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Another fascinating thing about the Newton story is its parallels to Archimedes and the "eureka" moment. Both stories involve the most famous physicist of the d

Another fascinating thing about the Newton story is its parallels to Archimedes and the "eureka" moment. Both stories involve the most famous physicist of the day being asked to protect the integrity of royal gold. (Archimedes was asked by the king of Syracuse to detect whether a goldsmith had been adding baser metals to an offertory gold crown.) And both involve famous scientists bending the rules of evidence and procedure to catch a thief – in Archimedes' case, the modern consensus is that simple water displacement would not be sufficient to distinguish pure gold from a gold/silver alloy.

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lifeisstillgood 3y ago
Wait what? Are you saying that the story (Archimedes invents theory of density, proves the crown is fake) is really Archimedes invents density, but then proves the fakery by ... finding the spare gold in the guys kitchen or something? I'm flabbergasted. I can of course believe it's true. I just never thought to question it.
- bryanrasmussen 3y ago
  I figured it was Archimedes invents theory of density, then he or someone else invents anecdote to show its use, anecdote actually wouldn't work though but theory of density still good so people use it.
- deleted 3y ago
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WalterBright 3y ago
I always wondered how he measured the displacement accurately enough.
- roflmaostc 3y ago
  You simply should use a vessel which gets narrower to the top. If you put the crown, the water level rises. The smaller the cross section of the vessel the more the height has to increase to amount the volume.
  - smolder 3y ago
    Old school liquid thermometers demonstrate this beautifully.
  - jl2718 3y ago
    We’re talking about clay pots here. How would you get the crown into the narrow opening? If you have two containers, one for displacement, the other for measurement, you would lose far more water in the pouring than the precision required. Here is an idea: I can imagine a vessel that looks like an elongated tetrahedron upside-down with one of the isosceles faces open and the point below it beveled to enable it to balance in two positions, position 1 with the long end slightly higher than the short end, and position 2 with the long end exactly the same height as the short end. Start in position 1, fill with water, place the crown to overflow it’s volume, then remove the crown, tip the vessel to position 2, mark the extent (rather than the height) of the water on the elongated end, repeat with the gold, compare. This could be improvised with something like a large urn and a block to lift the long end a little bit. I’m still not sure about the precision of the overflow and dripping off the water.
- jl2718 3y ago
  I assume he used a mechanical balance to measure the equal weight of gold. Couldn’t he then just submerge the balance? If the method from the story doesn’t work, is it possible that it was just a plausible-sounding cover for the actual method that they wouldn’t have wanted to disclose?
hddqsb 3y ago
Wikipedia has a good paragraph on this. It describes a very cool alternative method that has higher accuracy, and according to Galileo it's probable that Archimedes used this method: > The story of the golden crown does not appear anywhere in Archimedes' known works. The practicality of the method described has been called into question due to the extreme accuracy that would be required to measure water displacement. Archimedes may have instead sought a solution that applied the hydrostatics principle known as Archimedes' principle, found in his treatise On Floating Bodies: a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.[34] Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing it on a scale with a pure gold reference sample of the same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly.[12] Galileo Galilei, who invented a hydrostatic balance in 1586 inspired by Archimedes' work, considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself." -- https://en.wikipedia.org/wiki/Archimedes#Archimedes'_principle https://en.wikipedia.org/wiki/Archimedes#Archimedes'_princip...
- spacemule 3y ago
  > then immersing the apparatus in water I'm having trouble picturing what's going on here. I'm not sure what the apparatus is. The best I can figure, it's two containers of water with the reference gold in one and the crown in the other. However, this wouldn't be any different than just weighing the two pieces of gold (which are already known to be the same mass). I tried searching for "hydrostatic balance," but nothing relevant to this came up. Since you seem to understand this, would you mind explaining (or pointing to an explanation of) Archimedes's probable solution?
  - mafuy 3y ago
    The apparatus is the scale, on which the crown and the gold were placed. They balance out when it is in air. They do not (for a fake crown), when the scale is submerged in water.

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lifeisstillgood 3y ago

Wait what? Are you saying that the story (Archimedes invents theory of density, proves the crown is fake) is really Archimedes invents density, but then proves the fakery by ... finding the spare gold in the guys kitchen or something? I'm flabbergasted. I can of course believe it's true. I just never thought to question it.

bryanrasmussen 3y ago
I figured it was Archimedes invents theory of density, then he or someone else invents anecdote to show its use, anecdote actually wouldn't work though but theory of density still good so people use it.
deleted 3y ago
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WalterBright 3y ago

I always wondered how he measured the displacement accurately enough.

roflmaostc 3y ago
You simply should use a vessel which gets narrower to the top. If you put the crown, the water level rises. The smaller the cross section of the vessel the more the height has to increase to amount the volume.
- smolder 3y ago
  Old school liquid thermometers demonstrate this beautifully.
- jl2718 3y ago
  We’re talking about clay pots here. How would you get the crown into the narrow opening? If you have two containers, one for displacement, the other for measurement, you would lose far more water in the pouring than the precision required. Here is an idea: I can imagine a vessel that looks like an elongated tetrahedron upside-down with one of the isosceles faces open and the point below it beveled to enable it to balance in two positions, position 1 with the long end slightly higher than the short end, and position 2 with the long end exactly the same height as the short end. Start in position 1, fill with water, place the crown to overflow it’s volume, then remove the crown, tip the vessel to position 2, mark the extent (rather than the height) of the water on the elongated end, repeat with the gold, compare. This could be improvised with something like a large urn and a block to lift the long end a little bit. I’m still not sure about the precision of the overflow and dripping off the water.
jl2718 3y ago
I assume he used a mechanical balance to measure the equal weight of gold. Couldn’t he then just submerge the balance? If the method from the story doesn’t work, is it possible that it was just a plausible-sounding cover for the actual method that they wouldn’t have wanted to disclose?

hddqsb 3y ago

Wikipedia has a good paragraph on this. It describes a very cool alternative method that has higher accuracy, and according to Galileo it's probable that Archimedes used this method: > The story of the golden crown does not appear anywhere in Archimedes' known works. The practicality of the method described has been called into question due to the extreme accuracy that would be required to measure water displacement. Archimedes may have instead sought a solution that applied the hydrostatics principle known as Archimedes' principle, found in his treatise On Floating Bodies: a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.[34] Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing it on a scale with a pure gold reference sample of the same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly.[12] Galileo Galilei, who invented a hydrostatic balance in 1586 inspired by Archimedes' work, considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself." -- https://en.wikipedia.org/wiki/Archimedes#Archimedes'_principle https://en.wikipedia.org/wiki/Archimedes#Archimedes'_princip...

spacemule 3y ago
> then immersing the apparatus in water I'm having trouble picturing what's going on here. I'm not sure what the apparatus is. The best I can figure, it's two containers of water with the reference gold in one and the crown in the other. However, this wouldn't be any different than just weighing the two pieces of gold (which are already known to be the same mass). I tried searching for "hydrostatic balance," but nothing relevant to this came up. Since you seem to understand this, would you mind explaining (or pointing to an explanation of) Archimedes's probable solution?
- mafuy 3y ago
  The apparatus is the scale, on which the crown and the gold were placed. They balance out when it is in air. They do not (for a fake crown), when the scale is submerged in water.