Evangelista Torricelli: An Ocean of Air
In 1643 a Tuscan mathematician sealed mercury into a metre-long glass tube, upended it into a basin, and watched the column fall until it stopped at about seventy-six centimetres. The empty space above it should not, according to every authority since Aristotle, have been able to exist. Torricelli had made the first recorded lasting vacuum and had built, without quite meaning to, the instrument that would let humanity weigh its own atmosphere. "We live submerged at the bottom of an ocean of air," he wrote.
Early Life
He was born in Rome on 15 October 1608 to a poor family from Faenza: his father, Gaspare Ruberti, was a textile worker; his mother was Giacoma Torricelli. The boy's talent outran his family's means, and it was an uncle, Giacomo, a Camaldolese monk, who arranged his schooling. From 1624 to 1626 Torricelli studied mathematics and philosophy at the Jesuit college — a training that gave him the classical apparatus he would spend his career dismantling.
The Galileo Circle
In 1626 he moved to Rome to work under Benedetto Castelli, a Benedictine mathematician and former student of Galileo, initially serving as his secretary. He remained until 1632, and studied mathematics alongside Bonaventura Cavalieri, who became a close friend and whose method of indivisibles Torricelli would extend. Galileo affectionately referred to Torricelli, Raffaello Magiotti and Antonio Nardi as his "triumvirate" in Rome.
After reading Galileo's *Dialogue Concerning the Two Chief World Systems* in 1632, Torricelli wrote to declare himself a Copernican — the only such public declaration he ever made, and one that preceded the Vatican's condemnation of Galileo by a year. In 1641 Castelli forwarded Torricelli's manuscript on projectile motion to the old man in Arcetri. Torricelli spent the last three months of Galileo's life at his side, acting as amanuensis and completing the fifth dialogue, which Vincenzo Viviani eventually published in 1674.
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Galileo died on 8 January 1642. Later that year Torricelli was appointed grand-ducal mathematician and given the chair of mathematics at the University of Pisa — succeeding, in effect, to the most exposed scientific position in Italy. In 1644 he published *Opera Geometrica*, whose solutions to problems of the cycloid established his reputation among European mathematicians.
The Barometer
The experiment of 1643 grew out of a practical puzzle: suction pumps could not lift water beyond a certain height. Torricelli reasoned that if air had weight, the atmosphere pressing on an open reservoir would support a column of liquid only so tall. Mercury, roughly thirteen times denser than water, let him test the idea on a benchtop rather than in a well shaft. The column settled at about seventy-six centimetres, and the space above it — the Torricellian vacuum — was empty.
Two revolutions followed from one glass tube. The vacuum, which scholastic physics had declared impossible, was now sitting on a table in Florence. And the height of the column varied with conditions, which meant atmospheric pressure could be measured. Barometry, altimetry and scientific weather forecasting all descend from that afternoon. Torricelli went further still, giving the first scientific account of what causes wind: differences of temperature and density in the air between one region and another.
Mathematics of the Infinite
His mathematics was as bold. He advanced Cavalieri's method of indivisibles, a direct ancestor of the integral calculus. He worked out the envelope of the family of projectile trajectories — the "parabola of safety" beyond which no shot can reach. He proved convergence formulas for geometric series. And he produced the object that delighted and unsettled his contemporaries in equal measure: Torricelli's trumpet, later called Gabriel's Horn, a shape with infinite surface area but finite volume. It was a demonstration that infinity does not behave the way intuition insists, and it fed directly into the arguments from which calculus emerged.
Torricelli's Law and the Workshop
He also established the relation now called Torricelli's law: fluid escaping an opening in a vessel flows at a speed proportional to the square root of the depth of liquid above it — later recognised as a particular case of Bernoulli's principle, and the basis of practical hydraulics. Alongside the theory he was an outstanding craftsman, developing techniques for grinding small glass lenses and building telescopes and microscopes of exceptional quality. His formulation of the principle governing the centre of gravity in equilibrium rounds out an unusually complete physicist.
Death at Thirty-Nine
Torricelli died in Florence on 25 October 1647, ten days after his thirty-ninth birthday, probably of typhoid fever. When his lectures were published in 1715 they carried an inscription that measured the loss precisely: "Here blossoms another Galileo."
Why Torricelli Matters
In barely five productive years he handed physics an instrument, a vacuum, a law of fluids and a fistful of results at the frontier of the infinite. The barometer alone would secure him: it made the atmosphere a measurable object rather than a philosophical category, and it opened the line of investigation that Pascal, Boyle and von Guericke would pursue into the physics of gases. The torr, the lunar crater, the asteroid and the Italian Navy submarines that bear his name all point back to a poor boy from Faenza who noticed that air is heavy.
