Torricelli's Great Insight: The Ocean of Air

On June 11, 1644, Evangelista Torricelli (1608–1647) (FIGURE 1) wrote a remarkable letter to his friend Michelangelo Ricci, who was a mathematician and also a cardinal in Rome. Torricelli himself was a mathematician and physicist, originally from Faenza, but now in Rome. Both men were part of the extraordinarily effervescent scientific activity in Italy in the early and mid-17th century. The letter contained the wonderful statement, “We live submerged at the bottom of an ocean of the element air, which by unquestioned experiments is known to have weight” (FIGURE 2). This has to be one of the most dramatic statements in the early history of atmospheric science, and, therefore, by implication, in the early development of high-altitude medicine and physiology. One wonders how many medical and graduate students today appreciate the fact that they are living at the bottom of a sea of air that bears down upon them and is responsible for the barometric pressure. This remarkable insight apparently came right out of the blue. For example, it eluded the great scientist Galileo, who, as we shall see, only a few years before gave an erroneous explanation for related phenomena.

Torricelli then went on to describe how he made the first barometer and how he recognized that it was the weight of the air that supported the column of mercury. He took a glass tube ∼2 cubits (∼110–120 cm) long and filled it with mercury (FIGURE 3). He then placed a finger over the end and inverted the tube in a basin containing mercury. He saw that the mercury fell until its height above the surface in the trough was “a cubit and a quarter and an inch besides.” A cubit and a quarter is probably ∼73 cm, so he reported the height as in the region of 76 cm of mercury.

Torricelli correctly reasoned that the space above the mercury contained nothing and therefore was a vacuum. Previous experimenters using water (see below) had seen a similar behavior in much longer water-filled tubes, and it had been argued that the column of liquid was held up by the properties of the vacuum above it. Incidentally this is apparently why Torricelli used two tubes, one with a simple blind end and the other with a small sphere on the end as shown in FIGURE 3. He argued that if a vacuum was responsible for attracting the mercury, the heights of the columns would be different because the differences in shape of the end of the tube would change the properties of the vacuum. However, as FIGURE 3 shows, the heights were the same. Torricelli went on to argue that the vacuum was irrelevant to maintaining the height of the mercury column. After remarking that the space above the mercury contained nothing and therefore could have no attractive effect, he stated that “On the surface of the liquid which is in the basin, there gravitates a mass of air 50 miles high.” In other words he clearly saw that it was the pressure of the “ocean of air” on the mercury in the trough that was responsible for maintaining a column of ∼76 cm.

The actual experiment was not done by Torricelli himself but by his colleague Vincenzo Viviani (1622–1703). Viviani was an assistant to Galileo at Arcetri near Florence from the age of 17 to Galileo's death in 1642, and he went on to edit the first edition of Galileo's collected works. The fact that it was Viviani who actually carried out Torricelli's experiment emphasizes the close link between Torricelli and Galileo. Torricelli was invited to work with Galileo in Arcetri but arrived just a few months before the latter's death.

Galileo's View on the Force of a Vacuum

There was much interest at the time in the problem of raising water from a deep well by means of a pump. This was extensively discussed before Torricelli's experiment and it was well known that it was not possible to pump water from a well if the pump was more than ∼9 m above the surface of the water. A related interest was the behavior of siphons, which were used to transport water in a pipe over a small hill. In 1630, Giovanni Galliano (1582–1666) had written to Galileo asking him why a siphon that Galliano had designed to carry water over a hill 21 m high refused to work. If the tube of the siphon was filled with water by means of a pump, and then the pump was stopped, the water separated high in the tube and flowed out at both ends.

Galileo discussed this problem in some detail in his last book Discourses Concerning Two New Sciences (4). This was published in 1638 in Leiden, far from Rome. The reason is that Galileo had been under house arrest at Arcetri since 1633 because he was “vehemently suspected of heresy” by the Holy Office of the Inquisition. This came about because Galileo argued in his previous great book Dialogues Concerning the Two Chief World Systems (3) that the earth circled the sun. In fact, the original sentence was prison, but this was reduced to house arrest. Galileo was precluded from publishing anything after 1633, but since Leiden in the Netherlands was outside the influence of the Church, it was possible to have his book published there.

