A Sage taught in the Tosefta: And half of one half of its half, one-eighth of this loaf, is the minimum measure of food that contracts the ritual impurity of foods. The Gemara asks: And our tanna, in the mishna, for what reason did he did not teach the measure of the impurity of foods? The Gemara answers: He did not state this halakha because their measures are not precisely identical. The measure for the impurity of foods is not exactly half the amount of ritually impure food that disqualifies one from eating teruma.

As it was taught in a baraita: How much is half a peras? Two eggs minus a little; this is the statement of Rabbi Yehuda. Rabbi Yosei says: Two large eggs, slightly larger ones than average. Rabbi Yehuda HaNasi measured the amount of half a peras after calculating the number of kav in the se’a brought before him, and found it to be a little more than two eggs. The tanna asks: How much is this little more? One-twentieth of an egg.

In contrast, concerning the impurity of foods, it was taught in a baraita: Rabbi Natan and Rabbi Dosa said that the measure of an egg-bulk, which the Sages said is the amount that contracts the impurity of foods, is equivalent to it, i.e., the egg, and its shell. And the Rabbis say: It is equivalent to it without its shell. These amounts are not precisely half of any of the measurements given for half a peras.

As for the issue itself, Rafram bar Pappa said that Rav Ḥisda said: This baraita that clarifies the measure of half a peras is in accordance with the statements of Rabbi Yehuda and Rabbi Yosei, a measure that is identical to that of Rabbi Shimon in the mishna. But the Rabbis say: One and one half large egg-bulks. And who are these Rabbis? Rabbi Yoḥanan ben Beroka.

The Gemara registers surprise: This is obvious, as Rabbi Yoḥanan ben Beroka maintains that half a loaf is three egg-bulks, half of which is an egg-bulk and one half. The Gemara explains: The novel aspect of this teaching is not the amount itself; rather, he came to teach us that the measurement is performed with large eggs.

The Gemara relates that when Rav Dimi came from Eretz Yisrael to Babylonia, he said: A person named Bonyos sent Rabbi Yehuda HaNasi a measure [modya] of a se’a from a place called Na’usa, where they had a tradition that it was an ancient and accurate measure (Ritva). And Rabbi Yehuda HaNasi measured it and found it contained 217 eggs.

The Gemara asks: This se’a, from where is it, i.e., on what measure is it based? If it is based on the wilderness se’a, the standard measure used by Moses in the wilderness, which is the basis for all the Torah’s measurements of volume, the difficulty is that a se’a is composed of six kav, where each kav is equivalent to four log and each log is equivalent to six egg-bulks. This means that a se’a is equivalent to a total of 144 egg-bulks.

And if it is the Jerusalem se’a, then the se’a is only 173 egg-bulks, as they enlarged the measures in Jerusalem by adding a fifth to the measures of the wilderness.

And if it is a se’a of Tzippori, as the measures were once again increased in Tzippori, where another fifth was added to the Jerusalem measure, the se’a is 207 egg-bulks. The se’a measured by Rabbi Yehuda HaNasi does not correspond to any of these measures of a se’a.

The Gemara answers: Actually, this measure is based on the se’a of Tzippori, but you must bring the amount of the ḥalla given to a priest, and add it to them. That is to say, although this measure is slightly larger than a se’a, if it is used for flour and you deduct the amount due as ḥalla, you are left with exactly one se’a, or 207 egg-bulks.

The Gemara raises an objection: The amount of ḥalla, how many egg-bulks is it? Approximately eight egg-bulks, one-twenty-fourth of 207. Yet in that case, it remains less than 217 egg-bulks, for even if we were to add another eight egg-bulks for ḥalla to the 207 egg-bulks, we would have only 215 egg-bulks, almost 216 to be more precise, which is still less than 217.

Rather, you must bring the excess amounts of Rabbi Yehuda HaNasi, the little more he included in his measure, and add these to them. In Rabbi Yehuda HaNasi’s calculations, he did not factor in the ḥalla that had to be separated. Instead, the egg-bulks he used to measure the se’a were small egg-bulks. Consequently, one-twentieth of an egg-bulk must be added for each egg-bulk. Since one-twentieth of 207 egg-bulks is roughly ten, the total amount equals 217 egg-bulks.

The Gemara raises an objection: If so, it is still slightly more than 217 egg-bulks, by seven-twentieths of an egg-bulk, to be precise. The Gemara answers: Since it is not more than 217 egg-bulks by a whole egg, he did not count it.

The Sages taught in a baraita: A Jerusalem se’a is larger than a wilderness se’a by one-sixth, and that of Tzippori is larger than a Jerusalem se’a by one-sixth. Consequently, a se’a of Tzippori is larger than a wilderness se’a by one-third.

The Gemara inquires: One-third of which measurement? If you say it means one-third of a wilderness se’a, now you must consider: One-third of a wilderness se’a, how much is it? Forty-eight egg-bulks, and yet the difference between the wilderness se’a and the Tzippori se’a is sixty-three egg-bulks. As stated above, a Tzippori se’a is 207 egg-bulks, whereas a wilderness se’a is only 144 egg-bulks.

But rather, this one-third mentioned in the baraita is referring to one-third of a Jerusalem se’a, which is 173 egg-bulks, as stated above. The Gemara again examines the calculation: One-third of that se’a, how much is it? Fifty-eight less one-third, and yet the difference between the wilderness and the Tzippori se’a is sixty-three. Rather, you must say that it is referring to one-third of a Tzippori se’a. One-third of that se’a, how much is it? Seventy less one-third, and yet the difference between the wilderness se’a and the Tzippori se’a is sixty-three egg-bulks. The difference between the measures is not exactly one-third according to any of the known se’a measurements.

Rather, Rabbi Yirmeya said that this is what the tanna is saying: Consequently, a se’a of Tzippori is larger than a wilderness se’a by sixty-three egg-bulks, which is close to one-third of a Tzippori se’a of sixty-nine egg-bulks. And one-third of it, sixty-nine egg-bulks, is close to half of a wilderness se’a of seventy-two egg-bulks.

Ravina raised an objection to the opinion of Rabbi Yirmeya: Does the baraita state either: Close to one-third of a Tzippori se’a or: Close to half of a wilderness se’a? The wording of the baraita indicates an exact amount. Rather, Ravina said that this is what the tanna is saying: Consequently, one-third of a Tzippori se’a together with the excess amounts of Rabbi Yehuda HaNasi is greater than half of a wilderness se’a of seventy-two egg-bulks by only one-third of an egg. In other words, a Tzippori se’a of 207 egg-bulks added to the excess amounts of Rabbi Yehuda HaNasi of one-twentieth of an egg-bulk for each egg-bulk amounts to a total of 217 egg-bulks, one-third of which is seventy-two and one-third egg-bulks.

Our Sages taught a baraita: The verse states: “You shall set apart a cake of the first of your dough as a gift; like the gift of the threshing floor, so shall you set it apart” (Numbers 15:20).