The 1600s were marked by ferocious conflicts between old superstitions and new sciences. A small number of people began using observations and experiments to reveal how Nature worked and in doing so changed the way we understand our world.
Evangelista Torricelli was one of these people. He invented the mercury barometer and deduced from experiments that his device revealed the height of our planet’s atmosphere. In 1644, he concluded that we live at the bottom of a sea of air.
Torricelli’s hectic few years of scientific activity began when Galileo was an old man and ended when Isaac Newton was a young boy.
Torricelli was the first person to explain correctly why the wind blows, and he discovered an extraordinary and controversial geometrical figure, Gabriel’s horn, which has a finite volume but infinite surface area.
Evangelista Torricelli was born on October 15, 1608 in the great Italian city of Rome.
His mother was Giacoma Ruberti (born Torricelli). His father was Gaspare Ruberti, a weaver. Evangelista was the eldest of their three sons; he took his mother’s surname – it was not exceptionally rare in Rome for children to do this. Two of the family’s three sons took their mother’s surname, while one took the surname Ruberti.
Sometimes biographers incorrectly state that Evangelista was born in the small northern Italian city of Faenza. This is actually where he was educated and where his mother was born – he regarded Faenza as his spiritual birthplace.
Evangelista’s parents grasped that their son was unusually intelligent, but they were too poor to pay for school.
Enter Evangelista’s uncle, Gian Francesco Torricelli, priest of the Abbey of Saint Ippolito in Faenza, Evangelista mother’s birthplace. Gian Francesco was a graduate of the famous University of Padua and was ideally placed to help with Evangelista’s education.
Evangelista moved north to live with his Gian Francesco, who began his education by teaching him the basics.
In 1619, age 11, Evangelista began attending Faenza’s Jesuit school. In 1623, he began studying mathematics.
Gian Francesco soon learned from Evangelista’s teachers that his nephew was an extraordinarily talented mathematician. Gian Francesco got in touch with a friend, Professor Benedetto Castelli of Sapienza College in Rome – both men were in the same Catholic Camaldolese order.
Mathematics and Physical Sciences
In 1626, age 18, Evangelista Torricelli moved to Rome to be taught mathematics and physical sciences by Professor Castelli. This was a fantastic break for the young Torricelli: Castelli had been taught these subjects by Galileo.
Torricelli could not afford fees, so he worked as Castelli’s secretary for six years, until 1632. Near the end of this period, he took over Castelli’s lecturing duties whenever Castelli was sick or traveling.
Galileo: First Contact
At the beginning of 1632, Galileo Galilei changed the course of scientific and religious history by publishing Dialogue Concerning the Two Chief World Systems. Within a year, this book and everything else he had ever written were suppressed by the Catholic Church.
Galileo was declared “vehemently suspect of heresy.” The trigger for the Church’s outrage was that part of Galileo’s book discussed the Copernican view that the solar system is centered on the sun rather than the earth, a view Galileo said he agreed with.
Soon after the book was published and before it was banned, Torricelli, age 23, read it hungrily, working through all its implications for himself. He soon found himself in a position to write to the great man. In his professor’s absence, Torricelli replied to a letter Galileo had sent to Professor Castelli.
In the letter, Torricelli explains that Professor Castelli is absent and so he, as Castelli’s secretary, must reply. He introduces himself and tells Galileo that he has read his new book “with delight.” Torricelli’s letter is a gift for future biographers, because so little of his early life is recorded. Torricelli informs Galileo (and us) that he has studied the works of the great Ancient Greek mathematicians, such as Archimedes’, and has studied the works of Ptolemy, Tycho Brahe, and Kepler. He says that he agrees with the Copernican view of the solar system.
This was the only time Torricelli ever openly supported the Copernican view. Soon enough, to do so would risk death.
Torricelli’s Lifetime in Context
Evangelista Torricelli’s Contributions to Science
The Barometer and Earth’s Sea of Air
Torricelli is best known for his invention and, even more importantly, his explanation of the mercury barometer. He did this in in 1643.
Torricelli’s device measures atmospheric pressure, which is related to the weight of the miles of air in the atmosphere pressing down on us.
Looking at the results of his experiment, Torricelli rather brilliantly concluded that the barometer acts as a balance. On one side of the balance is the downward push of a column of mercury about 76 cm high. On the other is the downward push of Earth’s atmosphere.
Torricelli was right. In modern terms we can measure at sea level that the average weight of Earth’s atmosphere is 1.03 kg on every square centimeter of surface (14.7 lb on every square inch.)
Torricelli’s explanation contradicted Galileo’s theory that the mercury column was held in the tube by the suction power of the vacuum above it. Galileo had also been contradicted by Giovanni Baliani of Genoa in 1630, who advanced similar ideas to Torricelli, albeit less developed, about the effects of air pressure. Whether Torricelli had heard of Baliani’s ideas is unknown.
In a series of experiments Torricelli and his friend Vincenzo Viviani proved that the vacuum at the top of the tube was not the cause of the mercury column’s height.
Why does the Wind Blow?
In Torricelli’s day people believed that the wind was caused by vapors released by the damp earth.
Torricelli gave the correct explanation as part of a series of lectures. These were published in 1823, long after his death, as Lezioni accademiche di Evangelista Torricelli.
Torricelli observed prevailing wind directions for some time in the city of Florence and gathered reports from around Europe.
Moreover, he took into account his observation that when the doors of large buildings are opened on hot days, cold air rushes outward through the doorway.
