Philosophy 167: Class 6 - Part 13 - Inclined Plane Experiments- Galileo, Mersenne, and the Necessity of Low-Angle Inclines

Smith, George E. (George Edwin), 1938-


  • Synopsis: Examining the evidence provided by Galileo's inclined plane experiments

    Opening line: 'Now we look at his inclined plane experiment, okay?'

    Duration: 6:40 minutes.

    Segment: Class 6, Part 13.
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Now we look at his inclined plane experiment, okay? What he does is to announce in Day Two of the Dialog On The World Systems [Third Day of Two New Sciences] that he's done inclined plane experiments and found indeed that they agree with naturally accelerated motion, that is they have a one-three-five-seven progression.
Marin Mersenne - who liked to do experiments and did many of them - Mersenne did two things remarkably extensively. A correspondence that's past seventeen volumes now and still growing, and it's almost all technical science or philosophy correspondence. It's spectacular how many people he corresponded with.
And he liked to do experiments, many many of them. So this book - Harmonie Universelle 1636 - it's a book on the theory of musical instruments, and really is an extraordinary book with lots of experiments on musical tones, etc. He remarks in it, "I question whether Lord Galileo ever did the experiments of falls along the plane, since he nowhere says so, and the proportion he gives often contradicts experiment."
Now what I've done here - I'm not going to read the whole thing out - when Dominico Bertoloni Meli - who's a professor of history and philosophy of science at Indiana University - was at Dibner Institute in 2001, I was director, we had a little group doing research on this.
Mele took (it's Bertoloni Meli but I'm just going to call him Nico) Nico took Mersenne's data as reported and put it on the basis of seven for the reasons you see, to see how the variation went depending on the angle of inclination. So you notice the first two are very close to five-to-seven. Then as the inclination goes up it becomes much closer to six-to-seven. And at 50 it says five-to-seven, but Mersenne remarks he couldn't get repeatable results by 50 degrees at all.
But it's those data, the non-repeatability of those data, for the moment - I'll explain why it's five-to-seven very shortly - but the key thing is: they're not the same. But they should be the same if Galileo is right. So he's just saying it doesn't hold. So now I can tell you about Galileo's actual experiment as he describes it. You've read this.
"We made the same ball descend only one-quarter the length of this channel, and the time of its descent being measured, this was found always to be precisely one-half the other. Next making the experiment for other lengths, comparing now the time for the whole length with the time for one-half, or with that of two-thirds, or of three-quarters, and finally with any other division, by experiments repeated a full hundred times, the spaces were always found to be to one another as the squares of the times. And this for all inclinations of the plane. We observed also that the times of descent for diverse inclinations maintained among themselves accurately that ratio which we shall find later assigned and demonstrated by our author."
This, of course, is equal velocities acquired over equal heights, so it's a confirmation of that. Now, what did he do? In Two World Systems [Two New Sciences], that's his diagram. Nice steep inclined angles. So Mersenne did nice steep inclined angles and got problems. So what does Galileo now report? Inclined planes ranging from one to two braccia in height, twelve braccia long. This is to scale. That's the height of those inclined planes. They are very very shallow, less than ten degrees. Okay? And - if you... using what we know - that means the total time from full length was around four point nine seconds, and the least time - going for the least distance he did - was point nine seconds.
How did he measure time? With a water clock. How do you do that with a water clock? What is a water clock? You put a pail of water with a small orifice at the bottom, you collect the water running out. So you pull your finger, let water run out, put your finger back. In fact, if the amount of water in the container is kept high, it's a very very near uniform rate. So it's not a crazy thing to do.
Okay. So what he's done here is to get the one-three-five progression at - he says multiple, I don't care multiple, two are enough - at two different inclinations, to within - I didn't include that part of the quote - "to within a heartbeat" is what he says. And he can compare the two and show that that confirms as well.
Now there's a problem here. I'm going to mention it briefly and then go on to other things. Here's a problem. He gets one-three-five at very low levels of inclination; what happens if you raise to a higher level of inclination? He says nothing. Mersenne has already said you don't get good results. So he's telling you now how to do the experiment. The experiment works perfectly if you do very low angles of inclination. What kind of evidence is it where the experiment works only in certain conditions and you basically have to tinker to find those conditions?
Well one answer to that question is "a typical experiment" because most experiments are like that and very often when you finally get it to work and you have good results, it'll take twenty or thirty years - in this case it was actually just about... I have to think... fifty-five years - before they figured out what was going on. You know, it's a classic thing when you do experiments, you design an experiment that doesn't work, you start with tinkering it, suddenly you start getting well-behaved results, then you announce to the world, "This is the way you do this experiment." And what you have to... how to explain away when it doesn't work becomes a secondary consideration.
But you will get a chance to write on the question of what kind of evidence you get when you have to restrict it.