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1)

(a) Six Beitzim comprise a Log.

(b) From the fact that the Torah (in connection with the Lachmei Todah) writes "ba'Shemen" twice - Rebbi Akiva Darshens 'Ein Ribuy Ela Lema'et', reducing the Log of oil that other Menachos require to hlf a Log.

(c) The ojection to the initial wording 'Ilu Lo Ne'emar Ela "ba'Shemen" Echad' is - that if one "ba'Shemen" is needed for the intrinsic Halachah, then it cannot be considered a 'Ribuy Achar Ribuy'.

(d) We therefore amend the text to read - 'Ilu Lo Ne'emar ba'Shemen (Kol Ikar)', meaning that we would have learned the Din of Log Shemen from the other Menachos.

(a) We therefore reduce the amount of oil that is needed for the Todah - to half a Log.

(b) The Todah consists of - three kinds of loaves, Chalos, Rekikin and Murbeches.

(c) We reject the suggestion that the oil is divided into three equal portions (of one k'Beitzah each), one for each king of loaf - due to the fact that the Torah writes an extra "ba'Shemen" by the Revuchah loaves (intimating that they should receive more oil than the Chalos and the Rekikin).

(d) Consequentrly, it is distributed - half (one and a half k'Beitzim) for the Revuchh loaves, and a quarter for each of the Chalos and the Rekikin.

(a) Rebbi Elazar ben Azaryah disagrees with Rebbi Akiva's D'rashah from "ba'Shemen" "be'Shemen". He learns Rebbi Akiva's Din from - 'Halachah le'Moshe mi'Sinai'.

(b) Besides Revi'is Shemen le'Nazir, he adds - the eleven days (of Zivus) after the termination of the days of Midus, during which time she is subject to Zivus instead of Nidus.

(a) The Tana Kama of the Beraisa learns from the Pasuk (in connection with the Metzora Ani) "Isaron ... Balul ... ve'Log Shamen" - that each Isaron of flour requires a Log of oil.

(b) Whereas Rebbi Nechemyah and Rebbi Eliezer ben Ya'akov learn from the same Pasuk "le'Minchah ve'Log Shamen" - that even a Minchah of sixty Log requires only one Log of oil.

(c) Rebbi Nechemyah and Rebbi Eliezer ban Ya'akov maintain that the Torah needs "Isaron ... Balul ... ve'Log Shamen" to teach us - that a Minchas Ani requires one Isaron. The Rabbanan do not consider this necessary - because we could learn it from a Metzora Ashir, who brings three Korbnos consisting of three Esronos.

(d) However ...

1. ... Rebbi Nechemyah and Rebbi Eliezer ben Ya'akov disagree with that. In their opinion, we would not be able to learn Metzora Ani from Metzora Ashir - who might not have to bring a Minchah at all, because, as we see, the Torah takes pity on him (and permits him to bring a cheaper Korban). Maybe it also absolves from the Minchah altogether.
2. ... the Rabbanan do not accept Rebbi Nechemyah and Rebbi Eliezer ben Ya'akov's argument - because even though it allows him to bring a cheaper Korban, it does not follow that it exempts him from bringing any Minchah at all.

(a) The Rabbanan learn from the Pasuk "le'Minchah ve'Log Shamen" - that one is not permitted to donate a Minchah that requires less than a Log of oil (i.e. one Isaron).

(b) And Rebbi Nechemyah and Rebbi Eliezer ben Ya'akov know that from there two. Due to the principle 'Hei Minayhu Mafkas' (when one is faced with two equal D'rashos, one learns them both).

(c) We know that the Shemen ha'Mishchah consisted of a Hin - from a Pasuk in Ki Sisa ("ve'Shemen Zayis Hin").

(d) We then learn from the Pasuk in ...

1. ... Ki Sisa "Shemen Mishchas Kodesh Yih'yeh *Zeh* Li ... " - that a Hin is equivalent to twelve Lugin (the numerical value of "Zeh").
2. ... Pinchas "ve'Niskeihem Chatzi ha'Hin Yih'yeh la'Par ... " that the wine for a bull comprises six Lugin (for a ram, four Lugin and a lamb, three). And once we convert the liquid measure from a Hin to Lugin with regard to wine, it is obvious that the same will apply to oil.

