The Talmud, tractate Menachot 41b sets the relationship between Tefach (halachic handbreadth) and Etzba (halachic finger width). Menachot 97b and 98a explain the relationship of the handbreadth to the cubit. Thus if we could figure out the handbreadth we can determine also halachic finger values and cubit values.
The Talmud tractate Chulin 50b as translated by Sefaria.org states:
Geneiva says that Rabbi Asi says: If a round hole was bored through the external rumen as large as a sela coin, the animal is a tereifa, since if a hole of such size will be stretched, it will reach the length of a handbreadth. Rabbi Ḥiyya bar Abba said: This matter was explained to me personally by Geneiva himself, when we were on the ferry of Neharde’a: If the hole is exactly as large as a sela, the animal is kosher. If the size of the hole is greater than a sela, it is a tereifa. The Gemara asks: And how much is considered greater than a sela? Rav Yosef said: For example, if three date pits covered in remains of the date can fit through the hole with difficulty, or if, without being covered in any remains, they can fit comfortably, this is considered a hole larger than a sela.
Tosafot on that Gemara explains: when the hole of such size will be stretched, it will reach the length of a handbreadth – when you surround the sela coin with a string and then stretch it out, the length will be a handbreadth. Also the Rosh in his Tosafot HaRosh commentary agreed there, that a string that surrounds the Sela coin is equal to a Tefach.
Regarding Which Sela coin are we talking about?
The Gemara in tractate Bechorot (37b – 38a) discussed the size of a sela coin. According to Rav Chisda it is equal in size to a Nero sela coin, while Rav Nachman holds it is smaller than a Nero sela coin. Now Rashi to tractate, Bava Metzia 25b, starting from the word Neronit, explains that the Nero sela coin has the words Caeser Nero (or Neron as vocalized in Hebrew) written on it. And so holds Rabbeinu Chananel to Bava Metzia page 25, and Rambam, Rash, Rosh, and Rabbi Ovadia of Bartenura to the Mishna of Keilim 17:12. However, from the rest of the Rishonim we only learn the sela was made in the period of Caeser Nero but not what was written upon it.
What indeed is the circumference of the coin of Caeser Nero in order to establish the maximum size of the Tefach (handbreadth)?
Rabbi Hadar Yehuda Margolin wrote for the periodical, “Beit Aharon V’Yisrael 105, year 5763, pages 103 – 111 that the diameter of the sela coins found in caches is between 2.5 to 2.6 centimeters approximately. However, I brought to the attention of Rabbi Margolin, Shlit”a that this is imprecise.
According to the web site http://www.ancient-roman-coin.com/nero-coins-imperial :
The diameter of the coin of Caeser Nero in year 62 and year 63 according to the secular system of dating (8 and 7 years before the destruction of the Temple) was 29 millimeters / 2.9 centimeters. While in year 64 until the end of year 66 the diameter was reduced to 26 millimeters / 2.6 centimeters.
According to the true reality the circumference of a circle is equal to the diameter times pi which is about 3.14 or to be a little more accurate the value of 22/7.
22 divided by 7 times 2.6 centimeters produces a Tefach (handbreadth) of 8.1714 cm. and if I multiply this by six, I receive a cubit about 49.0285 cm. which is the larger value of the two cubit sizes, supported by Rabbi Chaim Naeh (see the endnote [i]for further elaboration). For those that support Rabbi Chaim Naeh’s viewpoint it is possible to explain that they used here the formula that the circumference of a circle is equal to the diameter times pi (22/7) because they measured with a string, the hole’s circumference in the animal that possibly received a wound making it into a Treifa and did not use the formula that the Diameter is exactly a third of the circumstance. And one is urged to see in the commentary of Rambam to Eruvin chapter 1, Mishna 5 that he too admits, that the diameter times the value of pi is more accurate than the diameter multiplied by 3 when you wish to determine the circumference.
The Rosh, after agreeing that a string encircling the area of a Sela coin equals a Tefach (handbreadth), determines using the inexact formula, that a third of the circumference of the circle equals the diameter, and thus according to his outlook is the rule that we practice in a number of areas of Halacha, namely, we consider the diameter to be a third of the circumference.
I searched and found that the Rosh too, was also aware of the fact that it is not scientifically precise that the diameter of the circle = one third of the circumference. And here I will quote a Hebrew article that I found at
https://www.kby.org/english/torat-yavneh/view.asp?id=5826
“On the topic in Eruvin (14a) regarding the Sea of Solomon, Tosafot HaRosh (authored by the Rosh) writes: “Anything that is three in circumference has a width of a Tefach (handbreadth), from where (in the Bible) do we know it? I’m wondering why is it relevant to look for a Biblical source on a matter that eyes can see and a man can measure himself. Let them bring an object which is one Tefach (handbreadth) wide and we will measure the circumference! And it appears to me to explain, because the calculation (made by the Talmud) is not exact; and the circumference is really greater than 3 handbreadths and what the Talmud is really asking, from where in the Bible do we have a precedent for the sages providing a limit and a measure for a certain matter, even though it is not precise, but only a close approximation to the true results, and they bring a precedent, that scripture itself did so regarding the Sea of Solomon…
These things wonderfully settle our three perplexities regarding the accuracy of calculating a circle (even though Tosafot HaRosh came to answer a completely different question…). It must be said that the Gemara did not bring the verse to teach a geometric value that can be easily measured, but to teach that there is no need to be more precise than that and it is possible to be satisfied with this approximation (that the ratio is 1 to 3) for the purpose of calculating the circle. And the truth is easily recognizable.
