SEEING THE EARTH ROTATE

FOUCAULT'S SUBLIME PENDULUM

THE TEN MOST BEAUTIFUL EXPERIMENTS IN SCIENCE)

Robert P. Crease

The first Foucault’s pendulum I ever saw was at the Franklin institute in Philadelphia, the city where I was born. The pendulum hung--and still hangs - in the well of a main stairway. Its thin wire cable was attached to the ceiling four stories up, while its silver bob glided silently back and forth over a compass dial (which has recently been replaced by a backlit globe) embedded in the floor. I can still recite the information on the first-floor sign: The pendulum's cable was eighty-five feet long and its bob--a steel sphere twenty-three inches in diameter and loaded with lead shot weighed 1,800 pounds. The bob swung back and forth in a straight line, silently and ponderously, once every ten seconds. The plane of its swing slowly shifted to the left (clockwise) at an unchanging rate throughout the day: 0.6 degrees per hour. The sign informed me that although the pendulum seemed to be changing direction, this was false; the pendulum always swung in exactly the same direction with respect to the stars. Instead, what the museum visitor was really seeing was the earth--and along with it the floor of the Institute building and the compass dial in that floor turning underneath the pendulum.

The pendulum had been installed in 1934, when the institute moved to its current building. Its installation was cause for an unusual parade. The wire, which weighed only nine pounds, could not be rolled up but had to he kept straight to prevent kinks and stresses that would interfere with its swing. It was therefore carried, fully stretched out, through the streets of Philadelphia from the manufacturer to the new building. The slow and bizarre procession of eleven men carrying a long wire was accompanied by a police escort and trailed by bemused onlookers and reporters.

The Franklin Institute's pendulum signaled its change of direction by knocking down, every twenty minutes or so, one of the set of four-inch steel pegs that stood in two semi-circles on the floor, tracing the outside of the dial. Whenever I visited the Institute, I would often pull myself away from the exhibit I was playing with to rush back and join the crowd of onlookers watching the swing of the silver bob and staring at the pegs, hoping to see one fall. First the bob would graze a peg, making it shiver. A few swings later, the peg would actively wobble. A few more and the tip of the bob would strike the peg solidly enough to make it rock back and forth. Not long now! One or two more swings and the peg would go over plink! - and the bob would begin to creep toward the next peg. Sometimes I'd just stare at the pendulum itself, trying to obey the sign and make myself see that it was I--and the solid floor beneath my feet--that was moving for reasons I did not understand, I never quite succeeded, though the pendulum did leave me with a feeling of mystery and awe.

The pendulum's movement was entirely beyond my control, as inexorable a performance as I knew, then or now. The only human influence on it was the museum staff member who started it swinging in the morning, in the north-south direction just before the opened at 10:00 A.M. Sometimes I would arrive at the museum early and wait for the door to open, so that I could race to the stairwell to try to catch the pendulum being started. I was always too late. Once I heard that a museum supporter had arranged, as a birthday gift, for his son to start the pendulum one day. How I envied that child! Other kids may have dreamed of tossing out the first pitch at a baseball game. I dreamed of starting a Foucault’s pendulum.

French scientist Jean-Bernard-Leon Foucault (1819-1868) was born in Paris. As a youth he built scientific and mechanical toys, and began studying medicine with the aim of exploiting his practical talents by becoming a surgeon-until he discovered his aversion to blood and suffering. His interest reverted to mechanical instruments and inventions and he became fascinated by the new photographic imaging processes developed by his fellow French- man Louis Daguerre. In work that successfully tapped his mechanical abilities, Foucault teamed up with another ex-medical student, Hippolye Fizeau, to improve what were known as daguerreotypes, which were predecessors of the modern photograph. The two took the first clear picture of the sun in 1845, and then-first working together, then separately after a personal dispute-showed that the speed of light was greater in air than in water, in 1850, before going on to measure the absolute speed of light in air still later, Foucault made significant contributions to the construction of mirrors for telescopes.

Foucault also took some of the earliest photographs of stars, a technical tour de force at the time. Normally one would photograph faint objects by opening the camera shutter for minutes at a time but because the earth rotates on its axis, the stars seem to slowly move in the sky making it impossible to simply leave the shutter open instead Foucault, reviving a once-discarded idea, built a pendulum-driven clockwork device that would keep the camera pointed at a star long enough for an exposure--though in place of a bob on a string he used a metal rod that vibrated like a pendulum when twanged. (I have read dozens of articles on pendulums, and spoken to many scientists about them, and I assure you that the technical term for starting a metal-rod pendulum is to "twang" it.)

