4.2 Experiment or Hoax?

Marin Mersenne, a contemporary of Galileo, was a friar and scientist who corresponded regularly with many of the leading scientists of his day. He had seen references to the experiment on the inclined plane already before the publication of Two New Sciences and had tried to perform it himself. Although Galileo had mentioned the experiment in other places, he had never given a description as detailed as that in his last book. We may even suspect that the detailed description there was an answer to Mersenne's criticism. As Mersenne had not succeeded in reproducing the experiment, he regarded it as incapable of founding a science. He even doubted that Galileo had performed it at all [3].

Perhaps inspired by Mersenne's failed attempts, the philosopher Alexandre Koyré provided outspoken criticism of Galileo's experiment in a 1953 paper [4]. Koyré was an eager advocate of the view that theory must precede observation in science and, judging from the paper, he even seems to have thought that empirical investigation was less dignified than theoretical speculation. Galileo's water clock was too primitive to have played a central role in the experiment, he thought. It lacked both precision and theoretical refinement. Indeed, he thought that the whole experiment was too crude to provide useful results. This was partly because he thought that Galileo had based it on faulty assumptions, and partly because of the “amazing and pitiful poverty of the experimental means at his disposal”. He even ridiculed the experiment:

A bronze ball rolling in a “smooth and polished” wooden groove! A vessel of water with a small hole through which it runs out and which one collects in a small glass in order to weigh it afterwards and thus measure the times of descent […]: what an accumulation of sources of error and inexactitude!

It is obvious that the Galilean experiments are completely worthless: the very perfection of their results is a rigorous proof of their incorrectness [4].

In other words, he accuses Galileo of academic dishonesty – of fabricating data to confirm a mathematical relationship that he had obtained by means other than experimentation. He also declares that this must be the reason why Galileo does not specify a concrete value for the acceleration of gravity.

Koyré points out that it is wrong to assume that a ball rolling down an inclined plane is equivalent to a body gliding down the plane without friction. Due to the ball's rotational inertia, the rotation requires energy and this affects the speed. His most serious criticism, however, is the assertion that Galileo lacked the means to measure time with the required precision. Rather than investigating the water clock Koyré seeks to prove his point by explaining how difficult it is to measure time with what he considered to be a much more refined instrument: a pendulum.

Galileo himself had established that a pendulum of a certain length has a constant period of oscillation, meaning that a cycle of back and forth swings always takes the same time. This fact is said to have dawned on Galileo while looking at a swinging candelabra in the cathedral of Pisa and timing the motion with his own pulse. It is also known that he established it by experimenting with pendulums that had the same length but different weights. Despite this, Koyré emphasizes that Galileo had arrived at the result “first and foremost by hard mathematical thinking”. In his eyes this seemed to make the pendulum a more worthy timekeeper than the water clock, and he thereby thought it rather strange that Galileo had not used it in his experiments with the inclined plane. The constant period made the pendulum a very suitable technology for timekeeping.

Figure 4.2 Mersenne found that the bob of the pendulum fell to its bottom position (left) in the same time that it would cover the same height in free fall (right). Something was obviously wrong with his measurements.

Father Mersenne had used a pendulum to measure time in his own experiments with free fall. According to him, the period of his pendulum had been exactly one second. When comparing his times of free fall with times measured by Galileo, Mersenne found large differences in the absolute numbers. Mersenne's measurements, which Koyré describe as progress compared to those of Galileo, also implied another, rather counter-intuitive result. Mersenne was forced to admit that the bob of the pendulum seemed to travel from its turning point to the bottom, along the curved path in Figure 4.2, in the same time that it would cover the same height vertically in free fall. Clearly, there must have been something wrong with these measurements. And using a pendulum to measure falling times in absolute units is challenging, to say the least. Those who have been working in a laboratory will have noticed that some people have a greater aptitude than others for standing up to such challenges. Koyré freely admits that Mersenne does not seem to have been one of them but he chooses not to pay this fact much attention. His preferred conclusion is rather that “precision couldn't be achieved in science and that its results were only approximately valid” [4]. If time could not be measured with a refined pendulum, it certainly could not be measured with a primitive water clock.

Koyré goes on to describe the work of the Jesuit scientist Riccioli, also known for being a persistent anti-Copernican (presumably, he may have felt compelled to hold that view). Needing an absolute timekeeper to determine the rate of acceleration in free fall he tried to build a pendulum with a period of exactly one second. Using a water-glass, he was able to confirm Galileo's finding that the period of the pendulum was constant. To calibrate the period, however, he needed to use the only exact time reference there was: the motion of the celestial bodies. First he used a sundial to count the oscillations for six consecutive hours. The result was disastrous, so he built a new pendulum and counted its beats for twenty-four hours, from noon to noon. Still dissatisfied, he adjusted the length of the pendulum and made a new attempt. To increase the measurement precision he now started counting when a certain star passed the meridian line and continued until it passed the line again, the following night. As the period still was not right, he made several new attempts. Despite heroic efforts, wearing down the patience of his assistants, he never managed to get the period right. Measuring time accurately with a pendulum was simply very difficult.

To finish the story off, Koyré turns his attention to Christiaan Huygens, the famed inventor of the pendulum clock. The work leading up to this invention included series of experiments but Koyré emphasizes the theoretical aspects. Huygens’ clock is important, he says, because “it is the result not of empirical trial and error, but of careful and subtle theoretical investigation of the mathematical structure of circular and oscillatory motions”. With his clock, Huygens could determine the exact period of a pendulum that he had used in his own experiments. On the other hand, Huygens did not have to measure the rate of acceleration in free fall, because through his work he had found a formula that related the period of a pendulum to its length and the acceleration of gravity, g. Using a pendulum and the clock he had invented, Huygens could thereby determine the value of g that is still accepted. This is what Koyré perceived as the final purpose of the Galilean experiment.

In Koyré's eyes this closed the circle. Through Huygens’ theoretical ingenuity there was, at last, a timekeeper with sufficient precision to determine the rate of acceleration in free fall. The argument is wrapped up in the following moral: “not only are good experiments based upon theory, but even the means to perform them are nothing else than theory incarnate” [4].