Before creating the 5 weights, The ancients had to create a 1 gram weight to measure out all their other weights.

So the ancients had a bunch of super fine sand which was made entirely of the same material, and every grain was its most basic material. They had 121 grams of this sand. They also had a tube which could hold exactly 121 grams of sand, no more, no less.

How do the ancients weigh out 1 gram of sand?

The ancients had to create a 1 gram weight, but maybe they don't need to weigh out one gram of sand to do it.

Say they have a balance, and they reconfigure it so the lengths of the balance arm on either side of the fulcrum have a 121:1 ratio. They place the empty tube on the short arm, and make a weight that counters the empty tube when placed on the long arm. Next, they fill the tube with sand and put it back on the short arm of the balance. They leave the first weight on the long arm (this counters the weight of the tube), and fashion a new weight to counter the 121g of sand. If balanced, this new weight will be 1g.

Posted by Bryan on 2003-04-14 08:51:37