1) "BIRUTZEI MIDOS"
OPINIONS: The Gemara analyzes the statements of Rebbi Yehudah and Rebbi Meir in the Beraisa (87b), who both say that seven liquid measures were used in the Beis ha'Mikdash. They also agree about the sizes of all seven measures. The only apparent difference between them is that Rebbi Yehudah lists the measurements from the smallest size up to the largest (Revi'is Log, Chatzi Log, etc.), while Rebbi Meir lists the sizes from the largest size down to the smallest (Hin, Chatzi Hin, etc.).
Rebbi Yochanan explains that the difference between them is whether "Birutzei Midos" are also Kadosh. Rebbi Yehudah, who lists the measures from smallest to largest, maintains that Birutzei Midos are Kadosh. He maintains that Hash-m showed Moshe Rabeinu that we should use a Revi'is, and that sometimes we will need a Chatzi Log which contains the contents of two Revi'is ha'Log, and so on. The significance of starting from the smallest measure is that the larger measures must be able to contain everything which is in the smaller vessels, including the Birutzei Midos. This position obviously maintains that the Birutzei Midos are Kadosh, since we are concerned that they should fit into the vessel.
Rebbi Meir, who lists the vessels from largest to smallest, apparently maintains that the Birutzei Midos are not Kadosh, since the Birutzei Midos of the larger vessel usually do not fit into the two smaller vessels. Rebbi Meir's list indicates that the Torah was not concerned about the Birutzei Midos, and that he maintains that they are not Kadosh.
What exactly are "Birutzei Midos"?
(a) RASHI (DH Birutzei ha'Midos) explains that Birutzei Midos refers to the part of the contents of a vessel that spill down the sides of the vessel. This is also the opinion of the RAMBAM (Hilchos Ma'aseh ha'Korbanos 2:9) and the ARUCH.
(b) RASHI KESAV YAD (DH Birutzei ha'Midos) apparently understands that Birutzei Midos refers to the part of the contents that pass above the lip of the vessel. Rashi in Zevachim (88a, DH Birutzei) makes a similar statement. This is also the explanation of the BARTENURA here (9:5). (According to the first opinion, this is considered part of the Korban itself and is not Birutzei ha'Midos.)
(c) RABEINU GERSHOM also explains that the Birutzei Midos refers to the contents in the vessel that reach past the top of the vessel, but he understands that it refers to the "foam" that is on top of the contents of the vessel. (According to the first opinion, this is considered part of the Korban itself and is not Birutzei ha'Midos.)
According to the last two opinions, why are the piled contents of the vessel not considered Kadosh? The Gemara earlier (87b) discusses the piled-up contents of a vessel that contains half an Isaron of the Chavitei Kohen Gadol. The Gemara there clearly maintains that it is Kadosh. Why is the Gemara here in doubt about this?
The EIZEHU MEKOMAN answers that when the Gemara earlier says that when the half-Isaron is piled up beyond the top of the vessel it definitely is Kadosh, it refers to when that half-Isaron of flour is the only flour in the vessel. The Gemara here refers to when there is more than the required amount piled up beyond the top of the vessel. (See YAD BINYAMIN, who infers this from the words of TOSFOS, DH Birutzei Midos, unlike the CHAZON ISH, Menachos 27:1.) The Gemara asks whether this amount is Kadosh.
This approach answers a different question on this opinion. The TIFERES YISRAEL (9:35) asks that if "Birutzei Midos" refers to the piled-up contents of the vessel, then why does the Gemara first call these piled-up contents the "Gadish" (87b), and then call it "Birutzei ha'Midos"? Based on the answer of the Eizehu Mekoman, the answer may be that "Birutzei Midos" refers to an extra amount of piled-up contents, while "Gadish" refers to any amount of piled-up contents. (Y. MONTROSE)

