract unit into a physical standard. Using a technique devised by Thomson, they spun a coil rapidly in the earth’s magnetic field and, by noting how a magnetized needle was deflected by the induced currents, calculated the absolute resistance of the coil. The committee issued its first tentative resistance standards at the end of 1863 and early in 1865 began sending certified copies of its official ohm to physicists, cable companies, and instrument makers around the world. Maxwell’s vortex model, with its whirling gears and idle wheels, has often been seen as a prime example of physics done in the style of a Victorian mechanical engineer, and so in a sense it was. But Maxwell’s work on the British 8. William Thomson (1862), quoted in Crosbie Smith and Norton Wise, Energy and Empire: A Biographical Study of Lord Kelvin (Cambridge: Cambridge University Press, 1989), p. 687.

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Association committee led him to think like an engineer in another and deeper sense as well. At least for a time, he put aside speculations about the unseen causes of phenomena and focused instead, as engineers generally do, on factors he could measure and control. Amid his work on the ohm, Maxwell set out to reformulate his theory of the electromagnetic field in a way that did not depend on hypothetical mechanisms in the ether and that tied his equations far more closely to measurable electric and magnetic quantities. Rather than imagining invisibly small vortices and idle wheels, he now assumed only that the electromagnetic field forms a connected mechanical system subject to the general laws of dynamics. On this basis he proceeded to work out exactly how changes in the electromagnetic state of one portion of the field would affect that of another. He still believed that the ether possessed a complex mechanical structure—indeed, he still thought it probably contained tiny spinning vortices—but he wanted to see how far he could go toward explaining observable electromagnetic phenomena without relying on any specific mechanical hypotheses. The result, completed toward the end of 1864, was “A Dynamical Theory of the Electromagnetic Field,” widely regarded as Maxwell’s greatest scientific paper. Using the techniques of Lagrangian analysis, he derived a set of equations that connected the electric and magnetic variables to each other and to the energy stored in the field. He also defined the “vector potential,” from which other electric and magnetic quantities could be mathematically derived, and clarified the nature of the displacement current he had first introduced in “On Physical Lines of Force.” Most notably, he expressed his theory of light in purely electromagnetic form, free of its previous reliance on mechanical waves in an elastic solid ether. When Maxwell wrote to friends about his “Dynamical Theory,” he cast his achievement in terms of electrical measurements and the ratio of units. He told Hockin, for example, that he had “cleared the electromagnetic theory of light of all unwarrantable assumption, so that we may safely determine the velocity of light by measuring the attraction between bodies kept at a given difference of potential, the value of which is known in electromagnetic measure.”⁹ He went on to do just that, devising a delicate electrical balance that he and Hockin used in 1868 to measure the ratio of units in terms of the British Association ohm. It came out as 28.8 ohms or, taking the ohm at its intended value of 10 million meters per second, 288,000 kilometers per second. This was 9. James Clerk Maxwell to Charles Hockin, 7 Sept. 1864, in Campbell and Garnett, Maxwell, p. 340.

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about 3 percent below the best recent measurements of the speed of light— fairly close, though not quite close enough to convince skeptics that the electromagnetic theory of light had been conclusively confirmed. Maxwell’s value for the ratio of units depended on that of the British Association ohm, however, and in the 1870s it became clear that the standards the committee had issued in 1865 were a little under their intended value. Once this was corrected, and as methods for comparing currents and charges were further improved, the best measurements of the ratio of units and of the speed of light gradually converged on a value of about 299,800 kilometers per second, or 186,300 miles per second. Maxwell regarded his theory of the electromagnetic field, his work on the ohm, and his measurement of the ratio of units as all of a piece, a confluence of high theory and practical technology in which each fed the other. Addressing the British Association in 1871, Thomson cited Maxwell’s work on electrical units and the electromagnetic theory of light as a prime example of how science gains from its ties to technology. “Those who perilled and lost their money in the original Atlantic Telegraph” had hoped both to improve communications and earn themselves a profit, Thomson said, but they scarcely realized that when in the wake of its failure they turned to the British Association for a practical standard of resistance, they were “laying the foundation for accurate electric measurement in every scientific laboratory in the world, and initiating a train of investigation which now sends up branches into the loftiest regions and subtlest ether of natural philosophy.”¹⁰ In 1865 Maxwell left King’s College London and retired to his Scottish estate to take up the life of a country gentleman. He continued to produce a stream of scientific papers, however, and returned to London at intervals to do experiments. He also began serving as an outside examiner for the Mathematical Tripos at Cambridge, helping reintroduce questions on electricity, magnetism, and heat. In part to meet the needs of students attempting to tackle such questions, he began writing his great Treatise on Electricity and Magnetism, published in two volumes in 1873. It was a rich but often confusing compendium of mathematical and experimental techniques, in which Maxwell put little real emphasis on his own distinctive ideas. Extracting “Maxwell’s theory” from Maxwell’s Treatise would prove to be a demanding task. In the 1860s, Cambridge was coming under pressure to modernize its teaching of scientific subjects to better serve the practical needs of industrial Britain. 10. William Thomson, 1871 address to the British Association, in Thomson, Popular Lectures and Addresses, 3 vols. (London: Macmillan, 1891–94), 2:161–62.

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The university responded by establishing a new professorship of experimental physics in 1871, with the promise of a laboratory to be funded by William Cavendish, the Duke of Devonshire, a prominent aristocrat who was also a leading industrialist. Thomson was the obvious first choice for the chair, but when he declined to leave Glasgow, the position was offered to Maxwell, who accepted and set about teaching in borrowed rooms until the new Cavendish Laboratory opened in 1874. Maxwell did surprisingly little to promote his new electrical theory at Cambridge. He lectured on it, but most students preferred the more structured teaching offered by specialized mathematics “coaches,” and by the late 1870s his classes often drew only three or four students. A few students came to work with him at the Cavendish Laboratory, but Maxwell left them to follow their own noses and made little effort to draw them into exploring his electrical theory. He began to revise his Treatise for a second edition, correcting many errors and obscurities along the way, but had made it only a quarter of the way through when he was struck down by cancer. He was 48 when he died in November 1879. Maxwell’s electrical teachings were eventually taken up at Cambridge, both by mathematical physicists in the colleges and by experimenters at the Cavendish Laboratory, where in the 1880s his successor, Lord Rayleigh (1842–1919), focused on precision electrical measurement and the redetermination of the ohm. But this was a slow process, and it was outside Cambridge, notably in the context of cable telegraphy, that many of Maxwell’s ideas were first and most fully explored. Maxwellian Waves At the time of his death in 1879, Maxwell’s theory of the electromagnetic field was neither well understood nor widely accepted. Most physicists looked on it as just one of several competing theories of electromagnetism. Indeed, other than a somewhat shaky coincidence between the speed of light and the ratio of electrical units, there was little direct empirical evidence in its favor. Ten years later, the status of the theory was completely different. In Britain, a group of young “Maxwellians” had traced out its chief implications and cast it into much clearer and more compelling form, while in Germany, Heinrich Hertz’s detection of electromagnetic waves in 1888 had given the theory the dramatic experimental confirmation it had previously lacked. By the mid-1890s, Maxwell’s theory was almost universally accepted as the theory of electromagnetism, and scientists and inventors were taking the first steps toward putting electromagnetic waves to use for wireless communications. Maxwell’s theory

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has been regarded ever since as one of the greatest achievements of modern science, ranking with Newton’s laws of motion; in 1964, the American physicist Richard Feynman (1918–88) went so far as to declare that “from a long view of the history of mankind . . . there can be little doubt that the most significant event of the nineteenth century will be judged as Maxwell’s discovery of the laws of electrodynamics.”¹¹ The “Maxwell’s theory” that passed into general circulation in the 1890s was not, however, quite the same as the one Maxwell had originally propounded. Many of its most distinctive features—the paths by which energy flows through the field, for example, and even the existence of electromagnetic waves longer than those of light—were not clearly recognized by Maxwell himself and had to be teased out later by others. Even the now standard form of “Maxwell’s equations,” as a set of four vector equations connecting the electric and magnetic field strengths, was taken not from Maxwell’s own writings but from those of Oliver Heaviside, a cable engineer turned mathematical physicist. Maxwell undoubtedly laid the foundations, but important parts of “Maxwell’s theory” were in fact the work of his successors. G. F. FitzGerald (1851–1901) was one of the first to add significantly to Maxwell’s theory. As a young physicist at Trinity College Dublin, he heard in 1876 of the discovery that reflection from the polished pole of a magnet could alter the polarization of light. The phenomenon was closely related to the Faraday effect, and FitzGerald thought Maxwell’s theory ought to be able to explain it. Maxwell, however, had never formulated a purely electromagnetic theory of the reflection of light, a gap FitzGerald filled by drawing on an almost forgotten theory of the ether that his Dublin predecessor James MacCullagh (1809–47) had devised in 1839. MacCullagh’s ether gave a good account of most optical phenomena, but it had such peculiar properties—its parts did not resist ordinary compression or distortion, but only rotation—that most physicists rejected it as unworkable. FitzGerald showed, however, that the equations of MacCullagh’s rotational ether could be directly translated into those of Maxwell’s electromagnetic field, and that they brought along a full mathematical theory of the reflection and refraction of light. FitzGerald went on to clarify and correct several other points in Maxwell’s theory, particularly concerning the effects of moving charges. FitzGerald went badly astray, however, on the subject of electromagnetic waves. In 1879 his friend and fellow Maxwellian Oliver Lodge (1851–1940), a 11. Richard P. Feynman, The Feynman Lectures on Physics, 3 vols. (Reading, MA: AddisonWesley, 1963–65), 2:1.11.

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London-trained experimentalist, hit on an intriguing idea. If Maxwell’s theory was right, Lodge suggested, any rapidly oscillating electric current ought to generate electromagnetic waves in the ether, and if we could push the frequency as high as 5  1014 cycles per second, corresponding to a wavelength of less than 106 meters (about 1⁄ 40,000 of an inch), the resulting waves ought to be visible as light. Lodge even proposed possible ways to produce such rapid oscillations, including using the discharge of a small condenser or Leyden jar. But FitzGerald quickly threw cold water on his friend’s idea, citing passages from Maxwell’s Treatise that showed, he said, that the energy of an electric circuit could never be radiated away in waves like those of light. Maxwell believed light to be waves in the electromagnetic medium, but he thought the waves were generated by an unknown molecular process rather than by electrical forces. He seems never to have considered that it might be possible to produce and detect electromagnetic waves longer than those of light—and so missed out on predicting the “radio waves” that in retrospect rank as the most distinctive and technologically important implication of his theory. Discouraged by FitzGerald’s negative verdict, Lodge dropped the idea of producing “electromagnetic light” and turned his attention elsewhere. In 1882, however, FitzGerald found he had blundered. On closer examination it turned out that Maxwell’s strictures against the possibility of a circuit radiating away its energy were based on an approximation that ignored the effect of displacement currents. Once he took these into account, FitzGerald found that almost any oscillating current would generate electromagnetic waves. Although he could see no practical way to achieve frequencies high enough to generate Lodge’s visible light, FitzGerald was able to show that the discharge of a small condenser would produce waves a few meters long, and even managed to calculate how much energy they would carry away. He could not devise a way to detect these waves of invisible “light,” however, and they remained tantalizingly out of reach for several more years. In the meantime, electromagnetic waves were taken up in a very different context by Oliver Heaviside (1850–1925). To call Heaviside eccentric would be an understatement; his best friend of his later years once described him as “a first rate oddity,” though “never a mental invalid.”¹² Personal quirks aside, Heaviside made enormous contributions to Maxwellian theory, particularly its application to telegraphic problems. The son of a London artisan, he left 12. G. F. C. Searle, “Oliver Heaviside: A Personal Sketch,” in Institution of Electrical Engineers, Heaviside Centenary Volume (London: IEE, 1950), p. 96.

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div E  0 div H  0 Maxwell’s Equations in Heaviside’s Vector Form Oliver Heaviside hit on this simple symmetrical form of Maxwell’s equations in 1885. The vector operations “div” and “curl” capture how the strength and direction of fields vary in space, while /t captures how they vary with time. These equations show how the electric field strength (E) and the magnetic field strength (H) are

curl H 

E t

curl E  H t related to each other when there are no charges or currents in the neighborhood; introducing such charges and currents adds additional terms to the equations. Notice that, except for a minus sign and the constants and , we can switch the places of E and H in all of these equations, giving them a powerful symmetry. Heaviside’s form of Maxwell’s equations became standard in the 1890s and, with small variations, is the form still used today.

school when he was 16 and was almost entirely self-taught in science and mathematics. He had the good fortune, however, to have Charles Wheatstone as an uncle and through him landed a job working on a telegraph cable that had been laid across the North Sea in 1868. He soon became fascinated by electrical phenomena and, after reading all he could find on the subject, began publishing his own analyses of telegraphic problems. Heaviside’s caustic wit and prickly self-regard made him an amusing writer but a difficult coworker. Conflicts on the job, together with ill health and a desire to devote more of his time to his electrical studies, led him to “retire” from the cable company when he was just 24. He spent the next 20 years living with his parents, first in London and later in Devonshire, and never again held a regular job. It was a pinched and difficult life, but Heaviside was sustained by the sense that he was making fundamental discoveries—as indeed he was. Heaviside’s first important work was a revision of Thomson’s 1854 theory of cable signaling. Thomson had shown that the resistance of a cable and its capacity to store charge combine to make signals diffuse along the line like heat passing along a rod. It was a useful theory as far as it went, but in the 1870s Heaviside showed that if we also take into account “self-induction,” a sort of electromagnetic inertia that opposes any sudden changes in the current, we find that the current does not simply diffuse along the cable but instead surges

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back and forth in a series of waves. To understand such waves more fully, and to carry his analysis outside the wire into the surrounding dielectric, Heaviside turned to Maxwell’s Treatise. Working alone in his room, Heaviside read Maxwell’s book with a probing intensity that few could match. Early on, he began to strip away what he saw as unnecessary mathematical baggage, paring down the often clumsy array of symbols in which Maxwell had dressed his equations and devising a simple vector algebra that scientists and engineers still use today. He also began to explore the physical workings of Maxwell’s field, particularly the distribution of energy. Maxwell had given formulas that specified how energy is stored in the space around currents and charges but had said little about how this energy gets from one place to another. Heaviside focused on precisely this question, for he regarded the clean transmission of energy along a wire—the energy needed to trip a lever or deflect a needle—as the key to effective telegraphy. His big breakthrough came in 1884. After laboriously manipulating Maxwell’s original formulas, he hit on a remarkably simple result: the flow of energy at any point in the field is simply the vector product of the electric and magnetic forces at that point: S  E  H. This led to some surprising results, in particular, that the energy conveyed by an electric current does not flow along within the wire, as everyone had always assumed, but instead passes through the surrounding space and converges on the wire, where it is converted into heat or work. This might seem odd to those who pictured electric power flowing in a wire like water in a pipe, but in the context of Maxwellian theory it made perfect sense, for it put the real action out in the field rather than in the currents and charges themselves. Heaviside thought a result as fundamental as his energy flow formula ought to follow directly from the basic equations of electromagnetism, and he proceeded to recast Maxwell’s theory so that it would. Working backwards, he derived the set of four vector equations now universally known as “Maxwell’s equations”—formally equivalent to Maxwell’s own set of equations based on the vector potential, but simpler, more symmetrical, and, as Heaviside insisted, far more closely related to the physical state of the field. He published these equations in a series of articles in The Electrician, a weekly electrical trade journal, early in 1885 and used them as the foundation on which to rebuild Maxwell’s theory in a clearer and more usable form. Heaviside did not know it, but a Cambridge-trained physicist, J. H. Poynting (1852–1914), had hit on the energy flow formula a few months before him, which is why it is now known as Poynting’s theorem rather than Heaviside’s. But while Poynting used the formula to clarify some important points in Max-

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well’s theory, it did not lead him, like Heaviside, to recast the basic equations. Poynting saw the flow formula as a pretty mathematical theorem that offered some useful physical insights; Heaviside, saturated as he was in problems of telegraphic propagation, saw it as the key to understanding electromagnetic theory as a whole. Heaviside’s recasting of Maxwell’s theory initially attracted little attention, perhaps in part because it first appeared in the pages of a trade journal, squeezed between business notices and advertisements for wires and insulators. Heaviside was a complete outsider, and it was all too easy for more established scientists and engineers to dismiss him as a crank. Consider his views on selfinduction. Telegraphers had long regarded it as an obstacle to clear signaling and tried to eliminate it whenever they could, yet in 1887 Heaviside said his theories showed that the best way to improve signaling on telegraph and telephone lines was to increase their self-induction. W. H. Preece, the chief engineer of the British Post Office telegraph department, denounced this as nonsense and took steps to block Heaviside from publishing further. Already marginalized, Heaviside might have been silenced altogether had it not been for two unexpected experimental developments: Lodge’s discovery of electromagnetic waves along wires and Hertz’s even more spectacular discovery of electromagnetic waves in air. Lodge’s discovery grew out of experiments on lightning protection he performed early in 1888 in which he simulated lightning strikes by discharging Leyden jars into long wires. He soon noticed some odd resonance phenomena and realized that the oscillatory discharge of his jars was sending electromagnetic waves skittering down the wires. By letting the waves reflect from the far end and set up interference patterns, he was able to measure their wavelengths and other properties. As a confirmed Maxwellian, Lodge looked on the waves as primarily field phenomena, with the wires serving solely to guide and concentrate them. When he set out to analyze the behavior of the waves, Lodge found exactly the theoretical tools he needed in Heaviside’s writings, and in March 1888 he publicly praised what he called Heaviside’s “masterly grasp” of Maxwell’s theory.¹³ Heaviside was grateful finally to have a scientific ally, and he and Lodge soon struck up a lively and mutually supportive correspondence. Lodge headed into the summer of 1888 thinking his discovery of waves on wires would be the hit of the upcoming British Association meeting, but he 13. Oliver J. Lodge, “The Protection of Buildings from Lightning,” The Electrician 21 (1888): 236.

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Hertz’s Electromagnetic Wave Apparatus In 1888, the German physicist Heinrich Hertz used the apparatus shown here to produce and detect electromagnetic waves. He connected an induction coil ( J ) to two metal sheets (A and A) that were separated by a small gap. The induction coil charged the metal sheets until the voltage between them became high enough to make a spark jump across the gap; the electric field around the sheets then collapsed, sending the outlying parts of the field flying off as electromagnetic waves. Hertz used handheld wire loops (B and C ) with small spark gaps to detect these waves. As the waves struck the loops, they induced electric currents that oscillated back and forth; if the resonant frequency of the loop matched that of the waves, the oscillations would build up until they made tiny sparks jump

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the gap in the loop. By moving a loop back and forth and squinting at sparks that were barely visible in a darkened room, Hertz was able to detect and measure the standing wave patterns that were set up when he bounced electromagnetic waves off a wall or when, as shown here, he sent waves both through the air and along a wire he had connected to the metal sheets. Hertz’s experiments were hailed as strong confirmation of Maxwell’s theory and soon led to the wide acceptance of field theory in Germany. His work also provided the starting point from which Oliver Lodge, Guglielmo Marconi, and others later developed wireless telegraphy and other forms of radio communications.

 Heinrich Hertz, Electric Waves, trans.

