The **Cartesian diver** is a classic science experiment that demonstrates the principles of buoyancy and pressure in a fun and engaging way. Named after the French mathematician and philosopher René Descartes, the experiment has been fascinating students and enthusiasts for centuries.

### What Is a Cartesian Diver?

A Cartesian diver is a small, sealed container that is partially filled with air and placed in a larger container of water. When you apply pressure to the container, the Cartesian diver sinks, and when pressure is released, it rises. The experiment demonstrates the relationship between volume, pressure, and buoyancy, and it is a practical application of the gas laws and principles discovered by Descartes and his contemporaries.

### The Name: Cartesian Diver

The Cartesian diver or Cartesian devil experiment got its name from René Descartes. Descartes may have invented the toy in the early 17th century, although Raffaello Magiotti gets credit for the first written description of its principles in his 1648 book *Renitenza certissima dell’acqua alla compressione* (Very firm resistance of water to compression). Descartes was a prolific mathematician, philosopher, and scientist, and his work laid the foundations for the development of the scientific method. The experiment is a fitting tribute to his legacy, as it showcases the interplay between observation, hypothesis, and experimentation that lies at the heart of the scientific process.

### Materials

To perform the Cartesian diver experiment, you need the following materials:

- A 2-liter clear plastic bottle with a cap (a smaller bottle works, but it’s harder finding a small enough diver)
- A “diver” that just barely floats in water (e.g., ketchup or soy sauce packet, small dropper, or plastic pen cap weighted with a blob of clay)
- Water
- Optional: food coloring to make the water more visible

The key to selecting a good “diver” is finding an object that fits through the bottle opening and just barely floats in the water because it contains an air bubble. Take-out sauce packets make great divers. Bite-size candy bars (in their wrappers) work, too, as do many small plastic objects. Hollow glass or plastic balls or bubbles are fancy options.

### How to Perform the Cartesian Diver Experiment

Performing the Cartesian diver experiment is easy:

- Fill the 2-liter bottle almost to the brim with water.
- Add the object you are using as your diver.
- Optional: Add a few drops of food coloring to the water in the bottle for easier observation.
- Top off the bottle with water so it is completely full and then seal it.
- Gently squeeze the sides of the bottle and observe the Cartesian diver.

### What to Expect

When you squeeze the bottle, the Cartesian diver sinks. When you release the pressure, the diver rises. This is due to the changes in pressure and buoyancy that occur within the system as a result of the applied force.

### The Science: How the Cartesian Diver Works

The Cartesian diver experiment demonstrates two key scientific principles: Boyle’s Law and buoyancy.

Boyle’s law is a special case of the ideal gas law that states that the pressure of a gas is inversely proportional to its volume, provided that the temperature remains constant. When you squeeze the bottle, you increase the pressure on the water and the air inside the Cartesian diver. This increased pressure compresses the air, reducing its volume. Because water is a liquid, it does not experience any appreciable compression and its volume remains unchanged.

Buoyancy, on the other hand, is the upward force exerted by a fluid that opposes the weight of an immersed object. An object will float if its buoyancy is greater than its weight and sink if its buoyancy is less than its weight. As the volume of the air inside the Cartesian diver decreases due to increased pressure, its buoyancy also decreases. As a result, the Cartesian diver becomes less buoyant and sinks. When you release the pressure, the air inside the diver expands, increasing its buoyancy, and the diver rises.

### Archimedes’ Principle

The Cartesian diver experiment also illustrates Archimedes’ Principle. Archimedes’ Principle states that the buoyant force acting on an object submerged in a fluid equals to the weight of the fluid displaced by the object. This principle relates directly to the concept of buoyancy, which plays a crucial role in the Cartesian diver experiment.

In the case of the Cartesian diver, the buoyant force acting on the diver depends on the volume of water displaced by it. When increasing pressure compressed the air inside the diver, the volume of the diver decreases. Consequently, the diver displaces less water, which reduces the buoyant force acting on it. When the buoyant force becomes less than the weight of the diver, it sinks.

Releasing the pressures lets the air in the diver expand, increasing its volume. The diver displaces more water and experiences a greater buoyant force. When the buoyant force is greater than the weight of the diver, it rises to the surface.

### A Neutral Buoyancy Diver

You may think a diver of neutral buoyancy (neither floating nor sinking) remains in the middle of the bottle, but this is not the case. If the diver starts out at neutral buoyancy where it displaces exactly the same weight as water, it still rises and sinks in response to the pressure change. This is because neutral buoyancy is an unstable equilibrium condition. If the diver rises the tiniest bit, pressure on the bubble decreases so it expands and displaces more water, making the diver rise even more. On the other hand, if the diver drops a bit, the pressure increases, the bubble contracts, more water enters, buoyancy decreases, and the diver drops even further.

### References

- Lima, F M S. (2012). “Using surface integrals for checking the Archimedes’ law of buoyancy”.
*European Journal of Physics*. 33 (1): 101–113. doi:10.1088/0143-0807/33/1/009 - Mohindroo, K. K. (1997).
*Basic Principles of Physics*. Pitambar Publishing. ISBN 978-81-209-0199-5. - Webster, Charles (1965). “The discovery of Boyle’s law, and the concept of the elasticity of air in seventeenth century”.
*Archive for the History of Exact Sciences*. 2(6) : 441–502.