He reported back to the Vice-Chancellor faithfully and in minute detail, but according to one anecdote, which may or may not be true, he said only one thing during the year-long proceedings. "Newton was an MP for almost exactly one year, but he seems to have contributed nothing personally to the proceedings of the new parliament. The Wikipedia entry for Newton mentions this and cites Michael White's book from 1997 - The last sorcerer. I’m still not sure about the precision of the overflow and dripping off the water. This could be improvised with something like a large urn and a block to lift the long end a little bit. 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. 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. 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. What we're actually trying to check is that the readout doesn't change when swapping the surroundings from air to water, ex:ĭiff_air = weight(real_gold, air) - weight(suspicious_crown, air)ĭiff_water = weight(real_gold, water) - weight(suspicious_crown, water)Īssert(diff_air = diff_water, "Error, density mismatch detected")Ī good counterfeiter will ensure diff_air=0, but that's just them trying to cheat a much-simpler "very similar mass" test, and it isn't a prerequisite for this "same density" test. It may help to consider that for this experiment we do not actually need to see an "equal" weight-measurement from any kind of scale. Perhaps not enough to see easily, but it's there. Once you apply the dissimilar samples (such as a known 1kg mass of styrofoam versus a known 1kg mass of steel) it will cease to read as perfectly even, because the air-buoyancy of the samples will be different. Both sides are made from the same materials with the same densities and displacements etc. As long as a scale is built symmetrically, an empty scale will read as balanced in any environment. I think you're confusing the tool-calibration step with the actual measuring. The two sides balance, because the weigher makes them balance. 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." The difference in density between the two samples would cause the scale to tip accordingly. 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. 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. The practicality of the method described has been called into question due to the extreme accuracy that would be required to measure water displacement. > The story of the golden crown does not appear anywhere in Archimedes' known works. It describes a very cool alternative method that has higher accuracy, and according to Galileo it's probable that Archimedes used this method:
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