Galileo's pendulum, or the clock he never lived to build
Sometime in 1583, a 19-year-old medical student sat through mass in the Cathedral of Pisa and watched the bronze lamp above him sway in a draft. He was not, by any surviving account, especially devout. He was bored, alert, and he had his fingers on his own pulse.
The student was Galileo Galilei, and he was timing a lamp. According to Vincenzo Viviani, his later pupil and biographer, Galileo noticed that the chandelier’s oscillations — wide at first, then narrowing as the motion died — seemed to keep the same duration regardless of how far the lamp swung. A long arc and a short arc each took the same number of heartbeats. The property he had stumbled on would later be called isochronism: from the Greek for “equal time.”
The physics is this: for small angles of swing, a pendulum’s period depends on its length and on gravity, but not on the width of its arc, and not on how heavy the bob is. A one-metre pendulum always takes almost exactly two seconds per full swing, whether the arc is wide or narrow. This was exactly the regulating property that every clock since the medieval escapement had been missing — a built-in corrector that needed no human hand to reset it. The verge-and-foliot clocks of the day drifted by as much as fifteen minutes in twenty-four hours. A pendulum-governed clock, in theory, promised seconds.
Galileo found an early, sideways use for the discovery. He built a device he called the pulsilogium — a short cord with a small weight, adjustable in length, that physicians could hold to a patient’s wrist and calibrate to count heartbeats. The man who had used his pulse to time a pendulum had invented a pendulum to time a pulse.
Turning isochronism into an actual clock proved harder than finding it in a lamp. The challenge was building an escapement that could sustain the pendulum’s swing without disrupting its period. Galileo worked at the problem for decades. It wasn’t until 1641 — when he was 77, blind, and under house arrest at his villa at Arcetri outside Florence, sentenced by the Inquisition — that he finally conceived the design. He described a pinwheel escapement mechanism to his son Vincenzio from memory; Vincenzio drew it up. Neither of them lived to build it. Galileo died in January 1642; Vincenzio in 1649. The drawings gathered dust.
Christiaan Huygens, working independently in The Hague, built the first functioning pendulum clock in 1656 — seventy-three years after that draft blew through the nave at Pisa. His clock reduced daily error from fifteen minutes to under a minute. Pendulum clocks would remain the world’s most accurate timekeepers for three hundred years, until quartz.
The man who found time’s steady beat inside a swinging lamp never heard it counted in a clock. Huygens built the first one fourteen years after Galileo’s death, and the quest for the next decimal place in timekeeping has not stopped since.
Sources
- Galileo’s escapement — Wikipedia — Galileo’s 1641 design at Arcetri, Vincenzio’s drawings, the comparison with Huygens’s 1656 clock.
- The invention of the pendulum clock — Seiko Museum Ginza — isochronism, the pulsilogium, daily error before and after, Huygens’s clock.
- Galileo and the pendulum clock — Royal Holloway, University of London — Viviani’s account of the Arcetri conversation and the 1641 escapement design.
- Pendulum — Wikipedia — the physics of isochronism, period dependence on length and gravity.