“[t]he mercury should enter and should rise in a column high enough to make equilibrium with the weight of the external air which forces it up?” [i]
Later tests with barometers proved that the height of the mercury lowered as elevation increased, confirming Torricelli’s hypothesis concerning the weight of the atmosphere. Torricelli’s explanation of atmospheric pressure as the weight of the air above was revolutionary and defined the idea of atmospheric pressure as we still understand it today. To get a sense of all that weight of air, recall that at sea level standard atmospheric pressure is 14.7 pounds per square inch (psi). Essentially, we all have the weight of a bowling ball pressing down on every inch of our bodies.
The barometer also showed unexpected behavior: the height of the mercury in the barometer fluctuated with changing weather conditions. Since the barometer itself wasn’t changing, Torricelli deduced that the change must be driven externally. The atmospheric pressure itself was changing, leading Torricelli to another revolutionary theory, this time concerning the wind. He posited in a later letter that:
“winds are produced by differences of air temperature, and hence density, between two regions of the earth.” [ii]
This was the first such scientific explanation, and has again turned out to be exactly the case. That principle is still one of the guiding factors in meteorology and weather prediction.
Improved versions of his mercury barometer are still in use today for pressure measurement and weather monitoring purposes, though many have switched to using a less-toxic liquid. Even the sensitive pressure transducers Glew Engineering uses in semiconductor equipment, which do not use a liquid, rely on the same principle of comparing varying pressures to a baseline vacuum. Torricelli is indeed honored with his own unit of measurement, the Torr: 1/760 of a standard atmosphere, or 1 mm of mercury (see Figure 2: the mercury in the meter-long tube stood 760 mm high, so the pressure was 760 Torr, or one standard atmosphere).
Contributions to Mathematics
Figure 3: Torricelli’s Trumpet AKA Gabriel’s Horn
Aside from physics, Torricelli also focused his talents and intellect on mathematics and geometry. His work on centroids (the geometric center of a shape) and centers of gravity in objects augmented and propelled forward a burgeoning field that joined mathematics and physics. He also assisted fellow mathematician Bonaventura Cavalieri in developing the first steps towards integral calculus, the lovely theory Isaac Newton and Gottfried Leibniz perfected in later decades.
Torricelli’s mathematics work threw fire on another hot topic among the scientists of the day: the nature of infinity. His work involved “volumes of revolution”, or the volume of an object formed by rotating a 2-dimensional shape around an axis (imagine taking a circle and rotating it through space about a line off to one side; your result would be a donut-shaped torus). He realized that by rotating the line formed by the equation y = 1/x for x ≥ 1 about the x-axis, he could form a theoretical object with a finite volume but with an infinite surface area (represented in Figure 3, above). That’s precisely as baffling as it sounds, a paradox which provoked many debates among his colleagues. The shape came to be known as Gabriel’s Horn, though some still referred to it as Torricelli’s Trumpet, in recognition of his work.
Although we remember Torricelli mainly remembered for his invention of the barometer and explanation of atmospheric pressure, his impact in math, science and engineering extends beyond pressure measurement. With his contributions to geometry, his initial steps in the development of calculus, and his ideas about the nature of vacuums and of infinity, Torricelli’s work continues to be felt in science, engineering and math today [iii].
Any other Italian scientists you think don’t get enough attention? Let us know in the comments below!