5 ms·

Very interesting article, would definitely like to read the paper when I get the time. Something I would like to understand is how these old systems scaled the

Very interesting article, would definitely like to read the paper when I get the time. Something I would like to understand is how these old systems scaled the reference measurements to order of magnitude larger/smaller weights to measure. Up until recently (before the SI redefinition of weight to physical constants) this was an issue even with the modern definition of the kg where for measuring larger and larger weights we essentially have to resort to larger reference weights. And in doing so the manufacturing complexity grows significantly if you want to hold the same uncertainty (as a %). And of course, this applies when measuring masses significantly smaller than the reference 1kg prototype.

myself248 5y ago
Is it really that hard? You make a lever/beam with notches at regular intervals. Move the hooks to set the ratio, and you can compare weights of arbitrary ratios. Sure there's some loss of precision at each step, but assuming you minimize the stacking of errors and return to the master reference whenever possible, I'd imagine it to be precise enough for pre-scientific uses. Note that many old measurement systems use factors other than 10, which happen to be easy to multiply/divide with ratios of 2 and 3, which happens to be very easy to make levers/beams for.
mikewarot 5y ago
Given the simple balance pictured in the article, it should be fairly easy to scale up or down by small integer ratios. First, you can put two equal weights on the scale, then swap them to make sure they are the same, AND the scale is fare. Next, you could make duplicates of that weight. You could then use some small number of them to make a heavier standard. You could also make some smaller weights, slightly heavier than 1/2 of the weight, and grind them down until they add up to 1 standard unit. You could then work on duplicating the heavier one, and then shave both of them down a bit at a time until they are equal, and match the standard weight. With time, you could probably come up with a fairly good set of standards, each up/down would be correct to a tolerance of the sensitivity of the scale. All of this without a modern beam balance.

myself248 5y ago

Is it really that hard? You make a lever/beam with notches at regular intervals. Move the hooks to set the ratio, and you can compare weights of arbitrary ratios. Sure there's some loss of precision at each step, but assuming you minimize the stacking of errors and return to the master reference whenever possible, I'd imagine it to be precise enough for pre-scientific uses. Note that many old measurement systems use factors other than 10, which happen to be easy to multiply/divide with ratios of 2 and 3, which happens to be very easy to make levers/beams for.

mikewarot 5y ago

Given the simple balance pictured in the article, it should be fairly easy to scale up or down by small integer ratios. First, you can put two equal weights on the scale, then swap them to make sure they are the same, AND the scale is fare. Next, you could make duplicates of that weight. You could then use some small number of them to make a heavier standard. You could also make some smaller weights, slightly heavier than 1/2 of the weight, and grind them down until they add up to 1 standard unit. You could then work on duplicating the heavier one, and then shave both of them down a bit at a time until they are equal, and match the standard weight. With time, you could probably come up with a fairly good set of standards, each up/down would be correct to a tolerance of the sensitivity of the scale. All of this without a modern beam balance.