The responsa of the Tashbetz (Volume 1, Chapter 165) answers someone who asked about this topic and he answered it is possible to accept one of the two following ideas:
“Their tradition was to go by these methods, and even though they are only an approximation, because halachic measurements are in the category of Halacha that was orally transmitted from Moshe from (the) Sinai (revelation) as we find in Eruvin (4a) … And it is possible to say that such was told to us as Halacha that was orally transmitted from Moshe from (the) Sinai (revelation) … And the reason is that the Torah was not given to the ministering angels … And perhaps thus was it transmitted to them, the following Halacha, namely, that they following these principles even though they are only an approximation as if they were precise. And there is a Biblical hint to this approach regarding the Sea of Solomon, that the scripture only used an approximation”….
“They when they had a back and forth discussion over these principles, did so, in order to make it more comprehensible for the students because as we learn in the first chapter of the Talmud Tractate Pesachim 3b “Always a person should teach his student in a concise manner … but when it comes to actual practical application, we have to be precise with the true precision and it was transmitted to the sages that know the measurements. It turns out that the (general) Halacha was given over to the new students, but the practical application was transmitted to the sages to be precise based on the truth and this is straight way in my eyes to rectify their words (of the sages) of blessed memory … And even though they raised in tractate Succa … Say that we say that the Sage was not precise when the result is a stringency, however, when the result is a leniency, do we say the Sage was not precise?
That is when it is a large amount but if it is a small amount, they won’t be concerned about it (to give an approximation) in order not to confuse the students … And furthermore there is to say that they found a verse to assist them (to give an approximation) by the precedent used for the Sea of Solomon …
The Amount of Caesar Nero Coins that They Have Found
The coins of Caesar Nero have been found among us abundantly, perhaps thousands (“Midot V’Shiurei Torah” page 17) and they are artifacts from the Second Temple where there are no doubts about their authenticity since they have the royal seal bearing the image of Caesar Nero.
The diameter of the Sela is suitable according to system of measurement of Rabbi Chaim Naeh and perhaps it can also fit with those who reduce the cubit to a greater degree than Rabbi Chaim Naeh did. But the diameter of the Nero sela coin, even if we choose the diameter of 2.9 cm that was used eight and seven years before the destruction of the Temple still does not work with the Tefach size assumed by the Chazon Ish. For behold 22/7 multiplied by 2.9 equals approximately 9.11 cm. far below the expected outcome using Chazon Ish standards.
The Ruling of the Rambam – Rambam Laws of Slaughtering 9:6 as translated by Eliyahu Touger, Moznaim Publishing at Sefaria.org
[The following rules apply if] a circular or oblong portion of this flesh was cut. If it was larger than a sela, i.e., large enough to fit tightly three date seeds next to each other, [the animal] is trefe. For when this size cut will be extended, it will be a handbreadth in length.The Thickness of Date Seeds According to Prof. Kislev
I asked Prof. Mordechai Kislev by e-mail, since there is a lack of clarity about the size of the sela coin that Rambam mentioned, “I wanted to ask you – do you know the thickness of date seeds at the time of Rambam?”
He answered:
To the Honorable …
We will attempt to answer you.
1 This is probably about the width of the seed, because it is difficult to stand the seed up on its side.
2 The variety of types dates in Egypt is large today and it is assumed that such was the same in the past.
3 I propose to take for the purpose of calculation the Hayani variety which is very common today in northern Egypt,
There is evidence of this variety growing there for hundreds of years. It has subspecies, it is not uniform.
4 In Zvi Bernstein’s book, 2004, The Tamar, p. 372, there us a photo of a Hayani seed in its natural size.
5 The width of the Date seed is about 8 mm.
In a separate e-mail Prof. Kislev added
In the (Hebrew) work of Dr. Bella Caspi, Jewish Year 5778 dealing with Morphologic and morphometric characterization of Date Palm seeds from Masada, published by University Bar-Ilan, page 77, I found on page 77, the following data (in millimeters) relating to ten date seeds/kernels of the Hayani, Retzanti variety.
(The last 3 columns of this chart are calculations made by Shlomo Scheinman and colored in blue).
| Length | Width | Thickness | Width of 3 Dates | Multiplied By 22/7 | Multiplied By 3 | |
| Average | 24.8 | 8.9 | 7.6 | 26.7 | ~83.91 | 80.1 |
| Standard Deviation | 1.4 | 0.5 | 0.5 | 1.5 | ~4.71 | 4.5 |
| Minimum | 22.8 | 8.4 | 7.0 | 25.2 | ~79.2 | 75.6 |
| Maximum | 28.0 | 10.0 | 8.5 | 30.0 | ~94.26 | 90.0 |
Note: In the Hebrew version of this article I also provided the calculation for the thickness of 3 Dates multiplied by 22/7 and multiplied by 3. In the English version, I will let the reader do the calculation if you think it is necessary.