1) HALACHAH: "MAYIM ACHARONIM"
OPINIONS: The Mishnah (17a) states that soldiers going out to battle are exempt from "washing the hands." Abaye (17b) explains that this refers only to Mayim Rishonim, the washing of hands before eating. Mayim Acharonim, however, is obligatory even for soldiers going out to battle. The Gemara explains that the reason for the strict obligation of Mayim Acharonim is that there might be some salt from the meal left on one's fingers, and if he wipes his eyes with his fingers he risks becoming blind from the corrosiveness of the Sedomis salt contained in table salt.
Common table salt nowadays does not contain Sedomis salt. Does the obligation to wash Mayim Acharonim still apply?
(a) The ROSH in Berachos (8:6), the RITVA, and other Rishonim write that in addition to the danger of Sedomis salt, there is another reason to wash Mayim Acharonim. Before one recites the blessings of Birkas ha'Mazon, he should wash his hands for the purpose of sanctity, as the Gemara states in Berachos (53b). Accordingly, even though we no longer have Sedomis salt at our meals, we should wash Mayim Acharonim in order sanctify ourselves before we recite Birkas ha'Mazon.
(b) TOSFOS (DH Mayim Acharonim, and in Berachos 53b, DH v'Hiyisem), however, says that it is no longer the practice to wash Mayim Acharonim, for two reasons. First, we do not use Sedomis salt at our meals. Second, it is not our practice to dip our fingers into salt and taste a little after eating a meal, as was the practice in the time of the Gemara. Washing Mayim Acharonim was an act which involved sanctity only when these two reasons applied, but not today.
(c) TOSFOS in Berachos (ibid.) and the ROSH (ibid.) add that even if we rule that it is not necessary to wash our hands for Birkas ha'Mazon since we do not use Sedomis salt at our meals and we do not consider our hands to be soiled, one who minds leaving his hands slightly soiled from the meal is obligated to wash Mayim Acharonim for Birkas ha'Mazon. For him, it indeed is a practice of sanctity to wash after the meal.
HALACHAH: The SHULCHAN ARUCH (OC 181:1) states that "Mayim Acharonim is obligatory." The MISHNAH BERURAH (181:1) records the reasoning of the Rosh (a) and the other Rishonim who say that washing is necessary in order to sanctify and purify our hands for the recitation of Birkas ha'Mazon. The Mishnah Berurah adds (in the name of the Rambam) that even if the only reason to wash Mayim Acharonim is to prevent blindness from Sedomis salt, and we no longer use Sedomis salt, we should still wash Mayim Acharonim because there might be other salt that has the same characteristics of Sedomis salt.
However, at the end of the laws of Mayim Acharonim, the Shulchan Aruch (181:10) cites the opinion of Tosfos (b) who says that the obligation of Mayim Acharonim no longer applies. He adds that one who is bothered by even a little soil on his hands and always washes them is obligated to wash Mayim Acharonim before he recites Birkas ha'Mazon, as Tosfos in Berachos rules (c).
The Mishnah Berurah there (181:22) cites the VILNA GA'ON, MAGEN AVRAHAM, MAHARSHAL, and BIRKEI YOSEF, who all maintain that Mayim Acharonim is still obligatory (even if one's hands are not dirty), like the first opinion (a).
In practice, some follow the first opinion as cited by the Shulchan Aruch (in 181:1), while others follow the opinion of Tosfos as cited by the Shulchan Aruch (in 181:10). Those who maintain that Mayim Acharonim is obligatory should wash each hand in its entirety with at least a Revi'is of water (BI'UR HALACHAH 181:4, DH Ad Perek; see also TESHUVOS V'HANHAGOS 1:173).
2) "PASEI BIRA'OS"
QUESTIONS: The Mishnah describes how to enclose the area around a well in a Reshus ha'Rabim in order to make it into a Reshus ha'Yachid to permit one to draw water from it on Shabbos. Four corner pieces, each comprised of two perpendicular boards (which are each one Amah wide and ten Tefachim tall), are placed at four vertices of a square surrounding the well. This area is considered "enclosed" by virtue of the corner pieces which constitute Mechitzos around the area. The distance between the corner pieces on each side may be up to 10 Amos according to Rebbi Meir, or 13 1/3 Amos according to Rebbi Yehudah. If the break between the corner pieces is too wide, a plank may be stood in the gap between the corner pieces in order to decrease the distance between the plank and the corner pieces.
