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Thread: Newton on Barycenter

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    Newton on Barycenter

    An alleged quote from Sir Isaac Newton's Principia Book 3 Proposition 11: “the common centre of gravity of the Earth, the Sun and all the Planets is to be esteemed the centre of the World”. (On the System of the World). (sample link)

    Since that makes no sense using our modern definition of world as planet, I am hoping someone can tell me what the original Latin word for world was that produced this seemingly misleading translation. Was it cosmos?

    And secondly, some years ago I saw a graph of the Solar System Barycenter allegedly by Newton, who of course could not incorporate Uranus and Neptune into his calculations, so it was just a simple sine wave. After looking again with google, I have not been able to find it. Does it exist?

    Newton explained in his Principia, as I understand it, in his discussion of the three body problem, that when Jupiter and Saturn are opposite each other, the SSB is near the heart of the sun, and when Jupiter and Saturn are together they pull the SSB out of the sun by about one solar width. Is that a correct summary?

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    That section is heavily linked to an image on the page, and verbally describes the image's construction with a mathematical proof. As near as I can tell, it doesn't actually contain any of the words from that book. There is a copy online via the Cambridge website, but it was poorly printed and or damaged so the text on many pages is not readable. It might not have ever been readable in that particular copy because a few pages before Prob VI, Prop XI, the printed text trails off into handwriting.

    Here is the text you are looking for:

    Prop. XI. Prob. VI.
    Revolvatur corpus in Ellipsi: Requiritur lex vis centripetę tendentis ad umbilicum Ellipseos.

    Esto Ellipseos superioris umbilicus S. Agatur SP secans Ellipseos tum diametrum DK in E, tum ordinatim applicatam Qv in x, & compleatur parallelogrammum QxPR. Patet EP ęqualem esse semiaxi majori AC, eo quod acta ab altero Ellipseos umbilico H linea HI ipsi EC parallela, (ob ęquales CS, CH) ęquentur ES, EI, adeo ut EP semisumma sit ipsarum PS, PI, id est (ob parallelas HI, PR & angulos ęquales IPR, HPZ) ipsorum PS, PH, quę conjunctim axem totum 2AC adęquant. Ad SP demittatur perpendicularis QT, & Ellipseos latere recto principali (seu 2BC quad. ÷ AC) dicto L, erit L × QR ad L × Pv ut QR ad Pv; id est ut PE (seu AC) ad PC; & L × Pv ad GvP ut L ad Gv; [51]& GvP ad Qv quad. ut CP quad. ad CD quad.; & (per Lem. VIII.) Qv quad. ad Qx quad. punctis Q & P coeuntibus, est ratio ęqualitatis, & Qx quad. seu Qv quad. est ad QT quad. ut EP quad. ad PF quad., id est ut CA quad. ad PF quad. sive (per Lem. XII.) ut CD quad. ad CB quad. Et conjunctis his omnibus rationibus, L × QR fit ad QT quad. ut AC ad PC + L ad Gv + CPq. ad CDq. + CDq. ad CBq. id est ut AC × L (seu 2CBq.) × CPq. ad PC × Gv × CBq. sive ut 2PC ad Gv. Sed punctis Q & P coeuntibus, ęquantur 2PC & Gv. Ergo & his proportionalia L × QR & QT quad. ęquantur. Ducantur hęc aqualia in SPq. ÷ QR & fiet L × SPq. ęquale SPq. × QTq. ÷ QR. Ergo (per Corol. Theor. V.) vis centripeta reciproce est ut L × SPq. id est reciproce in ratione duplicata distantię SP. Q. E. I.


    Eadem brevitate qua traduximus Problema quintum ad Parabolam, & Hyperbolam, liceret idem hic facere: verum ob dignitatem Problematis & usum ejus in sequentibus, non pigebit casus cęteros demonstratione confirmare.

