Using a water clock, Galileo measured the time it took for the ball to roll a known distance down the inclined plane. After many trials, he observed that the amount of time it took for the ball to roll down the entire length of the ramp was equal to double the amount of time it took for the same ball to only roll a quarter of the distance. In other words, if you doubled the amount of time that the ball was rolling, it would travel four times as far.

Through this experiment, Galileo concluded that if an object is released from rest and gains speed at a steady rate (as it would in free-fall or when rolling down an inclined plane), then the total distance, s, traveled by the object is proportional to the time squared needed for that travel:

$s\propto {t}^{2}$

The proportionality constant is exactly half of the acceleration a. For a ball rolling down an inclined plane, this acceleration relates to the gravitational acceleration g via

$a\=\frac{gh}{l}comma;$

where $h$ and $l$ are the height and length of the inclined plane. The resulting relationship

$s\=\frac{gh}{2l}{t}^{2}$

allowed Galileo to determine the value of the gravitational acceleration $g\.$