Evangelista Torricelli

1608-1647

Italian Mathematician and Physicist

Evangelista Torricelli is best known for inventing the mercury barometer (1644) and for his fundamental results in hydrodynamics. He also made important contributions to many areas of mathematics.

Torricelli was born on October 15, 1608, in Faenza, Italy. After Torricelli demonstrated his talents at an early age, his father, a textile artisan in modest circumstances, sent him to his uncle who supervised his education. He studied mathematics and philosophy at the Jesuit school in Faenza before going to Rome in 1627 to attended Sapienza College, run by Benedetto Castelli (1577-1644), a former student of Galileo (1564-1642).

In 1641 Torricelli completed De motu gravium, in which he developed some of Galileo's ideas on projectile motion. He experimentally verified many new conclusions and stated what is today known as Torricelli's law—a rigid system of bodies can move spontaneously on Earth's surface only if its center of gravity descends. Useful theorems of external ballistics followed, as well as artillery firing tables. He also propounded a fundamental hydrodynamic theorem that bears his name—the efflux velocity of a jet of liquid exiting a small orifice equals the velocity of a single drop of liquid falling freely in a vacuum from the same height as the liquid level at the orifice.

Castelli showed this work to Galileo. Suitably impressed, he engaged Torricelli as his personal assistant in 1641. They developed a close friendship, and Torricelli remained with Galileo until his death early the next year. Shortly thereafter Ferdinand II, Grand Duke of Tuscany, appointed him to Galileo's post of court mathematician.

After his death Galileo's followers in Rome and Florence continued a long-standing debate over why water in suction pumps would not rise more than 29.5 feet (9 meters). Galileo had argued that pumps created a vacuum, which in turn exerted a force on the water, thus preventing it from rising. Giovanni Battista Baliani (1582-1666) as early a 1630 maintained that it was the weight of air that was responsible. Torricelli undertook a series of experiments in 1643 to settle the issue.

The clearest evidence was provided by what now is readily recognized as the barometer. Torricelli filled a long glass tube with mercury. Placing his finger over the open end, he inverted the tube and inserted it in a large dish of mercury. As expected, the mercury began to drain out of the tube—all but 3 inches (76 millimeters) that is. Torricelli interpreted the result in accordance with Baliani's hypothesis, arguing that the weight of air pressing on the mercury in the dish balanced that of the mercury column. The discovery was announced in a 1644 letter to Michelangelo Ricci (1619-1692). (In fact, the letter suggests Torricelli, based on observations of various hydrostatic devices, was aware of variations in atmospheric pressure before the experiment and was more concerned with producing "an instrument that would show changes of air, now heavier and denser, now lighter and thinner.")

Torricelli also made significant contributions to the development of the calculus—a subject he possibly would have invented if he had lived long enough. He developed important results on maxima and minima, used infinitesimal methods to complete the first modern rectification of a curve (1645), and produced what is perhaps the first graph of a logarithmic function (1647). His independent discovery of the quadrature and center of gravity of the cycloid embroiled him in a bitter priority dispute with Gilles Persone de Roberval (1602-1675), who most certainly arrived at these results first. While in the process of assembling his correspondence and notes to defend his claims, Torricelli fell violently ill. He died, possibly of typhoid fever, in Florence on October 25, 1647.

STEPHEN D. NORTON