Come See the Earth Turn: How Foucault’s Pendulum Proved Our Planet Spins

On February 2, 1851, a handful of Paris scientists received one of the strangest invitations in the history of science. “You are invited to come and see the Earth turn,” it read, “in the Meridian Room of the Paris Observatory.” Those who went the next day found no telescope pointed at the sky and no chart of the stars. They found a heavy ball hanging from a long wire, swinging slowly back and forth. And as they watched, the line of its swing crept, almost imperceptibly, around the room.

Nobody in that room doubted that the Earth spins. Copernicus, Galileo and Newton had settled that long before. But for nearly three centuries, every proof had come from the sky: the motions of stars, planets and the Sun. No one had ever shown the planet’s rotation with an experiment you could do indoors, with the shutters closed. Léon Foucault, a 31-year-old physicist who had dropped out of medical school, had just done it with a weight and a piece of wire. Within weeks, all of Paris wanted to see it.

If you have read our stories on Euler’s Disk or the tippe top that flips itself over, you have met objects that spin in surprising ways. Foucault’s pendulum is the opposite kind of puzzle. The pendulum is the thing that isn’t turning. We are.

A doctor who couldn’t stand blood

Jean Bernard Léon Foucault was born in Paris in September 1819, the son of a publisher. He was a timid, sickly boy who did poorly at school and was taught largely at home. His mother hoped he would become a doctor, and he did enroll in medical school, but he found he could not stand the sight of blood and dropped out. What he did have was an unusually skilled pair of hands. As a teenager he built a boat, a telegraph and a small steam engine.

He drifted into physics through the new art of photography. With his friend Hippolyte Fizeau he made daguerreotypes of the Sun, among the first photographs ever taken of it, and studied the light of arc lamps. In 1850 he used a rapidly spinning mirror to show that light travels more slowly through water than through air, a result that helped finish off the old idea that light is made of tiny particles. He was becoming known as a brilliant experimenter. The scientific establishment, though, never fully accepted him, because he lacked formal scientific training.

Two o’clock in the morning, in the cellar

The idea seems to have started with a lathe. Foucault noticed that a thin steel rod clamped in a lathe and set vibrating kept vibrating in the same plane, even when he turned the lathe itself. The vibration did not care what its support was doing. A pendulum, he reasoned, should behave the same way. Hang one from a mount that lets it swing freely in any direction, and its plane of swing should hold steady while the building, and the Earth under it, rotates.

In January 1851 he set up a two-meter steel wire with a heavy weight in the vaulted cellar of the house he shared with his mother, on the rue d’Assas on the Left Bank. Everything had to be perfect. The bob had to be symmetrical, the mount could not twist or favor any direction, and the pendulum had to be released without the slightest sideways push. Early one January morning, at about 2 a.m. according to his notebook, he saw it: the line of the swing had shifted, a little, in the same direction that the stars move across the night sky. He later described the feeling of watching it happen:

“The phenomenon develops calmly; it is inevitable, irresistible… One feels, in seeing it born and grow, that it is not in the experimenter’s power to hasten or delay it. Anyone brought face to face with it stays pensive and silent for a few moments, and generally walks away with a sharper, keener sense of our ceaseless motion through space.”

Some of the best mathematicians of the day had argued that such an effect either would not exist or would be far too small to see. Others had tried to show the Earth’s rotation by dropping weights from towers and looking for a tiny eastward drift as they fell. Those tests were too crude to convince anyone. Foucault’s cellar pendulum was simple, and it worked.

“Come and see the Earth turn”

With the support of François Arago, the director of the Paris Observatory, Foucault moved his experiment into the observatory’s Meridian Room and lengthened the wire to 11 meters. A longer pendulum swings more slowly and drifts farther with every swing, so the effect was easier to see. That was the demonstration his invitation advertised. Arago presented Foucault’s paper to the Academy of Sciences on February 3, 1851, and within a week the mathematician Jacques Binet had worked out a full theory of the effect.

Then the head of state stepped in. Louis-Napoléon Bonaparte, the president of France’s young Second Republic and an amateur scientist, offered Foucault the Panthéon, the great domed monument in the Latin Quarter. On March 31, 1851, Foucault hung a 28-kilogram brass ball with a lead core from a 67-meter steel wire about 1.4 millimeters thick under its dome. The instrument maker Gustave Froment, who built much of Foucault’s equipment, helped make it. A wooden platform covered the marble floor, and a ridge of damp sand was laid where a pointer under the bob could scrape a fresh mark on each pass.

Each full back-and-forth swing took about 16 seconds. “After a double oscillation of 16 seconds,” Foucault wrote, the bob “was seen to return about two and a half millimeters to the left of its starting point,” and the drift kept growing with every swing. Crowds of Parisians came to watch the sand being cut, mark by mark. The plane of the swing turned about one degree every five minutes, or roughly 11 degrees an hour. Before air resistance wore the swing down, after about six hours, it had turned about 70 degrees.

