Philosophy 167: Class 14 - Part 2 - De Motu Sphaericorum Corporum in Fluidis: a New Version of De Motu Corporum in Gyrum, and Five Laws.
Smith, George E. (George Edwin), 1938-
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All right, this is a document you can see at the top, the title. So this document is written in the hand of Humphrey Newton, his amanuensis at the time, with Isaac going in and making the changes, and the principle change on this page, the change that stands out, is he's got hypothesis one, hypothesis two, hypothesis three, hypothesis four all crossed out to the word law lex.
And in a very real historical sense, the use of the word law in modern science, dates from the day Newton scratched those out, and changed it to law. Because from that time forward, these laws of motion were called laws by Newton. And that's where the tradition stems from, from his calling them laws at the beginning of the Principia.
Why he decided to change them to law, you'll have to decide that for yourself, okay? But he goes back after the document is complete and scratches it out, and down below, here, he inserts per lex too, which is by law too, etc. There are other changes to this document, and I'm gonna go through all of them versus.
What's interesting is the 11 proof propositions, remain word-for-word the same, and the proofs remain word-for-word the same. So Humphrey just copied over everything that was proven in we've got new material, and it's the new material that's interesting. The scholium after proposition five is replaced, all of the rest of the scholia stay in place, other than one of them is greatly augmented.
Okay. So we're just going to go through these changes. The changes are very dramatic. One last comment though before I go on, and I'll keep emphasizing this when I get to the changes. This document did not become public until 1893. It was among Newton's papers, we have no evidence anybody saw it, and the most extraordinary aspect of it, which I'll get to in a moment, nothing like it appears in the Principia.
So looking at this document changes something. The book in which the document first appears, it appears only in Latin in this, but I will pass it around. It was the first careful study of the genesis of the Principia, after his papers first became available through the Earl of Portsmouth, selling them to Cambridge University, that which then sold all of his theological and chemical manuscripts.
They kept the ones they thought were important, then they sold the others, so, all of his theological manuscripts, most of them sit in Jerusalem, at the Jewish National Library. And the chemical ones are scattered. Cain's had a fair number, I don't know where they all are at the present moment.
When we get to the Flamsteed correspondence, which starts on December 27th, it looks very clear that he's already thought through everything in this. And this surely postdates De motu corporum in gyrum. Okay. It has to postdate it, because he makes changes It makes no sense, unless it postdates it.
So most of us say, December 1684 question mark, that's the usual way to put it down. I actually sometimes drop the question mark, because it's hard to imagine. My picture of what happened, and I trust this has happened to all of you in this room. If not, you lead a cleaner life than I do.
Anytime I lose control of a paper, I hand it in and is no longer mine, I start having wonderful ideas about how I could do better with it. Okay? And my guess is, Newton sent off, and started having further thoughts. And already before sometime very, very early on, he had a new version of it.
But then things started changing so fast, that he didn't see the point of submitting it anywhere, and it sat there until it surfaced as a part of the Portsmouth collection in the 1880s. And then Ralph Spaul published this, what's it called, an essay on Newton's Principia, but published it only in Latin.
And you'll see, I mean I make a big deal of this one. We'll get a little further, you'll see what I mean. So this is the first page, nice and clean. You can see how clean, by the way, Humphrey's handwriting is. He does his job, if that's all he's supposed to do is write a clean manuscript that's readable.
He does it very well. All right, sorry, so what he's done here is there's a substantial change. Law one is the same as it was in the prior De Motu. Law two is new. It is a version of what we call Newton's Second Law. It's very close to the version in the Principia.
Newton never ever writes anything like F=ma. The first person to do that is Hermann, but nobody picked up on it, even Newton. Newton read Hermann's doing it, and paid little attention to it. So our tradition that Newton's Second Law is F=ma, actually derives from Euler, who when putting it forward doesn't mention Newton, much less call it Newton's Second Law.
He actually calls it a new principle, a discovery of a new principle that is fundamental to all mechanics, and it's F=ma. Make of that what you wish. You'll see that paper later in this course, next semester. So it's law two, it's the second law, changes in the state of motion or rest is proportional to the impressed force, and occurs along the straight line in which that force is impressed.
Law three and four are very different. The relative motions of bodies contained in a given space, are the same, whether that space is at rest, or whether it moves perpetually and uniformly in a straight line, without circular motion. And I'm worried about something. I'm gonna go back and look, just to make sure that Yeah, I thought so.
It's my fault for not changing this translation. The word relative does not occur in there. This is Heravel's translation. Everybody does this, and I've made a big production over the last 18 months pointing out that people have almost all mistranslated Newton time and again. The phrase is inter se, the correct translation is the motion of bodies among themselves.
I should have known, I should have checked that indeed. So it's inter se, the phrase is going to be used all over the place in the Principia. He's constantly talking about the motions of the bodies amongst themselves, which contrasts with the motions of these bodies, as affected by something outside of themselves.
And that's people including Bernard and Anne Whitman, have translated that as relative, because they're trying to make it clear to 20th century readers. Newton has a perfectly good word, relative, and you're gonna see him using it later tonight. He doesn't use it there. So I will change that, but I won't change it the next two minutes.
Go back and correct that. But it's the motions about these among themselves are even better. The motion of bodies contained in the, no it has to be among themselves, has to be right after bodies, are the same whether that space is at rest, or whether it moves perpetually and uniformly in a straight line without circular motion.
That's the added thing. You'll see later why he's thinking that way. That's of course Huygens's Principle of Relativity. Whether Newton saw that Huygens manuscript at the Royal Society and knew that Huygens had put this forward, or to the contrary, Newton was doing this entirely on his own, we have no way of knowing, but the phrasing here is reasonably close to Huygens's, other than the phrase inter se, that is not in Huygens.
Then law four, you've seen Huygens published it, Newton had it in the laws of motion paper. The common center of gravity does not alter its state of motion or rest through the mutual actions of bodies. This follows from law three. And the picture, what Newton ultimately says about this in the Principia, is this is a generalization of law one.
If a body could change its state of motion, which requires an external cause in an entire system of bodies, no matter how they're interacting with one another, for their center of gravity to change its motion, it's gonna require an external cost too. That's the thought on it. And then law five just spells out more fully that resistance of a medium, is as the the density of that medium, and as the spherical surfaces of the moving body, and its velocity conjointly.
And then the two principles that are used, that are put forward as hypotheses in are derived. And I'm not gonna do proofs of both. This is the proof of the second one, and you'll notice the other thing. We've now got limit three and four. They were submitted, this is the one about geometric progressions, and this is the one about areas of a parallelogram, a circumscribed parallelogram.
Notice we've got titles here, so that's now gonna be the motion of bodies in non-resisting media, and when we get to the last two propositions, problems six and seven, it's gonna be the motion of bodies in resisting media. Okay. And notice, he's got spherical bodies. He's gonna keep changing the titles here.
Finally, with the Principia it becomes book one. As he quits putting anything on the motion of bodies. And originally, that was going to be the title of the whole Principia. Late in the game, he decided to change it to mimic Descartes' title.