(a) The Torah writes in Tetzaveh (in connection with the oil for the Menorah) "me'Erev ad Boker". Besides the obligation to place sufficient oil in the lamps to burn all night, we also learn - that it can be performed after the Tamid shel Erev and right through the night (the only Avodah which enjoys this distinction).

(b) We learn from the first interpretation that each lamp requires half a Log - because the Chachamim assessed that this is how much oil is needed to burn for that period of time, in the long nights of Tekufas Teives.

(c) Some say that they arrived at the conclusion of half a Log 'mi'Lema'alah Lematah'; others 'mi'Lematah Lema'alah'.

1. 'mi'Lema'alah Lematah' means - that they began measuring with a Log, and when they discovered that oil remained in the morning, they tried again the following night with three quarters of a Log, and so on, until they arrived at half a Log, which was just right.
2. 'mi'Lematah Lema'alah' means - that they begn with a quarter of a Log, adding a little each night, until they arrived at half a Log.

(d) Those who say that one begins with a Log and works one's way downwards hold - that it doesn't matter if, in the process, some of the oil gets wasted, because we have a principle 'Ein Aniyus be'Makom Ashirus' (Hekdesh is considered wealthy, and it is not becoming for someone who is wealthy to behave like a poor man). Whereas, those who hold that one begins with a Revi'is ha'Log and works one's way upward - cite the principle (that we have already cited earlier) that the Torah 'has pity on the money of Yisrael'.

(e) Now that each lamp requires half a Log of oil during the long winter nights - one can either use the same amount all nights of the year, and simply burn the oil that is left over in the summer; or can avoid that by using progressively thinner wicks, so that the oil always burns out at daybreak.

7)

(a) Our Mishnah permits mixing the Nesachim of a bull with those of a ram (assuming that the respective Menachos have either been brought or that they too, got mixed up [Tif'eres Yisrael]). The Tana is referring to the wine and the oil of the Minchas Nesachim.

(b) The Tana permits it - because the proportion of the Nesech and the Minchah are the same in both cases (two Login per Isaron).

(c) The Tana also permits the Nesachim of one lamb with the Nesachim of another - even if one ...

1. ... belongs to a Yachid, and the other to the Tzibur (since the proportion of the Nesech and the Minchah of one is the still the same as the other (both are three Lugin per Isaron), and the same will apply if one of them ...
2. ... is from today's Korban, and the other, from yesterday's (since we have already learned that one may bring one's Minchah today and the Nesech anything up to ten days later.

(a) The Tana prohibits mixing the Nesachim of a lamb with those of a bull or a ram - because the proportion of the Nesech and the Minchah of one is different than the other.

(b) He permits the oil of the Nesech of a lamb that one did mix together with that of a bull or a ram - provided they were both already mixed together with their respective Menachos.

(c) Finally, the Tana says that ...

1. ... although the Minchas Nesachim of the lamb that accompanied the Omer is double (i.e. two Esronim) ...
2. ... the Nesech that comes with the Minchah is not ( i.e. it remains a quarter of a Hin).

(a) The Beraisa learns from the Pasuk (in connection with the Cheilev of the Shelamim) "Ve'hiktiro" (in the singular) - that one is not permitted to mix the Chalavim of two different Korbanos (but each should be burned independently).

(b) This poses a Kashya on our Mishnah - which permits mixing the Nesachim of two different Korbanos (provided the proportion between the Nesech and the Minchah is the same in both cases).

(c) Rebbi Yochanan answers - that whereas the Beraisa is speaking Lechatchilah, our Mishnah is speaking Bedi'eved.

(d) We query Rebbi Yochanan from the Seifa 'Balelan Eilu Bifnei Atzman ve'Eilu Bifnei Atzman Ve'nis'arvu Kesheirin' because then ...

1. ... the Reisha 've'Ein Me'arvin Niskei Kevasim be'Niskei Parim ve'Eilim' - must be speaking Lechatchilah, and so must ...
2. ... the Reisha de'Reisha 'Me'arvin Niskei Parim be'Niskei Eilim ... '.

