After covering the Addiator I was curious to see if there were similar devices in earlier times. Rome used primitive abacuses, just stones sliding in grooves on wood. Not really a device. Googling medieval abacus led solely to this gadget:
There’s only one source for the picture and description, a 1682 encyclopedia of ancient things by Marcus Welser. The British Museum has a photo that appears to be the real thing, but it’s described as a reproduction made in the 1800s. The British model showed me how the beads work, not clear in the original sketch.
Welser doesn’t say when or how it was used, only that it was made of brass, “of a form and size shown by the picture.” After cleaning up and separating the labels, here’s my model:
The long columns were obviously influenced by the soroban**, with one bead in heaven and four beads in earth. Roman stone-in-groove counters didn’t have separate heaven and earth. The eighth column has five beads in earth. The short columns on right suggest fractions, similar to the Hapennies and Farthings in the Addiator.
First I tried to work it out myself from the picture. Some parts are immediately obvious. C X I are columns for 100, 10, 1. To the left of C are variant symbols for the higher places. ‘Infinity’ is a condensed form of CIↃ for thousand, which may have helped to suggest M. CCIↃↃ is 10,000 and CCCIↃↃↃ is 100,000. IXI isn’t in the usual sources but must mean one million.
The Theta column to the right of I was completely unfamiliar, and the usual sources didn’t help. It has five beads in earth, which implies base 12 instead of base 10.
I translated Welser’s text, and after untangling I got it. The Theta column is calibrated in 1/12 increments like all Roman fractions. Welser says each bead in Theta represents one Sestertius, and the beads in the I column represent Asses.
Not donkeys or politicians! The roman As was a coin corresponding to the British pound, and these Sestertii were on the same weight level as Shillings, though they seemed to act more like Pence. Sources gave other proportions, usually 2.5 Sestertii in one As, but not 12. Nevertheless, Welser is certain on this point.
The fractions were still unclear. S was familiar: Semis for half or 6/12 of a unit, the base of the fraction system described in previous item. The other two seemed wrong. The Ↄ normally means thousand but couldn’t mean it here. The 2 was a total mystery. I translated Welser:
About the beads S, C, 2 it is not very clear, nor do I yet correctly understand their use.
He was just as puzzled as I was! But I have the Web, and Welser had only his books. The Web plus some interpolation yielded a partial answer.
S is Semis, half or 6/12 of a unit.
Ↄ is Sicilicus, 1/48 of a unit or 1/4 of 1/12.
2 must mean Ƨ for Sextula, 1/72 of a unit or 1/6 of 1/12.
Treating the unit as one As gives a consistent pattern that looks like coinage.
S, Semis, is a half-As or 6 Sestertii.
Ↄ, Sicilicus, is 3/12 or 1/4 of a Sestertius.
Ƨ, Sextula, is 2/12 or 1/6 of a Sestertius.
This system, base 12 for all parts and base 10 for all wholes, is more consistent than the British, which has 12 Pence in one Shilling but 20 Shillings in one Pound.
I still don’t know if this abacus was actually used, but it certainly looks like a practical tool for commerce. Most European money followed the Roman pattern, with changed names and later changed ratios. Symbols tend to stick around when the name changes, as with the P for Peso that remained after the name changed to Dollar, or the L for Libra after the name changed to Pound.
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Polistra and friends are using the abacus in the Pyx Chapel to calculate an unknown weight. Polistra has placed an unknown pile of coins in the left pan, and then balanced it with 28 Asses, 7 Sestertii, 1 Semis and 1 Sextula. Martian recorded the results on the abacus.
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** Later note: I tried to determine when the soroban could have influenced Roman or medieval merchants. It appears that the Roman Hand Abacus developed separately, perhaps earlier. If there was influence it might have been the other way around. This webpage on Ancient Computers discusses the Roman Hand Abacus and shows another model based on the Welser picture.
Polistra's Mill 