How did Newton discover his third law of motion?

Introduction

I restored the original title to show how interesting it is that a non-British student (18 at the time) can be more informed than a British physics graduate. He posted this comment:

*"The question before this must be whether it was his original or something like his 1st law, which was a restatement of the experimental findings of Galileo"* – Rijul Gupta Oct 26 '13 He then edited the title and the OP text adding: "Was it his original finding or was it a restatement of someone else's, like the first law coming from Galileo?"

This may seem a trivial detail in an answer but it is very important here: he knows that first law wasn't Newton's own (this is sometime acknowledged, though), but he expresses doubts that also third law might not be his own finding, whereas a U.S. academic is skeptical: "...I don't know if there's any evidence that he knew of them beforehand." – Ben Crowell

The historical truth is there, recorded in accessible documents and original texts, if one wants to look for it and is prepared to accept it, even if may be shocking for English eyes. I'll present the original documents, readers can draw their conclusions.

The historical facts

  • Christiaan Huygens [wiki (1)] was a good-natured, noble generous man, the son of a diplomat who was an advisor to the House of Orange. He was slow to publish his results and discoveries, in the early days his mentor , mathematicians Frans van Schooten was cautious for the sake of his reputation (1), this had the deplorable consequence that his ideas that he naively communicated to his contemporaries were plagiarized. He was too meek, he complained only to friends (even his patent was violated in Egland, France etc.) and therefore his great scientific merits are to date under-evaluated: he found the real law behind 'the conservation of momentum', discovered the formula of kinetic energy, the conservation of KE in elastic collisions, suggested the term 'vis viva' to Leibniz and taught him maths and helped him develop 'calculus', even he never believed in its usefulness.
  • during the years 1650 - 1666 [Enc. (2)] he lived at home, except for three journeys to Paris and London: an allowance supplied by his father enabled him to devote himself completely to the study of nature
  • between the years 1652-54, according to his own statements, he developped the theory of collisions in his work (in Latin): "De motu corporum ex percussione" (English translation: Chicago Journals), there is no proof of that, although :"... there are numerous indications that Huygens had established all the propositions and their proofs by 1656 at the latest (see the Avertissement in Oeuvres, Vol. XVI, pp. 3-14, for the evidence) (3, p. 574)

  • in 1661 he was already famous: in '55 he had discovered the satellite of Saturn (2), in '56 had invented the pendulum clock and in '57 had written his treatise on probability theory (1) . He went to Paris to meet Pascal as "He had been told of recent work in the field by Fermat, Blaise Pascal and Girard Desargues two years earlier" (1).

  • in May of that year he was in London " "..to observe the planet Mercury transit over the Sun, using the telescope of Richard Reeve in London, together with astronomer Thomas Streete and Reeve himself" (1). He also "..attended meetings in Gresham College, and met Moray, Wallis, and Oldenburg" (2). he told them about his findings and in particular about the theory of collisions". The scholars at Gresham had recently formed the Royal Society Henry Oldenburg (4) was "...one of the foremost intelligencers of Europe of the seventeenth century, with a network of correspondents .. At the foundation of the Royal Society he took on the task of foreign correspondence, as the first Secretary", he was the shady figure (shortly imprisoned as a suspected spy) that recruited scientists all over Europe, trying to entice them with a promise ".. they would be assured undying fame by the preservation of their results in the archives of the RS" and to convince them the could rest assured "that no harm to their discoveries would come about through divulging information in advance of publication" and that at RS each is certain of his due" [(5) p.53, passim]

  • the Royal Society, it is notorious, when Newton was a member "...in 1699 accused Leibniz of plagiarism. The dispute then broke out in full force in 1711 when the Royal Society proclaimed in a study that it was Newton who was the true discoverer and labelled Leibniz a fraud. This study was cast into doubt when it was later found that Newton himself wrote the study's concluding remarks on Leibniz"
  • in (June -September) 1663 "Huygens was made a member of the Society" (2), and was invited to London to illustrate his discoveries, in particular on the theory of collisions
  • in 1668 he was invited by the Society to publish his findings on collisions in the Philosophical Transactions of the Royal Society:"He presented the most important theorems to the Royal Society in 1668, simultaneously with studies by Wren and Wallis" (5 p.543). The Rules of Motion by these two, copied from Huygens' paper, were published while his original work was not. In this dishonest way the Society ensured the primacy of the theory to the English authors and Newton (of course, he can't ignore him altogether) can always cite :"In theoria Wrenni & Hugenii", "together with the third Law, Sir Christ. Wren, Dr. Wallis, and Mr. Huygens", ".. Dr. Wallis, indeed, was something more early in the publication; then followed Sir Christopher Wren, and, lastly, Mr. Huygens"
  • Huygens was saddened "...and publicly voiced his anger at being disadvantaged by not having his results published (in PT) at the same time as those of the opposite party" [5, p. 53]
  • in March 1669, having had no satisfaction, he published his paper in French in the Journal des sçavans
  • immediately after, his original Latin paper was published in the PT of the RS
  • in 1670, the following year, Huygens had already forgotten his anger and "... seriously ill, chose Francis Vernon to carry out a donation of his papers to the Royal Society in London, should he die." (1). If these historical reports are true, by 1671 (the RS and) Newton was in possess of the complete demonstrations concerning the theory of collisions (by Huygens and Mariotte): in 1669 Newton had already been appointed Lucasian Professor.