Foucault became a celebrity almost overnight. That same year, copies of his pendulum went up in Reims, Rome, Bristol, Dublin, London, New York, Rio de Janeiro and Ceylon (now Sri Lanka). The Panthéon show did not last, though. In December 1851, Louis-Napoléon seized power in a coup, soon to become Emperor Napoleon III, and the Panthéon was handed back to the Catholic Church as a place of worship. The pendulum came down.

Why the swing turns, and why it’s slower in Paris

The easiest place to picture a Foucault pendulum is the North Pole. Hang a pendulum there and set it swinging. Nothing pushes it sideways, so its plane of swing stays fixed with respect to the distant stars. The Earth, meanwhile, turns underneath it once a day. To someone standing on the ice, the pendulum’s path seems to rotate clockwise, making a full circle in about 23 hours and 56 minutes, the time it takes the Earth to spin once relative to the stars. At the South Pole, it turns the other way.

At the equator, the effect vanishes. The ground there is carried around the Earth’s axis, but it is not turning around the vertical line the pendulum hangs along, so the swing stays put. Everywhere in between, only part of the Earth’s spin counts, and the part that counts depends on the sine of your latitude. That is Foucault’s sine law, and he worked it out himself. In Paris, at almost 49 degrees north, the swing makes a full turn in about 32 hours, or roughly 270 degrees in a day. In New York it takes nearly 37 hours. In Los Angeles, about 43.

Strictly speaking, nothing makes the pendulum turn. The floor turns, and you turn with it. That is what made the demonstration so powerful. You did not have to trust an astronomer’s calculations. You could watch the room move under a swinging ball.

Foucault was not the first to see a pendulum veer. In 1661, the same year the Royal Society was puzzling over Prince Rupert’s drops, Galileo’s former student Vincenzo Viviani noticed a pendulum drifting sideways during his experiments. He treated it as a nuisance and fixed it by hanging the bob from two cords instead of one. As far as anyone knows, he never connected it to the Earth’s rotation.

Getting a clean result is harder than it looks. In his 1879 doctoral thesis, the Dutch physicist Heike Kamerlingh Onnes, who later discovered superconductivity and won the 1913 Nobel Prize in Physics, showed that tiny flaws in the mount or the wire can turn a straight swing into an ellipse within an hour and swamp the real effect. That is why the traditional launch is so ceremonial. The bob is pulled aside and tied back with a cotton thread, and when it hangs perfectly still, someone burns through the thread. The pendulum then starts without any sideways nudge from a human hand.

The other way to see the Earth turn

Foucault knew the pendulum was a slightly roundabout proof. In 1852 he came up with a more direct one. Instead of a swinging weight, he used a heavy metal wheel spun at high speed inside a set of rings that let it point in any direction. Once spinning, the wheel’s axis holds its direction in space, just as the pendulum’s swing does. Watched closely, it seemed to drift slowly relative to the room as the Earth carried the room around.

Foucault named the device after what it was for. He combined the Greek gyros, circle or rotation, with skopein, to see, and called it a gyroscope: an instrument for seeing the rotation. Spinning tops of this kind were not entirely new. The German astronomer Johann Bohnenberger had built a spinning sphere mounted in rings in 1817. But Foucault turned it into a scientific instrument, and his name for it stuck. Friction slowed the rotor within about ten minutes, which was just long enough to see the drift.

It was an idea with a long future. By the early 1900s, gyrocompasses built by Hermann Anschütz-Kaempfe in Germany and Elmer Sperry in the United States were guiding navy ships, and gyroscopes later went on to guide aircraft, missiles and spacecraft. The same family of spinning-wheel stability shows up in our stories on why bicycles stay upright, where scientists found that a bike’s spinning wheels matter less than most people think. The motion sensor in your phone does not have a spinning wheel at all. It uses a tiny vibrating element, and when the phone turns, the vibration is nudged sideways, the same effect that turns a Foucault pendulum.

Recognition came, slowly. The Royal Society in London awarded Foucault its Copley Medal in 1855, and Napoleon III gave him a post as physicist at the Imperial Observatory. In 1862 he measured the speed of light at 298,000 kilometers per second, within about 0.6 percent of the modern value. He also invented a simple knife-edge test for checking the shape of telescope mirrors, which amateur telescope makers still use today. The French Academy of Sciences finally elected him in 1865, after he had been passed over several times. He died in Paris in February 1868, aged 48, probably of a fast-moving form of multiple sclerosis. His name is one of the 72 engraved on the Eiffel Tower.

A pendulum in every lobby

Foucault pendulums never really went away. Kept swinging by an electromagnetic kick, a version of which Foucault himself designed for the Paris Exposition of 1855, they became a fixture of science museums, universities and grand public buildings. In 1955 the Netherlands gave one to the United Nations. Its 200-pound gold-plated ball hangs from a wire 75 feet above a staircase in the General Assembly building in New York. The UN says it takes about 36 hours and 45 minutes to complete its cycle. Its support carries a message from Queen Juliana: “It is a privilege to live this day and tomorrow.”