    First line roughly reads: "A body revolving in an ellipse is required by centripetal force to tend towards the focus." I could have that wrong.
    The middle section would be reduced to gibberish by me, as it contains math in Latin. The last line basically says that he proved it once and won't trouble to do it again.

    Whatever your source book is, it isn't a translation at all.

    Edit - Here is the link online to Cambridge - https://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00001/1 Go to page 126. The very next two pages are blank. I didn't bother translating the handwriting, as it is far less formal the than book itself. "When you want to center an ellipse..." This work has the dreaded s to f stuff that they did back then...
    Last edited by Solfe; 2018-Jan-01 at 02:31 AM.
    Solfe

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    On further research, that author is not a valid source of anything. He quoted the The Theogony of Hesiod, lines 104-110 in another book. It starts with the same words, then it stops being the same work. It isn't a translation error by any means.

    It is one thing for me to give a rough and snarky translation of Latin and then provide you with the text above plus links to a copy of the book. It is entirely different to say a book has X, when it simply doesn't. Even though I said my Latin was terrible, 147 different people on CQ can tell you exactly what is wrong with it. I'm not hiding anything, but trust me, this guy is.
    Last edited by Solfe; 2018-Jan-01 at 02:53 AM.
    Solfe

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    A better link to the quote is to Motte's 1846 translation of Newton at https://en.wikisource.org/wiki/The_M.../BookIII-Prop2

    The quoted translation is under PROPOSITION XII. THEOREM XII. That the sun is agitated by a perpetual motion, but never recedes far from the common centre of gravity of all the planets. (page 402)

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    The word is mundus, same is in De Mundi Systemate, "On The System Of The World" - which can mean "world" but which Newton is evidently using with its alternative meaning of "everything, the universe, the whole shebang".

    Prop. XI. Theor. XI.
    Commune centrum gravitas Terrę Solis & Planetarum omnium quiescere.
    Nam centrum illud (per Legum Corol. 4.) vel quiescet vel progredietur uniformiter in directum. Sed centro illo semper progrediente, centrum Mundi quoque movebitur contra Hypothesin quartam.
    The Project Gutenberg text is readily accessible and searchable. I think Solfe may have the wrong text.


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    Quote Originally Posted by Robert Tulip View Post
    A better link to the quote is to Motte's 1846 translation of Newton at https://en.wikisource.org/wiki/The_M.../BookIII-Prop2

    The quoted translation is under PROPOSITION XII. THEOREM XII. That the sun is agitated by a perpetual motion, but never recedes far from the common centre of gravity of all the planets. (page 402)
    Which is the next proposition, which contains the discussion of Jupiter, Saturn and barycentre:
    Prop. XII. Theor. XII.

    Solem motu perpetuo agitari sed nunquam longe recedere ą communi gravitatis centro Planetarum omnium.


    Nam cum, per Corol. 3. Prop. VIII. materia in Sole sit ad materiam in Jove ut 1100 ad 1, & distantia Jovis ą Sole sit ad semidiametrum Solis in eadem ratione circiter; commune centrum gravitatis Jovis & Solis incidet fere in superficiem Solis. Eodem argumento cłm materia in Sole sit ad materiam in Saturno ut 2360 ad 1, & distantia Saturni ą Sole sit ad semidiametrum Solis in ratione paulo minori: incidet commune centrum gravitatis Saturni & Solis in punctum paulo infra superficiem Solis. Et ejusdem calculi vestigiis insistendo si Terra & Planetę omnes ex una Solis parte consisterent, commune omnium centrum gravitatis vix integra Solis diametro ą centro Solis distaret. Aliis in casibus distantia centrorum semper minor est. Et propterea cum centrum illud gravitatis perpetuo quiescit, Sol pro vario Planetarum situ in omnes partes movebitur, sed ą centro illo nunquam longe recedet.
    Corol. Hinc commune gravitatis centrum Terrę, Solis & Planetarum omnium pro centro Mundi habendum est. Nam cłm Terra, Sol & Planetę omnes gravitent in se mutuņ, & propterea, pro vi gravitatis suę, secundum leges motūs perpetuņ agitentur: perspicuum est quod horum centra mobilia pro Mundi centro quiescente haberi nequeunt. Si corpus illud in centro locandum esset in quod corpora omnia maximč gravitant (uti vulgi est opinio) privilegium istud concedendum esset Soli. Cum autem Sol moveatur, eligendum erit punctum quiescens, ą quo centrum Solis quam minimč discedit, & ą quo idem adhuc minus discederet, si modņ Sol densior esset & major, ut minus moveretur.
    Grant Hutchison