Much of this work took place in a laboratory Foucault set up at his home on the rue Assas in Paris. One day he put a rod in his lathe, mounting it on a chuck or bit that could spin freely the way a skateboard wheel can spin freely on its mount. When he twanged the rod and turned the lathe slowly he was startled to see the rod continue to vibrate back and forth in the same plane. Curious, he experimented with a more conventional pendulum--a spherical weight suspended vertically with piano wire that could swing freely. He attached it to the mount of a drill press and turned the bit. The pendulum, too, continued to swing in the same plane.

If one stops to think about it, this is not surprising. According to Newton's laws, a body in free motion, such as a pendulum bob, moves in the same direction unless some force is applied to change it. Because turning the freely spinning bit did not apply any force to the rod or pendulum, they continued to oscillate in the same direction. But the unsurprising can still be unexpected. Foucault soon realized that this effect, if magnified enough, could be used to demonstrate the diurnal (daily) rotation of the earth on its axis.

Later he summarized the reasoning process rather elegantly as follows. Imagine we build a little pendulum on a table atop a freely and smoothly swiveling plate (we might say a lazy Susan). We have now what Foucault called petit theatre on which we are about to stage a performance. The lazy Susan is like the earth and the surrounding room like the rest of the universe. If we set the pendulum swinging in a plane-- let’s point it at the door- -and then slowly swivel the plate, what happens? At first we might expect that the pendulum's plane of oscillation would turn along with the base. Erreur profonde! The plane of oscillation is not a material thing attached to the plate. Because of the pendulum's inertia, the plane of its swing is independent of the plate--it now "belongs," so to speak, to the space around it rather than to the plate. Whichever way we turn the plate, the pendulum continues to point at the door.

This performance in the little theater demonstrates that the lazy Susan moves, while the pendulum's plane of oscillation is unchanged. But imagine that we make our little theater very big, Foucault says. Imagine, in fact, that we--as well an the rest of the room and everything we can see around us except for the sun, planets, and stars--are on board the turning plate. Now it will look to us like we are motionless and the pendulum's direction of oscillation is changing. Again- Erreur profonde! We are the ones who turn. But Foucault points out an additional complication. Our little pendulum is in the center of a flat plate, so that a complete turn would change the pendulum's plane of oscillation by 360 degrees, or a complete circle. But an earth-based pendulum is on the surface of a sphere. Depending on where the pendulum is located between pole and equator, a complete rotation of the sphere will make the pendulum's plane turn by different amounts and the sphere will have to turn by different amounts to get the pendulum's plane of oscillation to make a complete rotation. Doing the math, Foucault calculated that the number of degrees through which the pendulum's plane of oscillation would shift in twenty-four hours would be 360 degrees times the sine of the latitude--which thus provided a way to determine the person's north-south location on the globe. But the details of the calculation do not matter nearly as much as the visible demonstration of the effects of the earth's rotation.

Foucault wondered whether he could see the effect of the Earth’s rotation using a real pendulum. He suspended a pendulum from the vault of his basement, using a thin six-and-a-half-foot wire and an eleven-pound bob. On Friday January 1, 1851, he tried it for the first time. To make sure the pendulum's swing would be steady and straight, he tied the bob to the wall with a cotton cord, let its motion come to a complete halt, and then burnt through the cord with a candle. Although the experiment seemed to work, the wire broke. Five days later, an Wednesday, January 8, 1851, at 2:00 A.M., he got it working again, and within half an hour he found that the "displacement is such that it is evident to the eye," and that the pendulum turned in the direction of the diurnal movement of the celestial sphere." Ever methodical, however, he found it less interesting to watch the phenomenon on a grand scale and "more interesting to follow the phenomenon more closely, so as to be satisfied of the continuousness of the effect." He mounted a pointer on the floor so that it would just touch a point on the pendulum, and noticed that, in less than a minute, the pendulum was displaced toward the left of the observer meaning that the pendulum's plane of oscillation was moving with the apparent motion of the heavens.

A few weeks later, Foucault wrote:

The phenomenon unfolds calmly; it is inevitable, irresistible.... Watching it being born and grow, we realize that it is not in the experimenter's power to speed it up or slow it down... Everyone who is in its presence... grows thoughtful and silent for a few seconds, and generally takes away a more pressing and intense feeling of our ceaseless mobility in space.'