D. E. Jones (London: Macmillan, 1893), p. 108.

was soon upstaged by news out of Germany. Heinrich Hertz (1857–94) had been the top student in Helmholtz’s Berlin laboratory, excelling as both a theorist and an experimenter. In the early 1880s he set out to find an experimental test to decide among Weber’s, Neumann’s, and Maxwell’s electrical theories. He made little headway until 1886, when he took up a new job at an engineering school, the Technische Hochschule in Karlsruhe. While trying out some equipment, he noticed unexpected sparking when he discharged one coil

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of wire near another. Following this up, by late 1887 he had produced evidence of electromagnetic waves traveling along wires, and by March 1888 he was sending waves several meters long flying through the air and bouncing them off the walls of his lecture hall. Hertz’s key step was to achieve resonance between the source of his waves, essentially an opened-up condenser, and his detector, a loop of wire with a small adjustable gap. When waves of the right frequency struck the detector, tiny sparks, barely visible in a darkened room, would jump across the gap, enabling Hertz to trace the interference patterns set up by the waves reflected from his walls. In later terms, he was “tuning” his receiver to the frequency of his waves, about 50 million cycles per second or, as we would now say, 50 megahertz. There were some ambiguities in Hertz’s early results, and he only gradually came to see them as fully confirming Maxwell’s theory. The British Maxwellians showed no such hesitation, and at the September 1888 meeting of the British Association in Bath, FitzGerald made a point of hailing Hertz’s experiments as the long-sought proof that electromagnetic waves really exist. Though he was disappointed to see his own experiments overshadowed, Lodge soon joined in the chorus of praise for Hertz’s work, and “Hertzian waves” figured prominently in the discussions of self-induction, lightning conductors, and electromagnetic propagation that made the Bath meeting a watershed in the fortunes of Maxwellian theory and the Maxwellian group. Heaviside was not at Bath—he never attended scientific meetings—but his name came up frequently there and the meeting helped spark his transformation from obscure crank to recognized scientific authority. He began to correspond with FitzGerald and Hertz, as well as Lodge; his work began to draw favorable notices in scientific journals; and in January 1889 Thomson devoted much of his presidential address to the Institution of Electrical Engineers (formerly the Society of Telegraph Engineers) to praise for Heaviside’s theory of signal propagation. Over the next few years, Heaviside’s electrical writings were collected and published in two fat volumes, he was elected a Fellow of the Royal Society of London, and his version of “Maxwell’s equations” began to take its place in textbooks as the standard way of expressing the theory. His proposal to improve the clarity of telegraph and telephone signals by loading lines with extra self-induction was taken up in the late 1890s and made a fortune for AT&T and other corporations, though Heaviside, who had not patented the idea, never made a penny from it. Heaviside continued to hold a grudge against Preece and other “practicians” who had earlier opposed him, but after 1888 he could afford to make light of their resistance to the idea that scientific theory could ever have any-

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thing useful to contribute to engineering practice. Reports of the discussions at the Bath meeting even inspired Heaviside to burst into verse, in a pointed jab at Preece: Self induction’s “in the air,” Everywhere, everywhere; Waves are running to and fro, Here they are, there they go. Try to stop ’em if you can You British Engineering man!¹⁴

Electromagnetic waves were very much “in the air” after 1888, and Hertz’s experiments were soon repeated and extended by Lodge and others in Britain, Germany, the United States, and other countries around the world. Most of the scientists who performed these experiments were intent on exploring the properties of the waves and demonstrating their similarities to light by showing, for example, that they could be reflected, refracted, and polarized. The scientists gave little thought to using the waves to send signals, but in the mid1890s a young Italian, Guglielmo Marconi (1874–1937), set out to do just that. Starting with apparatus similar to Lodge’s and tinkering with it to find what worked best, Marconi did experiments on his father’s estate in which he managed to send and receive wireless signals over ranges of up to a mile. In 1896 he headed to London in hopes of attracting investors and tapping a potential market for ship-to-shore communications. Aided by others with more scientific expertise, particularly J. A. Fleming (1849–1945), a professor of electrical engineering who had studied under Maxwell, Marconi pushed his system forward rapidly, adapting it both for shipboard use and for long distance—eventually transatlantic—point-to-point wireless telegraphy. By the 1910s, new transmitters and receivers based on vacuum tubes made it possible to send and receive audible speech, and the rapid development of radio broadcasting in the 1920s transformed mass communications in ways that Marconi, not to mention Hertz or Maxwell, could scarcely have imagined. Electromagnetic waves soon became central to some of the most revolutionary technologies of the twentieth century. On the surface, the story of the prediction, detection, and commercial use of electromagnetic waves might look like a straightforward example of pure science leading to technological applications, in a sequence running from Max14. Heaviside notebook 7, p. 113, Heaviside Collection, Institution of Engineering and Technology, quoted in Bruce J. Hunt, The Maxwellians (Ithaca: Cornell University Press, 1991), p. 173.

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well and Hertz to Marconi and the first broadcasters. As we have seen, however, the development of Maxwellian theory and the discovery of electromagnetic waves were in fact the products of a complex interplay between science and technology, with important influences running both ways. Faraday’s field theory did not attract much real attention or support until telegraphers took it up by in the 1850s, while Thomson, Maxwell, and Heaviside were only the most prominent of the later electrical theorists whose work was shaped by demands and opportunities arising from the growth of the British cable industry. Maxwell was well aware of how deeply telegraphy had influenced the development of electrical science. In the preface to his Treatise on Electricity and Magnetism, he remarked: The important applications of electromagnetism to telegraphy have . . . reacted on pure science by giving a commercial value to accurate electrical measurements, and by affording to electricians the use of apparatus on a scale which greatly transcends that of any ordinary laboratory. The consequences of this demand for electrical knowledge, and of these experimental opportunities for acquiring it, have been already very great, both in stimulating the energies of advanced electricians, and in diffusing among practical men a degree of accurate knowledge which is likely to conduce to the general scientific progress of the whole engineering profession.¹⁵

The rise of field theory in the nineteenth century was closely tied to the rise of electrical technology, particularly cable telegraphy. As new technologies exposed scientists to phenomena they would never have encountered in the laboratory—the retardation of signals on long telegraph cables being the most notable example—they stimulated research that led on the one hand to deeper scientific insights and on the other to improved technologies. Electrical science and technology fed each other in a mutually reinforcing cycle that expanded the scale on which work on electricity was pursued, drove it forward into new areas, and shaped the directions in which it developed. As Maxwell noted, the rise of the telegraph industry had already sparked an enormous growth in the demand for electrical knowledge in the 1860s and 1870s. That demand would grow even more in the 1880s and 1890s, with consequences that would reach into every corner of both physics and technology, as a new and even larger industry emerged: electrical power and light. 15. James Clerk Maxwell, Treatise on Electricity and Magnetism, 2 vols. (Oxford: Clarendon Press, 1873), 1:vii–viii.

6 Electric Power and Light

For most of us, stepping into a room and switching on a light is such an everyday experience that we hardly give it a thought. We expect to be able to draw on abundant supplies of electric power virtually at will, and we take the vast network of power plants and transmission lines that makes this possible almost for granted—until it fails and we are suddenly plunged into a blackout. If most of us give little thought to the sources of the power we use or the paths by which it reaches us, we give even less to the long process, both scientific and technological, by which the modern electric power system came to be. Beyond a vague sense that Thomas Edison had something to do with it, most of us are in the dark. In cartoons, when someone has a sudden bright idea, a light bulb flashes on above his or her head. Besides evoking the traditional link between light and thought, the image harks back to Edison’s most famous invention. But the light bulb was not just a bright idea, and in any case it was only the shining tip of the much larger power system that lay behind it. That system, partly the work of Edison himself and partly that of many others, brought together the two great branches of nineteenth-century physics: energy and electricity. It provided striking examples of both the transformation of energy and the workings of the electromagnetic field, and it called for an unprecedentedly high level of scientific training on the part of the engineers who designed and ran it. As the new electric power system began to transform daily life in the last decades of the nineteenth century, it also set in train important changes in the practice of engineering—changes that also affected the scale and direction of work in physics. Beginnings The roots of the electric power and light industry stretch back to the 1830s, when the discovery of electromagnetic induction and the invention of the first electric motors led to a burst of electrical enthusiasm. Inventors from St.

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Petersburg to New York demonstrated electrically propelled boats and carriages to crowds of eager onlookers and boasted that railway trains, themselves still quite new, would soon be driven by electricity rather than steam. Early experiments suggested that there might be no limit to the power a properly designed motor could draw from an ordinary battery, and by the late 1830s the prospect of replacing coal with clean and cheap electricity seemed almost within reach. As we saw in Chapter 2, however, those hopes began to falter after James Joule subjected them to careful experimental test in the early 1840s. Joule showed that there were definite limits to the amount of work any battery could produce and concluded that, except for a few special purposes, it would not pay to generate power by burning zinc rather than coal. Even as hopes for a battery-powered utopia were fading, however, new sources of electrical power were opening up. Building on Michael Faraday’s 1831 discovery of electromagnetic induction, experimenters found they could produce electric currents without batteries simply by spinning a coil of wire between the poles of a magnet. In their simplest form, such magneto generators produced alternating currents that sloshed back and forth as the coils cut the magnetic lines of force first in one direction and then in the other. Using clever arrangements of brushes and commutators, inventors found ways to draw off currents that flowed in a single direction, though early magnetos still produced something more like a succession of electrical jolts than a truly constant direct current. In laboratories and lecture halls, experimenters used handcranked magnetos to produce spectacular sparks and shocks, and by 1850 industrialists were using big steam-driven magnetos to generate currents for use in electroplating, passing strong currents through special chemical solutions in order to deposit thin layers of gold, silver, or tin on the surfaces of objects made of iron or other metals. Useful as magnetos were, their reliance on inherently weak permanent magnets put fundamental limits on their power and efficiency. In the early 1860s several inventors toyed with the idea of replacing the permanent magnets with more powerful electromagnets, and in 1867 Werner von Siemens, Charles Wheatstone, and S. A. Varley all nearly simultaneously devised what became known as the “self-exciting dynamo-electric generator,” or “dynamo” for short. The basic principle was simple. Start with a regular magneto, crank it into action, and then feed some of the resulting current into coils of wire wrapped around the field magnets. The added current will turn the permanent magnets into much stronger electromagnets, and dynamo makers soon found they hardly needed the permanent magnets at all: the residual magnetism of ordi-

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nary iron was enough to get the process started. As the generator puts out more current and its electromagnets grow stronger, each turn of the crank will produce even more current. A dynamo will not, of course, give you something for nothing: as the currents and electromagnets grow stronger, the crank will become harder to turn and you will have to do more work to keep it going. In return, however, the dynamo will be able to put out far more current than an ordinary magneto ever could. Dynamos made it possible for the first time to convert mechanical work into electrical power on a really large scale. After 1867, inventors brought out a wide variety of new dynamo designs. Perhaps the most important improvement came in 1870, when a Belgian inventor, Zénobe-Théophile Gramme, devised a dynamo with many interconnected coils set around an iron ring. In place of the intermittent jolts produced by earlier generators, Gramme’s dynamo generated a steady direct current that was well suited to powering motors. In fact, if you fed current from one Gramme dynamo down a wire and into a second one, the second dynamo would run backwards as a motor. This gave a striking illustration of the conversion of energy from mechanical to electrical form and back again, and also a hint of the future electrical transmission of industrial power. The advent of improved dynamos like Gramme’s sparked a new burst of electrical enthusiasm, and by the mid-1870s proponents were again envisioning a world powered by electricity—and lit by it as well. As early as 1802, Humphry Davy had found that when he ran a current from a large battery through two carbon rods and then drew the rods slightly apart, the current continued to flow in a sustained spark or arc that gave off an extremely bright light. By the 1840s, arcs powered by huge batteries were being used to produce spectacular lighting effects at the Paris Opera and in London theatres, and by the late 1850s the first magneto-powered arc lights were being used in lighthouses. Current from batteries or magnetos was too expensive for most ordinary uses, however, and it was not until the development of more efficient dynamos like Gramme’s that arc lighting became a practical alternative to gas or oil lamps. By the late 1870s arc lights were being used to light streets and large buildings in cities around the world, and the future of electric lighting seemed dazzling. But that was just the problem: arc lights were too blindingly bright to use in any ordinary room. Nor could one simply make a small arc light, for if the current fell below a certain level, the arc went out altogether. There were great hopes for electric lighting in the late 1870s, but the way forward was far from clear.

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Edison’s System When Thomas Edison (1847–1931) took up the problem of electric lighting in 1878, he thought he was just the man to solve it—and in many ways he was right. Though only 31, he was already known as America’s top inventor, famous for a string of important telegraph and telephone devices and especially for the astonishing “talking machine,” or phonograph, he had devised the year before. Backed by Western Union, the giant telegraph firm, he had recently opened an “invention factory” at Menlo Park, New Jersey, declaring that he and his team of assistants would turn out “a minor invention every ten days and a big thing every six months or so.”¹ Brash, affable, and a skilled self-promoter, Edison knew how to give his friends in the press stories that would sell papers. They rewarded him with reams of free publicity and an evocative title: “the Wizard of Menlo Park.” Lighting was, of course, already a big business long before Edison took it up. Gas lighting systems had first appeared around 1800, and over the next few decades pipes began to snake their way beneath the streets of most European and American cities, supplying homes and businesses with “town gas” produced by heating coal in huge central gasworks. Gas was more convenient to use than old-fashioned lamps and candles, but it had serious drawbacks, particularly the heat, soot, and fumes the flaming gas gave off and the danger of asphyxiation or explosions from leaking pipes. Edison came to electric lighting armed with his characteristic drive and confidence but lacking much experience with dynamos or the strong currents required for lighting. Early in September 1878 he visited the workshops of William Wallace, a Connecticut maker of dynamos and arc lights. Edison was intrigued by what he saw and came away with a sweeping vision of a system that would supply both power and light from central generating stations. He would, he said, unite steam engines, dynamos, wires, and motors into one great electromechanical system. To make it work, however, he would need one more crucial ingredient: a small and readily controllable electric lamp, comparable to a gas light. Convinced that arc lights would not do, Edison thought the most promising alternative was the incandescent lamp, in which an electric current heats a coil of wire or other “burner” until it glows white hot. Several other inventors were already working on incandescent lamps, though so far without much success, and after his visit to Wallace, Edison told reporters he 1. Matthew Josephson, Edison: A Biography (New York: McGraw-Hill, 1959), pp. 133–34.

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was happy to see “the thing had not gone so far but that I had a chance.”² Not long after returning to Menlo Park, he hit upon what he felt sure was the perfect answer. He assured reporters that he would have it all worked out within a few weeks. Edison’s initial optimism was based on the platinum regulator lamp. Platinum was one of the few materials that could be heated to incandescence without burning up, but the trick was to get it hot enough to glow without letting it melt. Edison thought he saw a way—in fact, dozens of ways—to add a tiny thermostat that would momentarily shut off the current just before the white-hot filament could melt. Once the filament had cooled a little, the current would switch back on, reheating the filament and restoring its glow. This would all happen so quickly, Edison said, that the lamp would not even flicker. He lined up investors and in October 1878 launched the Edison Electric Light Company to finance further development. Lighting by gas, he declared, would soon be a thing of the past—a boast that quickly sent gas company stocks tumbling. It soon became clear, however, that Edison would need more than a few weeks to make his new system work. Edison was not a scientist, but he knew how to draw on scientific data and expertise when he needed them. He maintained a large scientific library at Menlo Park, and in December 1878 he hired Francis Upton (1852–1921), a young American physicist who had studied under Helmholtz in Berlin. Upton did important calculations on the lamp, dynamo, and wiring systems, bringing scientific knowledge and methods to bear on Edison’s design ideas. Edison was remarkably creative, but what really set him apart from other inventors was his access to resources and manpower. At Menlo Park, he was able to call not only on Upton, but on a crew of skilled machinists who could quickly turn his rough sketches into working models. Edison had a million ideas, and he also had the means to try them out virtually on the spot. Edison kept working on the platinum regulator lamp though the winter of 1878–79, confident he was on the right track. He invited investors and reporters to Menlo Park to see his glowing lamps, but the demonstrations, though impressive, were strictly temporary: the platinum filaments inevitably failed after just a few hours. Enclosing the filament in an evacuated glass bulb helped, and Edison’s men soon developed the best vacuum pumps in the world, but work on the platinum lamp itself began to stall out. Edison had been at it for 2. Robert Friedel and Paul Israel, Edison’s Electric Light: Biography of an Invention (New Brunswick: Rutgers University Press, 1986), p. 8.

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nearly a year, and by September 1879 both his investors and the public were growing restive. Edison had staked his reputation on delivering a working electric light, and if platinum would not do the job, he would try something else—preferably something cheaper. Carbon was fragile, but it was cheap and it could be made to incandesce in a vacuum, so Edison and his assistants gave it a try. In October 1879 they took a simple cotton thread, baked it in an oven to reduce it to a skeleton of pure carbon, clamped it to two electrical leads, and sealed it in an evacuated bulb. When they turned on the current, the new bulb glowed beautifully for more than 14 hours. Elated, Edison quickly patented the carbon filament bulb, and within a few months his crew was turning out lamps with filaments of carbonized bamboo that could stay lit for hundreds of hours. By later standards the bulbs were dim and woefully inefficient, drawing over 100 watts of power to produce no more light than a modern 25-watt incandescent bulb or a 4-watt compact fluorescent. To Edison and his contemporaries, however, the new bulb was a shining marvel. No light bulb was much good, however, without something to plug it into. From the first, Edison had set his sights on building a unified system to deliver electric power and light, but it took some time for him to grasp just how complex the task of integrating the necessary generators, lamps, and wiring would be. He modeled his plans closely on the gas system, with a centralized supply and individually controlled lamps. As first he even proposed running his wires through disused gas pipes and installing electric lamps in existing gas fixtures— ideas he soon gave up, though he stuck with running his transmission lines underground. Matching the flexibility of gas, while beating it on safety, cost, and convenience, always remained his goal. A key insight shaped Edison’s entire system: the lamps, he said, should be arranged in parallel circuits rather than in series, as arc lights generally were. With lamps arranged in parallel, like the rungs of a ladder, he could connect many lamps to a single generator while still allowing each lamp to be individually controlled; with a series circuit, in which the current passed directly from one lamp to the next, if a single lamp went out, they all did. To make a parallel system work, the individual lamps needed to be of high resistance, on the order of 100 ohms—a requirement Edison’s thin carbon filaments met nicely. Low-resistance incandescent lamps like those developed by Edison’s competitors, notably Joseph Swan in England, would have drawn enormous currents if arranged in parallel and would have required thick and expensive copper conductors to carry the load without suffering huge losses in transmis-

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sion. Edison made high-resistance lamps arranged in parallel circuits the foundation of his system and proceeded to design everything else around them. Edison always used direct current, regarding it as simpler, safer, and more efficient than alternating current. In addition, the electric motors available at the time worked only on direct current, and Edison saw such “motor loads” as a crucial part of his integrated system to supply both power and light—and as the main market for current during daylight hours, when few lights would be turned on. For safety, especially with underground conductors, he had to keep the voltage on the transmission lines relatively low, and he soon settled on 110 volts, a level that also worked well with his bulbs. This meant, however, that one of his central stations could serve customers only within a radius of about a mile; too much power would be lost in transmission at low voltages to be able to supply current to more distant customers and still turn a profit. Given the limited range of his direct current system, Edison needed to locate his power plants in areas with a high density of potential customers. That, combined with his desire to make an impression on investors, led him to pick lower Manhattan for his first installation, and in May 1881 he acquired a site on Pearl Street, just a few blocks from Wall Street. It took his crew months to install his special “Jumbo” dynamos and the big steam engines that would drive them, and months more to lay the underground transmission lines and wire up customers’ offices. Finally, on 4 September 1882, the crew at Pearl Street fired up its first engine, set its first dynamo spinning, and sent current coursing through the system. Edison was finally lighting up New York City—or at least a small corner of it. The Pearl Street station worked well, though it took several years for it to turn a profit. Edison ran it as a commercial operation, but it was essentially a demonstration project, intended mainly to test and show off the new system. The limited range of Edison’s direct current system made it difficult for him to expand much beyond the initial service area. Over the next few years Edison’s companies built similar power stations in several other cities and installed a large number of “isolated plants” in factories, hotels, and other businesses. Before the vision of giant integrated power systems could become a reality, however, electrical technology would need to take a step in a new and different direction. AC versus DC The 1880s and 1890s witnessed what became known as the “War of the Currents” or “Battle of the Systems,” as Edison’s direct current (DC) system was challenged by the upstart alternating current (AC) system. It was a long and

Electric Power and Light

Testing a Dynamo in Thomas Edison’s Workshop Thomas Edison is remembered as the inventor of the light bulb, but even the best bulb would have been useless without something to plug it into. Besides the bulb itself, Edison and his crew at Menlo Park devised a system to generate, distribute, and control electric power and, perhaps just as importantly, an “invention factory” to produce it all. Drawing on Faraday’s ideas about the flow of magnetic force, Edison developed a new form of dynamo, known as the “long-legged Mary-Ann”

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because of its unusually long field magnets; here, we see one being tested at the Menlo Park workshop in 1879 as Edison’s friend George Barker, physics professor at the University of Pennsylvania, looks on. Edison’s dynamos worked well enough, but his understanding of the underlying theory proved faulty; it turned out there was no real need for the magnets to be so long, and they were soon replaced by shorter ones.