At the Smithsonian’s Museum of History and Technology in Washington, now the National Museum of American History, a pendulum swung through the middle of the building from 1964 to 1998. It was so popular that the place was often called “the museum with the pendulum.” Its 240-pound brass bob knocked over a ring of red markers one by one as the day went on. It was taken down in 1998 to make room for the conservation of the Star-Spangled Banner.

In 1902, for the 50th anniversary, the astronomer Camille Flammarion and the French Astronomical Society hung a pendulum under the Panthéon dome again, and more than 2,000 people came to the opening. A permanent copy has hung there since 1995. Foucault’s own Panthéon bob went to the Musée des Arts et Métiers, where a pendulum swings in the nave of a former medieval church. That is where Umberto Eco set the climax of his 1988 bestseller Foucault’s Pendulum, in which conspiracy theorists gather around the pendulum at night.

On April 6, 2010, the steel cable holding the original 1851 bob at the museum snapped. The ball fell to the marble floor and was dented in three places, beyond repair. The museum’s curator admitted that it had been treated roughly at evening events in the chapel; in May 2009 a partygoer had grabbed the 28-kilogram ball and swung it into a security barrier. The historian Amir Aczel, who wrote a book about Foucault, said the accident was “a bit like hearing that one of the statues at the Vatican has been broken.” The damaged ball is now displayed in a case beside a working replica.

At the bottom of the world

The most extreme Foucault pendulum may be the one three researchers built at the South Pole in the winter of 2001. Allan Baker, John Bird and Mike Town hung a 25-kilogram weight on a 33-meter wire in the six-story stairwell of the new Amundsen-Scott station, which was still under construction and unheated. The temperature was about minus 90 degrees Fahrenheit, and the altitude was over 11,000 feet. They had to stop and warm up about every 10 minutes.

Their first try showed the Earth spinning backward. Their second showed it spinning twice as fast as it should. “We suspected some kind of government conspiracy,” they wrote, but after fixing the bob, the third run gave the right answer: one full turn in 24 hours, give or take 50 minutes. Even the launch was a challenge. The Antarctic rules banned open flames, so they could not use the traditional burning thread. One of them simply practiced dropping the bob until it swung cleanly.

What Foucault couldn’t see

Foucault assumed his pendulum held its direction in absolute space. Einstein’s general theory of relativity says that is not quite true. A massive spinning body like the Earth very slightly drags space and time around with it, an effect called frame-dragging. When the French physicist Thibault Damour was asked about the broken pendulum in 2010, that was the part of Foucault’s legacy he pointed to. Foucault’s question about what a swinging or spinning object really holds steady against, he said, lives on in Einstein’s thought and in modern experiments.

The most famous of those experiments used Foucault’s other invention. NASA’s Gravity Probe B, launched in 2004, carried four gyroscopes whose rotors were ping-pong-ball-sized spheres of fused quartz, among the roundest objects ever made. For about a year in orbit, the gyroscopes were kept pointed at a guide star, IM Pegasi, and researchers watched for drift. In 2011 the team reported that the gyroscopes’ spin axes had tilted by 6,602 milliarcseconds a year because the Earth warps space, and by 37 milliarcseconds a year because of frame-dragging. Einstein’s theory predicted 6,606 and 39. “Imagine the Earth as if it were immersed in honey,” said the mission’s principal investigator, Francis Everitt of Stanford University. “As the planet rotates, the honey around it would swirl, and it’s the same with space and time.”

That is a long way from a cellar on the rue d’Assas. But the question is the same one Foucault asked at two in the morning: if you set something moving and leave it alone, what does it keep pointing at?

See the Earth turn at home

The easiest way is to visit one. Many science museums, planetariums and university physics buildings have a Foucault pendulum, often with pegs that the bob knocks down over the day. Note where the swing is when you arrive and check again an hour later.

You can also build a small one. The Musée des Arts et Métiers suggests copying Foucault’s cellar setup: a heavy ball, such as a steel pétanque or boules ball, on about two meters of strong nylon line, attached to a solid ceiling hook through a fishing swivel so the line can’t twist. Pull the ball aside and tie it to a chair with a cotton thread, wait until it is completely still, then carefully burn or snip the thread. Mark the line of the swing on the floor with tape and check it again half an hour later. In Paris the museum expects about 6 degrees of drift. Across most of the United States you should see roughly 4 to 5 degrees. It is a small change, but it is real. You are watching the floor turn underneath you.

One thing your pendulum will not explain is your bathtub. The Coriolis effect that turns a Foucault pendulum also helps decide which way hurricanes spin, but in a sink or toilet it is far too weak to matter. The shape of the basin and the way the water was moving decide the direction. Foucault’s pendulum works because it is slow and patient, with a heavy bob swinging for hours. A bathtub drain is over in less than a minute.

Further reading