# Did Galileo perform an experiment at the Leaning Tower of Pisa?

Galileo's pupil Viviani said that Galileo dropped unequal weights from the Leaning Tower of Pisa and observed them to take equal times to hit the ground. Galileo's own writings do not describe such an experiment, but it is clear that he did quantitative experiments with balls rolling down inclined planes, which would make it natural to extrapolate to the same result for falling objects. (I suppose it's not a matter of pure extrapolation, since the acceleration of a sphere rolling without slipping is strictly less than $$g\sin\theta$$.) Wikipedia says that most historians of science think there was never any more than a thought experiment (e.g., Koyre seems to have thought this), but that Drake disagrees.

What would be the arguments for and against the actual existence of the experiment? What did Viviani claim Galileo actually did? (Apparently in some versions of the story, Galileo dropped his objects near the heads of professors emerging from their lectures!)

Is the only argument about whether the experiment took place at the Leaning Tower, or is there doubt about whether it happened at all? Galileo does describe such an experiment, in a line spoken by Simplicio:

But I, Simplicio, who have made the test, can assure you that a cannon ball weighing one or two hundred pounds, or even more, will not reach the ground by as much as a span ahead of a musket ball weighing only half a pound, provided both are dropped from a height of 200 cubits.

There seems to be room for doubt, since it's fictionalized as a dialog, and the words are spoken by Simplicio rather than by Salviati, who is Galileo's mouthpiece.

As a side issue, there appears to have been some controversy about what Aristotle had really claimed about this. Apparently there is a case to be made that he was only talking about terminal velocities. For translations of the relevant passages from Aristotle see this link.

• This letter from Cajori also seems relevant: books.google.com/… He argues that no, Galileo doesn't name the place: "But what other locality in Pisa would have been as favorable?" – Ben Crowell Feb 7 '15 at 20:41
• There is also "Vincenzio Renieri and the Law of Falling Bodies," Curtis V. Smith, kckcc.edu/docs/default-source/ejournal/… In De Motu, Galileo says that he dropped lead and wood weights from "a high tower" and that the lead weight hit first. – Ben Crowell Feb 7 '15 at 20:49
• You gave a rather complete account of "who said what" about this experiment. What else to you hope to find out with this question? Galileo used inclined planes instead of a tower, because this is a much more reasonable experiment. – Alexandre Eremenko Feb 7 '15 at 20:57
• @AlexandreEremenko: I don't have any confidence that my information is complete or that I understand the possibly relevant arguments, which seem to be complex. – Ben Crowell Feb 7 '15 at 21:34
• I don't see what's wrong with the question. If I understand right, Ben's saying that he has some information about it, but doesn't have a complete argument for or against it. What's wrong with that? – HDE 226868 Feb 7 '15 at 22:34

See the detailed discussion on :

In 1641 Galileo’s successor on the chair of mathematics at Pisa, Vincenzo Renieri, experimented with bodies made of different materials dropped from the leaning tower, finding that a lead ball fell faster than a wooden one.

Drake discuss at lenght about the fact that at that time Viviani was assistant and amanuensis of the old and blind Galileo; thus, it is quite certain that the lost answer to Ranieri was dictated to Viviani by Galileo.

If so, the lost reply to Renieri may include the account of the “real” Galileo's early Pisan experiment; if so, Viviani's recollection can be grounded by the original Galileo's words.

Drake's conjecture is plausible, but we still lack a definitive proof.

Check out the wikipedia article where they explain:

At the time when Viviani asserts that the experiment took place, Galileo had not yet formulated the final version of his law of free fall. He had, however, formulated an earlier version which predicted that bodies of the same material falling through the same medium would fall at the same speed.

This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to their weight. While this story has been retold in popular accounts, there is no account by Galileo himself of such an experiment, and it is accepted by most historians that it was a thought experiment which did not actually take place.

I don't actually agree with this - its Aristotelianism that taught this; and not Aristotle; one ought to recall that Aristotle was at the very beginning of science and he had was commenting on the problem of change, and he had elucidated that change had several modes, and the predominant mode of change was motion - this was a huge advance for the time and this is why his name is justly revered; that he got details wrong is not a good reason to knock him, as physicists often do today - after all, by this basis we could say that Newtons theory of gravity was wrong in the light of Einstiens theory - but this is not the proper mode of historical assessment as it is ahistorical.

An exception is Stillman Drake, who argues that it took place, more or less as Viviani described it, as a demonstration for students.

They also remark that

Galileo arrived at his hypothesis by a famous thought experiment outlined in his book On Motion.

and

This experiment runs as follows: Imagine two objects, one light and one heavier than the other one, are connected to each other by a string. Drop this system of objects from the top of a tower. If we assume heavier objects do indeed fall faster than lighter ones (and conversely, lighter objects fall slower), the string will soon pull taut as the lighter object retards the fall of the heavier object. But the system considered as a whole is heavier than the heavy object alone, and therefore should fall faster. This contradiction leads one to conclude the assumption is false.

In other words, the scholarly consensus is that he came to his hypothesis/conjecture about motion through a thought experiment based on continuity and symmetry rather than through direct experiment; and nor had he directly verified it. Given this, it seems likely that the notion that Galileo actually carried out this experiment at the leaning tower of Pisa is a type of scientific myth akin to urban myths; it really ought to have died a death by now.

On a personal note, I came up with more or less the same idea just as I was finishing high school; which suggests to me other people may have had the same idea; take three balls of plasticine of the same size and hold them above the earth at the same height and at equal distances from each other - obviously they will hit the ground at the same time. Then move the middle ball a little towards the left and repeat the experiment; obviously again they will hit the ground at the same time; eventually, the middle ball will be right next to the left ball; repeating the experiment again will show that the balls again hit the surface of the earth at the same time; now squeeze the middle plasticine ball into the left - again repeating the experiment we see there is no difference; eventually the left and middle ball merge and we have a ball twice the size of the right and they both fall at the same rate.

Galileo used weights and a string attached between them. as one can see, the argument hinges on symmetry and continuity (and the observation that how something falls does not actually vary by location).

Thinking about it, I think I used stones originally...