Soon thereafter, the director of the Paris Observatory asked him to repeat the experiment in its salle meridienne, its central hall, located on the meridian. Foucault used the same bob but was able to lengthen the wire to 36 feet. This was preferable, because a pendulum with a longer wire swings for a longer time--it is less affected by friction in the air and in the mount where the wire attaches to the ceiling-and this magnifies the opportunity to see its apparent change of direction.

On February 3, 1851, exactly a month after starting his experiment, Foucault officially reported the results of his work to the French Academy of Sciences. The academy sent out dramatic invitations: "Vous etes invites a venire voir tourner la Terre, dans la sale meridienne de l’Observatoire de Paris"- "You are invited to come watch the earth turn in the central hall of the Paris Observatory." At the gathering, Foucault told the crowd that most scientists studying pendulum behavior have focused on the time of their swing. Instead, his work had to do with the plane of their swing. Then, as his pendulum swung, he asked his audience to conduct a version of the thought experiment described above-to imagine building a pendulum "of the greatest simplicity" at the North Pole, setting its bob oscillating, and then leaving it abandoned to the action of gravity. Because the earth "does not cease turning from west to east," the plane of oscillation appears to turn to the left, from the observer's perspective, as if the oscillation were attached to the heavens themselves.

Few scientific experiments met with such instantaneous fame as Foucault’s pendulum. Although all educated Europeans in 1851 knew that the earth moved, all evidence for this fact-however incontrovertible-was based on inferences from astronomical observations. People without a telescope and the knowledge of how to use it had no way to see that motion for themselves. With Foucault's pendulum, the earth's rotation seems to become visible. A suitably educated person locked in a windowless room could prove that the room was rotating and, by careful measurement, even determine tile latitude of the room. The pendulum. Foucault liked to put it, speaks "directly to the eyes."

Or does it? One of the fascinations of Foucault’s pendulum is that it exhibits the ambiguities of perception. Foucault’s remark is philosophically disingenuous: Nothing speaks directly to the eyes. The remark is Cartesian; Foucault imagines that his eyes are geometric eyes, and he has convinced himself that he can see what he imagines ideally and geometrically. If we can imagine the situation of the pendulum oscillating against the background of the solar system as a geometric model, he thinks, we can "see" the earth turn. But perception is more complicated than that. Even perceiving what is in motion and what is at rest depends on what we take as the foreground and what as the background or horizon. Foucault’s pendulum seems to offer us the experience either of the pendulum turning in the gravitational field of the earth, or of the earth turning beneath our feet. This either-or seems to resemble French philosopher Maurice Merleau-Ponty's description of the familiar experience of being in a train stopped in a station beside another train on a nearby track--and when this other train begins to move we experience either that we are beginning to move or that the other train is beginning to move in the opposite direction. Which one, Merleau-Ponty writer, depends on where our perception is invested (in this train or the other), and what is its background or outer horizon. In order to see the plane of the pendulum's oscillation move, we need only do what perception habitually does, and take the object in question - the pendulum--as the foreground and the surrounding room as the background. Foucault's pendulum, like every instrument, shows what it does only within an appropriate environment. In order to "see" the earth moving, we would have to introduce a different and much bigger background in which the earth would show itself as moving, and the plane of oscillation of the pendulum would show itself as stationary. What if the pendulum were mounted nor inside but outside? Could one see the earth turn on a starry night?

As news of the demonstration filled Paris, Foucault was bombarded with correspondence from ordinary citizens, other scientists, and even interested government officials. Prince Louis-Napoleon Bonaparte-the President of the Republic, soon to become Napoleon III, Emperor of France--asked Foucault to set up a public demonstration in the Pantheon in Paris, a former church that had become the final resting place for many French national heroes. The Pantheon was, Foucault wrote, a marvelously appropriate location for the experiment, which now had a splendeur magnifigue. For the bigger the pendulum, the slower and more majestically it moved, and the more effectively it demonstrated the motion of everything around it. In an amazing display, Foucault attached a pendulum to the center of the Pantheon's huge dome. It had a 220-foot steel wire and a cannonball bob with a tiny, needle-like stylus attached underneath. Around the outer circumference of the circle where the pendulum was to travel, Foucault and his assistants built two semicircular banks lined with sand, which the stylus grazed at the extremity of each swing, marking the pendulum's position. In case the wire broke and the bob fell, Foucault protected the mosaic on the floor of the Pantheon directly underneath the dome by covering it with a layer of wood and several inches of densely packed sand. This was wise, for the first time the pendulum was installed the wire did in fact snap just below the dome, terrifying Foucault and his assistants as the 200-plus feet of wire whipped around the hall, convulsed with the pendulum's energy. When they reattached it, they installed a parachute up in the dome in case the wire broke again at the top.