 Scientific American 41 (18 Oct. 1879):

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bitter struggle, fought out mainly in the United States but with skirmishes elsewhere, and it came to involve everything from the first electric chair to the harnessing of Niagara Falls. The eventual victory of the more complex but flexible AC system had important consequences not just for the shape and workings of the electric power system, but for the whole profession of electrical engineering, and indirectly for physics as well. The main problem with Edison’s DC system stemmed from the basic relationship between voltage, current, and power. The power (measured in watts) that any current can deliver is given by the strength of the current (measured

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in amperes) multiplied by its potential or voltage (measured in volts). In symbols, taking P for power, I for current, and V for voltage, we have P  I • V. We can thus deliver, say, 1000 watts of power with a high voltage and a weak current (1000 volts and 1 amp), or a low voltage and a strong current (1 volt and 1000 amps), or any other combination of volts and amps whose product is 1000. As the current passes along the transmission line, however, some of its power is lost to resistance, going simply to heat up the wire. Joule had shown in 1840 that such losses were proportional to the resistance (R ) of the wire multiplied by the square of the current passing through it: P  I 2 • R. There are several ways to minimize transmission losses in DC systems. First, we can keep the resistance low by using thick (and expensive) copper conductors. Alternatively, we can hold down the total resistance by keeping the transmission wires short and serving only customers who are located near the power plant, as Edison had done at his Pearl Street station. A third option would be to raise the voltage and reduce the current. If we were to increase the voltage by a factor of 10, we could deliver the same power with one-tenth the current, and since the power goes by the square of the current, losses in transmission would drop by a factor of 100. If Edison had run his system at 1100 volts instead of 110, he could have reduced the power lost in transmission by 99 percent and so could have served a far wider area with the same amount of copper. Of course, Edison had found it hard enough to insulate his underground conductors when they were carrying 110 volts; insulating 1100-volt wires would have been far trickier. Nor could his carbon filament bulbs have stood up to such high voltages for long. More to the point, who would want a 1100 volt power line coming directly into his or her home? Most people regarded such high voltages as simply too dangerous for home use. It would be best, of course, if one could find a way to transmit power at a high voltage and then bring it into the home at a low voltage. Clever wiring arrangements enabled Edison to go a little way in that direction in the mid1880s, extending his radius of service from one mile to about two and quadrupling the area each power station could serve. But there seemed to be no practical way to go much further. Given his commitment to DC, Edison seemed to be stuck with his model of low voltages, small service areas, and numerous small power plants. There was, of course, an alternative to direct current. In the late 1870s, alternating current was already widely used for arc lighting, since it made the carbon rods burn down more evenly than did direct current. Alternating current also worked well with incandescent lamps; currents sloshing rapidly back

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and forth heated filaments to a white glow just as effectively as a steady current did. By the early 1880s, overhead AC power lines, many carrying thousands of volts, were going up in cities around the world. In Britain, the Electric Lighting Act of 1882 stipulated that electric supply companies could not force their customers to purchase any specific type of light bulb. The aim was to promote competition and consumer choice in the bulb industry, but the law also created a potential market for an adapter that could adjust voltages to suit different kinds of bulbs. Lucien Gaulard (1850– 88), a French inventor working in London, responded by developing a device whose eventual significance extended far beyond its original purpose. The “secondary generator” (or transformer, as it came to be called) that he patented with John D. Gibbs was a complex arrangement of coils and iron rods that a customer could use to step an incoming AC voltage either up or down to virtually any desired level. If your local electric company supplied alternating current at 200 volts but your favorite lamps worked best at 60 volts, you could simply change a few settings on your Gaulard-Gibbs transformer, wire it up, and proceed to plug in your bulbs. The working principle of the transformer was based directly on Faraday’s 1831 discovery of electromagnetic induction. Oersted had shown that an electric current produces a magnetic field, and Faraday had shown that a changing magnetic field can generate an electric current. Thus, if we wrap two coils of insulated wire around an iron ring and run an alternating current into the first coil, it will produce a changing magnetic field in the ring, which will in turn induce an alternating electric current in the second coil. No current actually passes from the first coil to the second, but power clearly does, showing in a striking way that energy flows through the surrounding electromagnetic field rather than just within the conducting wires. The power that passes between the coils is coupled through the changing magnetic field, and by adjusting the number of turns in each coil, we can step the voltage induced in the second coil either up or down. Crucially, the process works only with alternating currents; if we feed a steady direct current into the first coil, it will just set up a steady magnetic field in the iron ring, and as Faraday had shown, such a steady field is powerless to induce an electric current. Gaulard and Gibbs demonstrated their new transformer in London in 1883 and in Italy the next year. By then, Gaulard recognized that it could be far more than just an adapter for light bulbs: it might offer a way to solve the great problem of electrical transmission. After generating alternating current at a convenient voltage, one could use a transformer to step it up to thousands of volts for efficient transmission. Closer to the customer, one could then use a

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second transformer to step the voltage back down to a level that was safe to bring into the home. It seemed an almost perfect solution. Others soon picked up on Gaulard’s idea and developed it further. The American industrialist George Westinghouse and his engineer William Stanley, a group of Hungarian engineers at Ganz and Company in Budapest, and S. Z. de Ferranti in London all found ways to simplify and improve Gaulard’s original highly complex design and produce more efficient and reliable transformers. Ferranti and his backers even challenged Gaulard and Gibbs’s original patent, claiming (rather misleadingly) that the device was not really new, and in 1888 a British court threw the patent out. Gaulard, who had a history of mental problems, found this too much to bear. Not long after, he reportedly called at the Elysée Palace and demanded to speak to the president of France, declaring, “I am God and God does not wait.”³ He died in a Paris asylum later that year. By then AC systems based on improved versions of Gaulard’s transformer were already coming into commercial use. The Ganz engineers in Hungary, Ferranti in Britain, and Stanley in the United States had all demonstrated working systems by mid-1886. Westinghouse proceeded to push the new technology forward at breakneck speed, erecting his first commercial AC power plant just a few months after Stanley’s successful demonstration. By 1888 the Westinghouse Electric Company was building more electric power plants in a month than Edison did in year, and other firms, notably the ThomsonHouston Company of Massachusetts, were also jumping into the booming AC incandescent lighting business. It looked to many like Edison’s DC system might be left in the dust. The strong point of the AC system, of course, was its freedom from the high transmission losses that plagued Edison’s DC system. An AC power plant could reach a far wider area than a DC plant and could thus be located with an eye toward efficiency of production rather than proximity to customers. Alternating current still faced serious technical challenges, however, and as late as 1888, it still lagged badly in a very important area: direct current could be used to drive motors, while alternating current (with some minor exceptions) could not. Without a workable motor, alternating current could never replace direct current as the foundation of a unified system to supply both power and light. 3. Thomas Hughes, Networks of Power: Electrification in Western Society, 1880–1930 (Baltimore: Johns Hopkins University Press, 1983), p. 94.

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The AC industry faced another major obstacle in the late 1880s: opposition from Edison and his backers. Edison’s investors included some of the biggest money men on Wall Street, and they did not like to see their stake in the DC system devalued by an upstart competitor. Edison himself was understandably partial to his own DC system and skeptical that alternating current could really deliver all of the benefits its proponents claimed. He turned down all opportunities to get into the AC business himself, in part because he was convinced that high-voltage AC lines simply were not safe. “Just as sure as death,” he wrote in 1886, “Westinghouse will kill a customer within 6 months after he puts in a system of any size.”⁴ Early in 1888, the Edison Electric Light Company issued a pamphlet bearing a red cover and a stark title: “A Warning.” After laying out what it said were the legal, technical, and economic deficiencies of Westinghouse’s system, the pamphlet declared alternating current to be inherently dangerous. It drove its message home by reprinting newspaper accounts of gruesome accidents involving high-voltage AC lines. At just that moment, a new figure stepped forward as a self-appointed guardian of electrical safety. In June 1888 Harold P. Brown, a little-known electrical consultant who had worked in the arc lighting business, sent the New York Evening Post a letter in which he denounced alternating current as “damnable” and a serious hazard to the public. He called for a law limiting AC power lines to no more than 300 volts, a measure that would have crippled the AC industry by eliminating its chief advantage over direct current. Brown also maintained that alternating current was deadlier than direct current even at relatively low voltages, a claim he backed up by publicly subjecting dogs to jolts first of one kind of current and then the other. In the process Brown killed a number of the unfortunate animals, and many of the onlookers expressed their revulsion at his methods. The Edison interests were widely accused of being behind Brown’s efforts and of using his distasteful demonstrations to discredit alternating current. No direct pay-offs were ever proved, but Brown was certainly given every assistance at Edison’s new laboratory in West Orange, New Jersey, where many of the animal-killing experiments were in fact first performed by Edison’s staff. Killing dogs turned out to be just the start. In 1886, the state of New York had set up a commission to investigate possible new methods of capital punishment. Rejecting the noose as cruel and outdated, its members thought electricity might offer a clean, modern, and humane alternative. When they first 4. Josephson, Edison, p. 346.

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asked Edison for advice in November 1887, he declined to help, saying he opposed the death penalty altogether. When pressed, however, he replied that if the state insisted on executing people, then electricity would indeed be the best way to do it. Evidently seeing a chance to get in a dig at his chief competitor, Edison added that an especially deadly source of current was readily available: the AC dynamos “manufactured principally in this country by Geo. Westinghouse.”⁵ Swayed by Edison’s endorsement, the New York legislature passed the Electrical Execution Act in June 1888. The law did not specify the type of current to be used, but the board charged with working out procedures hired Brown as its consultant, and he soon steered them toward high-voltage alternating current—“the executioner’s current,” as he called it. He proceeded to design an electric chair, complete with straps, mask, and electrodes, and set about acquiring AC dynamos for the state prisons. Brown insisted on using Westinghouse machines, explicitly saying that he wished to bring the safety of Westinghouse’s system into disrepute and if possible secure a legal ban on the use of high-voltage alternating current for anything but executions. Westinghouse angrily refused to sell Brown any equipment, but with help from Edison, Brown managed to buy Westinghouse dynamos on the secondhand market. The bitter fight spilled over even into what to call the new process of electrical execution. There were many suggestions, ranging from “electrothanasia” and “dynamort” to “joltacuss” and “blitzentod.” Edison’s lawyer suggested that, just as the guillotine had been named for Dr. Joseph-Ignace Guillotin, so one who had been killed with electricity might be said to have been “westinghoused.”⁶ The other side shot back that “browned” would be a more fitting term. Eventually everyone settled on “electrocuted.” The first person to be executed with electricity was an axe-murderer from Buffalo named William Kemmler. After the courts rejected the argument that electrocution would be an unconstitutionally cruel or unusual form of punishment, he was duly strapped into the new electric chair at Auburn Prison on 6 August 1890. The first jolt of current made Kemmler’s body twitch and stiffen, but to the horror of the assembled officials, it left him still breathing. As he groaned hideously, they applied a second and much longer jolt that certainly killed him, but also seared his flesh and singed his hair. The stench was horrible; at least one reporter fainted. When Westinghouse read news ac5. Richard Moran, Executioner’s Current: Thomas Edison, George Westinghouse, and the Invention of the Electric Chair (New York: Knopf, 2002), p. 75. 6. Mark Essig, Edison and the Electric Chair: A Story of Light and Death (New York: Walker, 2003), p. 161.

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counts of Kemmler’s execution, he was disgusted. “It was a brutal affair,” he said. “They could have done better with an axe.”⁷ Despite such efforts to tag it as the killer current and ban its use, alternating current continued to capture an ever larger share of the electric lighting market in the late 1880s and early 1890s. Its lower cost and ability to reach wider areas evidently outweighed any safety concerns or unpleasant associations with executions, and Westinghouse and Thomson-Houston built hundreds of new AC power plants in the United States and abroad. In Europe, Ganz and Company and the German firm AEG installed AC systems in many cities and began laying plans to transmit hydroelectric power over long distances. They needed just one more piece to have a complete AC power system: a workable motor. The key figure in the development of the AC motor was a visionary Serbian-born engineer, Nikola Tesla (1856–1943). Trained in physics and engineering at the Polytechnic in Graz, Austria, he acquired a grasp of mathematics and electrical theory as well of the nuts and bolts of dynamo and motor design. He was impressed by the way a Gramme dynamo could be made to run backwards as a motor but saw its sparking brushes and commutator as a weak point. There must be a way to eliminate such troublesome components, he thought, and make a motor that could run on the alternating current that a dynamo with no commutator would produce. Tesla later said the idea for his revolutionary solution, an induction motor based on a rotating magnetic field, came to him in a flash of insight in 1882 while he was walking in a park in Budapest. It would be another five years, however, before he would seek to patent his idea. In the meantime, Tesla worked on DC systems, first for one of Edison’s companies in Paris and then in 1884 for Edison himself in New York. Edison was impressed with Tesla’s abilities but scoffed at his grand talk about the wonders of alternating currents. Tesla quit in disgust and was reduced for a time to working as a ditch digger. Finally in 1887 he lined up new backers, wrote up his ideas, and applied for patents on his motor. Shortly after his patents were issued in May 1888, Tesla demonstrated his new motor at a meeting of the American Institute of Electrical Engineers. He was a master showman, and the audience of elite electrical engineers and physicists was impressed. Tesla’s key idea was to take two alternating currents that were a quarter cycle out of phase and feed them into two pairs of coils set around a central rotor. As the current through each pair of coils rose and fell, 7. Ibid., p. 257 (quoting New York Times, 7 Aug. 1890).

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Lithograph of the Frankfurt Electrical Exhibition (1891) The international electrical exhibition held in Frankfurt, Germany, in 1891 marked a milestone in the development of alternating current power technology. The highlight of the exhibition, whose entrance is depicted in this lithograph, was the transmission of AC power at high voltage over

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110 miles from a hydroelectric plant at Lauffen on the Neckar River. The power was used not just to light lamps on the exhibition grounds but also to pump water for an impressive artificial waterfall, shown on the right.  Elektrizität: Offizielle Zeitung der Inter-

nationalen Ausstellung Frankfurt am Main, 1891, p. 828.

the resulting magnetic field within the motor would wheel around the axis, dragging the rotor with it. Tesla’s motor had no need for brushes or commutators, since it worked on induced alternating currents. When Westinghouse heard of Tesla’s invention, he saw that the new motor provided just what he needed to make his AC system complete. He quickly snapped up the rights to Tesla’s patents for a handsome royalty. Others in Italy, Germany, and Switzerland were also working on induction motors. In the early 1890s “polyphase” AC systems, some based on Tesla’s original two currents, others using three, scored a series of impressive triumphs in both Europe and America. The first came in 1891, when engineers from Swiss and German firms set up a high-voltage AC line to transmit over 100 kilowatts of power 110 miles from a hydroelectric site on the Neckar River to the Frank-

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furt Electrical Exhibition. Besides lighting the exhibits, the power drove a new three-phase induction motor designed by AEG engineer Michael DolivoDobrolowsky that was used to pump water for an artificial waterfall on the exhibition grounds—a dramatic foretaste of what the long-distance transmission of electric power might later achieve. In 1892, plans were being laid for the great Columbian Exposition to be held in Chicago the next year. General Electric, newly formed by the merger of Edison’s company with Thomson-Houston, initially offered to provide the fair with DC incandescent lighting for $1.7 million. When the fair managers balked, Westinghouse stepped in and offered to do the job with alternating current for just $400,000. He proceeded to install hundreds of thousands of incandescent bulbs, as well as thousands of arc lights and dozens of Tesla induction motors, all powered by enormous AC dynamos. The Chicago fair held the largest concentration of electrical technology ever seen up to that time, and its 27 million visitors came away enthralled by the prospect of a future lit and powered by electricity. Westinghouse made little if any profit on the Chicago contract, but the fair and its glittering “White City” provided better advertising for his AC system than any he could have bought. Perhaps the greatest triumph for alternating current came at Niagara Falls. In 1889, a group of New York financiers formed a company to harness the enormous power of the falls. Seeing no prospect of selling so much power at Niagara itself, they looked for a way to transmit the bulk of it to the booming city of Buffalo, some 20 miles away. The success of the Frankfurt demonstration line encouraged them to use electricity, and after an extensive and wellpublicized investigation, in May 1893 they settled on polyphase alternating current as the best option. The Niagara verdict, reflecting the considered judgment of those regarded as best informed on the subject, was widely seen as a decisive victory for alternating current in the battle of the currents. Huge tunnels were dug and turbines installed, and in August 1895 the first of the giant Westinghouse dynamos whirred into action. They were soon turning out far more power, at far lower cost, than any other power plant in the world. The availability of so much cheap electric power created new and unanticipated industries, and to the surprise of those behind the project, all of the power the Niagara plant initially produced—more than 10 megawatts—was bought by new aluminum smelters and electrochemical works in its immediate neighborhood. Ironically, most of these industrial customers needed direct current for their processes, so the alternating current from the power plant had to be run through rotary converters (essentially AC motors geared to DC dy-

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namos) to supply them. By 1896, however, substantial amounts of Niagara power were being sent to Buffalo, and within a few years the falls were supplying AC electric power to much of New York State and Ontario. By the mid-1890s, direct current was clearly losing ground. The prospect of such decline was one of the motives that had led Edison’s financial backers to force his company to merge with Thomson-Houston in 1892 to form General Electric. Edison was eased out, and the new company was run by the Thomson-Houston management, who went on to lead GE more fully into the AC business in the later 1890s. Similar trends were seen in much of Europe as the electrical industry consolidated into a relatively few large AC firms. Many smaller DC firms went under—including J. Einstein and Company of Munich, a once-promising maker of dynamos and lighting equipment that was owned and run by Albert Einstein’s father and uncle. Direct current did not disappear overnight. There were still large DC systems in place in New York and many other cities, and rather than ripping them out and replacing them at enormous cost, most power companies left them in service, using rotary converters to supply them with current from AC power plants. From the 1890s to the 1930s, power companies used the same method to supply the large market for DC power to drive electric streetcars; for all of their virtues, AC induction motors were not well suited to the demands of electric traction. One of the strengths of the AC system was its ability to supply a wide range of loads, including direct current, at relatively low cost, and after 1900 the electric power industry moved increasingly toward the unified system that would prevail throughout the twentieth century: huge power plants, long-distance transmission over high-voltage AC lines, and local distribution at lower voltages through substations and transformers. It was an effective system, but one that entrenched patterns of large-scale production and consumption that would later raise serious environmental problems. Designing and running the AC power system and its array of associated equipment proved to be an extremely demanding task. Engineers could no longer treat electricity simply like water flowing in a pipe, as they had often done with direct current; to make AC systems work, they also had to take into account complex inductive effects and field interactions. Successful AC engineering required a grasp of electromagnetic theory and a level of mathematical analysis that were beyond the reach of most of the older pioneers of direct current. In 1892, when one of his aides came to him with an electrical question, Edison told him to take it to Arthur Kennelly, the chief electrical expert at the West Orange laboratory and later a professor of electrical engineering at Harvard and MIT. When it came to electricity, Edison said, “he knows far more

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about it than I do. In fact,” he added, “I’ve come to the conclusion that I never did know anything about it.”⁸ Electrical Engineering and the Growth of Physics The growth of the electric power and light industry in the 1880s sparked a huge rise in the demand for trained electrical engineers. Edison himself felt it keenly. “I need the men,” he told the New York Tribune in 1883. “My work is seriously retarded by my inability to obtain competent engineers.”⁹ The later shift to polyphase alternating current exacerbated the problem, as firms now needed engineers trained to an even higher level. But where were such engineers to be found? Traditionally, especially in Britain and the United States, engineers had been trained largely through apprenticeship. After some initial schooling, a student would go to an established engineer, pay a substantial “premium,” and spend a few years learning the trade by working his way up through various jobs in workshops and drawing offices. This worked well enough for civil and mechanical engineering, which had long traditions and an ample supply of master engineers, but it failed badly for those looking to go into electrical engineering. The electric power and light industry was so new, and its growth in the 1880s so explosive, that there was essentially no pool of experienced electrical engineers to whom a student could apply. Without masters, there could be no apprentices, and beyond a handful of self-taught inventors, electrical engineering was not something one could readily pick up on one’s own. Many areas of electrical engineering also required mathematical skills that apprenticeship was ill-suited to convey. There were several potential alternatives to apprenticeship. Since the late eighteenth century, France had developed a system of technical schools to prepare civil and military engineers for government service, but these offered little to those looking to go into the electric power and light industry. In Germany and central Europe, many of the polytechnical schools, or Technische Hochschulen, provided excellent instruction in mechanical engineering, but without a store of specifically electrical knowledge, few mechanical engineers were equipped to train prospective electrical engineers. The same held true in American engineering schools, which in any case were generally less advanced than their German counterparts. Nor were telegraph engineers able to meet 8. Jill Jonnes, Empires of Light: Edison, Tesla, Westinghouse, and the Race to Electrify the World (New York: Random House, 2003), p. 242. 9. Robert Rosenberg, “Academic Physics and the Origins of Electrical Engineering in America” (Ph.D. dissertation, Johns Hopkins University, 1990), p. 64.

