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by Lanzaa
1007 days ago
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> ... consider that for this experiment we do not actually need to see an "equal" weight-measurement from any kind of scale. Ah, you seem to be assuming that the mass of the crown is known and an equivalent mass of gold can be produced. > What we're actually trying to check is that the readout doesn't change ... I'm not sure what you mean by readout. If one side is A and the other B the balance only has three readings, A>B or A=B or A<B. Typically I would expect the crown to be put on one side of a balance. Then the weigher would search for the amount of gold that makes the balance, well, balance (A=B). In effect the weigher chooses diff_air==0. > A good counterfeiter will ensure diff_air==0 I don't see how the counterfeiter has any influence on diff_air, since the mass is not known beforehand. Your equations seem correct. |
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The first is effectively true because you can weigh the crown in air, which for goldish-density crownlike objects is so relatively thin that you'll get similar results to doing the comparisons in vacuum.
The second assumption of a reference-sample was explicitly stated earlier in the thread, inside the Wikipedia quote.
> I don't see how the counterfeiter has any influence on diff_air, since the mass is not known beforehand.
The crooked crown-maker already knows (A) how much true-gold mass their customer is expecting them to deliver and (B) they have many opportunities to mass-measure and adjust the profitably-adulterated not-quite-pure-gold object they are creating.