Philosophy 167: Class 13 - Part 6 - Priority Dispute Over Inverse Square: the Conflict Between Newton and Hooke, and the Incipience of De Motu.

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


  • Synopsis: A dispute started over whether Hooke or Newton had first invented the inverse square law of force in orbital mechanics. Newton nearly stopped working on the project, but finally sent Halley a subsequently lost document believed to be titled De Motu.

    Opening line: "This story has become legendary. Many people have embellished it. What's fascinating about it is we have exactly one ... read more
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This story has become legendary. Many people have embellished it. What's fascinating about it is we have exactly one source of evidence about what happened. It's a letter Halley wrote on 29 of June, 1686. And it's about what happened in August, 1684. Why is this letter written in 29 June, 1686?
Couple weeks earlier Halley had very, very gently in a letter, informed Newton that Hooke had pretenses to priority on inverse square. All that was available in London at the time was Book One of the Principia, which is stuff you'll, the stuff you've read for tonight is typical of.
Newton blows up. And in a letter of, I think it's 22nd June, 1686, I'll put it on supplementary material next week. That's where he says Kepler only guessed on the ellipse, Newton proved it, Hook was only guessing on the inverse square, Newton proved it. Goes on and on.
To tell you how angry he is, the letter runs about three pages of vitriol. He signs it, and then there's a PS of another page and a half. Okay? That's when you're angry. When the PS runs another page and a half. So, and what he says is he's giving the project up.
You can publish Book One, Book Two. I have a short version of Book Two now, so, we're just gonna be two books. Short version of Book Two that weights only the figures, and I have a version of Book Three in the popular style, etc. Halley writes back trying to save the project.
He wants the whole Principia published, so this is a letter in which he's trying to assuage Newton, and convince Newton to go ahead and finish the whole project. So, this is, and as I say, this is the sole evidence we have of what transpired in 1684. Every other account you see is an embellishment of what's said here, and it is two years later.
According to your desire in your former, that's the letter where he said I wanna know what actually you think happened in all of this. I waited upon Sir Christopher Wrenn to inquire of him if he had the first notion of the reciprocal nuclear proportion for Mr. Hooke. His answer was that he, himself, very many years since, had had his thoughts upon making out the planet's motion by a composition of a descent toward the sun and an impressed motion, but that, at length, he gave over, not finding the means of doing it.
Since which time Mr. Hooke had frequently told him that he had done it, and attempted to make it out to him, but that he never satisfied him that his demonstrations were cogent. And this I know to be true, that in January 1683/84, I, having from the consideration of the sesquialteral proportion of Kepler, three-halves power of Kepler, concluded that the centripetal force decreased in proportion of the squares of the distances reciprocally, so that's when Halley concludes this on his own.
Came one Wednesday to town, where I met with sir Christopher Wren and Mr. Hooke, and falling into discourse about it, Mr. Hooke affirmed that upon that principle all the laws of the celestial motions were to be demonstrated and that he himself had done it. I declared the ill success of my attempts, and Sir Christopher, to encourage the inquiry, said that he would give Mr. Hooke or me two months time to bring him a convincing demonstration thereof, and besides the honor, he of us that did it should have from him a present of a book of 40 shillings.
40 shillings was not a trivial amount of money at the time. Mr. Hooke then said that he had it, but he would conceal it for some time, that others trying and failing might know how to value it when he should make it public. However, I remember Sir Christopher was a little satisfied that he could do it.
And though Mr. Hooke then promised to show him, I do not yet find that, in that particular, he has been as good as his word. The August following, when I did myself the honor to visit you, I then learned the good news that you had brought this demonstration to perfection and you were pleased to promise me a copy thereof, which the November following I received with a great deal of satisfaction from Mr. Padgett.
With you about it, excuse me, I'm sorry. And thereupon took another journey down to Cambridge on purpose to confer with you about it, since about that time it has been entered upon the register books of the Society as all the past Mr. Hooke was acquainted with it. So, it's December 12th that gets announced before the Royal Society and it's fully inscribed in the register book.
The actual copy that got sent to London is lost, but it was handwritten by the, whoever was keeping the register book simply copied the whole thing. There are details in my notes if you want more of it. Now picking up, all the time Mr. Hooke was acquainted with it, as Hooke could go read the register book anytime he wanted after 1684, and according to the philosophically ambitious temper he is of, he would, had he been master of a like demonstration, no longer have concealed it, the reason he told Mr Christopher and I now ceasing.
But now he says that this is but one small part of an excellent system of nature which he has conceived, but has not yet completely made out, so that he thinks not fit to publish one part without the other. But I have plainly told him that unless he produced another differing demonstration and let the world judge of it, neither I nor anyone else can believe it.
That's all we actually know about what happened. Years later Newton said the visit was in late spring. There's no reason to think Halley, two years later, can't tell the difference between May and August. So almost nobody counts late spring unless they have an ulterior motive, saying Newton needed more time to work out the De Motu.
But that's the genesis of De Motu. Okay? He leaves in August, promised to deliver a document. The document arrives in November. Halley reads it, decides time to go back to Cambridge to talk to Newton about this document. What we do know from another letter, that when he arrives in Cambridge, Newton is pushing the matter forward, he hasn't stopped with De Motu, he's going on.
He gets permission to register it and the rest is there. So that's the background to De Motu.