How did Newton discover his third law? Was it his original finding or was it a restatement of someone else's, like the first law coming from Galileo? What initiated the concept of what is now known as Newton's 3rd law?
Newtonian Mechanics – How Did Newton Discover His Third Law of Motion?
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Newton's 1st and 2nd laws weren't particularly revolutionary or surprising to anyone in the know back then. Hooke had already deduced inverse-square gravitation from Kepler's third law, so he understood the second law. He just could not prove that the bound motion in response to an inverse square attraction is an ellipse.
The source of Newton's second law was Galileo's experiments and thought experiments, especially the principle of Galilean relativity. If you believe that the world is invariant under uniform motion, as Galileo states clearly, then the velocity cannot be a physical response because it isn't invariant, only the acceleration is. Galileo established that gravity produces acceleration, and its no leap from that to the second law.
Newton's third law on the other hand was revolutionary, because it implied conservation of momentum and conservation of angular momentum, and these general principles allow Newton to solve problems. The real juicy parts of the Principia are the specific problems he solves, including the bulge of the Earth due to its rotation, which takes some thinking even now, three centuries later.
EDIT: Real History vs. Physicist's History
The real history of scientific developments is complex, with many people making different contributions of various magnitude. The tendency in pedagogy is to relentlessly simplify, and to credit the results to one or two people, who are sort of a handle on the era. For the early modern era, the go-to folks are Galileo and Newton. But Hooke, Kepler, Huygens, Leibniz and a host of lesser known others made crucial contributions along the way.
This is especially pernicious when you have a figure of such singular genius as Newton. Newton's actual discoveries and contributions are usually too advanced to present to beginning undergraduates, but his stature is immense, so that he is given credit for earlier more trivial results that were folklore at the time.
To repeat the answer here: Newton did not discover the second law of motion. It was well known at the time, it was used by all his contemporaries without comment and without question. The proper credit for the second law belongs almost certainly to the Italians, to Galileo and his contemporaries.
But Newton applied the second law with genius to solve the problem of inverse square motion, to find the tidal friction and precession of the equinoxes, to give the wobbly orbit of the moon (in an approximation), to find the oblateness of the Earth, and the altitude variation of the acceleration of gravity g, to give a nearly quantitative model of the propagation of sound waves, to find the isochronous property of the cycloid, and a host of other contributions which are so brilliant ad so complete in their scope, that he is justly credited as founding the modern science of physics.
But in physics classes, you aren't studying history, and the applications listed above are too advanced for a first course, and Newton did indeed state the second law, so why not just give him credit for inventing it?
Similarly, in mathematics, Newton and Leibniz are given credit for the fundamental theorem of calculus. The proper credit for the fundamental theorem of calculus is to Isaac Barrow, Newton's advisor. Leibniz does not deserve credit at all. The real meat of the calculus however is not the fundamental theorem, but the organizing principles of Taylor expansions and infinitesimal orders, with successive approximations, and differential identities applied in varied settings, like arclength problems. In this, Newton founded the field.
Leibniz gave a second set of organizing principles, based on the infinitesimal calculus of Cavalieri. Cavalieri was Galileo's contemporary in Itali, and he either revived or rediscovered the ideas originally due to Archimedes in "The Method of Mechanical Theorems" (although he might not have had access to this work, which was only definitively rediscovered in the early 20th century. One of the theorems in Archimedes reappear in Kepler's work, suggesting that perhaps the Method was available to these people in an obscure copy in some library, and only became lost at a later date. This is pure speculation on my part. Kepler might have formulated and solved the problem independently of Archimedes. It is hard to tell. The problem is the volume of a cylinder cut off by a prism, related to the problem of two cylinders intersecting at right angles). Cavalieri and Kepler hardly surpassed Archimedes, while Newton went far beyond. Leibniz gave the theory its modern form, and all the formalism of integrals, differentials, product rule, chain rule, and so on are all due to Leibniz and his infinitesimals. Leibniz was also one of the discoverers of the conservation of mechanical energy, although Huygens has his paws on it too, and I don't know the dates.
The mathematicians' early modern history is no better. Again, Newton and Leibniz are given credit for theorems they did not produce, and which were common knowledge.
This type of falsified history sometimes happens today, although the internet makes honest accounting easier. Generally, Witten gets credit for everything, whether he deserves it or not. The social phenomenon was codified by Mermin, who called it "The Matthew principle", from the biblical quote "To those that have, much will be given, and to those that have not, even the little they have will be taken away." The urge to simplify relentlessly reassigns credit to well known figures, taking credit away from lesser known figures.
The way to fight this is to simply cite correctly. This is important, because the mechanism of progress is not apparent from seeing the soup, you have to see how the soup was cooked. Future generations deserve to get the recipe, so that we won't be the only ones who can make soup.
Newton didn't say "change in momentum", he said "alteration in momentum", and whichever he said, this means clearly, and with no room for doubt, rate of change of momentum, the limit of small $\Delta t$ of $\Delta P \over \Delta t$. This was understood this way by everyone who read the book, there is no way to misinterpret if you follow the mathematical things.
The experiments of Galileo showed that bodies in gravity have the same acceleration. This means that the Earth is imparting changes in velocity to particles. The notion of "force" is already present to some extent in the theory of statics developed by Archimedes, and gravity produces a steady force in a static situtation, and this force is proportional to the mass. If you know force is proportional to the mass, and the acceleration is the same for all bodies, it is no leap to conclude that a force produces a steady acceleration inversely proportional to the mass.
The second law was not the major innovation in Newton, this was known to Hooke and Halley and Huygens for sure. Newton's innovation is the third law, and the system of the world, the special problems.
Best Answer
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:
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)
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.
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