Gemara

Bar Kapara: According to R. Meir, a separate Ma'arachah is made for leftover limbs, even on Shabbos.

Question: What is the Chidush? R. Meir explicitly said that every day there are four Ma'arachos!

R. Avin: This is even if they are Pesulim.

He argues with Rav Huna.

Rav Huna: The Tamid is Docheh at the beginning, but not at the end.

Question: What does this mean?

Answer #1 (Rav Chisda): (Haktarah of (leftover) limbs or Chelev of) the Tamid is Docheh Shabbos, but it is not Docheh Tum'ah.

Answer #2 (Rava; some texts say 'Rabah'): It is Docheh Tum'ah, but it is not Docheh Shabbos.

Question (against both of them - Abaye): The same source that the Tamid is Docheh Shabbos ("b'Mo'ado") teaches that it is Docheh Tum'ah. If it is Docheh one, it should be Docheh both!

Answer (Rava, for himself): The end is like the beginning. The beginning is Docheh Tum'ah (if we cannot bring the Tamid b'Taharah, we bring it b'Tum'ah), so also the end is;

The beginning (of the Tamid of Erev Shabbos) is not Docheh Shabbos, so also the end is not.

Answer (Rava, for Rav Chisda): Rav Chisda does not hold that the end is like the beginning. Rather, since Shabbos is Hutrah (totally permitted) regarding Avodas Tzibur, the end is Docheh Shabbos;

Tum'ah is not Hutrah, rather, Hudchah b'Tzibur. Since the primary Kaparah is the beginning of the Hakravah, it is Docheh Tum'ah. The end is not the primary Kaparah, therefore it is not Docheh Tum'ah.

Shabbos 20a: "Lo Seva'aru Esh b'Chol Moshvoseichem" - you may not burn in your dwellings, but you may burn limbs and Chelev on the Mizbe'ach (on Shabbos).

114a (Beraisa - R. Yishmael): "Olas Shabas b'Shabato" permits to offer Chelev of Shabbos on (another 'Shabbos', i.e.) Yom Kipur;

R. Akiva says, it permits to offer Chelev of Shabbos on Yom Tov.

Suggestion: Perhaps it may be offered even on Yom Kipur!

Rejection: "B'Shabato" excludes this.

Pesachim 46a - Mishnah: Five Korbanos (that are normally eaten) are brought b'Tum'ah but may not be eaten b'Tum'ah - the Omer, Shtei ha'Lechem, Lechem ha'Panim, Zivchei Shalmei Tzibur, and Se'irei Rosh Chodesh.

Rishonim

Rashi (DH Mai): It is best to explain that 'the beginning' refers to Zerikah, and 'the end' refers to Haktaras Eimurim. Some say that 'the beginning is Docheh Tum'ah' refers to Haktaras Chelev, and 'the end' refers to Haktarah of leftover limbs.

Rashi (Avos 5:5 and Ritva 21a DH v'Lo Nimtza): If the Omer, Shtei ha'Lechem or Lechem ha'Panim became Tamei, it could not be offered.

Note: According to Rashi's first explanation, this is like Rav Chisda. According to Rava, even if it became Tamei it is offered.

Question #1 (against Rashi's first explanation): A Mishnah (Pesachim 76b) teaches that five Korbanos are brought b'Tum'ah but may not be eaten b'Tum'ah. This implies that only eating is forbidden, but they are totally offered. If a Korban became Tamei in the middle, we tell the Kohen to offer it quietly (6a).

Answer (Tosfos DH Techilaso): The Kometz of a Minchah may be offered b'Tum'ah, for it is like the beginning, like Zerikah.

Question #2 (Tosfos ibid.): It is unreasonable to say that Rav Chisda discusses Hakravah in the proper time, and Rava discusses Hakravah of something left over!

Conclusion (Tosfos, ibid.): Rather, Rashi's second explanation is better.

Rambam (Hilchos Temidim u'Musafim 1:7): Limbs of the Tamid are Docheh Tum'ah, but they are not Docheh Shabbos. Limbs of the Tamid of Erev Shabbos may be burned only on Erev Shabbos. The beginning of the Tamid is Docheh Shabbos, but the end is not.

Ri Korkus: The Rambam explains like Rashi's first explanation. 'The beginning' refers to Shechitah and Zerikah; 'the end' refers to Haktaras Eimurim. The Rambam rules like Rava because he is Basra. Also, the Gemara said that Bar Kapara argues with Rav Huna, and this is only according to Rava.

Tosfos (ibid.): Bar Kapara (as explained by R. Avin) argues with Rav Huna also according to Rav Chisda, for Bar Kapara says that (according to R. Meir) a separate Ma'arachah is made even for leftover Pesulim.