Discourses Concerning Two New Sciences makes excellent reading. The format is a discussion between three people, Salviatti, who is a spokesman for Galileo, and two others, Sagredo and Simplicio, who continually challenge Galileo on various points. This is the same format that Galileo used in Dialogues Concerning the Two Chief World Systems.

Galileo takes up the issue of why water cannot be raised more than a certain amount from a well by describing a “thought experiment” illustrated in FIGURE 4. CABD represents the cross section of a cylinder either of metal or preferably of glass, hollow inside, and accurately turned. Into this is introduced a perfectly fitting cylinder of wood, represented in cross section by EGHF, and capable of up and down motion. A hole is bored through the cylinder to receive an iron wire carrying a hook at the bottom. The conical head at the top of the wire makes a perfect fit with the countersunk wooden cylinder. For the experiment, the cylinder is carefully filled with water so that no air remains, and weights are added gradually until the water separates and the weights fall. The weight of the stopper, wire, and bucket with its contents then measure the force of the vacuum (forza del vacuo).

Segredo, one of the discussants, then remarks, “Up to this time I had been so thoughtless that, although I knew a rope . . . if sufficiently long would break by its own weight when held at the upper end, it never occurred to me that the same thing would happen only much more easily to a column of water. And really is not that thing which is attracted in the pump [raising water from the well] a column of water attached at the upper end and stretched more and more until finally a point is reached where it breaks, like a rope, on account of its excessive weight.” To which Salviati responds, “That is precisely the way it works; this fixed elevation of 18 cubits [∼10 m] is true for any quantity of water whatever, be the pump large or small.” In other words, Galileo was thinking in terms of a force to break the vacuum rather like a force can break a wire by stretching it.

This section is quoted at some length to emphasize how revolutionary was Torricelli's new insight. Only some 6 or so years before Torricelli's experiment, one of the greatest scientists of all time held an entirely different view.

Gasparo Berti's Experiment With a Long Lead Tube

Torricelli's experiment was revolutionary, but as so often happens in science, it had been preceded by other somewhat similar activities. One of the most important of these was a remarkable demonstration by Gasparo Berti (c. 1600–1643), who was another Renaissance Italian mathematician and physicist. Unfortunately, the details of Berti's experiment are not as clear as those of Torricelli's because the accounts were written several years later. Indeed, the actual date of the experiment is uncertain but was probably between 1639 and 1644. The best account is by Emmanuel Maignan (1601–1676), who taught natural philosophy in a convent in Rome (6).

Maignan first refers to Berti as “indeed my greatest friend” and then goes on to describe how Berti erected a long lead tube on the outside wall of the tower of his house (FIGURE 5). The length was ∼11 m, and initially Berti filled it with water and sealed it at both ends. He then placed the bottom of the tube in a tank of water and opened the seal. Some of the water flowed out of the tube, but much remained so that the height of the column of water was ∼10 m. Berti referred to the space above the water as a vacuum.

A number of variations of this arrangement were made. One was to attach a large sphere at the top of the tube, which was initially filled with water as well and then became part of the container for the vacuum. The sphere can be seen in FIGURE 5. The properties of the space above the water created a great deal of controversy. One experiment was to place a bell in the sphere and arrange for this to be struck in some way, because it was argued that sound could not travel through a vacuum. However, there was no way of supporting the bell so that the sound could not travel along its support. Interestingly although this was a very remarkable experiment, it was not well known at the time, and, as indicated above, accounts were written only some years later. There was never any suggestion that the column of water was supported by air pressure.

Weighing the Air

Torricelli's letter (FIGURE 2) extends the passage quoted earlier as follows: “We live submerged at the bottom of an ocean of the element air, which by unquestioned experiments is known to have weight, and so much, indeed, that near the surface of the earth where it is most dense, it weighs [volume for volume] about four-hundredth part of the weight of water.” This raises the issue of how these early scientists were able to weigh air.

Torricelli is here referring to a section in Galileo's Discourses Concerning Two New Sciences where Salviati states, “But can you doubt that air has weight when you have the clear testimony of Aristotle affirming that all elements have weight including air, excepting only fire? As evidence of this, he cites the fact that a leather bottle weighs more when inflated than when collapsed.” Actually Aristotle's remarks on this are extremely brief. He states in De Caelo Book IV.4, 311b, lines 6–11, “Earth, then, and bodies in which earth preponderates, must needs have weight everywhere, while water is heavy anywhere but in earth, and air is heavy when not in water or earth. In its own place each of these bodies has weight excepting fire, even air. Of this we have evidence in the fact that a bladder when inflated weighs more than when empty” (1).