He said that winds are caused by what today we call convection currents, whose circulation he described. Put simply, he said that hot air is less dense than cold air, so hot air rises from the earth’s surface – he said it could rise to heights of three or four miles – and is replaced by cooler air. The result is that air moves from regions where its density is high to regions where it is low and this moving air is the wind.
Archimedes and Torricelli’s Principle
Torricelli made a number of startling discoveries in mathematics and mechanics, publishing many in his Opera geometrica (Geometry Work).
As a mathematician, his greatest influence was Archimedes, whose work by then was almost two millennia old. Torricelli believed Archimedes had worked “ad occultandum artis arcanum” – in other words using some hidden or secret art. Torricelli was right – Archimedes’ work The Method, in which he revealed his remarkable techniques, was only rediscovered in 1906 in the renowned Archimedes Palimpsest.
The concept of center of gravity was discovered by Archimedes. Torricelli, following in his footsteps, discovered a new principle, Torricelli’s principle, which says:
A system of bodies in equilibrium can only move spontaneously on the earth’s surface if its center of gravity descends.
How Fast Should Water Flow Through an Opening?
Torricelli observed water flowing through openings in water tanks and figured out that the water should move through the opening with the same velocity as if it had fallen under gravity from the height of the water above the opening.
This allowed him to prove in Opera geometrica that the rate a liquid flows through an opening is proportional to the square root of the depth of the liquid. This proportionality is called Torricelli’s law.
As a result of his law, Torricelli has a good claim to be recognized as the founder of modern fluid dynamics.
An Infinity Paradox
Gabriel’s horn (or Torricelli’s trumpet) starts wide and diminishes forever without reaching an end. Torricelli revealed this object to the world in 1644, provoking awe, bewilderment, jeers and acrimony.
The horn has finite volume, infinite length and infinite surface area.
In the 1600s, mathematicians were distinctly uncomfortable with infinity – Torricelli described his discovery as a paradox.
Some philosophers refused to believe Gabriel’s horn could exist at all. Thomas Hobbes, of the empiricist school, believed knowledge can only come from experience. Since we cannot experience infinity, Hobbes argued we cannot make any trustworthy statement about it in general or accept Torricelli’s discovery in particular. Attempting to defeat mathematics with mockery, Hobbes said of Gabriel’s Horn:
Modern mathematicians see infinity as an everyday aspect of their work.
Gabriel’s horn is made by taking the function y = 1⁄x and rotating it around the x-axis for x=1 to ∞.
Parabolas and Projectiles
The study of parabolas began with the Ancient Greeks. In renaissance Italy, parabolas once again fascinated mathematicians. Galileo, building on the work of Niccolo Tartaglia, showed that projectiles, such as cannon balls, follow a parabola-shaped path.
Torricelli made a number of advances in the study of parabolas and projectiles. He recorded these in De motu gravium, published as part of Opera geometrica. The gunnery tables he produced were not improved upon until the 1700s.
Below you can see his ‘safety parabola’ in blue. Torricelli imagined a cannon ball shot many times, always emerging from the cannon at the same speed, but at different angles to the ground. He deduced that you can draw a ‘safety parabola’ which will form an envelope around all the possible parabolic trajectories. Anyone outside the envelope is safe from the cannonball, whatever angle the cannon is fired at. The safety parabola is of mathematical interest because it was the first envelope discovered. Torricelli also showed that all possible parabolic trajectories of the cannonball are tangent to the safety parabola.
The torr unit of pressure is named after Torricelli.
Originally it was defined as the pressure equal to one millimeter of mercury at 0 °C. It is now defined as 1⁄760 of a standard atmosphere (101325 Pa).
In 1958, Italy issued a new stamp, shown here, to commemorate the 350th anniversary of Torricelli’s birth.
Some Personal Details and the End
Torricelli never married and had no children.
He loved old literature – many of the books he owned were Latin and Ancient Greek classics. His book collection also revealed his enthusiasm for architecture and military technology.
In 1641, three months before Galileo’s death, Torricelli traveled to live at his home in the city of Florence to act as his eyes and writer in his final days – Galileo had been completely blind for three years and under house arrest for eight years.
Despite his house arrest, Galileo was the mathematician and philosopher to the Grand Duke Ferdinando II of Tuscany. After Galileo’s death, Torricelli was appointed to the post, with an ample salary and an apartment in the Medici Palace in Florence. He was also appointed Chair of Mathematics at the University of Pisa. He remained in these posts until his untimely death.
Torricelli was acclaimed among his friends as a scintillating conversationalist. Before his death, he was working on comedies for performance. Sadly, they no longer exist.
Evangelista Torricelli died in Florence 10 days after his 39th birthday on October 25, 1647. He was feverish for about 20 days before his death, probably resulting from typhoid or pneumonia. During the fever he was sometimes rational, sometimes delirious.
Fearing he would not recover, he wrote his will 11 days before the end came. He left almost all he had to his two brothers, Carlo and Francesco, a sum to his great friend Doctor Buonaiuti, who had treated him during his illness, a sum to his servant Dianora, and his old shoes, socks and similar items to Ceccotto the sweeper.
To his friend Lodovico Serenai, who was responsible for executing his will, he left a ring and his books. He told Serenai to erase any and all the notes he had made in book margins criticizing the Jesuit scholars Niccolò Cabeo and Athanasius Kircher – Torricelli did not want future generations to learn of his profound contempt for them.
Evangelista Torricelli was buried in the Basilica of San Lorenzo in Florence. He died at the peak of his intellectual powers.
Author of this page: The Doc
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