Mishneh l'Melech: According to Tosfos, Rav Chisda holds that Pesulim are burned on the big Ma'arachah.

Question: What is the Gemara's source that Rav Huna argues with the previous teaching? Perhaps Rav Huna discusses limbs that did not catch fire, but he agrees that we Mechalel Shabbos for limbs that caught fire!

Answer (Mishneh l'Melech): He said 'they are not Docheh Shabbos'. This implies that they are never Docheh Shabbos.

Question: What is Tosfos' source to say that Rav Huna agrees that Pesulim may be burned on Shabbos, and that he argues only about burning on a separate Ma'arachah?

Answer (Mishneh l'Melech): We must say that Rav Huna discusses limbs that caught fire, for otherwise there is no source that he argues with Bar Kapara, who discusses only such limbs. Surely he agrees that leftover limbs may be burned on Shabbos - we learn from "Lo Seva'aru Esh b'Chol Moshvoseichem" (Shabbos 20a).

Question: The Rambam rules that leftover limbs may never be burned on Shabbos. How does he explain "Lo Seva'aru..."?

Answer (Mishneh l'Melech DH v'Ra'isi): The Rambam holds like R. Pores in Tosfos (46a DH Aval), who says that "Lo Seva'aru..." permits Eimurim of Korbanos of Shabbos (even though they could be burned at night). Tosfos concludes that R. Pores agrees that limbs that caught fire before Shabbos are burned on Shabbos, but this is according to Bar Kapara. The Halachah follows Rabah, who says that the beginning is Docheh, but not the end. Alternatively, Bar Kapara expounds "Lo Seva'aru" to permit leftover limbs on Shabbos, but Rav Huna disagrees. The Gemara (Kidushin 37b) learns that Beis Din need not Mekadesh Shabbos from 'Moshvos'. Rashi explains that 'Moshvos' refers to "Lo Seva'aru Esh b'Chol Moshvoseichem". This shows that the Halachah does not follow Bar Kapara.

Chidushei ha'Grach (Siman 330): The Chiyuv to burn limbs from yesterday that did not catch fire stems from yesterday's Chiyuv, and "Olas Shabas b'Shabato" forbids this on Shabbos. The Chiyuv to burn limbs that caught fire is because they became the Mizbe'ach's food. "Moshvoseichem" permits this on Shabbos.

Chazon Ish (OC 126:29 DH Docheh): The Gemara explained that Rav Chisda holds that 'the end' is not Docheh Tum'ah because it is not the primary Kaparah. This forced Rashi to say that he refers even to that day's Eimurim (for even they are not the primary Kaparah), even though this is unlike 'the end' regarding Rabah. Rashi holds that Rav Huna, Rabah and Rav Chisda are even according to Chachamim of R. Meir, for the Tana'im argue only about yesterday's Korbanos.

Aruch l'Ner (Sanhedrin 22b DH Kohen): A Beraisa (Ta'anis 17a) forbids Kohanim of the Beis Av that serves today to drink wine during the day or at night, for they constantly engage in Avodah. The Rambam (Bi'as Makdish 1:6) explains that they are forbidden the night before they serve, lest they be drunk when they get up for Avodah in the morning. The Ra'avad disagrees. Rather, it is lest they need to offer Eimurim. The Rambam disagrees because the Gemara forbids every Beis Av at night, even those who serve on Erev Shabbos, even though all agree that Eimurim of Chol may not be offered on Shabbos (Shabbos 114a). The Ra'avad (and Rashi, who mentioned Haktaras Eimurim and returning limbs that flew off the Mizbe'ach) hold like the Riva in Tosfos (Yoma 46a DH Aval) that Eimurim of Chol may be offered on Shabbos if they caught fire before Shabbos. Alternatively, Rashi and the Ra'avad agree that we are also concerned for drunkenness the next morning. Otherwise, it would be obvious that Kohanim may drink at night nowadays (but this is considered a Chidush of Rebbi - Sanhedrin 22b).

Rambam (ibid.): Chelev of (Temidim of) Shabbos may be offered at night, even if it is Yom Tov, but not if it is Yom Kipur. We learn from "Olas Shabas b'Shabato" that an Olah of Shabbos may not be offered on another Shabbos (i.e. Yom Kipur), and an Olah of Chol may not be offered on Yom Tov.

Question: The verse discusses Shabbos. What is the source to forbid an Olah of Chol on Yom Tov?

Answer (Tosfos Pesachim 59b DH v'Lo): R. Akiva expounds "Olas Shabas b'Shabato" to allow an Olah of Shabbos on Yom Tov. We infer that an Olah of Chol is forbidden on Yom Tov.