The problem of falling
For nearly two millennia, physics was governed by Aristotle's assertion that heavy objects fall faster than light ones. This idea, proposed around 330 BCE, was accepted without rigorous experimental proof. It took Galileo Galilei in the early 1600s to challenge this long-held belief. The core problem was that free-falling objects moved too quickly for the time-keeping technology of the 17th century to measure accurately.
To solve this, Galileo designed an experiment that "diluted" or slowed down gravity. He used an inclined plane. His insight was that a ball rolling down a gentle slope is still subject to gravity's acceleration, but at a rate slow enough to be measured. He described the apparatus in his 1638 book, Discourses and Mathematical Demonstrations Relating to Two New Sciences. The ramp was a wooden beam about 12 cubits long (roughly 6.7 meters or 22 feet). Along its length, he carved a smooth groove and lined it with parchment to reduce friction. A hard, polished bronze ball was then rolled down this channel.
Timing is everything
The most ingenious part of Galileo's experiment was his time-keeping method. Lacking a pendulum clock or a modern stopwatch, he invented a water clock. This was a large container of water placed in a high position, with a small pipe at the bottom that let out a thin stream of water. To time a trial, he would collect the escaping water in a small glass for the duration of the ball's roll. Afterwards, he weighed the collected water on a very accurate balance. The weight of the water was directly proportional to the time elapsed. He repeated each run many times, and his measurements were so consistent that he claimed an accuracy to within one-tenth of a pulse beat.
He released the ball from different points along the ramp—one-quarter, two-thirds, and its full length—and measured the time it took to reach the bottom. The data revealed a clear mathematical relationship: the distance traveled is proportional to the square of the time (s ∝ t²). This meant that if a ball traveled one unit of distance in the first interval of time, it would have traveled four total units of distance after two intervals of time, and nine units after three. This simple law describes uniform acceleration. Importantly, the law held true for balls of different weights, directly contradicting Aristotle.