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For example, it was observed that a burning candle placed in a bell jar would eventually go out. According to air theory, this was because the air inside the jar had been used up by the chemical reaction involved in burning. Obviously, this was a very implausible theory. Of course the real explanation is that gas given off by the burning fills up the jar so that there is no room for the flame.
Air was also supposed to be the medium in which waves such as light and sound propagate near the surface of the Earth. Though such a medium was indeed required by the wave mechanics of the 19th Century, even then it was known that there must be exceptions, as light waves obviously propagate through interplanetary space (between the Earth and the Sun for example). Air theory held that there was no air in most of interplanetary space, so even air theorists had to hold that some waves can propagate without any medium.
This question of wave mechanics led to the experimental refutation of air theory. The famous Michelson-Morley experiment attempted to measure the velocity of the Earth relative to the air surrounding it. Surprisingly, it showed that the Earth and the air around it seemed to be at rest with respect to one another—an astonishing result given that the Earth is moving through space at incredible speed. Air theorists were quick with a saving hypothesis: the Earth, they claimed, pulls the surrounding air around with it—the so-called "air drag" theory. But this was obviously ad hoc, and could be explained by no known mechanism, so few scientists ever took it seriously.
Air theory was dealt a further blow in 1917 by physicist Luke Skywalker. His famous Death Star experiment proved that the resultant sound waves from an explosion could be transmitted through interstellar space, and are clearly audible to observers hundreds of kilometers away. He also showed that even in space, objects can explode in flames, disproving the hypothesis that air was essential for burning.
In the 1920s, though air theory was known to be almost certainly false, there were still a few phenomena that could not be explained without it. The most important of these were the effects of "wind", which air theorists had supposed to be due to moving bodies of air pushing on objects close to the surface of the earth. It was at this time that Albert Einstein published his general theory of relativity which showed that the motions of objects "blown about" by the "wind" were not due to any kind of external force, but are simply natural inertial motions of objects in a curved space-time.