(a) Abaye answers 'Me'arvin Yeinan Im Nis'areiv Saltan ve'Shamnan', by which he means - that the Reisha 'Me'arvin Niskei Parim be'Niskei Eilim' is referring to the wines, which one is permitted to mix even Lechatchilah, provided their flour and oil were also mixed together (as indeed they should be [and as will be explained shortly]).

(b) We refute Abaye's answer however, from a Beraisa, which draws a distinction between mixing the flour and oil of two Korbanos - which is forbidden, and mixing their wines - which is permitted (irrespective of whether their flour and oil were mixed together or not).

(a) Abaye therefore reinterprets the Reisha of our Mishnah 'Me'arvin Niskei Parim be'Niskei Eilim' (even Lechatchilah) - confining it to where the flour and oil of the two Korbanos have already been burned (even if they were not actually mixed together).

(b) If they have not, one is forbidden to mix them.

(c) The Tana permits mixing the wines after the flour and the oil have been burned, but forbids it beforehand - on account of a decree, for fear that they might go on to mix the flour and oil of the two Korbanos (which is forbidden Lechatchilah).

(d) Mixing the wines Lechatchilah is not intrinsically included in the prohibition of mixing the Chalavim - because "Hukt'ru" is confined to Kodshim that are burned on the Mizbe'ach, whereas the wine is poured into the bowls on the Keren.

(a) Even though the Torah writes (in connection with the Keves ha'Ba im ha'Omer) "u'Minchaso Sh'nei Esronim", we know that the wine of its Nesech is not double too - because the Pasuk specifically writes there "ve'Nisko Yayin Revi'is ha'Hin".

(b) And Rebbi Elazar learns from the fact that the Torah writes "ve'Nisko" with a 'Hey' (as if it had written "ve'Niskah"), even though it is read with a 'Vav' - that the Nesech of the Minchah (i.e. its oil) is not double either.

(c) And this latter Pasuk is necessary, because we might have otherwise thought - that notwithstanding the fact that the wine is not double, the oil, which is mixed with the Minchah, is.

(a) An Asham that is Shechted she'Lo li'Shemo - is nevertheless brought on the Mizbe'ach, though the owner has not fulfilled his obligation, and is obligated to bring another one.

(b) Rebbi Yochanan rules that in the case of an Asham Metzora that is Shechted she'Lo li'Shemo - the Asham also requires Nesachim. He refers specifically to an Asham Metzora, because no other Asham requires Nesachim to begin with.

(c) Rebbi Yochanan gives his reason as 'she'Im I Atah Omer Kein, Paslaso'. That is because, without Nesachim, it is not fit to be brought as an Asham Metzora. Neither can it be brought as ...

1. ... an Olah - because it would then first require 'Nituk li'Re'ayah' (i.e. an Asham can only adopt the Kedushah of an Olah, once it has been sent into the field to obtain a blemish).
2. ... an Asham Nedavah - because an Asham cannot be brought as a Nedavah.

(a) Rav Menashya bar Gada asks - why Rebbi Yochanan does not also incorporate in his ruling where one Shechted she'Lo li'Shemo ...

1. ... Keves ha'Ba im ha'Omer - which ought to be brought together with its double Minchah?
2. ... Tamid shel Shachar - brought together with two blocks of wood carried by one Kohen?
3. ... Tamid shel Bein ha'Arbayim - brought together with two blocks of wood carried by two Kohanim.

(b) Abaye answers that this is indeed the Halachah in all three cases. Rebbi Yochanan however - only mentioned one of the four cases, and it is self-understood that the same applies to the other three.

(c) Rebbi Aba disagrees. All three cases that we queried, he explains, are Olos, and an Olah is different than Asham - inasmuch as if it cannot be brought as an Olas Chovah, it can still be brought as an Olas Nedavah (and does not therefore require the unique specifications that it needed as an Olas Chovah).

(d) We cite a Beraisa that corroborates Rebbi Yochanan. The Tana presents an alternative case with regard to the Asham, besides 'Shachto she'Lo li'Shemo'; namely - there where the blood was not placed on the right ear, the right thumb and the right big toe.