  • in 1670 Edme Mariotte had announced his intention to compose a major work on the impact of bodies. Completed and read to the Academy in 1671, it was published in 1673 as Traité de la percussion ou choc des corps. The first comprehensive treatment of the laws of inelastic and elastic impact and of their application to various physical problems". In order to verify his suppositions, he used " an experimental apparatus consisting of two simple pendulums of equal length, the replaceable bobs (the impacting bodies) of which meet at dead center". Here we found the real inventor of "Newton's 'cradle'. Newton cites Wrenn's experiments and Mariotte's book: ".*.veritas comprobata est a Wrenno ...quod etiam Clarissimus Mariottus libro integro exponere mox dignatus est**" (p. 37), but never Huygens'. Newton affirms that Mariotte had just divulged the findings of the British architect: ".. Wren confirmed the truth of the thing before the Royal Society by the experiment of pendulums, which Mr. Mariotte soon after thought fit to explain in a treatise entirely upon that subject." (p.90) enter image description here

  • Huygens was certainly saddened by the fact that Mariotte did not cite him as his source, but did not respond (the silence of the lambs) his nature was so meek that only " seventeen years later, in 1690, when Mariotte was dead, Huygens responded to this slight (see below) by accusing Mariotte of plagiarism. “Mariotte took everything from me,” he protested in a sketch of an introduction to a treatise on impact never completed" (ibidem, you can read about the 'slight'):

Clearly he knew of the work of Wallis, Wren, and Huygens published in the Philosophical Transactions of the Royal Society in 1668; and there are enough striking similarities between Mariotte’s treatise and Huygens’ then unpublished paper on impact (De motu corporum ex percussione, in Oeuvres, XVI) to suggest that *he knew the content of the latter, perhaps verbally from Huygens himself** Certainly his colleagues in the Academy recognized Mariotte’s debt to others while they praised the clarity of his presentation. And yet Galileo’s name alone appears in the treatise; Huygens’ in particular is conspicuously absent.

  • Since the first meeting in 1661 the RS group had tried to understand the profound meaning of 'conservation of momentum' and even after Huygens sent in his paper in 1668 with the complete list of the rules were not able to interpret them. "In a letter of Feb. 4, 1669, (one month before the delayed publication in RPRS of his submitted paper) Oldenburg "earnestly intreated" Huygens to publish his theory, but the reply ignored the point. Huygens himself explains his refusal to publish." (3, p. 575) The reason was not, as one might imagine, that he did not want to reveal the theory, but because he wanted to get to the bottom (penitus), to the metaphysical level: "he was concerned to determine the essence and true cause of motion and forces" (ibidem). He mentioned the true principle once, but never wrote it down.
  • from 1669 to 1687 Newton tried for 18 more years to figure out the true essence/law of motion, but lacked Huygens' metaphysical insight He tried to be original (as he had done with the 1st law) and produced a 3rd law which is partially in contrast with his own laws. (this will be discussed in a another answer, to separate facts from opinions)

conclusions

This is how Newton found the third law. Is "there enough evidence that he knew of them beforehand"?, I'll leave the answer to the readers, as this post is unpopular just as it is. Certainly if one should decide that


The third law states that to every action (force) there is an equal and opposite reaction.

According to "The historical context of Newton's Third Law and the teaching of mechanics" by Colin Gauld, Research in Science Education 1993, Volume 23, Issue 1, pp 95-103:

'[Newton] referred to the investigations, using pendulums, into "the rules of the congress and reflexion of hard bodies" carried out by Wren, Wallis, Huygens and Mariotte and he went on to describe his own experiments using tightly compressed bails of wool and balls of steel, cork and glass. He concluded "thus the third Law, so far as it regards percussions and reflexions, is proved by a theory agreeing with the experience"'

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