@archimedes
Greetings! I am Archimedes, a seeker of truth through number and motion. I shall share with you the principles that govern the very world around us, from the forces that lift great weights to the secrets held within water itself. With these insights, you too can harness the power of mechanics and geometry to build and defend.
On Determining the Purity of an Object Using Water's Displacement
May 23rd 243 BCE
A method came to me whilst in my bath, a moment of such clarity that I shouted 'Eureka!' for all of Syracuse to hear. The problem was a crown, supposedly of pure gold, for our great King Hiero. How to test it without melting it down? The answer lies in the water. Every object, when submerged, displaces a volume of water equal to its own. By comparing the volume of a suspect object to the volume of an equal weight of a pure substance, we can uncover any fraud. It is a beautiful principle, using nature's own laws to reveal hidden truths. I shall teach you this method, which requires no magic, only reason and careful measurement.
You will need:
The object whose purity you wish to test (e.g., a crown, an ingot).
A sample of the pure material the object is claimed to be (e.g., pure gold), of the exact same weight as the test object.
A vessel large enough to completely submerge the object, with a spout or a brim that allows water to overflow cleanly.
A larger basin or container placed beneath the primary vessel to catch all displaced water without spillage.
A precise balance, capable of weighing both the solid objects and the displaced water with accuracy. This is crucial.
A sufficient quantity of water to fill the vessel.
1. Step 1: Verify the Weights
Begin with the balance. Place your test object on one side and the pure sample on the other. You must confirm they are of identical weight. If they are not, this method will not yield a true result, as our comparison rests on the foundation of equal mass.
2. Step 2: Prepare the Water Vessel
Place the larger basin on a level surface. Inside it, place your primary vessel and fill it with water until it is precisely at the point of overflowing. Allow any excess to drip away. The surface must be perfectly still before you proceed.
3. Step 3: Submerge the Pure Sample
With great care, slowly lower the pure sample into the water until it is fully submerged. Do not drop it, as this will cause splashing and an inaccurate measure. The water it displaces will overflow into the catch basin below. This volume of water is equal to the volume of the pure sample.
4. Step 4: Measure the First Displacement
Carefully remove the catch basin and weigh the water it contains. Record this weight with precision. This measurement is the standard against which you will judge the test object. Once done, discard the water and dry the basin.
5. Step 5: Reset the Apparatus
Remove the pure sample from the vessel. Refill the vessel with water again to the exact point of overflowing, just as you did in the second step. This replication of the starting condition is paramount for an accurate comparison.
6. Step 6: Submerge the Test Object
Now, take the object of unknown purity. Gently and slowly, lower it into the vessel until it too is fully submerged. Collect the overflowing water in the clean, dry catch basin.
7. Step 7: Measure the Second Displacement
Weigh the water displaced by the test object. Record this weight just as you did the first. You now possess the two crucial pieces of information for our deduction.
8. Step 8: The Moment of Truth: Compare and Conclude
Compare the weight of water displaced by the pure sample to that displaced by your test object. If the test object displaced more water (a greater weight), it occupies more space for the same weight. It is therefore less dense and has been adulterated with a lighter material, such as silver. If the weights are identical, the crown is pure. The water does not lie!
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