You often see statements to the effect that “Galileo invented the pendulum in 1581, greatly improving the accuracy of clocks.” This is simply not true. Instead, sometime in the 1580s or later, Galileo, observing lamps swinging and other motion of this type, decided to claim that the time of a pendulum’s swing (its period) depends only on the length, not the size (amplitude) of the swing.
Some historians of science think that Galileo did not actually believe this statement (it is not true), but that he claimed it because it seemed more dramatic than the truth, which is that for small amplitudes the period is very close to dependent only on the length of the pendulum. Galileo suggested that this concept might be used to make a more accurate clock, but he never got around to constructing one (although his son experimented with pendulum clocks).
Interestingly, Leonardo da Vinci seems to have had the same idea a century earlier than Galileo, but he never got around to trying to build a clock using a pendulum either. Since the period of the pendulum varies somewhat with the amplitude, a clock using a pendulum for regulation needs a compensating mechanism. Unwittingly, Galileo suggested the idea that led to the first good compensating method. He called the attention of mathematicians to a curve called the cycloid, which is the curve generated by a point on the rim of a rolling wheel. Mathematicians in the 17th century were very interested in the properties of the cycloid.
In a famous incident in 1658, the mathematician Blaise Pascal, who had otherwise retired from mathematics for religious reasons, used solving the properties of the cycloid to keep his mind off a toothache. He published the results, which led to the realization by Christiaan Huygens that the cycloid is a isochrone (a.k.a. tautochrone) –– a curve through which an object falls in the same amount of time no matter how high. Again, the myth and the reality are somewhat different. The myth is that Huygens was unable to make a good pendulum clock until he found the tautochrone.
In reality, Huygens made the first good pendulum clocks with no thought of the cycloid. When he showed that the cycloid was a tautochrone –– two years later –– he made a few clocks that used this idea, but they were clumsy and did not work as well as those that just used a pendulum with small amplitude. Pendulum clocks that did not employ the cycloid were relatively accurate, but keeping the beat exact was still a problem. A few years later a series of little-known English craftspeople found various ways to handle the problems of the pendulum. William Clement developed an escapement that kept the amplitude of the swing small. Nearly 50 years later George Graham developed an escapement that nudged the pendulum at one point and braked it at another to make the whole operation more accurate. In addition to the ordinary pendulum, a different kind of pendulum, called a balance wheel, was used in small clocks from early in the 15th century.
Subject to the same problems as the ordinary pendulum, the balance wheel also needs compensation to make it accurate. George Graham found a way to do this, and 50 years later another obscure Englishman, Thomas Mudge, found a better way, one used in balance-wheel watches and small clocks to the present day. Even if Galileo had been correct in asserting that the pendulum swing depends only on its length, the pendulum could not be a perfect timekeeper because its length varies with temperature. The same English craftspeople who found ways to correct the variation caused by changing amplitude also found clever ways to correct the variation caused by temperature changes.
By the middle of the 18th century, the best pendulum clocks kept nearly perfect time, losing seconds per month. But the accuracy of these mechanical pendulum clocks was very much superseded in the 20th century –– first by accurate electric clocks, then by clocks in which the expansion and contraction of a quartz crystal acted as the “pendulum” for an electric clock, and finally by clocks that used the natural vibrations of molecules as pendulums, the so-called “atomic” clocks.