In fact Aristotle's statement that “a bladder when inflated weighs more than when empty” was the subject of much subsequent controversy. Even Galileo followed up his remarks cited above with the following: “I am inclined to believe that the increase of weight observed in the leather bottle or bladder arises, not from the gravity of the air, but from the many thick vapors mingled with it in these lower regions. To this I would attribute the increase in weight in the leather bottle.”

It is interesting that, today, teachers of elementary physics often use an experiment with an inflated balloon to make the point that air has weight. There are several examples of these on the internet. In a typical demonstration, two inflated toy balloons are suspended at the ends of a long stick such as a meter rule, and this is supported in the middle so that it is balanced. One balloon is then burst by putting a match under it, and the other balloon tilts the balance downward.

In fact, this is a misleading demonstration because the reason why the intact balloon falls is that it contains air under pressure. If the two balloons are inflated with air at normal atmospheric pressure, deflating one balloon will not change the balance. The reason is that a balloon at normal pressure, such as a thin plastic bag that has been partly inflated, receives support by buoyancy from the air around it, which cancels the weight of the air inside it.

Galileo presumably understood this, although he does not appear to state it. What he does do is describe in detail a method for measuring the weight of the air. This is included in Discourses Concerning Two New Sciences (4). Basically, he takes an empty bottle containing air at normal pressure and weighs it. He then blows air into it so that the pressure is increased and weighs it again. A second bottle filled with water is then connected to the first bottle so that the air escaping from the first bottle displaces water from the second, and the volume of the displaced water is measured. Now he has an accurate measurement of the weight of the air introduced into the first bottle and its volume measured from the displaced water. This allows him to determine the weight per unit volume or, as he actually calls it, the specific gravity of the air. At the end of the description, he states that this allows him to determine “definitely how many times heavier water is than air, and we shall find, contrary to the opinion of Aristotle, that this is not ten times, but as our experiment shows more nearly four hundred times.”

The last part of this statement is surprising because the actual value is ∼800 times at sea level at a temperature of 20°C. In other words, Galileo's figure is too low by a factor of about two. The procedure is described in such detail that it is difficult to understand how such a large error was incurred. One wonders whether this too was in part a “thought experiment” rather than something actually carried out as described.

The Decrease of Barometric Pressure With Altitude

In his letter, Torricelli makes an oblique reference to the fact that barometric pressure may decrease with altitude. First, he states, “Those who have written about twilight, moreover, have observed that the vaporous invisible air rises above us about 50 or 54 miles.” This statement implies that, above this altitude, there is no air, so that as we approach the altitude the pressure will fall. Torricelli goes on to say, “I do not, however, believe its height is as great as this, since if it were, I could show that the vacuum would have to offer much greater resistance than it does.” Here, Torricelli is presumably arguing that if the air extended as high as 50–54 miles, the height of the column of mercury in his barometer would be greater. He then continues, “The weight referred to by Galileo applies to air in very low places, where men and animals live, whereas that on the tops of high mountains begins to be distinctly rare and of much less weight than four-hundredth part of the weight of water.” In other words, Torricelli is certainly suggesting that barometric pressure declines with altitude.

The definite proof of the fall in barometric pressure with altitude is usually ascribed to Blaise Pascal (1623–1662). He was an infant prodigy, particularly in the area of mathematics, but he also did extensive work on pressure in fluids. Students are taught Pascal's Law, which states that the pressure at any point in a liquid is equally transmitted in all directions. Indeed, up to now, we have been concentrating on the intellectual ferment in Italy in the early and mid-17th century. However, French scientists such as Pascal and René Descartes (1596–1650) were also extremely active.

Pascal had the idea of taking a barometer up the Puy-de-Dôme near Clermont in central France where he was born. Rather than do this himself, he asked his brother-in-law Florin Perier, who lived in Clermont, to carry out the experiment. The results were subsequently sent to Pascal in a delightful letter by Perier dated September 22, 1648. Note that this is only 4 years after Torricelli's letter to Ricci, and this short period is further evidence of the lively intellectual activity of the time.