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the need; except in Britain, where the demands of cable telegraphy had produced a higher level of electrical competence, few telegraphers proved able to make the transition to power and light engineering. Frustrated by the lack of qualified engineers, Edison and Thomson-Houston set up their own in-house training programs in the early 1880s, followed a little later by Westinghouse. Such “test courses” did a good job of teaching employees how to install and operate their companies’ products, but they fell far short of meeting the wider need for electrical engineers. Almost by default, the task of teaching electrical engineering initially fell to physics professors. They alone possessed both the requisite electrical knowledge and the means to impart it to substantial numbers of students, and in the early 1880s physicists at universities and technical colleges in Britain, Germany, and the United States stepped forward to offer programs in “electrotechnology” or “applied electricity.” These programs often grew to dwarf the physics departments from which they had sprung, and in the 1890s most split off to become separate electrical engineering departments. The whole process generally took little more than a decade, but the fact that electrical engineering education often got its start within physics departments had important consequences for both disciplines. Physicists had been studying electricity in their laboratories for many years before 1880, of course, but except in the British cable industry, there had been little technological demand for the knowledge and skills physicists had to offer. Inventors had drawn on physicists’ discoveries, as we have seen, and physicists had taken up technological problems ranging from the efficiency of steam engines to the retardation of telegraph signals. Few engineers in the mid-nineteenth century, however, regarded advanced academic study in physics as the best path to success in their profession. Some physicists (notably William Thomson in Glasgow) made a pitch for the wider practical value of their work, but most were content to pursue scientific knowledge for its own sake. Physics—or “natural philosophy,” as it was often still called—occupied only a small place in the usual college curriculum. Although many students were exposed to a smattering of the subject in hopes it would give them an appreciation of the wisdom of God’s laws, very few were moved to study it further. Shortly after Johns Hopkins University opened in 1876 as the first real research university in the United States, the physicist Henry Rowland (1848– 1901) explained why his department could never expect to attract many graduate or “special” students. Advanced students in chemistry or biology could go into business or medicine, he said, “but in physics special students have no opening in life except as teachers, and as the demand for these is limited, so

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the number of special students must be.”¹⁰ Rowland wrote, however, at almost the last moment that such a statement could be made. In the early 1880s, the birth of the electric power and light industry set off a clamor for electrical expertise that drew large numbers of students into physics classrooms and gave the subject a more prominent place in the academic landscape. Britain got an early start on the process, as the rise of the submarine cable industry had led Thomson and others to open the first physics teaching laboratories in British colleges and universities in the 1850s and 1860s. The work in these laboratories focused on precision electrical measurement, and while it proved important for both physicists and cable engineers, it was pursued on a relatively small scale. It provided a solid grounding in electrical principles, however, and the laboratories established by Thomson and others helped lay the basis for later work in power and light engineering. Electrical engineering education in Britain developed along a curious path that led through Tokyo. In the 1870s, as part of a policy aimed at promoting rapid technological development, the Japanese government began to import European and American experts to serve as teachers. When Japanese officials asked Thomson for advice, he recommended a young Englishman, W. E. Ayrton (1847–1908), who had studied in Thomson’s Glasgow laboratory and had then spent several years as a telegraph engineer in India. Ayrton arrived in Tokyo in 1873 with a five-year contract to teach physics at the new Imperial College of Engineering. Given a free hand and eventually ample funding by the Japanese, he established one of the world’s best courses in electrical physics and telegraph engineering. After his contract ended in 1878, Ayrton returned to London and put the ideas he had developed in Japan into practice at Finsbury Technical College and, after 1885, at the new Central Institution at South Kensington. Equipped by Thomson with a broad view of electrical physics, Ayrton made a fairly smooth transition from telegraphy to power and light engineering and soon built the Central Institution into Britain’s leading center for electrical engineering education. His wife, Hertha Ayrton (1854–1923), was also an electrical engineer and did important work on arc lighting. Although he carried the process further than most, Ayrton was far from the only physics professor in Britain to take up teaching electrical engineering in the 1880s and 1890s. In Liverpool, for example, Oliver Lodge set up a successful program in “electrotechnics” that eventually outgrew his physics department and became a separate department of electrical engineering in 1901. 10. Ibid., p. 205.

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In Germany, the influential industrialist Werner von Siemens issued a call in 1881 for all Technische Hochschulen to offer instruction in electrical engineering. The next year the Technische Hochschule at Charlottenburg, just outside Berlin, began offering courses in dynamo and motor construction in its mechanical engineering department and soon developed close ties to AEG, Siemens, and other big German electrical firms. In 1887 a new government research institute, the Physikalisch-Technische Reichsanstalt, opened in Charlottenburg under the direction of Hermann von Helmholtz; its work on standards and measurement further strengthened the links between electrical science and technology. Other schools launched free-standing programs in electrical engineering, many of them directed by physics professors. In 1882 the physicist Erasmus Kittler was appointed to head the world’s first full department of electrical engineering at the Darmstadt Technische Hochschule, where he quickly built up a large and successful program. Among his many students was Michael Dolivo-Dobrowolsky, who went on to perfect the three-phase AC induction motor in 1890. As the demand for electrical instruction rose, more physicists were hired to teach in the growing Technische Hochschulen, as well as in German universities. The pattern of electrical engineering education getting its start in physics departments was strongest in the United States. At MIT, physics professor Charles Cross launched an “alternative course” in electrical technology that, after starting with 18 students in 1882, quickly grew to become the largest program in the school. By 1889, Cross’s electrical program had over 100 students, far more than the regular physics course, and it kept growing through the 1890s before finally breaking off as a separate department of electrical engineering in 1902. At Cornell University, William Anthony began offering electrical engineering courses in the physics department in 1883 and soon built up the largest and best-regarded program in the country. Although Anthony left Cornell for private industry in 1887, the electrical program he had founded continued to prosper: by the mid-1890s it had over 300 students, and demand for its graduates consistently exceeded the supply. Even after it became a separate department in 1888, electrical engineering at Cornell retained close ties to physics. Electrical engineering students outnumbered physics majors in many advanced physics courses, and much of the research in the Cornell physics department continued to focus on electrical problems. By 1900, substantial electrical engineering programs had sprung up at universities and technical colleges throughout the United States, most of them growing out of physics departments. Among the largest and most important were the programs at the state universities in Wisconsin, Ohio, Illinois, and

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Michigan. Each year, hundreds of students passed through these programs and took jobs with national electrical firms or regional utility companies. Led by the “electricals,” engineering shed its association with apprenticeship and inreasingly came to be seen as the preserve of college-educated professionals. Particularly at the big state universities, students looking to get ahead in the world increasingly chose engineering over more traditional courses in the humanities, leading a literature professor to grumble in 1908 that his field would soon be dismissed as fit only for “sissies.” Nowadays, he lamented, “the really virile thing is to be an electrical engineer.”¹¹ Virile or not, electrical engineering was certainly attracting more and better students. As the president of Cornell had observed in 1891, “The importance which electricity has recently assumed in so many ways, has drawn into special studies of the subject a large number of our ablest and most scholarly men.”¹² Electrical engineering departments retained close ties with physics long after their formal separation and long after the era of dynamos and light bulbs had given way to the age of radio, radar, and solid state electronics. The line separating advanced research in electrical engineering from work in physics was often thin or nonexistent. Physics, too, was deeply affected by its role in giving birth to electrical engineering as an academic discipline. Electrical technology had created the first real market for the expertise physicists had to offer; and the rise of the power and light industry in the 1880s and 1890s, with the concomitant rise in student numbers and public profile, drove an increase in the number of physicists and in the resources available to support their work. By the mid-1890s, physics was a significantly different and much stronger discipline than it had been just 20 years before. 11. Irving Babbitt, Literature and the American College: Essays in Defense of the Humanities (Boston: Houghton Mifflin, 1908), p. 119. 12. Quoted in Rosenberg, “Academic Physics,” p. 178.

7 Into a New Century

As the nineteenth century headed into its final decade, physicists could look back with satisfaction on what they had achieved. Guided in large part by the belief that all physical phenomena were ultimately mechanical, they had formulated sweeping laws of heat and energy, deciphered the workings of the electromagnetic field, and helped forge technologies that had transformed modern life. Their discipline had grown in size and stature and added greatly to humans’ understanding of the physical world and their practical power over it. Citing both Hertz’s discovery of electromagnetic waves and the recent harnessing of electricity to provide power and light, G. F. FitzGerald compared his fellow physicists to modern Prometheans; thanks to them, he declared in 1888, mankind had “snatched the thunderbolt from Jove himself and enslaved the all-pervading ether.”¹ One of the keys to this success had been their determined pursuit of purely mechanical explanations, and physicists fully expected that further progress, both intellectual and material, would come by continuing along the same path. In the 1890s, however, this sense of optimism and triumph was joined by an undercurrent of unease. When William Thomson was raised to the peerage as Lord Kelvin in 1892, he was recognized as the embodiment of the nineteenth-century union between physics and technology; he had also long been a leader in the quest for purely mechanical explanations. Yet he had to admit that, despite its many successes, the mechanical program had not managed to deliver the grand “theory of everything” it had long promised. When the University of Glasgow held a jubilee in 1896 to mark his fiftieth year as a professor there, Kelvin chose one word to sum up all of his efforts to grasp the ultimate foundations of physical reality: “failure.” “I know no more of electric and magnetic force,” he said, “or of the relation between ether, electricity, and ponderable matter, or of chemical affinity, than I knew and tried to teach to my 1. G. F. FitzGerald, “Address to the Mathematical and Physical Section of the British Association” (1888), in Joseph Larmor, ed., The Scientific Writings of the Late George Francis FitzGerald (Dublin: Hodges and Figgis, 1902), p. 240.

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students of natural philosophy fifty years ago in my first session as Professor.”² Kelvin never lost his own faith in the mechanical program, but as the century drew to a close, others increasingly asked whether physicists had perhaps been chasing a mirage. If the 1890s marked the end of one era in physics, however, the decade also saw the first stirrings of a new one. Between 1895 and 1900, physicists made a series of remarkable experimental discoveries, including X-rays, radioactivity, and the electron. Worlds of previously unsuspected phenomena suddenly opened before them, and as the nineteenth century gave way to the twentieth, physicists increasingly turned their attention to the new physics of atoms and radiations—realms where many of the old rules of mechanics no longer seemed to apply. The laws of energy and electromagnetism that they had forged amid the technologies of the nineteenth century survived, but in the new century physicists would find those laws cast into a new and unexpected light. Ether Winds When FitzGerald invoked it in 1888, most physicists looked on “the all-pervading ether” as a fundamental and well-established reality, as real, many said, as the air we breathe. The wave theory of light had been abundantly confirmed long before, and it seemed obvious that there could be no waves without a medium to carry them. The exact nature of that medium remained far from clear, however, and throughout the nineteenth century physicists struggled to devise a workable mechanical model of it. Fresnel had shown in the 1820s that to sustain waves like those of light, the ether had to have properties like those of an elastic solid or jelly. Yet it was difficult to see how planets and other bodies could move so freely through a solid medium, nor could any ordinary elastic solid support the forces required by Maxwell’s electromagnetic theory. In the 1880s a number of British physicists took up alternative theories, particularly the “vortex sponge,” which pictured the ether as a liquid filled with a tangle of squirming vortices. The whirling motion of such vortices could store enormous amounts of energy, and there were tantalizing hints that a vortex sponge might be able to account for Maxwell’s field equations. FitzGerald said in 1893 that he had “a sort of feeling in my bones” that it must be the true theory of the ether.³ It was extremely difficult to analyze the turbulent motion 2. Silvanus P. Thompson, Life of Lord Kelvin, 2 vols. (1910; repr., New York: Chelsea, 1976), 2:984. 3. G. F. FitzGerald to Oliver Heaviside, 25 Aug. 1893, quoted in Bruce J. Hunt, The Maxwellians (Ithaca: Cornell University Press, 1991), p. 103.

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of such a medium mathematically, however, and even the most enthusiastic proponents of the vortex sponge could not tell if they were on the verge of a fundamental breakthrough or off on the wrong track altogether. Whatever the ultimate structure of the ether, physicists were convinced that the earth was moving through it at enormous speed. Aside from any motion the solar system as a whole might have, they knew the earth was circling the sun at about 30 kilometers per second (18 miles per second), or about 1 ⁄ 10,000 the speed of light. According to Fresnel, the ether remains wholly stationary and slips between the atoms of the earth or any other moving body much like water passing through a net—or, from the other point of view, like wind blowing through a grove of trees. Ordinarily, we do not notice this flow of ether, but in principle it should affect our measurements of the speed of light, since light waves going against the ether wind would be slowed down, like a swimmer heading against the current in a river, while those going with it would be similarly sped up. If such a difference in speeds could be detected, it would provide direct evidence of our motion through the ether and so of the existence of the ether itself. Detecting a difference in speeds of one part in 10,000 would be a daunting task, given that direct measurements of the speed of light in the mid-nineteenth century often differed from one another by several percent. In fact, the problem was much worse than that. The only practical ways to measure the speed of light all involved reflecting a beam back to its starting point. For such a round trip, in which the beam is slowed down going against the flow of ether and sped up going back with it, the effect of the ether wind would be proportional not to the simple ratio of the speed of the earth (v) to that of light (c), but instead to its square (v 2/c 2)—not to one part in 10,000, but to one in 100 million. Detecting such a tiny difference seemed impossible, and Maxwell, for one, despaired of anyone’s being able to do it. In 1880, however, a young physics instructor at the U.S. Naval Academy, A. A. Michelson (1852–1931), took up the challenge. Already a master of precision optical measurement, Michelson saw that if he could split a beam of light, send its two parts off in different directions, and then recombine them, the waves would interfere and produce a pattern of fringes that would be exquisitely sensitive to any change in the speeds or path lengths of the beams. By noting the position of this pattern, turning his “interferometer” through a 90-degree angle, and then looking for any shift in the fringes, he should be able to detect a difference as small as one part in 100 million between the speed of a beam that went with and then against the ether wind and one that simply went back and forth across it. Michelson built his first interferometer while on

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Michelson’s Interferometer In 1881, Albert A. Michelson, a young American physicist studying in Germany, used his newly invented interferometer, pictured here, to try to measure how fast the earth was moving through the ether. By splitting a beam of light and sending the two resulting rays bouncing back and forth both with and across the earth’s line of motion, Michelson hoped to be able to detect the slight effect the “ether wind” blowing across the moving earth ought to have on the speed of light. He found no

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measurable effect, however, either in 1881 or when he repeated the experiment more carefully with E. W. Morley in 1887. Michelson’s results raised deep questions about the ether and our supposed motion through it that were not fully resolved until Albert Einstein formulated his theory of relativity in 1905.

 Albert A. Michelson, “The Relative

Motion of the Earth and the Luminiferous Ether,” American Journal of Science 22 (1881): 124.

a study trip to Germany and took careful observations with it early in 1881. To his surprise, he found no significant shift of the fringes and no sign of the expected ether wind. Michelson did not conclude that the ether does not exist, any more than that the earth stands still in the heavens. Instead, he took his null result as supporting a theory the Irish physicist G. G. Stokes had proposed in the 1840s. According to Stokes, the ether does not blow freely through the moving earth, as Fresnel had said, but instead is dragged along by it, both within the earth and for a substantial distance around it. On Stokes’s view, Michelson’s interferometer would no more be exposed to an ether wind than someone riding within a ship is exposed to the ocean breeze. A Dutch theoretician, H. A. Lorentz (1853–1928), read Michelson’s explanation but was not convinced. Lorentz reexamined the whole problem of motion through the ether and concluded that if the earth really dragged the ether along as Stokes had suggested, rays of light reaching us from distant stars would be affected in ways that astronomers do not observe. He also found an error in

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Michelson’s calculations that reduced the expected effect of the ether wind from one part in 100 million to one in 200 million, raising doubts that the 1881 experiment had really been conclusive. Convinced that the ether wind was real and must ultimately be detectable, Lorentz urged Michelson to repeat his experiment with a larger and even more sensitive interferometer. In 1887 Michelson, by then a professor at the Case Institute of Technology in Cleveland, teamed up with E. W. Morley to do just that. Starting with a thick block of stone five feet square, they fitted it with the finest optical apparatus and floated it in a tub of mercury so they could easily turn it without producing any stress or distortion, for they knew that even the tiniest change in the dimensions of the block would throw off their measurements. The new interferometer was much more sensitive than Michelson’s old one and should have been able to detect motion through the ether far slower than the known orbital speed of the earth. Yet when Michelson and Morley took their readings in July 1887, they again found no appreciable shift of the fringes. The expected ether wind evidently did not exist. As Oliver Heaviside later remarked, the Michelson-Morley experiment presented physicists with “a flat contradiction.”⁴ A wide array of experiments had confirmed Fresnel’s theory, which said there must be an ether wind; Michelson and Morley’s experiment, though evidently well designed and admirably performed, had failed to detect it. Something had to give. Seeking to draw the logical noose as tight as possible, Oliver Lodge set out in 1891 to test whether rapidly moving matter might drag along the ether near it—in effect, to test Stokes’s theory directly, instead of relying on Lorentz’s rather subtle astronomical arguments. Drawing on the latest technology, Lodge took a large electric motor, mounted two large steel discs on its axle, and set it spinning at thousands of revolutions per minute. He then ran a beam of light through the narrow space between the discs and used a type of interferometer to look for any sign that the light was dragged along by the spinning discs. He found none. The evidence for a stationary ether seemed overwhelming, with Michelson and Morley’s result as the one piece that stubbornly refused to fit. Exasperated, Lodge declared in 1893 that “this experiment may have to be explained away.”⁵ By then, as Lodge well knew, FitzGerald had found a surprising way to do just that. At the end of 1888, Heaviside had, for the first time, worked out the complete formula for the electromagnetic field around a moving charge. When 4. Oliver Heaviside to Oliver J. Lodge, 13 Nov. 1893, quoted in Hunt, Maxwellians, p. 191. 5. Oliver J. Lodge, “Aberration Problems,” Philosophical Transactions 184A (1893): 753.

