Philosophy 167: Class 10 - Part 3 - Huygens' Mechanics: Cycloidal Pendulums, and the Invention of an Extremely Precise Clock.
Smith, George E. (George Edwin), 1938-
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He, because of Alexandre Courrier writing on Descartes and Newton, he portrayed Huygens as a Cartesian. It's most unfortunate that he did. So Howard Stein, philosopher, of course, now retired at University of Chicago, but a name you'll hear again, in making the point that Huygens was very far from a Cartesian, published this.
This is from a letter to Bale. Bale asked Huygens to write a biography of himself. And to describe Descartes since he knew Descartes personally. And this is from that letter in reply to Bale. Monsieur Descartes had found a way to make his conjectures and fictions pass for truths.
And those who read his principles of philosophy, experience somewhat the same as do the readers of romances, which give pleasure and make the same impression as veritable histories. It seemed to me, when I first read this book of the principles that everything in it was as good as could be.
And I believed when I found some difficulty there, that it was my fault for not correctly understanding his thought. I was only 15 or 16 years old. But having since discovered there from time to time things visibly false and others highly improbable, I have retreated far from the predilection I then had.
And at the present hour, that's 1693, after Newton's Principia. I find almost nothing that I can approve as true in all his physics or metaphysics or meteors. Okay, so he was, he ceased being a Cartesian. You'll see the one element that looks like he's Cartesian, he has a vortex theory of gravity.
Not of planetary motion, of gravity. Fixing Descartes' theory. All right, this is the clock that's shown in Horologium Oscellatorium. It's not his original clock. When you say, he invented the clock. Let me start with what I mean by that. The trick is in the mechanism shown at the top on your left.
That has to work properly. And in particular, it has to work in a way that it does not cause the pendulum to slow down. So what Hoygan developed, it's an adaptation from prior clocks that are not pendulum clocks. But he neatly adapted it in such a way that as the thing at the top clicks.
Typically it's gonna be every half second. But it could be every second depending on the length of the pendulum. As it clicks over, the pendulum causes it to click over. But there's a rebound effect throwing energy back into the pendulum. And of course, you wind that up. So the pendulum does not tend to slow down significantly at all.
That was the invention in 1658. And again, I'm passing around this whole chapter is available, but it describes the escapement in the page I've singled out. That the Huygens’ escapement, which was the real breakthrough in having a successful pendulum clock. And probably, the real breakthrough in having successful clocks at all.
Because the prior ones, the purely mechanical ones just didn't have, they had two problems. They didn't have a means of keeping good time which the pendulum provides you. But secondly, they didn't really have a mechanism that didn't run down way to fast. Okay, I don't know that much about clocks.
So I'm not gonna do much more with it. In 1658, he knew the circular pendulum is not isochronous. So he knew he could not use an unrestricted circular arc pendulum and keep time. So he, by trial and error, put some cheeks up, like this. That would bend the string of the pendulum.
So that it would be shorter at higher, at higher arcs and it would disappear at low arcs. That's trial and error. He knew what he had to do to remove the non isochronism. But then, he decided that the friction of the string against those walls was sufficiently bad.
That instead he put out his first pendulum clocks which I repeat were very successful. Put them out basically, trying to keep a constant amplitude. Small amplitude. But constant so it wouldn't go down. And that's why the escapement was so important. In 1659, in a manner I'll get to in almost the very next slide.
He got very, very involved in the question of how to measure surface gravity. And along the way, managed to go back to the question, what is the isocranous path? That is, what path would a pendulum have to describe so that it beats the same, it has the same time of each arc, whether it's a large arc or a miniscule arc?
And he proved, it's the cycloid. The cycloid is the path described by a point on a rolling ball rolling on a flat surface. Then, he asked the question. And again, you'll see this in more detail later, asked the question, how do I make something describe a cycloid? And he discovered that if these cheeks are exactly the cycloid you want, you get the cycloid.
Technically, what I just said is, the cycloid is its own evolute. We'll come back to that. All his clocks afterwards always had these cheeks. That is, they were alway cycloidal pendulum clocks. And this is the one that's on display at the beginning of Horologium Oscillatorium. Three or four pages later, I'm not gonna do anything with it in this course, but three or four pages later, he shows a marine clock with triangular threads coming down again, with the cheeks.
Why two threads coming down? Because if you want to put it at sea, this is a maritime clock. And you think the waves are gonna be tossing it all over. So if you have two strings coming down to the pendulum, his thought was that would behave much better.
Now, why is it important to have a maritime clock? We'll hear about all the rest of this course. They were having trouble determining longitude at sea. The best way to describe this trouble is some 40 or 50 vessels that disappeared off the Antilles. And of course, the Dutch were the most heavy traders of anybody at the time.
The Dutch East India Company etc.was making Holland extraordinarily wealthy through their trading exploits. So there was a lot of demand for some way to be able to determine what longitude you are at sea. Well, if you have a clock that keeps Paris, I think Paris is the wrong place.
Keeps Leiden time all the way around the world. And you can get local time from the Sun or the Moon. Then the difference in those two is your longitude. So he thought, he had solved the problem of longitude at sea. And even at his death, he still thought he had solved it.
It turned out he had not, that the pendulum clocks were never quite well behaved enough at sea. He didn't realize that fully. And therefore, it ended up that John Harrison in. Yeah, this is a funny statement. John Harrison invented the temperature compensated spring clock that did provide longitude at sea in the manner that's described.
I said, it's funny, because in 1680's, Huygens invented the spring clock. Found it was too temperature sensitive and couldn't figure out how to make it temperature insensitive, by using multiple different metals, which is what Harrison did. So there's a whole story here, but this is a major event in human history, having a really successful, precise clock.
Of course, afterwards, there are any number of others. So it's not that big a deal. But the importance for our course is it altered astronomy, cuz you now had really reliable timing.