When did scientists first postulate that Earth's atmosphere might have an upper limit?

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Contrary to assertions above, the correct computation of the size of the atmosphere predates Kepler by five centuries. It is sometimes claimed that this computation was was performed (with a correct answer) by Al Hazen in Mizan al-Hikmah (Balance of Wisdom) around the turn of the Millenium but I could not find reputable sources for this claim. In fact, the earliest well-sourced evidence I found for the computation is found in a manuscript of Ibn Mu'adh (from the middle eleventh century), a single Hebrew copy of which can be found at the French National Library (Source).

However, an important point to note is that the idea that the atmosphere was finite was classical: Aristotle held it in part for philosophical reasons but Ptolemy gave hard physical evidence for the claim. Before explaining them, I will point out that until Pascal's work at least, the consensus was aether was found beyond the atmosphere, not void as the question presupposes (1600 years elapsed between the first physical proof that the atmosphere was finite and the first physical proof that void was found beyond).

Ptolemy's argument (which are not in fact the earliest recorded, Hipparchus knew some of them 200 years before) is simple: when stars appear near the horizon, they do not appear where they should but higher, and their position seem to oscillate. No such effect is discernible when the stars are close to their zenith. Likewise, the light of the Sun shines on the sky before the Sun appears and lingers on after it is has disappeared. Ptolemy correctly understood this to be the effect of the refraction of the light in the atmosphere.

Ibn Mu'adh computed the size of the atmosphere assuming that it was a h*m*geneous refracting material and that the aether beyond was non-refracting. Coupled with the observation that no lingering light is visible after the Sun has sunk deeper than around 18°, this yields a depth of the atmosphere of 80km.

The article here clearly shows that the knowledge of the fact that the atmosphere was finite was well-preserved during the European late middle-age and Renaissance.

In conclusion, the scientifically very well-grounded opinion that the atmosphere is finite is at least as old as Ptolemy, and the first scientifically sound computation at least as old as Ibn Mu'adh.

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It was Kepler who first computed the height of the atmosphere at between 40 and 50 miles based on the refraction of the light from the sun at twilight. A correlating study was also made by him on the magnitude of the shadow of the earth on the moon during a lunar eclipse. These computations were later elaborated by Philippe de la Hire, and were more or less correct. Later, Dr. Francis Wollaston took up the matter using the newly discovered powers of the barometer and confirmed that Kepler's estimates were essentially correct. It was Wollaston who was responsible for publicizing the finding and eventually making students and the public at large aware that there was a limit to the atmosphere.

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This goes back a lot earlier than Torricelli or Kepler. Aristotle taught that the tangible world is formed from the four sub-lunar elements: earth, water, air, fire. These occupy the space between the centre of the cosmos (that is: the centre of the earth) and the sphere of the moon. The heavenly bodies are made of the fifth element: aether. Thus, there is no air beyond the sphere of the moon. This remained the standard theory throughout antiquity and the Middle Ages.

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From THIS

It is a simple, seemingly obvious notion: air has weight; the atmosphere presses down on us with a real force. However, humans don’t feel that weight. You aren’t aware of it because it has always been part of your world. The same was true for early scientists, who never thought to consider the weight of air and atmosphere.

Evangelista Torricelli’s discovery began the serious study of weather and the atmosphere. It launched our understanding of the atmosphere. This discovery helped lay the foundation for Newton and others to develop an understanding of gravity.

This same revelation also led Torricelli to discover the concept of a vacuum and to invent the barometer, the most basic, fundamental instrument of weather study.

On a clear October day in 1640, Galileo conducted a suction-pump experiment at a public well just off the market plaza in Florence, Italy. The famed Italian scientist lowered a long tube into the well’s murky water. From the well, Galileo’s tube draped up over a wooden cross-beam three meters above the well’s wall, and then down to a hand-powered pump held by two assistants: Evangelista Torricelli, the 32-year-old the son of a wealthy merchant and an aspiring scientist, and Giovanni Baliani, another Italian physicist.

Torricelli and Baliani pumped the pump’s wooden handlebar, slowly sucking air out of Galileo’s tube, pulling water higher into the tube. They pumped until the tube flattened like a run-over drinking straw. But no matter how hard they worked, water would not rise more than 9.7 meters above the well’s water level. It was the same in every test.

Galileo proposed that, somehow, the weight of the water column made it collapse back to that height.

In 1643, Torricelli returned to the suction pump mystery. If Galileo was correct, a heavier liquid should reach the same critical weight and collapse at a lower height. Liquid mercury weighted 13.5 times as much as water. Thus, a column of mercury should never rise any higher than 1/13.5 the height of a water column, or about 30 inches.

Torricelli filled a six-foot glass tube with liquid mercury and shoved a cork into the open end. Then he inverted the tube and submerged the corked end in a tub of liquid mercury before he pulled out the stopper. As he expected, mercury flowed out of the tube and into the tub. But not all of the mercury ran out.

Torricelli measured the height of the remaining mercury column, 30 inches, as expected. Still, Torricelli suspected that the mystery’s true answer had something to do with the vacuum he had created above his column of mercury.

The next day, with wind and a cold rain lashing at the windows, Torricelli repeated his experiment, planning to study the vacuum above the mercury. However, on this day the mercury column only rose to a height of 29 inches.

Torricelli was perplexed. He had expected the mercury to rise to the same height as yesterday. What was different? Rain beat on the windows as Torricelli pondered this new wrinkle.

What was different was the atmosphere, the weather. Torricelli’s mind latched onto a revolutionary new idea. Air, itself, had weight. The real answer to the suction pump mystery lay not in the weight of the liquid, nor in the vacuum above it, but in the weight of the atmosphere pushing down around it.

Torricelli realized that the weight of the air in the atmosphere pushed down on the mercury in the tub. That pressure forced mercury up into the tube. The weight of the mercury in the tube had to be exactly equal to the weight of the atmosphere pushing down on the mercury in the tub.

When the weight of the atmosphere changed, it would push down either a little bit more or a little bit less on the mercury in the tub and drive the column of mercury in the tube either a little higher or a little lower. Changing weather must change the weight of the atmosphere. Torricelli had discovered atmospheric pressure and a way to measure and study it.

Home barometers rarely drop more than 0.5 inch of mercury as the weather changes from fair to stormy. The greatest pressure drop ever recorded was 2.963 inches of mercury, measured inside a South Dakota tornado in June 2003.

So once you know that the atmosphere has finite, and changeable weight at any one point, all the other items become necessary followups. As T himself wrote:

Noi viviamo sommersi nel fondo d'un pelago d'aria. (We live submerged at the bottom of an ocean of air.)

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