On March 26, one of Foucault's assistants tied the bob to a wall with a cord and waited for it to come to rest. This time, the cord was burnt through with a match rather than a candle (safety matches had been invented that year). The pendulum moved ponderously magnificently, somberly crossing twenty feet of floor with each swing, making one back-and-forth oscillation every sixteen seconds. Its thin wire, less than a millimeter and a half in diameter, was practically invisible against the grand setting, and the gleaming bob looked like it was suspended in the void. When the bob reached the banks at the end of its swing, the stylus cut a tiny narrow in the wet sand, each about two millimeters to the left of the previous one. At the latitude of Paris (about 49⁰ N), the pendulum moved about one degree every five minutes--a little over eleven degrees an hour, a rate that would carry it around a complete circle in about thirty-two hours, provided the pendulum did not first come to rest.

The Pantheon demonstration was not perfect; the furrow cut by the stylus slowly broadened into an extremely narrow figure eight, evidently due to imperfections in the wire on the support. And the distance covered by the bob with each oscillation gradually shortened due to air resistance-though the time required for each swing remained the same (again, the principle of isochrony, discovered by Galileo, valid for all pendulums making small amplitude oscillations. Still, the pendulum continued to make the change of direction apparent for about five or six hours, in the course of which the direction shifted to the left in a clockwise direction (in the southern hemisphere, the direction would be counterclockwise) around the floor about 60 to 70 degrees. Enchanted, Louis-Napoleon rewarded Foucault by appointing him to a covered position as a physicist in the Observatory, allowing him to move from his home basement laboratory

The year 1851 was a year of marvels. The Crystal Palace exhibition in London opened, which marked a new era in display and visibility, and in the management of space and time. It was the first exhibition, for instance, at which audience tickets had time stamped on them, to manage traffic flow. Many historians, indeed, date the rise of modern mass society from this exhibition.

The year 1851 was also the Year of the Pendulum, Foucault pendulums proliferated all over the world: Oxford, Dublin, New York, Rio de Janeiro, Ceylon, and Rome. Cathedrals with their high ceilings and air of stability and authority were perfect setup locations. In May 1851, one was set up in the cathedral of Notre Dame in Reims (forty meter wire, 19.8 kilogram bob. more than 1 millimeter deviation each swing), one of the most beautiful Gothic cathedrals in France and the place where the kings of France were crowned. In June 1868, a Foucault pendulum was set up in the cathedral of Notre Dame in Amiens, another Gothic masterpiece. And while the Crystal Palace exhibition was too long in the planning to exhibit a Foucault pendulum, one was featured at the Paris Exposition of 1855. For this event, Foucault invented an ingenious device that gave the bob a small electromagnetic boost on each swing to keep it from slowing down. That same year, his original pendulum was installed in the Musee des Arts et Metiers in Paris, an institution founded as a "depository for new and useful inventions," where it can still be seen.

But Foucault's pendulum was more than merely an interesting public demonstration. Like any scientific discovery, it reached back to the past and forward to the future. Researchers poring through the writings of earlier scientists uncovered evidence that others had noticed the direction of pendulums slowly drift to the left--including Viviani, the devoted disciple of Galileo who had been the first to study pendulums seriously. Foucault, however, had been the first to connect this leftward drift with the rotation of the earth. Meanwhile, Foucault pointed out that the basic idea of his work had been anticipated by the late mathematician and physicist Simeon-Denis Baron Poisson (1781-1840). Poisson had calculated that cannon balls fired in the air should appear to veer slightly to the side as the earth rotated beneath them, though he had thought the deflection too slight to be observable. Poisson had also realized that the earth's rotation would affect pendulums--but had not grasped that the small effect on each movement of the hob would increase with each swing, allowing the motion, as Foucault put it, to accumulate the effects and allow them "to pass from the domain of theory into that of observation." Later, as the range of cannons increased; it became necessary for gunners to compensate for the effect described by Poisson. As physicist H. R. Crane noted,

During the naval engagement near the Falkland Islands early in World War I, British gunners were surprised to see that their salvos fell to the left of the German ships. They had followed the tables [for correcting their aim] prepared according to Poisson's formula, but had not remembered to change the signs for the corrections, to make them valid in the southern hemisphere.