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an electric charge moves, it sets up a magnetic field; the motion of that magnetic field then sets up a further electric field, and so on in an infinite series of ever smaller correction terms, each of them proportional to higher and higher powers of v/c, the ratio of the speed of the charge to that of light. To Heaviside’s surprise, this cumbersome infinite series converged to a very simple result: the electric field around a moving charge is just like that of an ordinary charge at rest, but compressed along its line of motion by a factor of (1  v 2/c 2). Heaviside made a point of telling his friends about this result, and FitzGerald thus had it fresh in his mind when, in the spring of 1889, he paid a visit to Lodge in Liverpool. As they sat in Lodge’s study discussing Michelson and Morley’s experiment, it suddenly occurred to FitzGerald that if matter is held together by electromagnetic forces, then these forces ought to be affected by motion through the ether. In fact, he said, we should expect a body moving through the ether to contract along its line of motion (or, what came to the same thing, to expand laterally) by the factor of (1  v 2/c 2) given by Heaviside’s formula. For ordinary speeds, this contraction would be very small; even for a body moving at 30 kilometers per second, it would come to only about one part in 200 million, so that the entire diameter of the earth would shrink by only about 6.4 centimeters (2.5 inches). But a contraction of one part in 200 million would, of course, be just enough to mask the effect Michelson and Morley had been looking for. A beam of light going against the ether wind would indeed go a little more slowly, as Michelson and Morley had assumed, but it would have a slightly shorter distance to travel, and the two effects would cancel each other out. FitzGerald concluded that this contraction must be real and that Michelson and Morley’s experiment was almost the only way to detect it—though seeing no effect at all certainly counted as an odd way of “detecting” something. FitzGerald was a firm believer in both the reality of the ether and the validity of Maxwell’s laws of electromagnetism. He was pleased that those laws allowed him to “explain away” Michelson and Morley’s troublesome result so neatly and thus save the ether from an experiment that seemed to tell against it. In many ways, however, FitzGerald’s explanation made the ether seem more elusive and inaccessible than ever. When they performed their experiment, Michelson and Morley were not trying to probe the inner structure of matter, but simply to measure the speed of the earth through the ether. For FitzGerald, however, the contraction hypothesis put the focus firmly on the question of just what holds a piece of matter together. It took several years before other physicists began to pick up on the idea that motion through the ether might affect the size of a body, but

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by the mid-1890s, several lines of inquiry were converging to focus physicists’ attention on the underlying structure of matter and the relationship between atoms and fields. Electrons Electrons were invented by theoreticians before they were discovered by experimentalists. In his electromagnetic theory, Maxwell had generally treated material bodies as simply portions of the ether that possessed different electric and magnetic properties—the ability to conduct a current, for example, or to sustain extra polarization. Maxwell was well aware that matter is made up of molecules, of course, but he set that knowledge aside in formulating his general laws of electromagnetism. After the basic framework of Maxwellian theory was consolidated in the late 1880s, however, theorists began to probe the connection between ether and matter more deeply. In the early 1890s, Lorentz in Holland and Joseph Larmor (1857–1942) in Britain took the lead in creating what became known as electron theory: the idea that ordinary matter contains swarms of tiny charged particles that act on one another through the electromagnetic field. Electron theory proved immensely fruitful, and it was soon backed up by direct experimental evidence that such particles—or at least negatively charged ones—really exist. Initially, electron theory was the purest of abstract physics, pursued with no thought of practical application. Within a few decades, however, the manipulation of electrons in vacuum tubes and later in transistors and integrated circuits would become central to the most important new technologies of the twentieth century. Work on electrons also marked one of physicists’ first major steps into the world of atomic and subatomic phenomena that would absorb so much of their attention in the new century. The idea that matter contains electric particles was of course not new in the 1890s. In some form it could be traced back at least to the eighteenth century, and between the 1840s and the 1870s Wilhelm Weber and other German physicists had worked out sophisticated mathematical theories based on the assumption that tiny particles of electricity exert forces on one another directly across empty space. In the last decades of the nineteenth century, however, such action-at-a-distance theories were largely displaced by Maxwell’s field theory, particularly after Hertz’s discovery of electromagnetic waves in 1888. The Maxwellians’ chief point was that electric and magnetic forces act through the field rather than directly at a distance, but they also attacked the idea that there was really such a thing as “electricity.” Electric charge, they said, is just a superficial effect of tensions in the surrounding field, and an electric current

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results not from any real flow of electric particles but simply from the breakdown of electric tension within a conductor. Strict Maxwellians looked on the whole idea of “electric fluids” or “particles of electricity” as badly outmoded. Lodge spoke for many, especially in Britain, when he declared in 1889 that “few things in physical science appear to me more certain than that what has so long been called electricity is a form, or rather a mode of manifestation, of the ether,” and not itself a real thing at all; the word “electrification” might survive, he said, but “‘electricity’ may gradually have to go.”⁶ No sooner had Lodge dismissed electric particles as obsolete relics, however, than they began to make a comeback, with Lorentz leading the way. Like many Continental theorists, he had always found Maxwell’s ideas about charges and currents to be vague and unsatisfactory. It was all very well to say that a current results from the breakdown of tension within a conductor, but until one could say just what that tension was and exactly how it broke down, the process remained mysterious. In the wake of Hertz’s experimental confirmation of Maxwell’s field theory, Lorentz looked for a way to graft what he saw as the best parts of the older German particle theories onto a solid new Maxwellian foundation. Lorentz’s basic idea was simple: ordinary matter, he suggested, is filled with tiny charged particles—he began to call them “electrons” in the late 1890s—that are able to move freely in conductors but are bound in place in insulators. One could look on an electron either as the source of the electromagnetic field around it or, as Faraday and Maxwell would have preferred, as simply the center on which the surrounding lines of force converge. Most bodies contain equal numbers of positive and negative electrons, Lorentz said, and so are electrically neutral; those with more of one kind than the other carry a net charge. Lorentz looked on an electric current not as a mysterious breaking down of tensions in the field, but as simply a flow of electrons within a conductor; polarization, he said, was just the elastic displacement of electrons from their equilibrium positions within an insulator. Armed only with his hypothetical electrons and Maxwell’s field equations, Lorentz proceeded to give clear and consistent explanations for all of the main phenomena of electromagnetism, as well as for such optical effects as reflection, refraction, dispersion, and Faraday’s magneto-optical rotation. Lorentz always treated ether and matter as completely separate, with the ether remaining wholly stationary while matter, sprinkled with electrons, moved freely through it. This led him quite directly to the contraction hypothesis, which he 6. Oliver J. Lodge, Modern Views of Electricity (London: Macmillan, 1889), p. ix.

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hit on independently of FitzGerald in 1892: if matter is held together by the forces between electrons, Lorentz reasoned, then motion through the ether ought to cause bodies to contract along their line of motion by just the factor of (1  v 2/c 2) needed to “explain away” Michelson and Morley’s result. Lorentz published a first version of his electron theory in 1892 and a fuller account in 1895. By then, the Cambridge mathematical physicist Joseph Larmor had begun to develop his own ideas about electrons, led to them not by German theories about electric particles but by a peculiar kind of ether theory. More than 50 years before, the Irish physicist James MacCullagh had proposed an ether whose parts did not resist being compressed or distorted, as those of an ordinary elastic solid do, but instead resisted being turned in space. Although this concept accounted very well for optical phenomena, and FitzGerald later showed that its equations closely paralleled those of Maxwell’s electromagnetic theory, MacCullagh’s theory attracted little support at the time, largely because no one could picture how a real mechanical medium could possess such purely rotational elasticity. When Larmor took it up in 1893, however, he saw great possibilities in MacCullagh’s ether, especially when he realized that it could support permanent vortex rings, whirling structures much like smoke rings. Building on an earlier idea of Kelvin’s, Larmor suggested that such vortex rings might constitute atoms of ordinary matter, with the added bonus that rings in MacCullagh’s ether would form little loops of electric current that could interact electromagnetically. Larmor initially thought he had found the key to a theory of everything; as he wrote to Heaviside in October 1893, “I fancy I have got a grip of the aether, and I am full of the matter.”⁷ Larmor soon ran into problems, however. His theory implied that ether must flow along lines of magnetic force, yet when Lodge looked for evidence that light waves were affected by such a flow, he found none. It also turned out that the forces between Larmor’s vortex rings were in the wrong direction: two rings in the rotational ether whose flows ran in the same direction would repel one another, whereas the corresponding loops of electric current would attract. FitzGerald sent Larmor piles of letters on the subject in the spring and summer of 1894 and eventually convinced him that the only way to make his theory work would be to replace his vortex rings with isolated electric charges—kinks in the rotational ether that would be able to move freely through it, rather like knots sliding along a rope. Borrowing a word first coined by his uncle, the physicist G. J. Stoney, FitzGerald dubbed these charges “electrons,” a name that soon stuck. Many things now fell into place, and though Larmor contin7. Joseph Larmor to Oliver Heaviside, 12 Oct. 1893, quoted in Hunt, Maxwellians, p. 213.

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ued to cite the rotational ether, after July 1894 he put most of his efforts into working out the consequences of introducing electrons into Maxwell’s field theory. Working independently of Lorentz, he reached many of the same conclusions, and by the time they became aware of each other’s work in 1895, the two men had produced comparably well developed versions of electron theory. To this point, electrons remained purely hypothetical. Lorentz and Larmor had shown that a wide range of electromagnetic and optical phenomena could be explained by assuming that matter contains tiny electrified particles, but they could not point to any direct evidence that such electrons actually existed, nor could they say much about their possible size or mass. In the later 1890s, however, the situation changed rapidly. Experimentalists began to turn up abundant evidence that electrons—or at least negatively charged ones— were not only real but ubiquitous, filling and perhaps constituting all of the matter around us. The first direct evidence for the existence of electrons was brought to light in the fall of 1896 by a Dutch physicist, Pieter Zeeman (1865–1943), who had studied under Lorentz. Physicists had long known that, when heated in flames, chemical elements give off light at characteristic frequencies; sodium, for example, emits yellow light that forms a well-defined double line in the spectrum. Following up a suggestion Faraday had made many years before, Zeeman placed a sodium-laced flame between the poles of an electromagnet and used a diffraction grating to examine the spectrum of the light it emitted. When he switched on the magnet, he saw the previously sharp sodium lines spread to three times their former width. On hearing this, Lorentz quickly showed that it followed directly from his theory: the magnetic field would act on the electrons oscillating or orbiting within the sodium atoms, he said, and slightly alter the frequency of the light they gave off. In fact, Lorentz said, a magnetic field should not just widen the spectral lines but actually split them apart—a prediction Zeeman confirmed when he repeated his experiment with a more powerful magnet early in 1897. By carefully measuring the polarization and other properties of the split spectral lines, Lorentz and Zeeman were able to show that the oscillating electrons must carry a negative charge and have a ratio of mass to charge less than 1⁄ 1,000 that of an ordinary hydrogen ion. Zeeman’s experiments helped turn electrons from mere theoretical constructs into real objects that physicists could measure and manipulate. Zeeman’s electrons were bound within atoms. The other main line of evidence for their reality emerged from work on cathode rays, in which electrons fly freely across space. As far back as the eighteenth century, experimenters had

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noticed a strange glow when they applied an electric charge to a pumped-out glass tube. In the nineteenth century, physicists in Germany and Britain inserted wires and plates into such tubes and studied the cascades of glowing colors that appeared when they ran electric currents through the rarefied gases within them. In the 1870s, as improved vacuum pumps (similar to those Edison used for his first light bulbs) made it possible to achieve lower pressures, physicists increasingly turned their attention to the mysterious rays given off by the negatively charged plates, or cathodes, within the tubes. Though themselves invisible, these cathode rays produced a glow where they hit the glass of the tube, and objects placed in their path cast sharp shadows. Moreover, a magnet held outside the tube deflected the rays, suggesting that they carried an electric current or at least marked the path of one. Most British experimenters believed the rays to be tiny bits of electrified matter thrown off from the cathode, while most of their German counterparts thought the rays were more likely to be waves or other disturbances in the ether. J. J. Thomson (1856–1940) was just 28 when he was appointed Cavendish Professor of Experimental Physics at Cambridge University in 1884. Under Maxwell, and especially under his successor Lord Rayleigh, work at the Cavendish had focused on precision electrical measurement, including an important redetermination of the ohm. Thomson had little flair for such exact measurement and turned instead to more rough-and-ready qualitative experimentation, particularly on electrical discharges and cathode rays. Although he and Larmor were close contemporaries and lived just a few blocks apart in Cambridge, they had little contact in the 1880s and 1890s. Thomson worked out his ideas about electrified particles—or “corpuscles,” as he called them— quite independently of Larmor’s electron theory. In 1897, Thomson succeeded in deflecting cathode rays with an electrostatic field, strongly reinforcing the argument that they were charged particles rather than waves in the ether. Moreover, by comparing these electrostatic deflections with those produced by a magnetic field, he was able to find a rough value for the corpuscles’ ratio of mass to charge: about 1011 kilograms per coulomb. This ratio was the same regardless of what metal he used for the cathode and what residual gas remained in the tube; it was also not far from the value Zeeman and Lorentz had found spectroscopically a few months before. By April 1897 Thomson felt his experimental evidence was strong enough that he could publicly suggest that negatively charged corpuscles, much smaller than atoms and all possessing identical mass and charge, are elementary constituents of all matter. (Positive charges were less accessible and evidently remained locked within atoms.) In later years Thomson’s 1897 announcement

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was often said to mark “the discovery of the electron.” In fact, there was no single dramatic moment of discovery, and it was only two or three years later, as evidence piled up from several other directions, that most physicists became convinced that electrons really existed. As electrons came to be accepted as real, they increasingly came to be viewed as truly fundamental. In their mathematical explorations of Maxwell’s theory in the 1880s, J. J. Thomson and Oliver Heaviside had noticed that electric charges possessed “electromagnetic mass,” as their interaction with the surrounding field gave the charges just the sort of resistance to any change in their speed or direction of motion that ordinary particles of matter have by virtue of their inertial mass. In a sense, the mass of a charged particle seemed to reside not within the particle itself but in the field or ether around it. It did not take long before theorists began to suggest that there might be no such thing as mass in the ordinary sense, but only the electromagnetic mass of the tiny charged particles that clump together to form material bodies. Many physicists continued to look on this in terms of a mechanical ether whose parts possessed ordinary mass, but others went further and advocated what became known as the “electromagnetic view of nature.” We should give up trying to derive the laws of electromagnetism from the workings of a mechanical ether, they said, and instead take Maxwell’s equations as fundamental. They could then hope to reduce the laws of mechanics, and ultimately all the rest of physics, simply to the interactions of fields and electrons. In 1889, Oliver Lodge had hailed Hertz’s discovery of electromagnetic waves and the consequent confirmation of the electromagnetic theory of light in very up-to-date language: “The whole domain of Optics,” he declared, “is now annexed to Electricity, which has thus become an imperial science.”⁸ By the end of the 1890s, it appeared that electricity was on the verge of annexing virtually everything else and extending its empire over the full reach of the physical world. Invisible Rays and Unstable Atoms The electron was an important experimental discovery but not an especially surprising one. There had been hints that matter contained tiny charged particles long before Zeeman, Thomson, and others first demonstrated their existence. By contrast, the discovery of X-rays at the end of 1895 came out of the blue. It was positively startling and soon set off a chain of other surprising discoveries, including that of radioactivity. It seemed for a time that previously 8. Lodge, Modern Views, p. 336.

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unsuspected properties of matter and radiation were turning up every month, and these discoveries, along with continuing research on electrons, served to focus physicists’ attention far more closely than ever before on atoms and the energies they contained. X-rays, radioactivity, and electrons also provided experimenters with powerful new tools they could use to probe the inner workings of atoms, and led as well to important new technologies. Wilhelm Röntgen (1845–1923) discovered X-rays in November 1895 while experimenting with cathode rays in his laboratory at the University of Würzburg in Germany. Like many physicists of the time, he was intrigued by the fluorescent glow that appeared where cathode rays struck the glass walls of their tubes. Other physicists had already found that if they inserted a thin aluminum “window” into the wall of a tube, they could shoot cathode rays right through the metal and into the surrounding air, though the rays went only a few centimeters before they were all absorbed. Physicists detected the rays by letting them fall on a piece of paper coated with a fluorescent compound, rather like the material used on blacklight posters. To make the fluorescence more easily visible, Röntgen darkened his laboratory and wrapped his tube in cardboard to block out the light it gave off directly. When he did so, he noticed a faint glow coming from a spare piece of fluorescent paper several feet from his tube. Sure that ordinary cathode rays could not possibly reach so far through air, he examined the phenomenon more closely. He soon established that penetrating rays of some kind—he called them “X-rays” to emphasize their unknown nature—were emanating from the glowing spot where the cathode rays struck the glass. The X-rays passed through paper, wood, even solid walls, and not only lit up a fluorescent screen but left an image on ordinary photographic film. Some materials were more transparent than others, and dense metals such as lead blocked almost all of the rays. Röntgen found he could use X-rays to take shadow photographs of metal objects within a closed wooden box, and even of his own bones through the flesh of his hand. After Röntgen made his initial discovery, he worked in complete secrecy for several weeks, intent on confirming as much as he could before announcing such a startling result. He later said he was afraid people would think he was crazy, and at first he did not tell even his wife what he was up to. Finally, just before Christmas 1895, he brought her to his laboratory, showed her what he had found, and, placing her hand on a photographic plate, took an X-ray picture that clearly showed every bone. Röntgen intended simply to give a dramatic demonstration of the penetrating power of his new rays, but his wife was reportedly disturbed by the sight, seeing in the shadow of her bones a premonition of her own death.

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Röntgen’s X-Ray Picture of His Wife’s Hand The German physicist Wilhelm Conrad Röntgen took this X-ray photograph of his wife Berthe’s hand in his Würzburg laboratory in December 1895. Its publication the next month touched off a worldwide sensation; people were intrigued and morbidly fascinated by the prospect of being able to see the bones beneath their skin.  Nature 53 (23 January 1896): 276.

Röntgen sent a brief account of his findings to the local Würzburg scientific society, which published it at the very end of December 1895. On New Year’s Day 1896 he sent copies, including a few X-ray photographs, to leading physicists in Germany and elsewhere. The news created an immediate sensation. Within a week, breathless reports were appearing in newspapers across Europe, and Kaiser Wilhelm soon called Röntgen to Berlin to deliver a special lecture about his discovery. It was the photograph of his wife’s hand that did it. People were fascinated by the prospect of being able to see the bones beneath their flesh, and more broadly by the idea that unseen realities might now suddenly be made visible. News accounts excitedly discussed the possible medical uses of X-rays, and within weeks of Röntgen’s first announcement, physicists and physicians were using the new rays to locate bullets lodged in victims’ flesh and aid in setting broken bones. Engineers soon developed special-purpose X-ray tubes and turned Röntgen’s laboratory discovery into a practical medical tool. As X-ray machines were integrated into medical practice, they proved enormously useful, though physicians eventually recognized that overexposure to the rays could pose serious dangers. X-rays were fascinating and useful, but just what were they? The idea of invisible rays was not entirely new, of course; infrared and ultraviolet light had been known since the early nineteenth century, and physicists had shown that Hertz’s long electromagnetic waves could readily pass through solid walls. At

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first Röntgen thought his rays might be a kind of pressure wave in the ether, but it soon became clear that X-rays were ordinary electromagnetic waves with extremely short wavelengths—in effect, ultra-ultraviolet light. The wavelengths of X-rays were, in fact, comparable to the spacing between atoms in ordinary matter, enabling many of the waves to pass right between the atoms. If the atoms in a body were arranged in a regular pattern, some of the X-rays could bounce off and interfere with each other, producing “X-ray diffraction patterns” that could be used to work out how atoms were arranged within crystals and molecules. Decades later, X-rays would be used in this way to find the double helix structure of DNA. Röntgen’s discovery soon sparked a search for other kinds of invisible rays. Some of these proved illusory, such as Gustave le Bon’s “black light” and later René Blondlot’s “N-rays,” both of which turned out to owe more to a will to believe than to any real physical phenomenon. In early 1896, however, the French physicist Henri Becquerel (1852–1908) made a discovery that proved far more consequential. Noting that Röntgen’s X-rays emanated from the fluorescent spot where the cathode rays struck the glass wall of the tube, Becquerel asked whether naturally fluorescent materials might give off similar rays. He placed samples of various fluorescent minerals on top of sealed photographic plates, left them there for a day or so, and then developed the plates. Most of the plates came back blank, but one on which he had placed a piece of a uranium compound came back fogged. On investigating further, he found that the fogging had nothing to do with ordinary fluorescence, but was caused by rays emanating directly from the uranium. Becquerel had discovered what soon came to be dubbed “radioactivity.” Becquerel’s discovery did not stir up anything like the excitement Röntgen’s had, but it drew the attention of a young Polish-born physicist, Marie Curie (1867–1934, born Marya Sklodowska) and her husband Pierre Curie (1859–1906). Marie Curie began to study not just uranium but the ore it came from, looking for signs of other radioactive substances. Following up Becquerel’s finding that the rays from uranium could ionize air and discharge an electrometer, she conducted tests that showed uranium ore (pitchblende) to be substantially more radioactive than uranium itself. Determined to isolate the source of this additional radioactivity, she set about laboriously extracting, purifying, and testing the various components of the ore. Pierre joined in, and by 1898 they had isolated a tiny speck of a new and highly radioactive element, which they named “polonium” in honor of Marie’s native country. Yet the remaining residue was still strongly radioactive, and the Curies tentatively identified another element in it, thousands of times as radioactive as uranium, to

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Caricature of Marie and Pierre Curie with Radium By the time Marie and Pierre Curie were awarded the Nobel Prize in Physics in December 1903 for their discovery of radium, the mysterious radioactive element was already becoming an object of public fascination. This caricature of the Curies holding a glowing vial of radium appeared in a popular British magazine of the day and reflected public interest not just in the new element and its surprising properties but also in the married pair of researchers who had discovered it.  Vanity Fair, 22 Dec. 1904.

