Q&A: Old-Time Scales, and Deciding the Weight by a Deviation of a Handbreadth
Old-Time Scales, and Deciding the Weight by a Deviation of a Handbreadth
Question
Hello Rabbi,
I was asked the following question: old-time scales, with two pans. I was told that the Jewish law is that if there is up to a handbreadth between one pan and the other, the weighing is valid. In Choshen Mishpat 231:13, scales are mentioned with a beam length (a cubit times two) that differs for each type of merchandise: 12 handbreadths, 9 handbreadths, etc. As far as I know, if there were not a bit of friction at the central pivot of the beam, then even the smallest difference in weights would cause one pan to go down and the other to rise. So one must assume there is a bit of friction. What is unclear is how they gave a measure of a handbreadth between the pans when the arm length was not defined. If the arm length is great, then a handbreadth expresses a relatively small difference in weight, but if the arm length is short, a handbreadth could indicate a large difference between the pans. Therefore, the same difference between the weight of the merchandise and the weight in the other pan would be considered a valid weighing on small scales, but on scales with a long beam the weighing would be invalid. Have you come across such a question? I would be glad for an answer or some thoughts on the matter. In my opinion, every scale would need its own special calibration with a table, and the permissible difference between the weights as a percentage would determine whether that is a handbreadth more or less. I hope the question is clear. Thanks in advance,
Ze’ev
Answer
The question is completely clear, and I noticed it myself in the past. Some of the medieval authorities understood that the scales were shaped like the letter chet, and then this is possible. But according to the medieval authorities for whom it was a bar with two cords on the sides, this has no meaning at all.
Discussion on Answer
It means that this is a mistake and such a criterion has no significance. That ruling is null and void because it is based on an error.
There are some of the medieval authorities there in the Talmudic passage who speak about scales in the shape of a chet, meaning that the pans hang by a cord from the bottom of each leg of the chet. In that situation it is clear that the scales stop at a height that depends on the differences in weight.
Sorry for the bother. I drew the situation. I compared the torque of the heavier weight m1 to the torque of the lighter one m2 and, with a bit of trigonometry, I got that the angle of tilt of the beam, alpha, does indeed depend on the difference in masses divided by their sum, but also on the beam length L. The difference in height between the two pans is the sum of how much one descended and how much the other rose, and that sum equals twice the drop of the end of the beam.
And that drop depends on the beam length. In short, I didn’t manage to get a dependence only on the two masses. I’ll check myself again. In any case, thank you. Ze’ev
These calculations are completely unnecessary. You do not know what the dimensions were there, and it is possible that they were talking about standard scales. What is the point of all these calculations?
Thank you very much. I really thought that perhaps they were referring to certain specific scales, and that it is not relevant to other scales.
All the best.
Thank you for the quick response. From the rabbi who wrote to me, I understood that this is the accepted halakhic ruling, so what does “has no meaning” mean? I would ask to understand, or for you to point me to where it is suggested that this is talking about scales in the shape of a chet, and to understand how that helps, because there too there are presumably arms.
Have a good week.