    Last edited by grant hutchison; 2018-Jan-01 at 03:13 AM.
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    So, this then:

    Prop. XII. Theor. XII.
    Solem motu perpetuo agitari sed nunquam longe recedere ą communi gravitatis centro Planetarum omnium.


    Nam cum, per Corol. 3. Prop. VIII. materia in Sole sit ad materiam in Jove ut 1100 ad 1, & distantia Jovis ą Sole sit ad semidiametrum Solis in eadem ratione circiter; commune centrum gravitatis Jovis & Solis incidet fere in superficiem Solis. Eodem argumento cłm materia in Sole sit ad materiam in Saturno ut 2360 ad 1, & distantia Saturni ą Sole sit ad semidiametrum Solis in ratione paulo minori: incidet commune centrum gravitatis Saturni & Solis in punctum paulo infra superficiem Solis. Et ejusdem calculi vestigiis insistendo si Terra & Planetę omnes ex una Solis parte consisterent, commune omnium centrum gravitatis vix integra Solis diametro ą centro Solis distaret. Aliis in casibus distantia centrorum semper minor est. Et propterea cum centrum illud gravitatis perpetuo quiescit, Sol pro vario Planetarum situ in omnes partes movebitur, sed ą centro illo nunquam longe recedet.


    Corol. Hinc commune gravitatis centrum Terrę, Solis & Planetarum omnium pro centro Mundi habendum est. Nam cłm Terra, Sol & Planetę omnes gravitent in se mutuņ, & propterea, pro vi gravitatis suę, secundum leges motūs perpetuņ agitentur: perspicuum est quod horum centra mobilia pro Mundi centro quiescente haberi nequeunt. Si corpus illud in centro locandum esset in quod corpora omnia maximč gravitant (uti vulgi est opinio) privilegium istud concedendum esset Soli. Cum autem Sol moveatur, eligendum erit punctum quiescens, ą quo centrum Solis quam minimč discedit, & ą quo idem adhuc minus discederet, si modņ Sol densior esset & major, ut minus moveretur.

    Latin is a smidgen poetic. I wouldn't say "the common centre of gravity of the Earth", I would say "THE center of gravity of the earth, sun and planets in the universe must be considered..." There is a slight distinction there, he means the center of them all. It is not clear where he places that center and if he equates that center with all of "space", a word he doesn't use at all. He said "universe" or "world". I would say that "world" and "universe" are approximations for "solar system". The reason I take this stance on the reading of this work is that he goes on to reduce "planets", "sun" and "earth" to "particles" and that one should be at the center. He selected the sun as the obvious one, but then declares that it can't be at the exact center because of the pull from other "particles".

    Why is my reading so different than others? English is an extra language to me, after Italian and Latin. Since I learned English by immersion, I can be horribly wrong in translation.

    (Edit - plus I am drunk posting. I shouldn't do that.)
    Solfe

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    IIRC, Copernicus, Galileo, and others commonly used "world" to apply to Earth and beyond, like a greater family.
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    Quote Originally Posted by George View Post
    IIRC, Copernicus, Galileo, and others commonly used "world" to apply to Earth and beyond, like a greater family.
    I think that even today, the meaning of world is ambiguous. I think it can mean both the earth and everything.
    As above, so below

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    Quote Originally Posted by Jens View Post
    I think that even today, the meaning of world is ambiguous. I think it can mean both the earth and everything.
    A world of difference between the two. (Ok, actually the opposite, but punetic license and all that.)
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    Newton is certainly making a distinction between the planet Earth, which he calls Terra, and "the world", which is Mundus.