which they gave the name “radium.” To nail down the case, they obtained over a ton of pitchblende and began the arduous work of isolating the radium within it. By 1900 the Curies had extracted a few tenths of a gram of nearly pure radium, enough to establish its main chemical and physical properties. It was soon clear that they had isolated one of the most extraordinary substances ever discovered. The Curies’ radium continually poured forth energy, though it did not seem to be itself consumed or altered in any way. It made fluorescent materials glow in the dark (leading to its later use in luminous watch dials) and remained measurably warmer than its surroundings. According to the first law of thermodynamics, energy could neither be created nor destroyed, yet radium seemed to create energy out of nothing. The Curies’ tiny speck of radium threatened to undermine one of the foundations of nineteenth century physics. Many other physicists and chemists soon joined Becquerel and the Curies in studying the strange new phenomena of radioactivity. One of the most active was Ernest Rutherford (1871–1937), a young New Zealander who had

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arrived in Cambridge in 1895 to work with J. J. Thomson. Rutherford worked first on a detector of radio waves, and for a time could achieve greater ranges than Marconi. In 1896, however, he switched to the hot new subject of X-rays and radioactivity and soon made it his own. Rutherford and others showed that radioactive substances give off three different kinds of radiation: gamma rays, which are essentially very powerful X-rays; beta rays, which are simply high-speed electrons; and the far more massive alpha rays, which were eventually identified as the nuclei of helium atoms. In 1898 Rutherford moved to McGill University in Montreal, where he teamed up with the chemist Frederick Soddy (1877–1956). By 1903, they had reached a radical conclusion: radioactive substances, they said, were not as unchanging as they first appeared but were in fact continually decaying away. As radioactive atoms gave off alpha and beta rays, Rutherford and Soddy said, they were actually disintegrating and changing into different elements—an especially startling idea for chemists, committed as they were to the permanence of chemical elements, but one that saved the physicists’ law of the conservation of energy. Radium and other radioactive substances were thus not generating energy out of nothing but simply releasing stores of energy that had somehow been locked inside them. Each kind of radioactive atom—and some elements evidently came in several distinct varieties, which Soddy dubbed “isotopes”—decayed at a characteristic rate into a lighter atom, which in turn decayed until the chain terminated in a stable isotope. It would take over four billion years for half of any given quantity of uranium to decay, through a long series of steps, into stable lead. Radium, one of the intermediate steps in this chain, has a half-life of about 1600 years; it decays, in turn, into radon, a radioactive gas with a half-life of just 3.8 days. Rutherford left Canada in 1907 to take a position at Manchester in England; he later succeeded Thomson as Cavendish professor at Cambridge. He continued to work on radioactivity, using alpha rays to probe the structure of atoms and showing in 1911 that they consist of a massive central nucleus surrounded by a swarm of lighter electrons. Soddy returned to Britain in 1904 and took up the broader implications of radioactivity in a popular book, The Interpretation of Radium (1909). Atoms, he said, hold far more energy locked within themselves than can be released in any ordinary chemical reaction. A kilogram of radium or uranium contains, and very gradually releases, millions of times as much energy as we could obtain by burning a kilogram of coal or even detonating a kilogram of dynamite. If we could find a way to release the energy within an atom all at once, rather than waiting for it to dribble out on its own over billions of years, we could, Soddy said, make the world a paradise—or

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perhaps destroy it. H. G. Wells took up Soddy’s ideas in his novel The World Set Free (1914), picturing a future that included both devastating atomic bombs and peaceful atomic power plants. It would be several decades before physicists would find ways to release atomic energy at will, but by the end of the 1890s they could already sense that vast new possibilities, for good or ill, lay before them. Atoms, long a matter of theoretical inference, were now experimental facts, rendered palpable in the laboratory. Just as physicists were finally bringing them into focus, however, atoms of such elements as uranium and radium were visibly slipping away, decaying into bursts of energy and streams of rays. Having at last penetrated to the apparent bedrock of the material world, physicists found it to be disconcertingly unstable. Quanta The most far-reaching departure in twentieth-century physics, the birth of quantum theory, had important roots in work on a seemingly mundane topic: light bulbs. The tradition of precision measurement that marked so much of nineteenth-century physics, from Joule’s work on heat and energy to the determination of the ohm and other electrical units, was closely tied to the technologies of steam power and telegraphy. By contrast, the new work in the 1890s on electrons, X-rays, and radioactivity had relatively little connection to practical technologies and often involved only rough measurements; many of J. J. Thomson’s measurements of electrons, for example, were accurate to no more than a factor of two or three. Other physicists continued to practice precision measurement, however, and it sometimes led them to important new discoveries. A case in point came in 1900, when German physicists analyzed the energy radiated by heated bodies—in effect, by the filaments of light bulbs. Deep within their careful measurements of “blackbody radiation” lay the first clues that energy is not continuous and infinitely divisible, but instead is parceled out in discrete quanta. It took several years for theorists to grasp the full implications of this discovery; when they did, the resulting quantum theory revolutionized their understanding of how, at the most basic level, the physical world works. It had, of course, long been known that bodies glow when heated, emitting radiant heat and light across the spectrum. In 1859 Gustav Kirchhoff had used the laws of thermodynamics to prove that the total amount of energy given off by a “blackbody” (defined as a body that absorbs all light and radiant heat that falls on it) does not depend at all on its material composition but solely on its temperature. By the mid-1890s, physicists had extended this to show that the

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amount of energy a blackbody emits at any particular wavelength—in effect, the color of the light it gives off when heated—must also be a function solely of its temperature, though they could not yet reduce the relationship to an exact formula. Finding the blackbody radiation formula was of fundamental theoretical importance, for it promised to shed light on the basic relationship between matter and energy. Max Planck (1858–1947), a leading theorist at the University of Berlin, saw this clearly and wrestled with the problem throughout the 1890s, striving to understand how bodies exchange energy with the electromagnetic field and eventually come into thermal equilibrium with it. Beyond its purely scientific interest, however, the blackbody problem also had practical implications relating to the efficiency of both electric light bulbs and the newly invented incandescent gas mantles, which produced light by heating metallic compounds to a white hot glow. To produce the most abundant and pleasing light for the least expenditure of energy, manufacturers needed to know how much light incandescent filaments and mantles would emit at different temperatures and what colors would predominate. For that, they needed accurate measurements and reliable standards of comparison, backed up if possible by theoretical understanding. At the behest of the German lighting industry, physicists at the Physikalisch-Technische Reichsanstalt (PTR), or Imperial Institute of Physics and Technology, near Berlin took up the light emission problem in the mid-1890s. The German government had established the institute in 1887 after a long campaign by the industrialist Werner von Siemens, who also contributed much of the money to get it started. Siemens had always advocated close relations between science and technology, and he hoped the PTR would strengthen both German industry and the German state. He persuaded Hermann von Helmholtz, Germany’s most eminent physicist, to serve as its first director, and the new institute soon set to work as both a national bureau of standards and a center for original research. Otto Lummer headed the optical laboratory at the PTR and was a master of precision measurement. In the late 1890s he and his collaborators devised sophisticated techniques for measuring the intensity of light emerging from a small hole in a hollow chamber held at a high temperature—the hole serving as the nearest practical equivalent of an ideal blackbody, in that it “absorbed” all of the radiant energy falling on it. Lummer and his group were happy to have their work serve the needs of the German lighting industry, but it is clear that they were motivated mainly by a desire to use their skills and resources to solve a significant scientific puzzle. It is just as clear, however, that they would

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not have been able to use the resources of the PTR to tackle that puzzle had not those in charge seen their blackbody measurements as having practical value.⁹ In the late 1890s, German theorists worked out formulas for blackbody radiation that seemed to fit well with both the available measurements and the known laws of energy and electromagnetism. Since the energy radiated by a blackbody was independent of its physical composition, theorists were free to assume whatever structure they found simplest to analyze. In 1899 Planck gave what appeared to be a particularly good derivation of the blackbody formula based on treating the body as made up of an immense number of tiny “Hertzian oscillators,” essentially small electric circuits that could resonate to produce electromagnetic waves. It was like picturing the blackbody as covered with tiny tuning forks and then analyzing how it would ring when repeatedly struck. With his derivation of the blackbody formula, Planck appeared to have finally given mathematical form to one of the basic relationships between matter and energy. Late in 1900, however, new and better measurements came to hand from the PTR experimentalists, and these no longer quite fit the formula Planck had so carefully derived. The difference was small, and had the data from the PTR been less precise or reliable, the discrepancy would no doubt have been ignored and the old formula retained. Planck, however, took the new measurements very seriously and felt compelled to find a theory that could account for them. Finding a formula that fit the new data was not hard; Planck came up with one within a few days. Making sense of it was another matter, and in December 1900, after trying every trick he could think of, Planck was driven to what he later called “an act of desperation.”¹⁰ Physicists had always assumed that the energy of an oscillator could have any value within its range, from zero up to the maximum the oscillator could hold. This was just common sense, like assuming that a pendulum can swing through any angle. Planck had made the same assumption in his original theory, but the result it led to did not fit the new measurements. Now he found he could derive the correct formula only by assuming that the oscillators in his blackbody could only possess certain amounts, or “quanta,” of energy, proportional to the frequency of the oscillations multiplied by a very small number, h, that came to be called “Planck’s constant.” It was as if energy came in lumps, or as if a body could have a tem9. David Cahan, An Institute for an Empire: The Physikalisch-Technische Reichsanstalt, 1871– 1918 (Cambridge: Cambridge University Press, 1989), pp. 156–57. 10. Helge Kragh, Quantum Generations: A History of Physics in the Twentieth Century (Princeton: Princeton University Press, 1999), p. 62.

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perature of, say, exactly 20 degrees or exactly 30 degrees but nothing in between. It was a startling assumption and one with far-reaching consequences. Planck had not set out to overturn the basic structure of physics, and at least at first, he did not think he had. He fully expected that the apparent division of the energy of his oscillators into discrete quanta was illusory and that he would eventually find a way to explain it in terms of ordinary physical mechanisms. Try as he might, however, he could never find such a solution. Quanta, it seemed, were real. Planck’s blackbody theory looked at first like a small and tentative adjustment in a specialized corner of physics; only in retrospect did it appear as the starting point of a great revolution. Albert Einstein took an important step toward that revolution in 1905 when he applied Planck’s idea of quanta not just to oscillators but to radiation itself, suggesting that the energy carried by light is not spread uniformly across the wave front but is bundled in packets, later known as “photons.” The idea was gradually taken up by others and applied to problems of atomic structure, most notably by the Danish theorist Niels Bohr (1885–1962) in his 1913 model of the hydrogen atom. Here, the ordinary laws of mechanics that Newton had laid down more than two centuries before no longer seemed to hold. In the 1920s physicists formulated a new set of laws, quantum mechanics, that proved spectacularly successful in accounting for atomic phenomena, but at the expense of some startling assumptions. Not only did energy come in packets, but both light and electrons seemed to behave sometimes like waves and sometimes like particles. Probability replaced strict causality, and physical reality itself seemed to fuzz out and become indeterminate when one attempted to examine it on the smallest scale. In the opening years of the twentieth century the old mechanical program, as conceived and pursued with such success in the nineteenth century, seemed to be breaking down completely.

Epilogue

Einstein at the Patent Office

In June 1905, a young patent examiner at the Swiss federal patent office in Bern sent the Annalen der Physik, the leading German physics journal of the day, a paper entitled “On the Electrodynamics of Moving Bodies.” Albert Einstein (1879–1955) had been wrestling with problems of motion and electromagnetism for years, since his student days at the Polytechnic in Zurich, and he had hit on a surprising solution, based on the “principle of relativity,” only a few weeks before. Einstein’s paper passed almost unnoticed when it first appeared, but it later came to be seen as marking one of the great revolutions in modern science. Those who look on Einstein as an icon of pure science are sometimes surprised to learn that he discovered the theory of relativity while working in a patent office, examining designs for electrical machinery. In fact, however, some of the chief roots of relativity lay precisely in the analysis of the workings of dynamos and electric motors. Many paths led Einstein to his relativity theory; one of the main ones led straight through the Swiss patent office. Einstein was born in March 1879 in Ulm in southern Germany. His father, Hermann, was a partner in a firm that sold featherbeds, but Einstein’s uncle Jakob was an ambitious engineer who soon convinced his brother to quit the bedding business and join him in a booming new field: electric power and light. The families moved to Munich in 1880 and launched J. Einstein and Company. Over the next decade, the firm prospered by providing both arc and incandescent lighting and by selling dynamos and other electrical equipment of Jakob’s design. The company displayed its wares at international electrical exhibitions and reached a high point in 1889 when it won the contract to light the Schwabing district of Munich. Living as he did among the new electrical technology, Albert was exposed to spinning coils and magnets from an early age, both in the factory that stood near the family home and in conversations with his uncle Jakob. He showed early ability in mathematics and physics and reportedly helped solve electrical design problems while still a schoolboy.¹ 1. John Stachel, Introduction to Stachel, ed., Einstein’s Miraculous Year, Centenary Edition (Princeton: Princeton University Press, 2005), p. xxx.

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(Stories that Einstein was considered slow in school have no basis in fact. He was late to begin to speak, but once he started school he excelled in the sciences, mathematics, and most other subjects. He chafed under the rigid discipline of German schooling, however, and his teachers sometimes complained that he did not show them proper respect.) J. Einstein and Company made direct current equipment, and when alternating current began to win out in the early 1890s, the firm proved unable to make the shift. The Einsteins had counted heavily on landing the Munich municipal lighting contract; when, amid a general consolidation of the electrical industry, the contract went to a larger firm in 1893, their company was forced into bankruptcy. Hermann and Jakob moved to northern Italy and tried to open a factory and power station at Pavia, but that effort failed as well, and by 1896 they were forced out of business for a second time. When his family moved to Italy, 15-year-old Albert was left behind in Munich to complete his schooling at the Luitpold Gymnasium, an elite secondary school. Lonesome and unhappy, he dropped out after a few months and joined his family in Italy. There, he helped around the electrical workshops and studied on his own in hopes of entering the Polytechnic in Zurich and becoming an engineer. Regarded as a very promising youth, he was allowed to take the entrance examination in 1895 when he was only 16, but while he did well in mathematics and physics, he fell short in other subjects. He spent the next year studying at a Swiss secondary school, passed his examinations, and entered the Polytechnic in October 1896, still several months shy of the official minimum age of 18. Modeled after both the French Ecole Polytechnique and the German Technische Hochschulen, the Zurich Polytechnic was one of the top science and engineering schools in Europe, with a particularly outstanding electrical laboratory. Einstein often skipped classes, but he studied hard on his own and completed his degree on time in 1900. His interests had shifted from engineering to theoretical physics even before he entered the Polytechnic, and he now set his sights on an academic career. There were few positions available in the field, however, and after two years of scrapping for short-term teaching jobs, he counted himself lucky when the Patent Office in Bern hired him as a “technical expert third class” in 1902. Einstein would remain there until 1909, years he later recalled as the happiest of his life. Switzerland was then emerging as an important center of the electrical industry, its mountain streams powering numerous hydroelectric projects and its engineers taking the lead in building electrical systems of all kinds. Designs for new types of dynamos, motors, and other electrical machinery poured into the

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Albert Einstein at the Swiss Federal Patent Office in Bern In June 1902, when he was 23 years old, Albert Einstein was hired as a “technical expert third class” at the Swiss Federal Patent Office in Bern, where he specialized in examining patents for dynamos, motors, and other electrical devices. The job paid well, and once he had mastered the routine, he was able to use his free time to pursue nagging problems in theoretical physics—including some concerning the relative motion of coils and magnets that also cropped up when he was analyzing dynamo designs. This photograph was taken during Einstein’s years at the patent office, which he later described as the happiest of his life.

 Hebrew University of Jerusalem Albert

Einstein Archives, courtesy AIP Emilio Segrè Visual Archives.

Bern patent office, where Einstein’s command of Maxwell’s theory made him a valued member of the staff. He soon learned the craft of the patent examiner, subjecting each application to searching criticism and insisting that inventors explain every point as clearly and rigorously as possible. Nothing was to be taken for granted and every assumption was to be carefully scrutinized. Einstein turned the same critical eye on problems in theoretical physics, delving deeply into statistical mechanics, blackbody radiation, and the photoelectric effect. He focused especially on a problem that had been troubling physicists for years: how to reconcile electromagnetic theory with the ordinary laws of motion. In Newtonian mechanics, only the relative motions of bodies really count, yet in Maxwellian field theory, the ether appeared to provide a universal standard of rest, a backdrop to which all motions had to be referred. This was not a purely abstract question, fit only for speculative philosophers. As a patent examiner, Einstein faced the problem of relative motion every time he had to analyze closely the workings of a dynamo. When Einstein finally hit on his solution to the problem in 1905 and wrote up his paper for the Annalen, he did not open with a discussion of the Michelson-Morley experiment or the latest measurements of the deflection of cathode rays. Instead, he started by describing a seemingly simple case of electro-

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magnetic induction, the effect Faraday had discovered in 1831 and that now provided the basis for the electric power industry. Consider a magnet moving near a conductor—a bar magnet, for example, being plunged into a coil of wire. “If the magnet is in motion and the conductor at rest,” Einstein noted, “there arises in the neighborhood of the magnet an electric field with a certain definite energy,” which then produces a current within the conductor. But if we hold the magnet stationary and instead move the coil over it, Maxwell’s theory tells us that something quite different happens: “If the magnet is at rest and the conductor is in motion, no electric field arises in the neighborhood of the magnet.” Instead, as the conductor moves through the magnetic field, an electromotive force, to which there is no corresponding field energy, acts to produce an electric current within the conductor. If the relative motion of the magnet and conductor is the same in the two cases, the current will be the same as well, but its source will be explained very differently: in the first case, the motion of the magnet will produce a new electric field, presumably involving a real change in the ether, while in the second case the electrons within the conductor will simply be pushed sideways as they move through the magnetic field, with no new electric field being produced at all. Of course, there was no way to tell whether it was the magnet or the conducting coil that was “really” at rest, and it was hard even to say exactly what it meant to say so. Clearly, Einstein said, simply applying Maxwell’s theory to moving magnets and conductors led to “asymmetries that do not seem to be inherent in the phenomena.”² In tracking down and eliminating those asymmetries, Einstein was led to reexamine basic assumptions about space and time and to redefine what it meant for two events to be simultaneous. The result was a remarkably elegant and self-consistent theory, but one in which electric and magnetic fields, mass and energy, and even space and time themselves were mixed together in surprising ways. Moreover, Einstein declared that in his theory, “the introduction of a ‘light ether’ will prove to be superfluous,” in that there would be no need either to assume a universal stationary frame of reference or to ascribe velocities to points in the electromagnetic field—that is, to treat the field as an ether whose parts can swirl or flow. At a stroke, Einstein had brought together two of the great branches of physics, mechanics and electromagnetism, and resolved the long-standing tensions between them. In many ways he had set the capstone to what later came to be called “classical” physics—but in the process 2. Albert Einstein, “On the Electrodynamics of Moving Bodies” (1905), in Stachel, Einstein’s Miraculous Year, p. 123.

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had eliminated the mechanical ether on which so much of classical physics had been based. Einstein did not develop his theory of relativity in an effort to improve the design of dynamos, nor did it have that effect. Although he said in his paper that his theory served to dissolve persistent controversies about the true “seat of electromotive force” in unipolar dynamos (generators in which the conductor slides along the surface of the magnet, producing a strong current at low voltage), he saw this as at most a side issue. Einstein was fascinated by technological problems, but he was not motivated by technological aims. As was so often the case in the history of physics, dating back to the work of Carnot, Clausius, and Thomson on steam engines and thermodynamics and of Thomson, Maxwell, and Heaviside on telegraphs and electromagnetism, new technologies had brought intriguing new phenomena to the fore, and physicists had responded by making them the focus of their research. Technology provided many of the most important tools for scientific research and much of the environment within which physicists’ thinking developed. Einstein would eventually leave the patent office and take his place as the most revered scientist of the twentieth century. By the 1930s he was widely viewed as a sort of holy man of science, dwelling in a rarefied intellectual realm far above the mundane world. It is worth remembering, however, that some of Einstein’s most important insights were rooted in the spinning coils and magnets of ordinary dynamos and motors, in the practical technologies that had brought the world both power and light.

