A depiction of Blaise Pascal's 1648 atmospheric pressure experiment, wherein he had his brother-in-law Florin Perier carry a Torricelli barometer to the top of Puy de Dome, France, to see if the height of the mercury column would fall as a result of decreasing atmospheric pressure, as he predicted.
In experiments, Pascal atmospheric pressure experiment, aka “Puy-de-Dome experiment” (Hall, 1970), refers to a 19 Sep 1648 test in which Florin Perier, brother in law of Blaise Pascal, took a Torricelli barometer to the base of Puy de Dome, France, then, per the instructions of Pascal, recorded the reading, i.e. height of the mercury, after which he climbed to the top, a height of 4,800 feet, and then recorded the reading of the mercury height again, finding that the column of mercury had dropped by 3 inches and 1.5 lines of height; this result therein was the first proof that atmospheric pressure decreases with height.

Overview
In 1644 to early 1648, Evangelista Torricelli told Marin Mersenne, someone characterized as having the “biggest address book of amateur scientists” on the continent, about his mercury column experiment. [1] Mersenne, in turn, was the first to draw the attention of Blaise Pascal to the work of Torricelli and the mercury column. [2]

In 1647 (Hosson, 2009), or early 1648, Pascal reasoned that if it were true that earth's atmosphere has a maximum height, based on he logic of the according to the results of the Torricelli vacuum experiment, then air pressure on a high mountain must be less than at a lower altitude. The following are his thoughts on this:

“I have thought of an experiment which will remove all doubt, if it be executed with exactness. The experiment should be made in vacuo several times, in one day, with the same quicksilver, at the bottom and at the top of the mountain of Puy, which is near our town of Clermont. If, as I anticipate, the height of the quicksilver be less at top than at the base, it will follow that the weight or pressure of the air is the cause of this; there certainly is more air to press at the foot of the mountain than at its summit, while one cannot say that nature abhors a vacuum in one place more than in another.”
— Blaise Pascal (1648), “Letter to Florin Perier” (Ѻ)

As Pascal resided near the Puy de Dome mountain, which is 4,790 feet (1,460 m) tall, and wanted to bring a mercury column to the top to test his theory, but his health was poor, so could not do the climb.

On 19 Sep 1648, after many months, Pascal convinced Florin Perier, husband of Pascal's elder sister Gilberte, to make the climb; Perier described the results as follows: (Ѻ)

“At eight o'clock, we met in the gardens of the Minim Fathers, which has the lowest elevation in town. First, I poured 16 pounds of quicksilver into a vessel, then took several glass tubes, each four feet long and hermetically sealed at one end and opened at the other. Then placed them in the vessel of quicksilver. I found the quicksilver stood at 26" and 3​1⁄2 lines above the quicksilver in the vessel. I repeated the experiment two more times while standing in the same spot. They produced the same result each time. Taking the other tube and a portion of the quicksilver, I walked to the top of Puy-de-Dôme, about 500 fathoms higher than the monastery, where upon experiment, and found that the quicksilver reached a height of only 23" and 2 lines. I repeated the experiment five times with care. Each at different points on the summit, found the same height of quicksilver, in each case.”

Pascal replicated the experiment in Paris by carrying a barometer up to the top of the bell tower at the church of Saint-Jacques-de-la-Boucherie, a height of about 50 metres. The mercury dropped two lines.

In 1651, or shortly before, Pascal, in his De l’equilibre des liqueurs and De la Masse d’air, wrote up the Dome experiment, as well as how he tried the experiment in several towers in Paris; two books were published (Ѻ) posthumously in 1663. [3]

References
1. Winston, Morton and Edelbach, Ralph. (2013). Society, Ethics, and Technology (pg. 29). Cengage Learning.
2. Conlon, Thomas. (2011). Thinking About Nothing: Otto von Guericke and the Magdeburg Experiments on the Vacuum (pg. 44). Saint Austin Press/LuLu.
3. Pascal, Blaise. (c.1651). The Physical Treatises of Pascal: the Equilibrium of Liquids (De l’equilibre des liqueurs) and the Weight of the Mass of the Air (De la Masse d’air) (Puy de Dome, pgs. 96-112). Octagon Books.