4.3 Reconstructing the Experiment

Koyré leaves us with a couple of central questions. Could Galileo have conducted the experiment with his limited means? And was the aim really to measure the acceleration of gravity? In response to the criticism, Thomas Settle reconstructed the Galilean experiment in 1961. Then a graduate student in the history of science, he staged the experiment in the common living room he shared with other students [1]. The purpose was to get a better appreciation for some of the problems that Galileo had faced. Both the equipment and the procedures were kept as close as possible to Galileo's description in Two New Sciences. It turned out that he could easily reproduce the results with the precision claimed by Galileo [3].

Settle points out that Koyré had fundamentally misunderstood the purpose of the experiment. It was true that Galileo's apparatus was not capable of establishing the gravitational constant, but he was not trying to do that. He was interested in the ratios given in Equation 4.1. He was thereby not dependent on measuring time in standard units and could be completely arbitrary in his choice of measures. Furthermore, there had been little justice in Koyré's criticism of Galileo failing to account for the rotational inertia of the ball. Not only did this problem not exist in his mind, in this experiment it was even irrelevant. As the factor that accounts for rotational inertia is a constant, it does not affect the proportionalities of the law. Taking the ratios in Equation 4.1, the rotational inertia of the ball cancels out of the equation [3].

His reconstruction is interesting from many points of view. One is to see that it was technically feasible to establish the law of free fall from the experiment. The actual performance of an experiment also brings out many more of its dimensions than reading about it. Conceiving an experiment is only part of the effort. A number of practical and conceptual problems must be solved to bring it to full maturity. For example, as we noted in connection with Mersenne's measurements, the operator is clearly an integral part of the experiment. Settle notices the importance of being allowed a few practice runs before each test to obtain consistent results. It would be valuable, he writes, to have a more detailed account both of Galileo's thinking and practical work around the experiment:

There is […] a fascinating and vastly important body of knowledge concealed in the “conceiving” and “bringing to maturity” of both the theoretical and empirical aspects of this experimentation […] For each step of original work we would like to know the mistakes and dead ends, the contributions and limitations of the existing technology and mathematics, the many conceptual aids as well as hindrances inherited from his contemporaries, and the nature and significance of his own predispositions.

Settle did his best to choose equipment and procedures that were no better than those available to Galileo. He used an 18-foot pine plank and cut a 1/4-inch groove in it with a circular saw. After sanding it he applied wood filler and rubbed the surface with wax to make the edges hard and smooth. Although there were irregularities where knots or the grain crossed the groove, he made no further attempts to make the edges exactly parallel. Instead of Galileo's bronze ball he used a standard billiard ball and a steel ball. An ordinary flowerpot was used as a water container for the timekeeper. He threaded a small glass pipe through its bottom hole for the outflow. Its upper end was positioned high enough in the pot for him to cover it easily with a finger while his palm rested on the rim of the pot. Lifting the finger, the water flowed out into a graduated cylinder under the pot and was “weighed” by reading its volume in milliliters. For each run, Settle placed a wooden block at a predetermined distance down the slope of the plank and filled the pot with water. He simultaneously released the ball and lifted his finger from the pipe. At the sound of the ball striking the block he replaced the finger and the “time” of the descent was read in milliliters on the graduated cylinder. He estimated that this method for measuring the time was about five times as crude as the one available to Galileo.

The time measurements were the most difficult part of the experiment. A uniform water flow had to be kept at least for the duration of the longest readings. He also found it necessary to practice releasing the ball and the water flow at the same time, and stopping the flow immediately at the strike of the ball. The operator “must spend time getting the feel of the equipment, the rhythm of the experiment”, he said. Sticking to techniques available in Galileo's time, he confirmed that the water flow was uniform by timing it with a pendulum. He made the pendulum from the billiard ball and kept the length a little less than a meter. This would make it beat at about the same rate as the pulse, which was appropriate since Galileo stated his precision in terms of “pulse beats”.

Watching the shadow of the bob against vertically lined paper he could accurately lift and reset his finger on the pipe at the end of a beat. This procedure showed that the water flow was indeed constant within one tenth of a second. When rolling the ball he took several readings for each distance, just as Galileo had described, and sight-averaged them. (The technique of calculating means to get more precise values than single measurements was not established in Galileo's days.) With this simple method, even the largest deviation from the theoretically expected value was less than a tenth of a second.

Settle emphasized the simplicity and ease with which his results were obtained. He said that he maintained a “deliberately cavalier attitude towards procedures and measures” because he “wanted to give ‘error and inexactitude’ every reasonable chance to accumulate. And yet they did not” [3].

Not only did Settle highlight Koyré's misunderstanding of the purpose of the experiment. The reconstruction also showed that it was technically feasible for Galileo to make the measurements. But one central question remained unanswered. Was it an experiment? Historians of science have regarded the inclined plane as a way for Galileo to demonstrate the truth of a law that he had obtained by abstract reasoning, not by explorative tests. As we will see, a page in Galileo's notebook from 1604 casts some light over this question.