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Suggested Further Reading

Introduction There are several good surveys of nineteenth-century physics on the one hand and of the associated technologies on the other, but very few books connect the two. Well-informed introductions to the histories of most areas of modern physics and chemistry can be found in Mary Jo Nye, ed., The Modern Physical and Mathematical Sciences, vol. 5 of the Cambridge History of Science (Cambridge: Cambridge University Press, 2003). P. M. Harman’s Energy, Force, and Matter: The Conceptual Development of Nineteenth-Century Physics (Cambridge: Cambridge University Press, 1982) focuses, as its subtitle suggests, on the development of theories and concepts, while Robert D. Purrington’s Physics in the Nineteenth Century (New Brunswick: Rutgers University Press, 1997) examines experimental work as well. Emilio Segrè’s books From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries (San Francisco: Freeman, 1984) and From X-Rays to Quarks: Modern Physicists and Their Discoveries (San Francisco: Freeman, 1980) provide engaging accounts that reflect a leading physicist’s perspective on the history of his field. Mary Jo Nye’s Before Big Science: The Pursuit of Modern Chemistry and Physics, 1800–1940 (Cambridge: Harvard University Press, 1996) ties physics more closely to chemistry than do most other accounts, while Iwan Rhys Morus, When Physics Became King (Chicago: University of Chicago Press, 2005), examines how and why physics became “king” of the sciences by the end of the nineteenth century. Christa Jungnickel and Russell McCormmach’s Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, 2 vols. (Chicago: University of Chicago Press, 1986), provides a comprehensive institutional and intellectual account of the rise of theoretical physics in Germany. On the technological side, Ben Marsden and Crosbie Smith’s Engineering Empires: A Cultural History of Technology in Nineteenth-Century Britain (New York: Palgrave Macmillan, 2005) puts nineteenth-century technology in an imperial context. For a provocative and thoroughly documented account of shift-

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ing views on the relationship between science and technology and of how these have affected historians’ treatments of the subject, see Paul Forman, “The Primacy of Science in Modernity, of Technology in Postmodernity, and of Ideology in the History of Technology,” History and Technology 23 (2007): 1–152. 1 Steam and Work On early steam power, see Richard Hills, Power from Steam: A History of the Stationary Steam Engine (Cambridge: Cambridge University Press, 1989), and Ben Marsden’s brief Watt’s Perfect Engine: Steam and the Age of Invention (New York: Columbia University Press, 2002). The approach taken in the present book owes much to Donald Cardwell’s masterly account of the role of steam technology in the development of thermodynamics in From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age (London: Heinemann, 1971). Robert Fox’s extensive notes to his translation of Sadi Carnot’s Reflexions on the Motive Power of Fire (Manchester: Manchester University Press, 1986) provide the best introduction to Carnot’s work; Eric Mendoza’s earlier edition, Reflections on the Motive Power of Fire and Other Papers on the Second Law of Thermodynamics (New York: Dover, 1960), includes translations of important papers by Clapeyron and Clausius. The classic account of Laplacian physics is Robert Fox, “The Rise and Fall of Laplacian Physics,” Historical Studies in the Physical Sciences 4 (1974): 89–136. Two papers by Eugene Frankel, “Corpuscular Optics and the Wave Theory of Light: The Science and Politics of a Revolution in Physics,” Social Studies of Science 6 (1976): 141–84, and “J. B. Biot and the Mathematization of Experimental Physics in Napoleonic France,” Historical Studies in the Physical Sciences 8 (1977): 33–72, focus on the contest between the wave and particle theories of light. In The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century (Chicago: University of Chicago Press, 1989), Jed Z. Buchwald presents an alternative view, arguing that adherents of the wave and particle theories largely talked past each other in the 1810s as they pursued incompatible approaches to the analysis of rays and wave fronts. 2 Energy and Entropy Thomas Kuhn’s essay “Energy Conservation as an Example of Simultaneous Discovery,” first published in 1957 and reprinted in Kuhn, The Essential Tension: Selected Studies in Scientific Tradition and Change (Chicago: University of Chicago Press, 1977), identifies various claimants to the title of “discoverer of the conservation of energy” and asks what such a discovery really amounts to.

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In Robert Mayer and the Conservation of Energy (Princeton: Princeton University Press, 1993), Kenneth Caneva tells the story of one of those claimants, and the essays in David Cahan, ed., Hermann von Helmholtz and the Foundations of Nineteenth-Century Science (Berkeley: University of California Press, 1993), explore aspects of the wide-ranging work of another. Donald Cardwell recounts Joule’s life and work in James Joule: A Biography (Manchester: Manchester University Press, 1989), while in “Reworking the Mechanical Equivalent of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England,” Studies in History and Philosophy of Science 26 (1995): 73–106, Heinz Otto Sibum closely examines Joule’s famous paddle wheel experiment and describes a careful effort to recreate it. Crosbie Smith, The Science of Energy: A Cultural History of Energy Physics in Victorian Britain (Chicago: University of Chicago Press, 1998), gives a comprehensive account of what the science of energy meant to its “North British” proponents in the nineteenth century. The writings of two of the most important of those proponents can be found in James Prescott Joule, Scientific Papers of James Prescott Joule, 2 vols. (London: Taylor and Francis, 1884); William Thomson, Mathematical and Physical Papers, 6 vols. (Cambridge: Cambridge University Press, 1882–1911); and William Thomson, Popular Lectures and Addresses, 3 vols. (London: Macmillan, 1891–94). For intriguing reflections on the larger cultural significance of thermodynamics, see Stephen G. Brush, The Temperature of History: Phases of Science and Culture in the Nineteenth Century (New York: B. Franklin, 1978). 3 The Kinetic Theory Stephen G. Brush, ed., The Kinetic Theory of Gases: An Anthology of Classic Papers with Historical Commentary (London: Imperial College Press, 2003), includes papers by Clausius, Maxwell, Boltzmann, and other pioneers of kinetic theory, as well as Brush’s own incisive commentaries on them and an extensive bibliography. Brush’s other writings on the history of thermodynamics and kinetic theory are collected in The Kind of Motion We Call Heat, 2 vols. (Amsterdam: North Holland, 1976). On Maxwell’s demon, see Martin J. Klein, “Maxwell, His Demon, and the Second Law of Thermodynamics,” American Scientist 58 (1970): 84–97; Edward Daub, “Maxwell’s Demon,” Studies in History and Philosophy of Science 1 (1970): 213–77; and the mix of historical and contemporary writings collected in Harvey S. Leff and Andrew F. Rex, eds., Maxwell’s Demon: Entropy, Information, Computing (Princeton: Princeton University Press, 1990), and Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing (Bristol, UK:

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Institute of Physics, 2003). Leff and Rex bring out how interpretations of Maxwell’s demon were affected by the rise of quantum theory and modern ideas about information and computing. Most of Maxwell’s published papers can be found in W. D. Niven, ed., Scientific Papers of James Clerk Maxwell, 2 vols. (Cambridge: Cambridge University Press, 1890), and many of his letters and manuscripts in P. M. Harman, ed., Scientific Letters and Papers of James Clerk Maxwell, 3 vols. (Cambridge: Cambridge University Press, 1990–2002). On Boltzmann, see David Lindley, Boltzmann’s Atom: The Great Debate That Launched a Revolution in Physics (New York: Free Press, 2001), and Ludwig Boltzmann, Lectures on Gas Theory (1896–98), trans. Stephen G. Brush (Berkeley: University of California Press, 1964). On Gibbs, see Lynde Phelps Wheeler, Josiah Willard Gibbs: The History of a Great Mind (New Haven: Yale University Press, 1952). 4 Electricity Volta’s invention of the battery is recounted in Giuliano Pancaldi, Volta: Science and Culture in the Age of Enlightenment (Princeton: Princeton University Press, 2003). The best brief biography of Faraday is Iwan Rhys Morus’s Michael Faraday and the Electrical Century (London: Icon Books, 2004). L. Pearce Williams’s Michael Faraday (London: Chapman and Hall, 1965) emphasizes the supposed philosophical antecedents of Faraday’s field ideas, while Geoffrey Cantor, Michael Faraday: Sandemanian and Scientist (London: Macmillan, 1991), focuses on his religion. Henry Bence Jones, Life and Letters of Faraday, 2 vols. (London: Longmans, Green, 1870), is the standard older source. Faraday’s own writings on electricity can be found in Michael Faraday, Experimental Researches in Electricity, 3 vols. (London: Quaritch, 1839–55), while his letters are collected in F. A. J. L. James, ed., Correspondence of Michael Faraday (London: IEE/IET, 1991–). Iwan Rhys Morus examines the work of other electrical experimenters of the time in Frankenstein’s Children: Electricity, Exhibition, and Experiment in Early-Nineteenth-Century London (Princeton: Princeton University Press, 1998) On early telegraphy, see Brian Bowers, Sir Charles Wheatstone, FRS, 2nd ed. (London: IEE, 2001), and Tom Standage, The Victorian Internet (New York: Walker, 1998). On cable telegraphy, the best single source is still Charles Bright, Submarine Telegraphs: Their History, Construction, and Working (London: Lockwood, 1898); see also Bruce J. Hunt, “Michael Faraday, Cable Telegraphy, and the Rise of British Field Theory,” History of Technology 13 (1991): 1–19, and “Scientists, Engineers, and Wildman Whitehouse: Measurement and Credibility in Early Cable Telegraphy,” British Journal for the History of Science

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29 (1996): 155–70. A rich source on the life and wide-ranging work of William Thomson (Lord Kelvin) is Crosbie Smith and Norton Wise, Energy and Empire: A Biographical Study of Lord Kelvin (Cambridge: Cambridge University Press, 1989); see also Silvanus P. Thompson, Life of Lord Kelvin, 2 vols. (1910; repr., New York: Chelsea, 1976). On the strategic importance of cable telegraphy, see Daniel R. Headrick, The Invisible Weapon: Telecommunications and International Politics, 1851–1945 (Oxford: Oxford University Press, 1991); on its effects on work in science, see Bruce J. Hunt, “Doing Science in a Global Empire: Cable Telegraphy and Victorian Physics,” in Bernard Lightman, ed., Victorian Science in Context (Chicago: University of Chicago Press, 1997). 5 Electromagnetism Olivier Darrigol’s Electrodynamics from Ampère to Einstein (Oxford: Oxford University Press, 2000) provides an outstanding guide to a demanding subject; the first volume of E. T. Whittaker’s History of the Theories of Aether and Electricity, 2 vols. (London: Thomas Nelson, 1951), is also useful. On the ether, see the essays in G. N. Cantor and M. J. S. Hodge, eds., Conceptions of Ether (Cambridge: Cambridge University Press, 1981). The Cambridge Mathematical Tripos did much to shape British work in mathematics and physics in the nineteenth century; Andrew Warwick gives a masterly account of its origin and influence in Masters of Theory: Cambridge and the Rise of Mathematical Physics (Chicago: University of Chicago Press, 2003). Lewis Campbell and William Garnett’s Life of James Clerk Maxwell (1882; repr., New York: Johnson, 1969) remains the standard biography of Maxwell; for briefer and more recent accounts, see C. W. F. Everitt, James Clerk Maxwell, Physicist and Natural Philosopher (New York: Scribner, 1975), and Basil Mahon, The Man Who Changed Everything: The Life of James Clerk Maxwell (Chichester: Wiley, 2003). Maxwell’s Treatise on Electricity and Magnetism, 2 vols. (Oxford: Clarendon Press, 1873; 2nd ed., 1881; 3rd ed., 1891), is a sprawling work that requires close study; for guidance to it, see Thomas K. Simpson’s Figures of Thought: A Literary Appreciation of Maxwell’s Treatise on Electricity and Magnetism (Santa Fe: Green Lion Press, 2005) and Maxwell on the Electromagnetic Field: A Guided Study (New Brunswick: Rutgers University Press, 1997). Daniel M. Siegel subjects Maxwell’s famous vortex model to detailed analysis in Innovation in Maxwell’s Electromagnetic Theory: Molecular Vortices, Displacement Current, and Light (Cambridge: Cambridge University Press, 1991), while Peter Harman examines Maxwell’s philosophical views in The Natural Philosophy of James Clerk Maxwell (Cambridge: Cambridge University Press, 1998). On electrical measurement and the determination of the ohm, see Bruce

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J. Hunt, “The Ohm Is Where the Art Is: British Telegraph Engineers and the Development of Electrical Standards,” Osiris 9 (1994): 48–63, and Simon Schaffer, “Accurate Measurement Is an English Science,” in M. Norton Wise, ed., The Values of Precision (Princeton: Princeton University Press, 1995). On the work of Maxwell’s successors, see Jed Z. Buchwald, From Maxwell to Microphysics: Aspects of Electromagnetic Theory in the Last Quarter of the Nineteenth Century (Chicago: University of Chicago Press, 1985), and Bruce J. Hunt, The Maxwellians (Ithaca: Cornell University Press, 1991). For the Maxwellians’ own writings, see Oliver J. Lodge, Modern Views of Electricity (London: Macmillan, 1889); Joseph Larmor, ed., The Scientific Writings of the Late George Francis FitzGerald (Dublin: Hodges and Figgis, 1902); Oliver Heaviside, Electrical Papers, 2 vols. (London: Macmillan, 1892), and Electromagnetic Theory, 3 vols. (London: Electrician Co., 1893–1912); and Heinrich Hertz, Electric Waves: Being Researches on the Propagation of Electric Action with Finite Velocity through Space, trans. D. E. Jones (London: Macmillan, 1893). On Hertz’s life and work, see Charles Susskind, Heinrich Hertz: A Short Life (San Francisco: San Francisco Press, 1995), and Jed Z. Buchwald, The Creation of Scientific Effects: Heinrich Hertz and Electric Waves (Chicago: University of Chicago Press, 1994). For a fascinating account of a most unusual personality, see Paul J. Nahin, Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age, 2nd ed. (Baltimore: Johns Hopkins University Press, 2002). 6 Electric Power and Light The best account of the history and early development of the electrical power system is Thomas Hughes, Networks of Power: Electrification in Western Society, 1880–1930 (Baltimore: Johns Hopkins University Press, 1983). Jill Jonnes’s Empires of Light: Edison, Tesla, Westinghouse, and the Race to Electrify the World (New York: Random House, 2003) provides a lively narrative focused on personalities. Paul Israel, Edison: A Life of Invention (New York: Wiley, 1998), is the best recent biography of Edison; see also Matthew Josephson, Edison: A Biography (New York: McGraw-Hill, 1959). Robert Friedel and Paul Israel give a blow-by-blow account of the invention of the light bulb in Edison’s Electric Light: Biography of an Invention (New Brunswick: Rutgers University Press, 1986). Masses of material on Edison and his co-workers can be found in Reese Jenkins et al., eds., The Papers of Thomas A. Edison (Baltimore: Johns Hopkins University Press, 1989–) and at the associated website. On the “battle of the currents” and the adoption of the electric chair, see

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Richard Moran, Executioner’s Current: Thomas Edison, George Westinghouse, and the Invention of the Electric Chair (New York: Knopf, 2002), and Mark Essig, Edison and the Electric Chair: A Story of Light and Death (New York: Walker, 2003). Robert Rosenberg’s 1990 Johns Hopkins University dissertation, “Academic Physics and the Origins of Electrical Engineering in America,” provides the fullest account of this important subject; on the British side, see Graeme Gooday, “Precision Measurement and the Genesis of Physics Teaching Laboratories in Victorian Britain,” British Journal for the History of Science 23 (1990): 25–51. On the history of the physics discipline in the United States, Daniel Kevles, The Physicists: The History of a Scientific Community in Modern America (New York: Knopf, 1978; 2nd ed., Cambridge: Harvard University Press, 1995), is unsurpassed. 7 Into a New Century On the Michelson-Morley experiment, see Loyd Swenson, The Ethereal Aether: A History of the Michelson-Morley-Miller Aether-Drift Experiment, 1880–1930 (Austin: University of Texas Press, 1972); Dorothy Michelson Livingston, The Master of Light: A Biography of Albert A. Michelson (Chicago: University of Chicago Press, 1973); and the essays in Stanley Goldberg and Roger Stuewer, eds., The Michelson Era in American Science, 1870–1930 (New York: American Institute of Physics, 1988). On Lorentz, see Russell McCormmach, “H. A. Lorentz and the Electromagnetic View of Nature,” Isis 61 (1970): 459–97; on the electron, see Per Dahl, Flash of the Cathode Rays: A History of J. J. Thomson’s Electron (Bristol, UK: Institute of Physics, 1997), and Jed Z. Buchwald and Andrew Warwick, eds., Histories of the Electron: The Birth of Microphysics (Cambridge: MIT Press, 2001). Perhaps the best of the many biographies of Marie Curie is Susan Quinn, Marie Curie: A Life (New York: Simon and Schuster, 1995). On the PTR and early experiments on blackbody radiation, see David Cahan, An Institute for an Empire: The Physikalisch-Technische Reichsanstalt, 1871–1918 (Cambridge: Cambridge University Press, 1989). Martin J. Klein analyzed Planck’s role in the origins of quantum theory in “Max Planck and the Beginnings of Quantum Theory,” Archive for History of Exact Sciences 1 (1962): 459–79; Thomas Kuhn offered an alternative interpretation in BlackBody Theory and the Quantum Discontinuity, 1894–1912 (Oxford: Clarendon Press, 1978). For an excellent short biography of Planck, see John Heilbron, The Dilemmas of an Upright Man: Max Planck as a Spokesman for German Science (Berkeley: University of California Press, 1986). Helge Kragh, Quantum

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Generations: A History of Physics in the Twentieth Century (Princeton: Princeton University Press, 1999), provides a good survey of quantum theory and atomic physics. Epilogue The literature on Einstein is enormous. Among the best starting points are the biographies by Walter Isaacson, Einstein: His Life and Universe (New York: Simon and Schuster, 2007), and Abraham Pais, ‘Subtle is the Lord . . .’: The Science and Life of Albert Einstein (Oxford: Oxford University Press, 1982). On the origins of relativity theory, see Arthur I. Miller, Albert Einstein’s Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905–1911) (Reading, MA: Addison-Wesley, 1981), and Richard Staley, Einstein’s Generation: The Origins of the Relativity Revolution (Chicago: University of Chicago Press, 2008). For a particularly interesting perspective, see Alberto A. Martínez, Kinematics: The Lost Origins of Einstein’s Relativity (Baltimore: Johns Hopkins University Press, 2009). John Stachel, Einstein’s Miraculous Year: Five Papers That Changed the Face of Physics (Princeton: Princeton University Press, 1998), provides translations of Einstein’s most important early papers; the 2005 Centenary Edition includes a useful new introduction by Stachel. Stachel was the first editor of The Collected Papers of Albert Einstein (Princeton: Princeton University Press, 1987–); the published volumes and associated website make available an abundance of material on Einstein’s life and work.

