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It has been said that Galileo’s experimentation with pendulums began when he observed an overhead light fixture swaying back and forth one afternoon, with some regularity. Published in “Dialogues Concerning Two New Sciences” in 1638, one of Galileo’s simplest experiments was how he found the period of the pendulum to be completely independent of the amplitude: a concept that became better known as isochronism.
Galileo actually introduced pendulum motion as a subset of free fall in his study. Galileo’s line of thought was that as he observed two objects of different mass but similar material dropped from the same height, they hit the ground at approximately the same time, but he wanted to confirm that there was absolutely no difference in their arrival times. First he tried to do this by reducing the heights the objects were dropped from, and then by using shallow inclined planes (to further reduce the speed at which the objects were traveling) using components – another revolutionary development. His hope here was to increase the time it took for the objects to complete their motion and to minimize air resistance. Though this notion was valid, he also found that friction from the plane would interfere and possibly alter his results. Here is where the pendulum came into play. Galileo selected to very different materials; cork and lead, attached each to string and hung them from overhead. To Galileo, he had now created what was essentially a frictionless, curvilinear inclined plane. Here is where some of Galileo’s assumptions fall a little short.
Galileo was absolutely certain that gravity accelerated all objects, regardless of their weight, in the same way. He was also absolutely certain that all pendulums, released from the same angle, regardless of their weights, would have the same decent times. His “findings” were described in the form of an experiment, which was unlikely to have ever been performed in reality. From Drake’s 1974 translation of “Two New Sciences,” Galileo was found to have stated (presented as having been said by Salviati):
Removed from the vertical, these were set going at the same moment, and falling along the circumferences of the circles described by the equal strings that were the radii, they passed the vertical and returned by the same path. Repeating their goings and comings a good hundred times by themselves, they sensibly showed that the heavy one kept time with the light one so well that not in a hundred oscillations, nor in a thousand, does it get ahead in time even by a moment, but the two travel with equal pace. (Drake, p. 87)
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As we now know, and can (and have – see Erlichson, 2006) recreated in experiments, the above situation is incorrect. Though Galileo acknowledged that the oscillations of the lighter material would damp more quickly, he failed to mention that the two pendulums would ultimately end up out of synchronization. Interestingly, this was a result of Galileo’s acceptance of previous theories. Had actual experimentation taken place, he would have found quite a different result.
Given the observable, testable and sometimes mathematical issues with Galileo’s claims, many of them have become a central part of what we refer to as the Scientific Revolution. Highly involved in this debate is Aristotelian Guidobaldo del Monte (1545 – 1607). Guidobaldo was a great mathematician and creator. He translated a number of Archimedes and published works on mechanics, mathematics and timekeeping. Interestingly enough, he was also the individual responsible for helping secure Galileo’s major jobs at both Pisa University and Padua University.
Given the observable, testable and sometimes mathematical issues with Galileo’s claims, many of them have become a central part of what we refer to as the Scientific Revolution. Highly involved in this debate is Aristotelian Guidobaldo del Monte (1545 – 1607). Guidobaldo was a great mathematician and creator. He translated a number of Archimedes and published works on mechanics, mathematics and timekeeping. Interestingly enough, he was also the individual responsible for helping secure Galileo’s major jobs at both Pisa University and Padua University.
Throughout Galileo’s research and experimentation, he and del Monte exchanged many communications on their studies. Sometimes contrary to Galileo, del Monte firmly believed that theory and application should not be separated. In one publication he noted, “For mechanics, if it is abstracted and separated from the machines, cannot even be called mechanics” (Drake & Drabkin 1969, p. 245).
Galileo and del Monte’s largest difference of opinion revolved around Galileo’s pendulum experiments as previously described, as del Monte felt that Galileo was a brilliant mathematician but poor physicist. Galileo believed that pendulum motion was “tautochronous” or that the curve where a body falling freely reaches the lowest point in the same time, regardless of where on the curve it was released. Del Monte argued this notion with experiments involving balls rolling inside an iron hoop. Galileo simply dismissed these tests as having been ill-formed and thus incorrectly executed.
The banter continued and so did the exchange of ideas. In 1602, Galileo published his ideas of isochrony based on chords within a circle. He noted two points:
1. That in a circle, the time of descent of a body freefalling along all chords terminating at the nadir (base), is the same regardless of the length of the chord.
2. In the same circle, the time of descent along two composite chords is shorter than along a single chord joining the beginning and end of the composites, even though the composite route is longer than the direct route.
Though Galileo had very strong beliefs that his isochrony of circular motion, he was ultimately incorrect, though for small amplitudes, most of his findings hold. Christiaan Huygens was able to show that the motion not circular but cycloid is isochronic, and to prove that at small amplitudes circles and cycloids agree. This proof was made a few decades Galileo’s claims. Still, in 1633 Galileo stubbornly tried to argue his tautchrony as follows:
Galileo and del Monte’s largest difference of opinion revolved around Galileo’s pendulum experiments as previously described, as del Monte felt that Galileo was a brilliant mathematician but poor physicist. Galileo believed that pendulum motion was “tautochronous” or that the curve where a body falling freely reaches the lowest point in the same time, regardless of where on the curve it was released. Del Monte argued this notion with experiments involving balls rolling inside an iron hoop. Galileo simply dismissed these tests as having been ill-formed and thus incorrectly executed.
The banter continued and so did the exchange of ideas. In 1602, Galileo published his ideas of isochrony based on chords within a circle. He noted two points:
1. That in a circle, the time of descent of a body freefalling along all chords terminating at the nadir (base), is the same regardless of the length of the chord.
2. In the same circle, the time of descent along two composite chords is shorter than along a single chord joining the beginning and end of the composites, even though the composite route is longer than the direct route.
Though Galileo had very strong beliefs that his isochrony of circular motion, he was ultimately incorrect, though for small amplitudes, most of his findings hold. Christiaan Huygens was able to show that the motion not circular but cycloid is isochronic, and to prove that at small amplitudes circles and cycloids agree. This proof was made a few decades Galileo’s claims. Still, in 1633 Galileo stubbornly tried to argue his tautchrony as follows:
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Take an arc made of a very smooth and polished concave hoop bending along the curvature of the circumference ADB, so that a well-rounded and smooth ball can run freely in it (the rim of a sieve is well suited for this experiment). Now I say that wherever you place the ball, whether near to or far from the ultimate limit B … and let it go, it will arrive at the point B in equal times … a truly remarkable phenomenon. (Galileo 1633/1953 p. 451 in Matthews, 2004).
Galileo’s world was largely one of philosophy. He felt no need to produce experiments as he relied on the mathematics and theory to prove his beliefs. When experimentation lacked agreement, particularly done by someone else, he was known to find sources of error to account for the disagreement, but rarely questioned his own work on paper.