In the beginning of the fourth perek we learn that nisuch hamayim – the water libations unique to sukkot – were performed each of the seven days of sukkot. Once we reach the ninth Mishnah we learn that the number of days it was performed is really the subject of debate. While the Chachamim indeed maintains that it was performed each of the seven days, R' Yehuda argues that it was also performed on the eighth day - on Shemi Atzeret. The debate appears to extend to the volume of water that was used. The Chachamim understand that it was three log while R' Yehuda maintains a single log was used. How do we understand this debate?
Rav Soleveitchik ztz"l (Harerei Kedem I, 152) connects the debate to the nature of Shemini Atzeret itself. The Gemara explains that Shemini Atzeret is an independent festival with respect to six matters following the acronym "pazar kashav". It has an independent "lottery" (payis) referring to system used to determine the work performed by the Kohanim. It is independent with respect to “time” (zeman). Rashi explains this refers to requirement to recite shehechiyanu. Shemini Atzeret is an independent “festival” (regel). Rashi explains that this refers to not sitting in the sukkah. Finally it has an independent sacrifice (korban), an independent song (shir sung by the Levi’im) and has an independent blessing (beracha). The Gemara in Yoma (2b) however explains that with respect to tashlumin, bringing the shalmei Simcha that should have been brought during sukkot, it extends to Shemini Atzeret.
The Rav notes that the way Shemini Atzeret is listed in the Torah differs with context. In Parashat Emor, that discusses the prohibition of melacha and Parashat Pinchas that lists the korban mussaf, Shemini Atzeret is mentioned as an independent festival. However, in Parashat Reah, Shemini Atzeret only appears by way of an exposition
The Rav concludes then that with respect to kedushat ha'yom (sanctity of the day), prohibition of melacha and korban mussaf, Shemini Atzeret is treated independently. However, regarding the olot re'iyah, chagigah and Simcha, Shemini Atzeret acts as a tashlumin for sukkot.
The Rav uses this dual nature of Shemini Atzeret to explain our Mishnah. According to the Chachamim, nissuch ha'mayim is connected to the kedushat ha'yom, much like the korban mussaf. That being the case, since Shemini Atzeret is considered independent in that respect, the nissuch ha'mayim is only performed during that seven days of sukkot. This also explains why they maintain three log was used. Since the nissuch ha'mayim is part of the family of korbanot of the day, it follows that the volume that matches another libation, the nisuch ha'yayin (wine libation), would be used.
R' Yehuda however understand the obligation of nissuch ha'mayim stems from the kedushat ha'regel, as in Parashat Re'eh; in the family of re'iya and Simcha. That being the case, since Simcha extends to Shemini Atzeret, so does the nissuch ha'mayim. Since it not connected to the kedushat ha'yom, the volume does not need to follow the nissuch ha'yayin and a log can be used instead.
Based on the above, according to R' Yehuda why was a log used and not any other volume? The Tosfot Yom Tov also understands that R' Yehuda includes nissuch ha'yamim on Shemini Atzeret much like Simcha is extended. When addressing why a log is used, he suggests that perhaps R' Yehuda agrees with R' Eliezer ben Yaakov (Menachot 9:3) who maintain that along with a voluntary mincha offering, irrespective of the volume of flour, one log of oil was used. Consequently, since the volume of oil in a voluntary offering is assumed to be a log, in the absence of a specified volume for nissuch ha'mayim, we use a log. Alternatively, he suggests that we find that a poor metzora would bring one log of oil as part of his korban. Consequently, in the absence of a volume, we select the smallest volume that we find elsewhere.
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