Perier described the project in considerable detail. A group of people met early in the morning in a garden in Clermont and filled several mercury barometers, which gave a pressure of ∼710 mmHg. One barometer was left in the garden where it was observed all day by the Reverent Father Chastin who reported that there were no changes in the height of the mercury. However, on the summit of Puy-de-Dôme, the altitude of which was described as 500 fathoms above the garden, the mercury had a height of only ∼625 mmHg. This meant that there was a fall in barometric pressure of ∼12%. The result was considered so remarkable that the experiment was repeated a number of times. In fact, Perier subsequently ascended to the summit again and found the same result.

Perier was so impressed by the results of this experiment that he then took the barometer up the tower of the cathedral in Clermont to see whether there would be a measureable change of pressure as a result of this much smaller ascent. Indeed, there was a fall of ∼5 mmHg, which gave him great satisfaction. Perier's letter of 1648 to Pascal is so beautifully written that it is embarrassing to state that there is some doubt about its authenticity (6). Some historians have contended that Pascal's request to Perier to carry out the experiments could not have been as early as November 1647 as he claimed. Other commentators have argued that the whole idea of the experiment came from Descartes rather than Pascal.

Torricelli's experiment had an enormous effect on the scientific community, not only in Italy but throughout Europe. This was in contrast to the experiment of Gasparo Berti described earlier, which resulted in little interest and in fact was only reported several years later. However, Torricelli's discovery had rapid repercussions.

Demonstration of the Enormous Force That Is Developed by the Barometric Pressure

One of the most colorful and best known subsequent experiments was carried out in 1654 by Otto von Guericke (1602–1686), who was the mayor of the city of Magdeburg in central Germany (FIGURE 6). He has the distinction of making the first air pump. He did this by modifying a water pump that previously had been used for fighting fires. Von Guericke then constructed two copper hemispheres that fitted together so accurately that they were airtight when they were evacuated. When he pumped the air out of the hemispheres, which had diameters of ∼50 cm, the force developed by the pressure of the air was so great that two teams of horses were unable to pull the hemispheres apart. As can be expected, this dramatic demonstration provoked widespread interest.

It is interesting to put some numbers on von Guericke's experiment. First, why did he need two teams of horses? One team would have given the same result, although the demonstration would perhaps have been less arresting. In fact, one team of horses would have resulted in the same tensile force on the hemispheres if they had been fastened to a solid structure such as a large wall. The second team simply provided a counterforce that otherwise would have been provided by a wall.

Another interesting point is how close did the horses come to separating the two hemispheres? Probably not close at all. If we assume as a first approximation that von Guericke's pump was capable of removing all of the air, the force holding the two hemispheres together was equal to the barometric pressure times the area of a circle of 50-cm diameter. Using English units and taking the radius as 10 in., the area of the circle is πr² or 3.14 × 100, that is 314 in.². The barometric pressure is 14.7 lb./in.², giving a total force of ∼46,000 lb. weight. In SI units, the area of the circle is 0.0625 m², and the total force is ∼10,300 N.

Next, how much force can be developed by a horse? There is a competition in some rural areas known as “horse pulling” in which the maximum force developed by a horse is measured by a dynamometer. A medium sized horse can pull ∼1,500 lb. weight. Therefore, it would take 46,000/1,500 horses, that is ∼30 horses in one team to separate the hemispheres. Von Guericke's team of 8 horses on one side (FIGURE 6) was therefore far less than required. Of course, if the air in the hemispheres could only be pumped down to half the normal pressure, the force required to separate them would be reduced to one-half.

Subsequent Studies of the Effects of Reducing the Barometric Pressure

One person who was greatly influenced by the news of von Guericke's demonstration was Robert Boyle (1627–1691) in England. He read about the new pump in a book by Schott (7) and realized the potential of making scientific studies in an experimentally produced low-pressure environment. He then persuaded his brilliant colleague Robert Hooke (1635–1703) to make an air pump that could evacuate a glass sphere into which small animals and other objects could be introduced. This was impossible with the metal hemispheres used by von Guericke. Boyle's experiments were initially described in his influential book New Experiments Physico-Mechanicall, Touching the Spring of the Air and its Effects (2). This publication marked the beginning of a new era of what we now know as high-altitude physiology (10).

FOOTNOTES

• No conflicts of interest, financial or otherwise, are declared by the author(s).