Index

Academy of Sciences (Paris), 16, 18 action-at-a-distance theories, 14–15, 69, 72, 75–79, 94–95, 148 AEG, 135, 140 Airy, G. B., 79 alternating current, 121, 126–36, 164; and induction motors, 133–36, 140; polyphase, 133–35, 137, 140; and transformers, 75, 129–30 Ampère, André-Marie, 71–73, 75, 80, 95 Annalen der Chemie, 30 Annalen der Physik, 29, 31, 163, 165 Anthony, William, 140 Arago, François, 16–18, 72 arc lighting, 122–23, 125, 128, 131, 135, 139, 163 Arcueil, Society of, 16–17, 20 Associated Press, 84 Atlantic telegraph cables, 85–93, 98, 104–6, 109 Atlantic Telegraph Company, 86, 89, 91–92 Ayrton, Hertha, 139 Ayrton, W. E., 139 Bacon, Francis, 2, 48 Barker, George, 127 Becquerel, Henri, 156–57 Bernoulli, Daniel, 48–51 Berthollet, Claude Louis, 14, 16–17 Biot, Jean-Baptiste, 16–18, 71 Black, Joseph, 9–10 blackbody radiation, 159–62, 165 Blondlot, René, 156 Bohr, Niels, 162 Boltzmann, Ludwig, 62; and atoms, 62, 65– 67; and H-theorem, 63–64; and kinetic theory, 47, 62–67; and second law of thermodynamics, 62–65 Boltzmann’s constant, 64–65 Boulton, Matthew, 10; and Watt, 10, 12, 24

Boyle, Robert, 47 Boyle’s law, 47–48, 50–51, 53 Brett, J. W., 86 Bright, Charles, 105 British Association Committee on Electrical Standards, 92, 105–8 British Association for the Advancement of Science, 33, 35, 105, 109, 115, 117 Brown, Harold P., 131–32 Brownian motion, 66 caloric, 15, 20, 28, 46, 48; in Carnot’s theory, 21, 23–24, 35, 37 Cambridge University, 97, 109–10, 152; Mathematical Tripos, 36, 53, 109. See also Cavendish Laboratory Campbell, Lewis, 99 Carnot, Lazare, 19 Carnot, Sadi, 19–25, 35–39, 67, 167 Carnot cycle, 21–24, 37, 41, 58 cathode rays, 151–52, 154, 156, 165 Cavendish Laboratory, 110, 152, 158 Central Institution (London), 139 Chappe, Claude, 79 Chicago Columbian Exposition, 135 Christie, S. H., 82 Clapeyron, Emile, 22–24, 35, 37 Clark, Latimer, 87, 105 Clausius, Rudolf, 38; and kinetic theory of gases, 47, 50–56, 67; and second law of thermodynamics, 36, 38–41, 45, 67, 167 Colding, Ludvig, 28 Cooke, W. F., 80–81 Copleston, Edward, 85 Cornell University, 140–41 Coulomb, Charles, 15, 72, 75, 100; and electric and magnetic force laws, 15, 69, 71, 79, 95–96, 106 Cross, Charles, 140

178 Curie, Marie, 156–57 Curie, Pierre, 156–57 Dancer, J. B., 33 Darmstadt Technische Hochschule, 140 Darwin, Charles, 1, 43–44 Davy, Humphry, 74, 122 dielectric, 77–78, 96, 102; and telegraphy, 87, 89, 94, 114 direct current, 121–22, 129, 135–36, 164; Edison and, 126–28, 130–31 displacement current, 103, 108, 112 Dolivo-Dobrolowsky, Michael, 135, 140 dynamos, 121–27, 132–33, 135–36, 140–41, 163– 65, 167 earth, age of the, 40, 42–45 Ecole Polytechnique (Paris), 16, 18–20, 164 Edison, Thomas, 75, 120, 123–28, 131–33, 136– 37, 152; and direct current system, 126–28, 130–31; and Menlo Park laboratory, 123–24; and Pearl Street power station, 126; and West Orange laboratory, 131, 136 Edison Electric Light Company, 124, 131, 135– 36, 138 Einstein, Albert, 66–67, 76, 136, 145, 162–67 Einstein, Hermann, 163–64 Einstein, Jakob, 163–64 electrical engineering education, 137–41 electrical measurement, 81–82, 85, 108–10, 119, 139, 152, 159; Coulomb and, 15, 69, 71; telegraphy and, 81–82, 85, 91–92, 94, 104– 6, 109, 119; Weber and, 95, 103–4, 106 electrical units, 92, 104–10, 159; ratio of, 103– 6, 108–10. See also British Association Committee on Electrical Standards; ohm electric chair, 127, 132 electric charge, 15, 69–70, 78, 106, 153; and electron theory, 148–52; field theory of, 73, 77, 87, 94, 100, 103; motion of, 106, 111, 146–47; particle theory of, 15, 76–77, 95, 100, 106, 148 electric current, 27, 32, 70–71; and electromagnetic forces, 27, 70–73, 80, 106; field theory of, 76–78, 87, 94, 101, 114, 148–49; particle theory of, 75–77, 101, 106, 149. See also alternating current; direct current electric generators, 27, 32. See also dynamos; magnetos Electrician, The (journal), 114

Index electric motors, 27, 75, 120–23, 126, 130, 163– 64, 167; Joule and, 31–32. See also induction motors Electric Telegraph Company, 81, 84 electromagnetic field. See field theory electromagnetic induction, 27, 74–76, 95, 100, 120–21, 129, 165–66 electromagnetic mass, 153 electromagnetic theory of light, 2, 94, 97, 108–9, 111–12, 153; and Maxwell’s vortex ether, 101–4, 107 electromagnetic waves, 94, 118–19, 156, 158, 161; FitzGerald and, 111–12, 117; Hertz and, 110, 115–118, 142, 148, 153, 155; Lodge and, 111–12, 115, 117–18 electrons, 68, 100, 148, 153–54, 158–59, 162, 166; FitzGerald and, 150; Larmor and, 150– 51, 152; Lorentz and, 149–52; J. J. Thomson and, 152–53, 159; Zeeman and, 151–53 electroplating, 121 electrostatic force, 15, 69, 95–96, 102–3, 106, 152 Elementary Principles in Statistical Mechanics (Gibbs), 66 energy, 8, 24–25, 38, 40–41, 66, 107, 162; of atoms, 44, 157–59; conservation of, 19, 25– 26, 30–32, 38–39, 41, 57, 75, 95, 157–58; dissipation of, 35, 39–42, 45, 59–60, 62; of electromagnetic field, 94, 108, 111–12, 114– 15, 129, 160, 166; of ether, 100, 102, 143; and heat, 32–33, 46, 57–58, 142, 159; and kinetic theory, 51–52, 57–58, 63–64; radiant, 159–61; transformation of, 25–26, 30, 40, 45–46, 120, 122. See also heat; thermodynamics English Channel telegraph cable, 85–86 entropy, 25, 41–42, 45, 57–58, 60, 62–66. See also thermodynamics ether, 28, 96, 109, 142–3, 156, 166–67; electromagnetic, 72, 94–95, 98–104, 107–8, 112, 142, 148–50; MacCullagh’s rotational, 111, 150–51; Maxwell’s vortex model of, 99–104, 107–8; motion through, 144–47, 149–50, 165–66; vortex sponge, 143–44; and wave theory of light, 18, 72, 94, 99, 143, 156 evolution, theory of, 40, 43–45 Experimental Researches in Electricity (Faraday), 98 Faraday, Michael, 27–28, 71, 73–74, 78–80, 86–88, 151; and electromagnetic induction,

Index 27, 74–76, 121, 129, 166; and field theory, 73, 78–79, 94–98, 119, 149; and lines of force, 75–78, 95–98; religious views of, 27, 34, 38, 73 Faraday effect (magneto-optic rotation), 95– 99, 104, 111, 149 Ferranti, S. Z. de, 130 Feynman, Richard, 111 Field, Cyrus, 86, 88–89, 92 field theory, 2, 94, 120, 153, 166; and electron theory, 148–51, 153; Faraday’s, 73, 78–79, 94–98, 119; Maxwellian, 68, 110–15, 117, 146–49, 165; Maxwell’s, 94–105, 108–17, 143, 147–51, 153, 165–66; and telegraphy, 85, 94, 119 Fin du Monde, La (Flammarion), 43 FitzGerald, G. F., 111, 142; and contraction hypothesis, 146–47, 150; and electromagnetic waves, 111–12, 117; and electrons, 150; and ether, 111, 142–43, 147, 150; and Maxwellians, 111–12, 117 Fizeau, Hippolyte, 103 Flammarion, Camille, 43 Fleming, J. A., 118 force, lines of, 75–79, 94–99, 149 Frankfurt Electrical Exhibition (1891), 134–35 Fresnel, A.-J., 18, 27, 72, 143; and motion through ether, 144–46 Gale, Leonard, 83 Galvani, Luigi, 69–70 Ganz and Company, 130 gas lighting, 123–25, 160 Gaulard, Lucien, 129–30 Gauss, C. F., 80, 106 Gay-Lussac, Joseph, 16, 18, 47–48 Gay-Lussac’s law, 47, 51 General Electric Company, 135–36 Germain, Sophie, 17 Gibbs, John D., 129 Gibbs, J. Willard, 62, 66 Glasgow, 9, 36–37, 89 Glasgow University, 9, 35–38, 93, 99, 110, 138– 39, 142 God, 130, 138; and conservation of physical powers, 27, 34, 38; and creation, 42; and heat death, 45 Gordon, Lewis, 38 Gramme, Zénobe-Théophile, 122 Gramme dynamo, 122, 133

179 Great Eastern (ship), 92 Grove, William Robert, 28–29 Guillotin, Joseph-Ignace, 132 gutta-percha, 86, 88–89, 92, 105 heat, 19–24; bodily, 29–30; and energy, 40–41; frictional, 28–29; kinetic theory of, 28, 31, 46–67; latent, 9, 48, 52; mechanical equivalent of, 30–35; wave theory of, 27–28; and work, 29–32, 35–39 heat death, 25, 40–45 Heaviside, Oliver, 88, 111–15, 117–19, 146–47, 150, 153, 167; energy flow formula of, 114– 15; and Maxwellians, 115, 117; and “Maxwell’s equations,” 111, 113–15, 117 Helmholtz, Hermann von, 30–31, 63, 95, 116, 124, 140, 160 Henry, Joseph, 80, 83 Herapath, John, 49–51 Hero of Alexandria, 4 Hertz, Heinrich, 110, 115–19, 142, 148–49, 153, 155 H.M.S. Agamemnon, 88 Hockin, Charles, 107–8 Hutton, James, 40, 42 Imperial College of Engineering (Tokyo), 139 indicator diagram, 13, 22, 24 induction motors, 133–36, 140 Institute of France, 16–17 Interpretation of Radium (Soddy), 158 J. Einstein and Company, 136, 163–64 Jenkin, Fleeming, 92, 105, 107 Johns Hopkins University, 138 Joint Committee on Submarine Telegraph Cables, 91–92, 105 Joule, James, 31, 34, 37–41, 98; and electric motors, 31–32, 121; and kinetic theory of heat, 32, 45, 49, 52; and mechanical equivalent of heat, 31–35, 159; paddle wheel experiments of, 33–36; and William Thomson, 35–38, 40, 98 Joule’s law, 32, 107, 128 Kelvin, Lord. See Thomson, William Kelvin temperature scale, 37, 41, 48 Kemmler, William, 132–33 Kennelly, Arthur, 136

180 kinetic theory of gases, 46–47, 50–51; Bernoulli’s, 48–50; Boltzmann’s, 62–67; Clausius’s, 38, 50–54; Herapath’s, 49; Maxwell’s, 53–62; and second law of thermodynamics, 57–65, 67; Waterston’s, 49–50. See also MaxwellBoltzmann distribution; Maxwell’s demon King’s College London, 56, 81, 107, 109 Kittler, Erasmus, 140 Kohlrausch, Rudolf, 103 Krönig, August, 51 Lagrange, J. L., 14 Laplace, Pierre-Simon, 14–18 Laplacian physics, 14–20, 30, 48, 69, 71–72, 75, 95, 107 Larmor, Joseph, 148, 150–52 Lavoisier, Antoine, 15, 29 Le Bon, Gustave, 156 Lectures on Gas Theory (Boltzmann), 65 Leyden jar, 69–70, 77–78, 87, 102 Liebig, Justus von, 28, 30 light: electromagnetic theory of, 94, 99, 101– 4, 107–9, 111–12, 153; particle theory of, 17– 18, 27; polarization of, 17, 27, 94, 96, 111; speed of, 103–10, 144; wave theory of, 17– 18, 27, 72, 94, 96, 143. See also arc lighting; gas lighting; light bulbs light bulbs, 120, 123, 129, 152; and blackbody radiation, 159–60; carbon filament, 125, 128; platinum regulator, 124–25 lines of force, 75–79, 94–99, 149 Locke, John, 48 Lodge, Oliver, 139, 149–50; and electromagnetic waves, 112, 115–18, 153; and Maxwellians, 111–12, 115, 117; spinning disc experiment of, 146; and wireless telegraphy, 116, 118 Lorentz, H. A., 145–46; contraction hypothesis of, 149–50; and electron theory, 148–51; and Zeeman, 151–52 Loschmidt, Josef, 60, 62–64 Lummer, Otto, 160 Lyell, Charles, 42–43 MacCullagh, James, 111, 150 Mach, Ernst, 65, 67 magneto-optic rotation (Faraday effect), 95– 99, 104 magnetos, 75, 121–22 Malus, Etienne, 17

Index Marconi, Guglielmo, 116, 118–19, 158 Mathematical Physics (Herapath), 49 Maxwell, James Clerk, 53, 56, 72, 109–10, 118, 144, 152, 167; and British Association Committee on Electrical Standards, 56, 92, 107– 9; and electromagnetic theory of light, 94, 97, 103–4, 108–9, 111–12, 153; and Faraday’s theories, 79, 94, 97–98; and field theory, 94–105, 108–17, 143, 147–51, 153, 165–66; and kinetic theory of gases, 47, 50, 53–63, 66–67; and telegraphy, 109, 119; and William Thomson, 60, 63, 92, 94–95, 98, 109; Treatise on Electricity and Magnetism, 109– 10, 112, 114, 119; and vortex model of ether, 99–104, 107 Maxwell, Katherine, 56 Maxwell-Boltzmann distribution, 54–55, 57, 63–64, 67 Maxwellians, the, 110–12, 115, 117, 148–49 Maxwell’s demon, 57–58, 60–64 “Maxwell’s equations,” 111, 113–14, 117 Mayer, Robert, 29–31 Mécanique céleste (Laplace), 14 mechanical equivalent of heat, 30–35 mechanical program of explanation, 46, 56, 94, 99, 102, 142–43, 153, 162 Michelson, A. A., 144–47 Michelson-Morley experiment, 145–47, 150, 165 Miner’s Friend, The (Savery), 5 MIT (Massachusetts Institute of Technology), 136, 140 Morley, E. W., 146–47 Morse, Samuel F. B., 82–83, 86 Napoleon Bonaparte, 15–17, 19, 74 Neumann, Franz, 75, 95, 116 Newcomen, Thomas, 6–7, 9 Newcomen steam engine, 6–11, 13 Newton, Isaac, 13–14, 72, 162 Newtonian physics, 14, 19, 111, 165 Niagara Falls, 127, 135–36 Oersted, Hans Christian, 27, 70–71, 74, 76, 129 ohm, 56, 92, 105, 107–10, 152, 159 Ohm, G. S., 82 Ohm’s law, 81–82, 105, 106 On the Connexion of the Physical Sciences (Somerville), 26

Index On the Correlation of Physical Forces (Grove), 28 Origin of Species (Darwin), 43 Ostwald, Wilhelm, 65–67 Pender, John, 92 perpetual motion machines, impossibility of, 23, 35–37, 39–40, 58, 60 Perrin, Jean, 67 Philosophical Transactions, 50 Physikalisch-Technische Reichsanstalt, 140, 160–61 Planck, Max, 160–62 Planck’s constant, 161 Poisson, Siméon-Denis, 16–18, 95 polonium, 156 Poynting, J. H., 114–15 Preece, W. H., 115, 117–18 Principia (Newton), 13 quantum theory, 52, 159, 161–62 Quetelet, Adolphe, 53 radioactivity, 44–45, 67, 143, 153–54, 156–59 radium, 44, 157–59 Rankine, W. J. Macquorn, 40, 99 ratio of electrical units, 103–6, 108–10 Rayleigh, Lord (J. W. Strutt), 50, 59, 110, 152 Reflexions on the Motive Power of Fire (Carnot), 19, 23–24, 37–38 Regnault, Victor, 36–37 retardation of telegraph signals, 87–89, 98, 119, 138 Ronalds, Francis, 80 Röntgen, Wilhelm, 154–56 rotary converters, 135–36 Rowland, Henry, 138–39 Royal Institution, 73–74, 87, 98 Royal Society of London, 33, 49–50, 81, 117 Rumford, Count. See Thompson, Benjamin Rutherford, Ernest, 44–45, 157–58 Sandemanians, the, 73 Savart, Felix, 71 Savery, Thomas, 5–7 Savery steam engine, 5–7, 11 Schilling, Pavel, 80 Schweigger, J. S. C., 71 science: attempts to define, 2; and relationship to technology, 2–4, 67–68, 109, 118– 19, 141, 167

181 self-induction, 113, 115, 117–18 Siemens, Werner von, 86–87, 106–7, 121, 140, 160 Smeaton, John, 7–8, 10, 13 Soddy, Frederick, 158–59 Somerville, Mary, 26 Stanley, William, 130 statistical mechanics, 62, 64–66, 165 statistics, 53–54; and kinetic theory of gases, 47, 51, 54, 62–66 steam engine, 5–13, 35; and British Industrial Revolution, 4, 11, 20; Carnot’s analysis of, 19–24, 37; efficiency of, 7–8, 10, 22–23, 32, 35; and indicator diagram, 13, 22–24; Newcomen’s, 6–11; Savery’s, 5–7; and thermodynamics, 4, 19, 26, 40, 67; Watt’s, 10–13, 20 Stewart, Balfour, 107 Stirling engine, 37 Stokes, G. G., 145–46 Stoney, G. J., 150 Sturgeon, William, 71 Submarine Telegraph Company, 86 sun, age of the, 42–44 Swan, Joseph, 125 Swiss federal patent office, 163–65 System of the World (Laplace), 15 Tait, P. G., 60 technology: attempts to define, 2; and relationship to science, 2–4, 67–68, 109, 118– 19, 141, 167 telegraph, 1, 68, 80, 84–85, 123; Cooke and Wheatstone’s, 80–81; and electrical measurement, 81–82, 85, 91–92, 104–6, 109, 119; and field theory, 2, 79, 85, 87, 94, 112, 115, 119; Gauss and Weber’s, 80; Morse and Vail’s, 82–84; optical, 79–80; and signal propagation, 87–89, 98, 113–15, 117, 119; submarine, 85–95, 98, 104–5, 113; wireless, 1–2, 94, 110, 116, 118–19 Telegraph Construction and Maintenance Company, 92 telegraph engineers, 105–6, 137–39 telegraph industry, 79, 81, 84–85, 92–94, 119, 123 Tesla, Nikola, 133–35 thermodynamics, 2, 51, 66, 107, 167; first law of, 25–26, 39, 41, 157–58; second law of, 25, 36, 39–43, 45–47, 57–67; and steam engines, 4, 19, 26, 40, 67. See also entropy; heat; kinetic theory of gases

182 Thompson, Benjamin (Count Rumford), 28–29, 74 Thomson, James, 36–37 Thomson, J. J., 152–53, 158–59 Thomson, William (Lord Kelvin), 35–37, 53, 110, 138–39, 142–43, 167; and age of the earth, 42–45; and Atlantic telegraph cables, 89, 91–93, 98, 109; and British Association Committee on Electrical Standards, 92, 105–7; and electrical measurement, 91–92, 105–7, 109, 139; and Faraday’s theories, 79, 88, 94–99, 119; and Joule, 35–37, 40; and Maxwell, 92, 94–95, 98, 109; and Maxwell’s demon, 58–60, 63; and telegraphic theory, 88–89, 91, 113, 117; and thermodynamics, 35–42, 45, 47, 67, 107 Thomson-Houston Company, 130, 133, 135– 36, 138 Thoreau, Henry David, 85 transformers, 75, 129–30, 136 Treatise on Electricity and Magnetism (Maxwell), 109–10, 112, 114, 119 Trevithick, Richard, 12

Index vector analysis, 111, 113–114 Volta, Alessandro, 27, 70, 80 Wallace, William, 123 Waterston, J. J., 49–51 Watt, James, 9–13, 20, 47 Watt steam engine, 10–13 Weber, Wilhelm, 75; and electrical theory, 75, 95, 98, 100, 104, 106–7, 116, 148; and electrical units, 103, 106–7; and telegraph line, 80 Wells, H. G., 159 Western Union Company, 84, 123 Westinghouse, George, 130–35 Westinghouse Electric Company, 130, 133, 138 Wheatstone, Charles, 81–82, 85, 86, 106, 113, 121 Wheatstone bridge, 82 Whitehouse, E. O. Wildman, 89, 91, 105 wireless telegraphy, 1–2, 94, 110, 116, 118–19 Woolf, Arthur, 12 Wordsworth, William, 74 World Set Free, The (Wells), 159

Upton, Francis, 124 uranium, 44, 156, 158–59 U.S.S. Niagara, 88

X-rays, 143, 153–56, 158–59

Vail, Alfred, 83 Varley, S. A., 121

Zeeman, Pieter, 151–53 Zurich Polytechnic, 163–64

Young, Thomas, 18