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    In more modern times, he might have written "the origin of this coordinate system". He's just defining it as a convenient point of reference.

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    And yet we see further evidence there that Newton does not take the modern view on the relative arbitrariness of coordinates-- he is attributing actual importance to "the center" of the universe. This maintains the issue from Galilean times, where the debate was around what is the actual center, rather than what is meant by a center in the first place. Newton tended to take coordinates as real literal things, not just language we use, because of his famous argument about a spinning bucket. He knew that it is possible to attach coordinates to the bucket that spin with the bucket, but in those coordinates, he could not see why the water in the bucket would crawl up the edges, so he felt that such "noninertial coordinates" were fundamentally different from inertial ones. Such coordinates needed to be corrected by the inclusion of fictitious forces to get the right results, results that do not obey Newton's laws without said corrective terms. Einstein made his remarkable correction to gravity, instead of to the coordinates, to get the right behavior in all coordinates, completely removing the distinction between a coordinate as a language choice and a coordinate as a description of "how things really are." So with Einstein's view, we hardly care what we decide to call the center of the "world," a concept that would certainly have blown Newton's mind to no small degree.

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    Quote Originally Posted by Ken G View Post
    And yet we see further evidence there that Newton does not take the modern view on the relative arbitrariness of coordinates-- he is attributing actual importance to "the center" of the universe. This maintains the issue from Galilean times, where the debate was around what is the actual center, rather than what is meant by a center in the first place. Newton tended to take coordinates as real literal things, not just language we use, because of his famous argument about a spinning bucket. He knew that it is possible to attach coordinates to the bucket that spin with the bucket, but in those coordinates, he could not see why the water in the bucket would crawl up the edges, so he felt that such "noninertial coordinates" were fundamentally different from inertial ones. Such coordinates needed to be corrected by the inclusion of fictitious forces to get the right results, results that do not obey Newton's laws without said corrective terms. Einstein made his remarkable correction to gravity, instead of to the coordinates, to get the right behavior in all coordinates, completely removing the distinction between a coordinate as a language choice and a coordinate as a description of "how things really are." So with Einstein's view, we hardly care what we decide to call the center of the "world," a concept that would certainly have blown Newton's mind to no small degree.
    I sense that Newton was struggling with both language and concepts. In one line, he seems to have problems with the word "gravitation" and seeming privilege it gives more massive objects. I am not sure what sort of mood this comment has:

    "Si corpus illud in centro locandum esset in quod corpora omnia maximč gravitant (uti vulgi est opinio) privilegium istud concedendum esset Soli."

    He says worth, gravitate, and privilege. He's the author of this piece, but he doesn't like something. His conclusions, or how other people do it or maybe the words used. When it comes to the words, it could be either his native language terms or how they were commonly translated to Latin. I am leaning on the linguistics of new ideas. He was being forced to use terms of things he didn't write himself so that others would understand. I still can't tell if that is a commentary on jargon, English or Latin.

    I'm not a scientist, but I love documents like this because they show a certain amount of richness which is not entirely about the subject matter, but a reflection of changing ideas and an internal dialog.
    Solfe

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    Ummm, where would that barycenter be, if nobody minds a side question?
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    Quote Originally Posted by BigDon View Post
    Ummm, where would that barycenter be, if nobody minds a side question?
    The Solar System Barycenter is the arc that our solar system follows around the galaxy. It varies between very close to the heart of the sun when Jupiter and Saturn are opposite and about one solar radius outside the sun when Jupiter and Saturn are together. As I mentioned in my opening question, since Newton did not know of the existence of Uranus and Neptune he could not factor them into his calculation of "the centre of the world".

