Koyré has this book in French studies, Galilean Studies. My French is so bad I won't try to pronounce it, but you can sort of picture it. And argued in that, very outspokenly, about Galileo in general. Galileo didn't really do experiments, he said. Galileo was a Platonist. He thought everything could be done by reason.
He was just like Descartes. His experiments are really all thought experiments. Don't take them seriously, and about this one, he said, anyone knows, you can't measure time this way. This can't be right. You can't put a water clock into these kind of measurements. We shouldn't take them seriously.
That started the whole idea that Galileo didn't really do experiments and it's Stillman Drake responding to that. Time and again showing Koyre wrong but there's a beautiful paper that appeared in Science Magazine. I think the next page will give the date. No it didn't. I think it's 69, but you can look, I can look.
61. Good. Tom Settle, then at Brooklyn Tech, decided to redo this experiment. Now, I don't use the word replicate because I'm dubious whether experiments are ever replicated. Reproduced is a reasonable word, but to literally replicate, you may have to use the same equipment, you may have to have the same day.
But he reproduced the experiment, so he trained his students and him with a water clock. Discovered he could do very, very well against a stopwatch once you had some training at it and got careful with it. He then re-does the experiment with multiple trials going all the way down, these are the individual trials.
These are the averages of the trials and these are the calculated values. And he is indeed, as Galileo put it, within a pulse beat. So what, and I put this whole paper on reserve, on supplementary materials. A beautiful paper showing that, indeed, whether Galileo could not only have done the experiment, he could have done the experiment quite, quite well, and gotten a very good result.
So, that's put to rest. There's every reason to think he did the experiment. What about the low inclination? Well, that's a different problem and I put this paper on reserve as well. What Hahn has done is simply do an exaggerated version. When Kuhn and I taught this course, it was Kuhn's standard course, but I did the Newton part.
We got to the inclined plane experiment and I made the remark, Tom, it's rolling instead of falling. And he actually said to me as a PhD in Physics, what difference does it make? And I can't believe, well, he had not actually thought through what the problem was in Galileo's experiment.
The problem is, if you're rolling, and I've now done it the modern way. You get five-sevenths of the speed you get in fall, if it's a sphere and it's rolling on its bottom. If it's rolling in a V-gutter or a wedge you get these formulas which are out of Hahn's article, which again is put in supplementary material.
So if you are rolling all the way you get a nice clean 1, 3, 5, 7 progression. But it is not the same velocities as in vertical fall, and they had no way of recognizing that. They did not recognize that. They had ways you'll see in a moment of recognizing it but they didn't recognize it.
In fact next week you'll see Galileo had every reason to recognize it and didn't recognize it. Because he didn't experiment and expose this and then decided not to publish that experiment, for whatever reason. Now go back to Cory's question, what happens is you go up in inclination. It's very hard to maintain perfect rolling for the reason you gave, friction isn't so uniform.
So if you bounce even slightly you get a domain of going in pure fall and then you resume rolling and you go back and forth and its a mixed domain. And it's next to impossible to control. Okay, you can go to very, very heavy weights. You can try to do things, but it's very hard to control.
We don't know which of these he did, but I'll show you next week reason to think he was doing it with kind of trough at the top. He describes the trough, he describes the vellum he put in it to keep the friction smooth, to keep it smooth all the way.
They didn't understand what friction was doing here, but this now, let me make the point. I've got plenty of time, I'll be able to do everything I want. What we've got here is go back to my discussion of parameters. We have the need to make a distinction between two domains, rolling and falling.
The need is imposed on us by empirical considerations, not something you see at first sight. They didn't see it, and they didn't see it for a long time, is the simple answer. Okay so that's explains retrospectively, not too far retrospectively, 1693, it's clear, retrospectively, why Mersenne got lousy results.
Galileo got good results by staying at very low angles of inclination, and simply didn't report what happens at higher angles of inclination. Either because he didn't do it or he didn't get good enough results, and chose not to report them. For those who know, I actually defend this one.
Millikan threw out the measurements of charge that didn't fit nicely with the others, and that's what Galileo was doing, throwing out. So what do we have here? We have 1, 3, 5, 7, actually takes place in a well designed experiment, therefore what? I leave that for you to conclude as part of your second paper.
But it's something to actually get the 1, 3, 5, 7 progression to within a heartbeat. That's a spectacular result, not to be expected. So back, mid 1990s I offered a $200 reward for any historian who could find me a published paper before 1765 that explained the difference between rolling and falling from a specific experimental result showing the contrast.
I still have not seen such an experiment, which is a comment you'll see in a couple of moments, a comment about experimental practice. Because by 1651 it was an easy experiment to do, and either people didn't did it, and didn't like the results and didn't report it, or they didn't do it.
Either way it's a comment about experimental practice. Nico Berloni Maylee got the $200 because he found these two pages in Huygens's notebooks published in this form, where Huygens in early 1690s, they can't say which year, 92 or 93, figured out the difference between rolling and falling. You'll see later why he was in a perfect position to do it.
He was in a singular position to see that some of the motion goes into rolling, and you'll notice he's very close to the right number. He says roughly seven to five. He can't do the calculus needed to get the exact seven to five, so he's only approximating it, but approximating it to the right numbers.
And he also figured out that the shape makes a difference. What we call these, are moments of inertia, and the different moments of inertia give you different ratios for them. So 1693, somebody actually figured it out, but they didn't publish. So the only place I know for sure that it's 100% clear is in Euler's 1765 publication on rigid body motion, where it just pops out.
It's almost clear the in 1750 paper. I think he knows a lot about Euler on this. It's almost clear from the 1750 paper, but the 1765 monograph, it's completely clear. But, really, it took that long to figure out the difference between rolling and falling? Okay, that's a striking thing.