1. The 1851 Experiment at the Paris Observatory: What Did an Unknown Experimenter Show?
On February 3, 1851, the meridian room at the Paris Observatory was said to be filled with excitement. The witnesses were the observatory director Arago and Poiret [2]. The person conducting the experiment was Léon Foucault, an amateur scientist who was unknown in academic circles. The tool he used was a pendulum 11 meters high [2].
Foucault is said to have tested his idea earlier that year in his home basement. At that time, he used a steel wire 2 meters long with a brass weight of 5 kilograms [4]. He gained confidence with this small pendulum before moving to the large one at the observatory.
The pendulum was simply swinging quietly. Yet, the direction of its swing gradually rotated. Many physicists watching were reportedly devastated, thinking, "Why did no one think of such a simple thing before?" This is how a science museum document describes their reaction, rather than a direct quote from the time [2]. So, why does the direction of a pendulum that has no force applied to it appear to rotate?
2. Why the Pendulum Keeps Its Direction While the Ground Beneath It Rotates
A pendulum has a property that it continues to swing in the same direction unless a sideways force changes that direction. This means the direction of the swing remains constant relative to space [1].
On the other hand, the ground beneath the pendulum is moving due to the Earth’s rotation. When you view a pendulum swinging in a constant direction relative to space from the moving ground, the direction of the swing appears to rotate. In the Northern Hemisphere, it appears to rotate clockwise (to the right) [1].
Note that the pendulum is not changing its direction by itself. It is the ground beneath the observer that is changing. For example, if you move a pencil back and forth in the same direction on a paper plate while slowly rotating the plate, overlapping lines with changing directions remain on the plate. The relationship between the pendulum and the Earth is similar to this paper plate. However, this is just an analogy to help understand why the direction appears to rotate.
3. The 67-Meter Pendulum Hung in the Pantheon in Paris
About a month after the observatory experiment, in March 1851, a larger public experiment took place at the Pantheon in Paris. Because the building is huge, the pendulum used was 67 meters long, made of piano wire with a weight of about 28 kilograms [2][5].
It is reported that the then-President Louis Napoleon (later Napoleon III) gave permission for its use [2]. A large crowd of spectators is said to have gathered.
There was also a clever method for releasing the weight. If released by hand, sideways force would enter the swing. To avoid this, the string holding the weight was burned through, starting the swing from zero speed [5]. This shows that doing "nothing" was the key to this experiment.
In front of the spectators, the direction of the swing gradually rotated. In Paris, it rotates at a pace of about 11 degrees per hour [5]. So, how does this number change depending on location?
4. How Latitude Decides How Many Hours One Rotation Takes in Tokyo
At the North and South Poles, the direction of the pendulum’s swing completes one rotation in about one day. As latitude decreases, the speed of rotation slows down [3].
The speed of rotation can be expressed by the formula "15 degrees × sin (latitude)" per hour [3]. The Earth rotates once in a day, or 360 degrees in about 24 hours, which is about 15 degrees per hour. At the North Pole, it is about 15 degrees. As latitude decreases, the speed of rotation slows down.
Let’s calculate for Tokyo (latitude about 35.7 degrees North). The sine of 35.7 degrees is about 0.58, so 15 × 0.58 gives about 8.8 degrees per hour. Dividing 360 degrees by 8.8 degrees gives about 41 hours for one rotation. This value for Tokyo is listed in dictionaries [3].
In Paris (latitude about 48.9 degrees North), the sine is about 0.75. 15 × 0.75 gives about 11 degrees per hour, and one rotation takes about 32 hours. This value is calculated by myself. It also matches the numbers in the English Wikipedia [5]. Paris rotates much faster than Tokyo. This means that if the observer’s latitude is different, the same pendulum will look different. So, what happens at the equator, where latitude is zero?
5. Why the Swing Direction Does Not Rotate at the Equator and Reverses in the Southern Hemisphere
If we apply latitude 0 degrees (the equator) to the formula, the sine of 0 degrees is 0, so the speed of rotation is also 0. At the equator, the direction of the pendulum’s swing does not rotate [3].
South of the equator, in the Southern Hemisphere, the direction of rotation is reversed. While the Northern Hemisphere rotates clockwise, the Southern Hemisphere rotates counterclockwise (to the left) [2][3].
Because the equipment for this experiment is simple, it was quickly verified in various places. Documents from the Osaka City Science Museum state that it was conducted not only in France but also in the UK and South America, and that the reversal of rotation direction in the Southern Hemisphere was confirmed [2].
At the North Pole, it takes about one day; in Tokyo, about 41 hours; at the equator, it does not rotate; and in the Southern Hemisphere, it reverses. The way it rotates changes clearly with numbers depending on the location. The way it rotates changes with location because it is linked to the Earth’s rotation beneath your feet. This difference in rotation based on latitude became evidence that the Earth is rotating.
6. Reproducing the Pendulum's Direction with a Paper Plate, and Checking at a Science Museum
You can try the relationship between the pendulum and the ground using a paper plate and a pencil you have at home. Make a small dot in the center of the paper plate, and draw a line back and forth through that dot, keeping the pencil’s direction constant relative to the desk. With your other hand, slowly rotate the paper plate.
Lines with shifting directions will remain on the plate. The direction of the pendulum’s swing does not change, but as the ground below rotates, the direction seen from the ground rotates. This relationship becomes visible. The tip of the pencil is sharp, so do not point it at anyone.
There are places where you can see a real pendulum. The Nagoya City Science Museum has a pendulum with a length of 27.9 meters and a weight of 81 kilograms, which is started every morning [1]. In Japan, it is said that pendulums have been installed in science museums across the country since before the war, such as at the National Museum of Nature and Science [2].
If you go to a science museum, try comparing the direction of the pendulum’s swing with marks on the floor several times. After some time, you might notice that the direction has shifted slightly. Comparing this with the value calculated from the formula for your own latitude should also be fun.