88b----------------------------------------88b

2) REKINDLING THE MENORAH AT NIGHT
OPINIONS: Rebbi Aba says that if a flame of the Menorah becomes extinguished, the leftover oil and wick are considered like ashes. The Kohen cleans it out and puts in new oil (in the original amount) and rekindles the wick. RASHI (DH Keitzad) explains that all of the contents of the candle are discarded, and new oil and a new wick are added, and then the flame is rekindled.
When must this process be done? Does Rebbi Aba refer to a flame that becomes extinguished only during the day, only during the night, or at any time?
(a) The RAMBAN in Shabbos (22b) writes that Rebbi Aba refers only to a case in which a flame of the Menorah becomes extinguished during the day. Only when the candle is found extinguished during the day must its oil and wick be changed and the flame rekindled towards night.
(b) The RASHBA (Teshuvos 1:309) explains that there is no obligation to rekindle the Menorah when one of its flames becomes extinguished, whether it becomes extinguished during the day or during the night. The Gemara is discussing the Ner Ma'aravi, the westernmost flame. The Kohen is obligated to ensure that the Ner Ma'aravi is always lit, even during the night.
(c) RASHI (DH Ner she'Kavsah) and RABEINU GERSHOM explain that the Gemara is discussing a case in which any one of the flames of the Menorah became extinguished in the middle of the night or before daylight. They understand that an extinguished flame on the Menorah must be attended to and rekindled immediately. (See, however, the YA'AVETZ, who has difficulty with this explanation. How is it possible to find a flame that went out at night, when one is forbidden to enter the Heichal at night for any purpose other than Hatavah, Hadlakah, or Haktarah?) However, the fact that they mention that the case refers to a flame that becomes extinguished during the night implies that they maintain that when the flame becomes extinguished during the day, it does not need to be rekindled in the same manner as it was lit originally (that is, perhaps the oil does not need to be changed, or perhaps it does not need to be rekindled at all.)
(d) The MINCHAS CHINUCH (98:12) infers from the words of the RAMBAM (Hilchos Temidin u'Musafin 3:12) that he understands that the Gemara means that whenever any flame is discovered to have become extinguished, whether it was during the day or during the night, it must be changed and rekindled. The Minchas Chinuch points out that most Rishonim disagree with this view.
Why does the Rambam rule that the flame must always be rekindled?
1. The Minchas Chinuch (98:15) understands this argument may depend, at least partially, on the interpretation of the verse, "l'Ha'alos Ner Tamid" -- "to kindle the lamp continually" (Shemos 27:20). The Rambam understands that the verse refers to all of the flames of the Menorah, and not just to the Ner Ma'aravi (as the other Rishonim explain). He also understands that the word "Tamid" means literally "always," while the other Rishonim maintain that being lit every night until the morning is considered "Tamid."
2. The Rashba quotes "HA'CHACHAM" who gives a slightly different explanation for the view of the Rambam. He understands that the Rambam maintains that the requirement to rekindle an extinguished flame applies to the Ner Ma'aravi only during the day, and to all of the other candles during the night. He explains that this is the meaning of the Gemara (89a) which discusses the verse, "me'Erev Ad Boker" -- "from evening until morning" (Shemos 27:21). The Gemara quotes a Beraisa which says that one must "place in it the proper amount [of oil] so that it should be lit from evening until morning." The Beraisa continues with another explanation and says that "there is no Avodah which is valid from evening until morning besides this." What does this Beraisa mean? It cannot be referring to when the Menorah is lit, because the verse clearly states that this is supposed to be done towards night. Moreover, if the Mitzvah is done in the evening, the second statement of the Beraisa is not accurate, because the Mishnah in Megilah (20a) says that "any Mitzvah that is supposed to be done at night may be done the entire night," and thus the lighting of the Menorah is not unique in this regard. The Chacham cited by the Rashba therefore understands that the Rambam infers from the Gemara that although the Mitzvah of lighting the Menorah is performed towards evening, the Menorah must remain lit the entire night. This is unlike any other Mitzvah, since this Mitzvah must be done during the day and be maintained throughout the night.
The Rashba responds to the Chacham's approach by saying that although he understands why one would learn this way, he prefers not to learn this way because we never find that the term "Hatavah" refers to changing all of the wicks of the Menorah at night. The Rashba rules that if one finds that a flame became extinguished, he does not need to exchange the wicks. Rather, he merely needs to rekindle the existing wick. This is why the Rashba understands that the Gemara refers only to the Ner Ma'aravi; he maintains that the Ner Ma'aravi is supposed to be aflame at all times. (See also TOSFOS to 86b, DH Mimenah, in contrast to TOSFOS to Chagigah 26b, DH Menorah.)
The Rashba also writes that the proofs of the Chacham from the Gemara later (89a) are not valid. When the Gemara says that the only Avodah that is valid from evening until morning is the Avodah of lighting the Menorah, it means merely that there is no other Avodah done during the day that can be done continuously from the day until the next morning. It does not mean that one must rekindle any flame that goes out during the night. (See EVEN HA'AZEL, Hilchos Temidin u'Musafin 3:12, and YAD BINYAMIN to 86b at length.) (Y. MONTROSE)

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