    Newton's use of 'mundus' to mean 'solar system' looks like a deliberate rejection of Aristotle's old idea of 'supramundane' perfection as referring to everything above the sublunary level.

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    Quote Originally Posted by Robert Tulip View Post
    Newton's use of 'mundus' to mean 'solar system' looks like a deliberate rejection of Aristotle's old idea of 'supramundane' perfection as referring to everything above the sublunary level.
    Aristotle, being an Ancient Greek, certainly wouldn't have used "supramundane", though. Presumably that's a translation of the Greek word he did use, which may also have had nuances of meaning that need to be explored.

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    Aristotle would also have objected to being called "Ancient".

    -- Jeff, in Minneapolis
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    Quote Originally Posted by BigDon View Post
    Ummm, where would that barycenter be, if nobody minds a side question?
    Newton would have had no trouble balancing the masses of the Sun and planets to note that the center would not be at the center of the Sun. Knowing the locations of the planets, he would still need to know all their masses to derive the barycenter. This is just like a see-saw where the fulcrum shifts as one side gets a greater weight, which is another way to answer your question.

    In early time, Copernicus, for instance, understood that there are centers of gravity for objects and the world. They also held two other concepts of centers including the geometric center and the "center of magnitude". The later seems to be the 3D balance point of the accumulation of things (water, land, etc.). An homogeneous object would have all three centers at the same point.

    In the old mechanistic view of planets on spherical shells, the fact that planets varied in distance from Earth over time is yet another argument against the Earth holding the center point.
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    Quote Originally Posted by Jeff Root View Post
    Aristotle would also have objected to being called "Ancient".
    Not now, he doesn't.

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    Quote Originally Posted by George View Post
    Newton would have had no trouble balancing the masses of the Sun and planets to note that the center would not be at the center of the Sun. Knowing the locations of the planets, he would still need to know all their masses to derive the barycenter. This is just like a see-saw where the fulcrum shifts as one side gets a greater weight, which is another way to answer your question.

    In early time, Copernicus, for instance, understood that there are centers of gravity for objects and the world. They also held two other concepts of centers including the geometric center and the "center of magnitude". The later seems to be the 3D balance point of the accumulation of things (water, land, etc.). An homogeneous object would have all three centers at the same point.

    In the old mechanistic view of planets on spherical shells, the fact that planets varied in distance from Earth over time is yet another argument against the Earth holding the center point.
    But, but...if, according to relativity, *everywhere* is the center of the Universe, how is this wrong?
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    Quote Originally Posted by BigDon View Post
    But, but...if, according to relativity, *everywhere* is the center of the Universe, how is this wrong?
    It's not wrong. Just catastrophically unhelpful.

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    Quote Originally Posted by BigDon View Post
    But, but...if, according to relativity, *everywhere* is the center of the Universe, how is this wrong?
    I assume you mean any one spot can be treated as a legitimate center. GR allows this but with a caveat regarding something to do with Mach and a rotating universe. Regardless you will be forced to use fictitious forces if you elect to model the solar system from beyond the barycenter, no doubt (which means probably I'm right).

    The argument itself is perhaps more against the transparent shells since Ptolemy got around the orbital variations with his addition of the deferent and his odd equant, which can simulate an ellipse fairly accurately.

    What's fun about being here is when you stumble across things that surprise you; some of my google-fu searches, fu becomes more than fodder (fu for thought, I suppose ). Copernicus noted (Revolutionibus) that Philolaus (ancient Greek) believed the planets orbited about the "fire" in an oblique circle. I wonder if Kepler ever noted this suggestion?
    Last edited by George; 2018-Jan-03 at 11:10 PM.
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    Quote Originally Posted by BigDon View Post
    But, but...if, according to relativity, *everywhere* is the center of the Universe, how is this wrong?
    To me, the key shift here is a shift in the important question, moreso than a shift in its answer. For millennia, everyone thought the question we should be asking is, "where is the center?" So the significant thing is not that the answer to this question has changed, it is that the question itself has been found to be somewhat irrelevant. The question is now, "what is a center?" This is related to a point I often try to make, which is, we should not assume the language is set and we are merely seeking to navigate it. The hardest and most important thing is figuring out what our own words mean, and how they acquire those meanings.
    Last edited by Ken G; 2018-Jan-04 at 04:20 PM.

