The fifth Mishnah in the thirteenth chapter of Maseches Menachos continues to deal with vague vows - commitments whose contents are not clearly defined, and how they are to be fulfilled. First a vow of wine, and then a vow of oil.
"Harei alai yayin" - "It is upon me to bring wine":
A person who takes upon himself to bring wine as an offering that stands on its own, without attaching it to a zevach or to any other minchah. This possibility was already learned at the end of the twelfth chapter from the verse "Kol ha'ezrach ya'aseh kachah es eileh" - "every native shall do so with these," a seemingly superfluous verse that comes to teach that one may imitate the minchas nesachim and bring it on its own, without the zevach - the olah or the shelamim - that it is meant to accompany. This law applies not only to the minchah itself, but to the wine as well.
The amount of wine that accompanies an olah or a shelamim depends on the type of animal. The smallest of them - the lamb and the goat - have nesachim of a quarter of a hin, which is three lugin. Therefore the Mishnah says: "lo yifchos mi'shloshah lugin" - he must not bring less than three lugin, since this is the smallest offering whose wine can stand on its own.
"Harei alai shemen" - "It is upon me to bring oil":
One who obligates himself to bring oil as a separate offering standing on its own. At the end of the previous chapter, Rabbi Akiva and Rabbi Tarfon disagreed about whether this can be done at all, and from our Mishnah, which is taught in accordance with the view of Rabbi Tarfon, it emerges that the halachah follows him - that it indeed can be done. What remains to be clarified is the required amount, and that depends on which verse the law is derived from:
From the verse "V'nefesh ki sakriv korban minchah la'Hashem" - "And a soul who brings a meal offering to Hashem." This is the source of Rabbi Tarfon, since the word "korban" is superfluous, and it comes to teach that one may bring an offering that consists not of food but of oil alone. According to this, he brings it in place of the minchah, but only the oil component of it, and therefore its measure is the amount of oil in the smallest minchah - one log, which is the standard measure in most menachos.
From the verse "Kol ha'ezrach ya'aseh kachah es eileh" - the verse of imitation, which operates here as well. And if one is imitating the minchas nesachim, then although most menachos contain one log of oil, the menachos of the nesachim contain more than that: the smallest of them, that of a goat or a lamb, is made of fine flour mixed with a quarter of a hin of olive oil (in addition to the quarter of a hin of wine for the libation). According to this, the measure of an oil offering standing on its own is three lugin.
Hence the dispute in the Mishnah: the Tanna Kamma says "lo yifchos mi'log" - he must not bring less than a log, based on the verse "V'nefesh ki sakriv korban minchah la'Hashem"; and Rabbi disagrees and says three lugin, relying on the verse of imitation, "kachah ya'aseh." The halachah follows the Tanna Kamma and not Rabbi Yehudah HaNasi, and therefore even a single log alone is valid.
He specified but does not remember - "yavi k'yom hameruban":
One who says: "My commitment to bring wine (or oil) was for a particular amount that I had in mind, and not merely for three lugin, but I do not remember what it was" - regarding him the Mishnah says: "yavi k'yom hameruban" - he brings the amount of the fullest day, the measure of wine brought on the busiest day of the year.
And which day is that? As was explained at the end of chapter twelve, it is the first day of Sukkos that falls on Shabbos, the most heavily laden day of the year in terms of obligatory offerings. On it there are:
Thirteen bulls for olos.
Two rams.
Eighteen lambs: the fourteen mussaf lambs brought on each day of Sukkos, the two temidim, and the two lambs of the Shabbos mussaf.
The amount of fine flour for that day was already calculated in the previous mishnayos, and it came to sixty-one esronim. Here we focus on the quantity of wine and oil: half a hin - six log - for a bull; a third of a hin - four log - for a ram; and a quarter of a hin - three log - for a lamb. And this is the calculation:
Thirteen bulls, six log for each one - seventy-eight log.
Two rams, four log for each one - eight log, for a running total of eighty-six.
Eighteen lambs, three log for each one - fifty-four log.
The result of the calculation: one hundred and forty log of wine are brought as libations on that day. Therefore, one who says "I take upon myself wine" and does not remember what amount he specified brings one hundred and forty log of wine - and the same law applies to oil - and thereby he fulfills his vow, since we never assume that he intended to obligate himself in more than that.