|A diagram illustrating the atmospheric pressure, i.e. the weight, or force per unit area, of a column of air pressing down on the surface of the earth, per unit area.|
In 1614, Isaac Beeckman, in his journal notes, according to William Middleton (1964), had correctly explained the action of a suction pump by an appeal to the pressure of air, and compared air to a sponge, which can be condensed, but because of its elasticity tries to return to its previous state; in 1618, Beeckman, supposedly, began to communicate some of these ideas to Rene Descartes.
On 24 Oct 1630, Giovanni Baliani, communicated to Galileo that, after shortly after he came to know that air had weight, that he began to believe in the existence of the vacuum; the following is an excerpt:
“The higher we go in the air, the less heavy it is.”— Giovanni Baliani (1630), “Letter to Galileo”, Oct 24 
In 1630, Jean Rey, in his Essay on Tying to Find out why Tin and Lead Increase Weight when Calcined, supposedly, was thinking about the weight and pressure of air. 
In 1631, Rene Descartes, in a letter, supposedly to his pupil Reneri, stated the following ideas, illustrated with a diagram (as shown adjacent): 
“To resolve your difficulties, imagine the air to be like wool, and the aether which is in its pores to be like eddies of wind which move hither and thither in this wool; and consider that this wind, which acts from all sides between the little fibers of the wool, prevents them from pressing as hard against one-another as they might do without it. For they all have weight, and press upon one-another as much as the agitation of this wind can let them, so that the wool which is upon the earth is compressed by all that which is above, even to beyond the clouds; and this makes a great weight.
Descartes' 1631 illustration of a column of mercury in air.
So that if we had to raise a part of this wool which is, for example, at the point marked O (see adjacent figure), with all that above on the line OPQ, we should need a very considerable force. Now this weight is not commonly felt in the air when we push it upwards; because if we raise a part, for example that which is at the point E towards F, that which is at F goes in a circle towards CHI and comes back to E; and so its weight is not felt at all, no more than that of a wheel is felt in turning it, when it is perfectly balanced on its axis. But in the example that you bring forward of a tube DR closed at the end D, where it is attached to the plane AB, the quicksilver which you suppose to be in it cannot begin to descend all at once unless the wool which is near R goes towards O, and that which is at ) goes towards P and Q, and so on, till all the wool in the line OPQ is raised, and this, taken all together, is very heavy. For, the tube being closed at the top, no wool—I mean air—can come in to replace the quicksilver when it descends. You will say that wind—I mean aether—can very well enter through the pores of the tube. I admit this; but consider, that the aether which will come in can come only from the sky above; for although there is some everywhere in the pores of air, nevertheless there is no more than is necessary to fill them. Consequently, if there is a new space to fill the tube, aether which is in the sky above the air must come in, after the air has risen in its place.
And so that you will make no mistake, you must not think that this quicksilver cannot be separated from the top of the tube by any force, but only that it needs as much force as is required to raise all the air which there is from that point to the above clouds.”
Of note, meteorology instrument historian Ernst Gerland (1893), stated that in this letter, Descartes had “given out the idea of the barometer, still without having been proven by trial”. 
“Surely it is unreasonable to see in this a prevision of the barometer. Apart from the fact that nothing is said about a cistern, there is no indication that Descartes realized that if the tube wee long enough only part of the quicksilver would come out.”— William Middleton (1964), The History of the Barometer (pg. 8)
Gerland's classification of Descartes as being the originator of the idea of the barometer, in short, has since been classified as an over-reading of the above. 
|Otto Guericke's c.1662 column barometer, from Illustration X, Figure IV, of Schott diagrams, which varied up or down by sever hand lengths, according to atmospheric pressure, which he used to predict when storms were near.|
“The weight of air on the earth’s surface is as great as the weight of water about 20 Magdeburg cubits deep. In other words, if water should rise 20 cubits above the earth’s surface, the pressure it would exert on all things beneath is the same as the pressure of air.”— Otto Guericke (1663), Magdeburg Experiments on the Vacuum of Space (pg. 113)
and had built a column barometer, shown adjacent, attached to his house, for measuring changes in atmospheric pressure
● Atmospheric thermodynamics
1. Middleton, William E. (1964). The History of the Barometer (pgs. 7-8) (Amz). Publisher.
2. (a) Gerland, Ernst. (1893). Report of the International Meteorological Congress, Chicago Illinois, Aug 21-24 (editor: O.L. Fassig) (pg. 690). U.S. Weather Bureau Bulletin, number 11, part 3. Washington.
(b) Gerland, Ernst. (1896). “Historical Sketch of Instrumental Meteorology” (§13:687-98), Bulletin, Issue 11, Part 3.
(c) Middleton, William E. (1964). The History of the Barometer (pg. 6-7) (Amz). Publisher.
3. Frisinger, Howard. (2018). History of Meteorology to 1800 (pg. 70). Springer.
4. (a) Rey, Jean. (1630). Essay on Tying to Find out why Tin and Lead Increase Weight when Calcined (Essai sur la recherche de la cause pour laquelle l’estain et le plomb augmentent de poids quand on les calcine). Bazas.
(b) Middleton, William E. (1964). The History of the Barometer (pg. 8) (Amz). Publisher.
5. (a) Baliani, Giovani. (1630). “Letter to Galileo”, Oct 24.
(b) Galilei, Galileo. (1904). Le Opere de Galileo Galilei, Volume 14 (20 volumes) (editor: Antonio Favaro) (pg. 157-60). Barbera. (c) Middleton, William E. (1964). The History of the Barometer (pg. 9) (Amz). Publisher.
● Atmospheric pressure – Wikipedia.