The “Cup of Pythagoras” is a vessel with a mechanism that prevents you from filling it more than you should. Far from having a sophisticated sensor system to control the liquid level, it is based on something as simple as the principle of communicating vessels, known for millennia. Legend says this cup was devised about 2,500 years ago by the mathematician and Greek philosopher Pythagoras of Samos, and it still amazes those who see it work.
Some ancient mechanisms are astonishing because of the skill with which they were built. The so-called “Cup of Pythagoras”, which some authors call the “Tantalus cup” and others claim was invented by Archimedes, is one of them. It is a very special wine cup that empties itself when the liquid inside exceeds a certain level. Legend says that Pythagoras of Samos (the Greek mathematician and philosopher best known for his famous theorem relating the lengths of the hypotenuse and legs of a right triangle), during the water supply works on Samos about 2,500 years ago, restricted the amount of alcohol the workers could drink by inventing what he called “the just cup”. This vessel emptied completely when the wine passed a mark, punishing the drinker’s greed. There is no general agreement on the truth of this story, but it is known that the invention is very old and works perfectly. But how does it do it?
How does the Cup of Pythagoras work?
Actually, the working principle can now be understood by anyone and is nothing more than a practical application of a basic principle of hydrostatics. From a construction point of view, the Cup of Pythagoras consists of a glass with an internal column that has an internal tube. This tube has a hole inside the glass near the bottom, rises up the interior of the column to the top, and then descends again to exit through the lower part. The second opening of this tube is on the outside of the cup, and it is through this that the contents will drain when the liquid level allows it. When water is added to the glass, it remains inside until the level exceeds the point where the internal tube of the central column turns 180 degrees, at which moment the cup empties completely. This happens because, as the cup fills, the tube also fills, displacing the air inside. The moment the water in the tube starts to fall, all the liquid in the glass follows, leaving it empty.
The fundamental principle on which the cup is based is what we commonly know as the ‘siphon principle’, the same one we use in almost all the drains in our homes. It consists of an inverted U-shaped tube through which liquid can rise to a certain height and then fall a greater one. The system works thanks to gravity, the force responsible for making the liquid fall, and also atmospheric pressure, which pushes on the free surface of the liquid and — thanks to Pascal’s Principle — ‘is transmitted with equal intensity in all directions and at all points of the fluid’.
Today it has become a simple but curious vessel sold in novelty shops or as a souvenir for tourists visiting Samos. But it is interesting to know that behind its development there may have been none other than Pythagoras. Don’t you think?
