Fig. 3.1
Evangelista Torricelli (1608–1647). (From (Lezioni d’Evangelista Torricelli and available at http://en.wikipedia.org/wiki/File:Libr0367.jpg))
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 about 2 cubits (about 110–120 cm) long and filled it with mercury (Fig. 3.3). 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 about 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 Fig. 3.3. 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 Fig. 3.3 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 about 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 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.
3.2 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 suction 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 about 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 Fig. 3.4. CABD represent 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].
Fig. 3.4
Galileo’s drawing of the “thought experiment” to measure the force of a vacuum. See text for details. (From [4])
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 (about 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 six or so years before Torricelli’s experiment, one of the greatest scientists of all time held an entirely different view.
3.3 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].
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