Foucault applied the same principle on which his pendulum had been based to invent the gyroscope, a word of his own coinage. A gyroscope consists of a spinning wheel mounted so that it can turn freely regardless of the direction of its support structure, and the spin axis of such a wheel always points in the same direction. Foucault predicted, correctly but decades prematurely, that it could and would be used as a directional device. The gyroscope principle, too, was found elsewhere in nature; scientists found, for instance, that common houseflies navigate with the aid of their own tiny twangers in the form of stiff stalks (rear vestigial wings) known as "halteres."

Today, Foucault pendulums exist all over the world in science museums, universities, and other institutions. During the past half-century, many of them were made by the instrument shop of the California Academy of Sciences, which is a specialized manufacturing service if there ever was one--has made nearly a hundred Foucault pendulums for institutions around the globe, including ones in Turkey, Pakistan, Kuwait, Scotland, Japan, and Israel. Often clients purchase the critical components, and then embellish them with their own stylized interpretations. The pendulum at the Boston Museum of Science moves back and forth over a brightly colored model of the Aztec Calendar Stone, with the bob crossing over the head of the Sun God Tonatiuh. The pendulum at the Lexington Public Library in Lexington, Kentucky, which was inaugurated with a cable cutting ceremony at midnight on New Year's Eve 2000, has sensors in the floor to monitor tile pendulum's motion instead of the usual pegs. The Montefiore Children's' Hospital in New York had New York City artist Tom Otrerniss design its bob and surrounding structure. The bob looks like an upside-down happy face, surmounted by a pointed conical hat that knocks over pegs. It swings over a silver-and-bronze relief map of the world centered on the Bronx, where the hospital ii located. Meanwhile, little bronze sculpted characters, made of geometrical solids, are attached in various comical poses to the bob, wire, railing, and surrounding area. Nearly all visitors to the hospital stop to ask about it. Although Montefiore is but one of many institutions whose pendulum swings over a map centered on the building housing the display, the pendulum actually illustrates that every location on this rapidly spinning world is in motion-all are, to that extent, equal. Most appropriately, the United Nations headquarters in New York has a Foucault pendulum in the grand ceremonial staircase of its lobby, a 200-hundred-pound gold-plated sphere twelve inches in diameter that swings from the ceiling seventy-five feet above. The Smithsonian institution, the United States national museum, used to have a Foucault's pendulum on display, but it was removed to make way for the restoration project of the Star Spangled Banner, the national symbol. The pendulum lies in a museum storage area.

Like Young's experiment, Foucault's pendulum has to he executed with more care than it seems. In a public setting, a major problem is protecting a pendulum from visitors who seem to find irresistible the urge to reach out and touch it. And even though a pendulum is one of the simplest devices in science, a pendulum in the real world is affected by air currents, the internal structure of the wire, the way the wire is suspended, and how the bob is started; most of these things can easily throw off a pendulum or guide it into a figure eight pattern. (A tip-off to a figure-eight pattern is that the knocked-over pins point inward.) At Stony Brook University where I teach, a physicist demonstrating the Foucault principle to an introductory physics class once had a technician tie a bowling ball to the ceiling of the lecture hall, explained the principle to the class, and worked out how much of an angle it would travel during the forty-minute class time. At the end of the period, he measured the deviation and to his satisfaction found that it was exactly the calculated amount--but in the wrong direction! The erroneous amount was evidently due to some combination of a bad suspension system and the air currents in the drafty auditorium.

A Foucault's pendulum is quite different from other museum displays. Its sheer size is one factor: It cannot be enclosed in a booth or mall display but demands a huge open space like a nave or stairwell. It makes no sparks, hums, or noises but moves with a solemn majesty and most important, it is not only non-interactive but seems to ignore us altogether, disclosing something radically counterintuitive to human experience. This--and its connection to vast physical forces-may be why people tend to remember their first Foucault's pendulum.

Mine put on the same performance every time I went to the Franklin Institute. But it never failed to enthrall me with its unsettling simplicity. It moved but stayed the same. It turned but told me that I was the one who was turning. I looked at it, and what it reflected back was my mobility and that of everything else around me--providing me with a clear and dramatic sense, whose true meaning I sensed I would never entirely fathom, of the deceptions and limits of my own perception and experience.

End