QUESTIONS: The Beraisa quotes Rebbi who says that the Shi'ur for all Halachos that involve food is a k'Zayis. The only exception to this rule is the Shi'ur for Tum'as Ochlin, which is a k'Beitzah. Rebbi Avahu says that the source for the Shi'ur of a k'Beitzah for Tum'as Ochlin is the verse, "mi'Kol ha'Ochel Asher Ye'achel" -- "All food that is eaten... will become Tamei" (Vayikra 11:34). This verse teaches that the amount of food which can be swallowed at one time is Mekabel Tum'as Ochlin, and the Chachamim assessed this Shi'ur to be a k'Beitzah.
The Gemara continues and discusses the Mishnah (73b) which teaches that the amount of liquid for which a person is liable for drinking on Yom Kippur is "Melo Lugmav," a mouthful. Rav Yehudah in the name of Shmuel says that the Mishnah does not mean an actual mouthful of liquid. Rather, it refers to the amount which, if concentrated to one side of the mouth, would create the appearance of a full mouth.
The Gemara notes that the Mishnah implies that a "Melo Lugmav" is an actual mouthful and not the amount that merely appears to be a mouthful. The Gemara responds that the Mishnah means "k'Melo Lugmav," not an actual "Melo Lugmav." The Gemara challenges this statement from the Beraisa, in which Beis Shamai says that one is liable for drinking a Revi'is on Yom Kippur, and Beis Hillel says that the Shi'ur is a "Melo Lugmav." If "Melo Lugmav" means "k'Melo Lugmav," then the Shi'ur that Beis Hillel prescribes is less than the Shi'ur of Beis Shamai. Consequently, Beis Hillel is more stringent than Beis Shamai. If, however, Beis Hillel means literally a "Melo Lugmav," then his Shi'ur -- two cheeks-full -- is more than a Revi'is, and he is more lenient than Beis Shamai. The Gemara clearly implies that a person can hold more than a Revi'is in both of his cheeks at one time.
The Gemara here apparently contradicts the famous opinion of the Noda b'Yehudah with regard to the size of a Beitzah.
The NODA B'YEHUDAH (d. 5553/1793; see TZELACH to Pesachim 109a and 116b) used his thumbs (Etzba'os) to determine the volume of an egg, based on the figure that the Chachamim set for the size of an egg. The Gemara in Pesachim (109a) describes a Revi'is (which is a measure of liquid volume) in terms of a cubic Etzba (which is a measure of length). Rav Chisda there explains that a Revi'is is equal to the volume contained within a box that is 2 Etzba'os long, 2 Etzba'os wide, and 2.7 Etzba'os high (2 X 2 X 2.7 cubic Etzba'os), or 10.8 cubic Etzba'os.
He then measured the volume of an average egg and found that it was only half of the volume that he calculated with his thumbs. He deduced that either thumbs had become larger than they were in the times of the Gemara, or eggs had shrunk. He argued that it is illogical to presume that thumbs had grown larger, because it is known that each generation is weaker than the previous one. Rather, he concluded that modern-day eggs are only half as large as ancient ones. Therefore, for any Mitzvah that involves the Shi'ur of a Beitzah (or Revi'is), one should use twice the amount that the Gemara requires. (For example, since the Gemara says that one must eat "one k'Beitzah" of Matzah on the first night of Pesach, today one must eat two k'Beitzim of Matzah, based on today's average egg size, in order to compensate for the decrease in the size of eggs.) This opinion is cited as the Halachah by the CHASAM SOFER (Teshuvos OC 127), the VILNA GA'ON (Ma'aseh Rav #105), and the CHAZON ISH (Kuntrus ha'Shi'urim OC 39).
(a) The MINCHAS BARUCH challenges the Noda b'Yehudah's opinion from the Gemara's statement that "the opening to one's esophagus (Beis ha'Beli'ah) cannot hold more than one Beitzah," which implies that it can hold exactly one Beitzah. However, it is clearly impossible to fit two modern eggs at once into the Beis ha'Beli'ah.
(b) The CHAFETZ CHAIM in BI'UR HALACHAH (OC 271:13, DH Shel Revi'is) notes that the Gemara here says that a person can hold more than a Revi'is (or the volume of 1.5 eggs) in both of his cheeks at one time. The Chafetz Chaim further writes that after considerable experimentation, he observed that the average person can hold, at most, the volume of two modern eggs in his mouth at once. According to the Noda b'Yehudah, who says that a Revi'is contains twice the amount of eggs than it did in the times of the Gemara, a person should be able to hold at least three modern eggs in his mouth at once. No average-sized person is able to do this.
(The TOSFOS RID here preceded the Chafetz Chaim with this observation. He writes that even 1.5 eggs cannot be held in the cheeks at once unless a person holds his head in an unnatural downwards position in order to prevent himself from swallowing the liquid in his cheeks. The Tosfos Rid suggests that the words "Im Ken" ("if so") are a mistake and should be omitted from the text of the Gemara. According to this Girsa, the Gemara would maintain that not only is a single cheek-full less than a Revi'is, but even "Melo Lugmav" (two cheeks-full) is less than a Revi'is. Accordingly, the Gemara here would not contradict the Noda b'Yehudah.)
ANSWERS: The CHAZON ISH (Kuntrus ha'Shi'urim OC 39) addresses both questions.
(a) The Chazon Ish (ibid. 39:10) answers the first question with the idea that "Beis ha'Beli'ah" refers to the area of the throat which holds all of the chewed-up food which can be swallowed in a protracted act of swallowing, and not only the amount that fits into the entrance to the esophagus.
(b) He (ibid. 39:16) answers the second question by suggestion that the Chafetz Chaim's measurement might not have been accurate. Perhaps the people whom the Chafetz Chaim asked to fill their cheeks did not stuff them to their absolute capacity. The Chazon Ish cites the RAN who implies that the amount which the average person can hold in his cheeks cannot be measured by experimentation. Apparently, either the amount that it takes to fully stuff a mouth is not measurable, or the definition of an average-sized person is not quantifiable.
(RAV YOSEF BEN-ARZA points out that the proof from the Ran that the amount the mouth can hold is not measurable may not be accurate, because the Ran refers to the minimum amount for which one is liable on Yom Kippur. The Ran says that the exact amount is not measurable because perhaps it is actually less than experimentation shows. However, the Shi'ur which the Chazon Ish says is not measurable is the maximum amount the cheeks can hold.) (See Insights to Pesachim 109:1.)