6.2 Galileo and the pendulum

Galileo was taught Aristotelian physics at the university of Pisa. But he quickly began questioning this approach. WhereAristotle had taken a qualitative and verbal approach, Galileo developed a quantitative and mathematical approach. Where theAristotelians argued that heavier bodies fell faster than lighter ones in the same medium, Galileo, early in his career,came to believe that the difference in speed depended on the densities of the bodies. Where Aristotelians maintained that inthe absence of the resisting force of a medium a body would travel infinitely fast and that a vacuum was thereforeimpossible, Galileo eventually came to believe that in a vacuum all bodies would fall with the same speed, and that this speedwas proportional to the time of fall.

Because of his mathematical approach to motion, Galileo was intrigued by the back and forth motion of a suspendedweight. His earliest considerations of this phenomenon must be dated to his days before he accepted a teaching position at theuniversity of Pisa. His first biographer, Vincenzo Viviani , states that he began his study of pendulums after he watched a suspended lamp swing backand forth in the cathedral of Pisa when he was still a student there. Galileo's first notes on the subject date from 1588, buthe did not begin serious investigations until 1602.

Galileo's discovery was that the period of swing of a pendulum is independent of its amplitude--the arc of the swing--the isochronism of the pendulum.

The motion of the pendulum bob posed interesting problems. What was the fastest motion from a higher to a lower point, along acircular arc like a pendulum bob or along a straight line like on an inclined plane? Does the weight of the bob have an effecton the period? What is the relationship between the length and the period? Throughout his experimental work, the pendulum wasnever very far from Galileo's thought. But there was also the question of its practical use.

A pendulum could be used for timing pulses or acting as a metronome for students of music: its swings measured out equaltime intervals. Could the device also be used to improve clocks? The mechanical clock, using a heavy weight to provide the motivepower, began displacing the much older water clock in the High Middle Ages. By incremental improvement, the device had becomesmaller and more reliable. But the accuracy of the best clocks was still so low that they were, for instance, useless forastronomical purposes. Not only did they gain or lose time, but they did so in an irregular and unpredictable manner. Could apendulum be hooked up to the escape mechanism of a clock so as to regulate it?

In 1641, at the age of 77, totally blind, Galileo turned his attention to this problem. Vincenzo Viviani describes the events as follows, as translated by Stillman Drake :

One day in 1641, while I was living with him at his villa in Arcetri, I remember that the idea occurred to him that thependulum could be adapted to clocks with weights or springs, serving in place of the usual tempo , he hoping that the very even and natural motions of the pendulumwould correct all the defects in the art of clocks. But because his being deprived of sight prevented his makingdrawings and models to the desired effect, and his son Vincenzio coming one day from Florence to Arcetri, Galileotold him his idea and several discussions followed. Finally they decided on the scheme shown in the accompanying drawing,to be put in practice to learn the fact of those difficulties in machines which are usually not foreseen in simpletheorizing.