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    Quote Originally Posted by Ken G View Post
    To me, the key shift here is a shift in the important question, moreso than a shift in its answer. For millennia, everyone thought the question we should be asking is, "where is the center?" So the significant thing is not that the answer to this question has changed, it is that the question itself has been found to be somewhat irrelevant. The question is now, "what is a center?" This is related to a point I often try to make, which is, we should not assume the language is set and we are merely seeking to navigate it. The hardest and most important thing is figuring out what our own words mean, and how they acquire those meanings.
    Not helpful in the situation was the intentional use of "code words" among philosophers and alchemists that later authors didn't realize were code words, then more time passes between the later authors and ourselves.

    I barely recall a poem by an Alchemist, the gist being how to identify gold through chemical rather than physical means, but the words themselves were in a coded poem.

    About a King being eaten by a wolf.

    but "King" stood in for gold, and the "wolf" was aqua regent.

    The wolf had to be eaten by something else to bring the King back.

    Sorry for absolutely mauling this bit of information.

    (There's also a fifty dollar wager that Dr. Grant knows the poem, and has it as a wall embroidery.)
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    Quote Originally Posted by BigDon View Post
    I barely recall a poem by an Alchemist, the gist being how to identify gold through chemical rather than physical means, but the words themselves were in a coded poem.
    Yes, that's more or less what "jargon" is. Used well, it allows more rapid communication among experts. Used poorly, it can manipulate access to information.
    About a King being eaten by a wolf.
    Sometimes there has been a need to protect information, moreso than control it, in times when people couldn't distinguish science from witchcraft.
    (There's also a fifty dollar wager that Dr. Grant knows the poem, and has it as a wall embroidery.)
    I wouldn't take the former wager, though the latter I would!

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    Tapestries!!
    We know time flies, we just can't see its wings.

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    Quote Originally Posted by BigDon View Post
    (There's also a fifty dollar wager that Dr. Grant knows the poem, and has it as a wall embroidery.)
    Sounds like Michael Maier's Atalanta Fugiens (1617). Take a look at "Emblem 24: A wolf devoured the king, and being burnt restored him to life again."
    Supposedly the dead king represents impure gold and the wolf is some sort of reagent. Heat the combination and pure gold (a live king) is restored.

    No embroidery, sadly.

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  29. #29
    Join Date
    Jul 2006
    Posts
    12,235
    Oh, "The Wolf" is most definitely Aqua Regent.

    Wait a sec, did I just inform Dr. G of something he didn't know before?

    And snow flurries are forecast today in Tartarus, Detroit and Pandemonium...
    Time wasted having fun is not time wasted - Lennon
    (John, not the other one.)

  30. #30
    Join Date
    Jul 2005
    Posts
    16,974
    Quote Originally Posted by BigDon View Post
    Oh, "The Wolf" is most definitely Aqua Regent.
    Aqua regia? It certainly dissolves out gold.

    But the "burning" part of the story (rather than "boiling") suggests to me that it's describing one of the other method of "gold parting". If you add elemental sulphur or antimony sulphide to impure gold and then heat it, the metal impurities form sulphides and leave the pure gold behind. There's also something complicated you can do by heating the impure gold with various salt mixtures, which does the same thing except by forming metal chlorides.

    Grant Hutchison
    Blog

    Note:
    During life, we all develop attitudes and strategies to make our interactions with others more pleasant and useful. If I mention mine here, those comments can apply only to myself, my experiences and my situation. Such remarks cannot and should not be construed as dismissing, denigrating, devaluing or criticizing any different attitudes and strategies that other people have evolved as a result of their different situation and different experiences.

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