(a) How can such a method permit one to carry water from the well into the enclosed area around it? The Gemara earlier (15b) teaches that Hash-m taught Moshe Rabeinu that in order to make a Reshus ha'Yachid, the combined length of the breaches in the partitions that enclose the Reshus ha'Yachid may not exceed the combined length of the partitions (Mechitzos). Here, however, the length of the breach between the corner pieces is considerably longer than the fenced section (the corner pieces themselves)!
(b) In addition, we have learned that there is a concept of "Asi Avira d'Hai Gisa v'Hai Gisa." This teaches that if the breach between the standing plank and the corner pieces is greater than the width of the plank, the plank is considered non-existent. Why, then, is one permitted to decrease the breach between the the Pasei Bira'os by merely standing a plank one Amah wide in the middle of each side of the enclosure?
(a) TOSFOS (DH Osin and DH v'Arba'ah), the RITVA and other Rishonim answer that according to Torah law, when two one-Amah-wide planks are placed at each corner of an area to be enclosed, those planks create actual "doorways," and the distance between the planks is considered to be the threshold of a doorway. (The planks at the corners do not form mere "entranceways," such that the area between them is considered a breach in a wall.) The rule that the length of the breaches must not exceed the length of fence applies only when the opening is considered a "breach," as opposed to a "doorway." A doorway is defined by the Rabanan as a Tzuras ha'Pesach (Eruvin 11a), and defined by the Torah as two one-Amah-wide planks separated by less than 10 Amos (or 13 1/3, according to Rebbi Yehudah. A doorway does not invalidate a Mechitzah regardless of how wide the doorway is.
(The RA'AVAD, cited by the RASHBA and others, suggests another possibility. He asserts that the rule of "Parutz Merubah Al ha'Omed" in all circumstances is only an invalidating factor mid'Rabanan, and thus the Rabanan did not apply it in the case of Pasei Bira'os. Hash-m taught it to Moshe Rabeinu just as He taught Moshe Rabeinu all of the other Halachic innovations that would be introduced throughout history, as mentioned in Megilah 19b.)
(b) The principle of "Asi Avira d'Hai Gisa" does not invalidate the planks (and, subsequently, the Pasei Bira'os) around the well, because this principle is only mid'Rabanan. Mid'Oraisa, open spaces on each side of a Mechitzah do not annul the Mechitzah (especially when the Mechitzah forms a doorway, such as when there are one-Amah-wide posts on the two sides of an open section). For the benefit of the Olei Regalim, who needed to carry water from a well on Shabbos, the Rabanan were lenient and required that one satisfy only the mid'Oraisa conditions. As long as the area enclosed by the planks is a Reshus ha'Yachid mid'Oraisa, the Rabanan permitted one to draw water there and to place the buckets down in the area enclosed by the planks in order for the animals to drink.
3) HALACHAH: "PASEI BIRA'OS" NOWADAYS
OPINIONS: The Rabanan permitted the Olei Regalim to carry water for their animals from public wells on Shabbos by constructing a Mechitzah with bare minimum dimensions (see previous Insight). Does this Halachah apply nowadays? Is it possible to make an area into a Reshus ha'Yachid in such a manner in order to permit one to carry within that area on Shabbos?
(a) The Gemara later (21a) explains that outside of Eretz Yisrael and Bavel one is not permitted to use Pasei Bira'os because "there are not many Yeshivos" outside of Eretz Yisrael and Bavel. Rashi explains that since there are not many Talmidim traveling from one place to another to learn Torah who would need the amenities of such a Mechitzah, the Rabanan did not permit one to erect Pasei Bira'os. They permitted Pasei Bira'os only for the Olei Regalim and for those traveling in order to fulfill a Mitzvah.
The Gemara says that Pasei Bira'os are not allowed in Chutz la'Aretz only because there are no Yeshivos in Chutz la'Aretz. This implies that if students do travel from Yeshiva to Yeshiva to learn Torah in Chutz la'Aretz, or to perform any other Mitzvah, it should be permissible for them to make Pasei Bira'os. This indeed is the opinion of the RITVA, RASHBA, and OR ZARU'A (cited by the HAGAHOS ASHIRI).
(b) The RAMBAM, RIF, and ROSH do not mention any of the laws of Pasei Bira'os. Their omission of the laws implies that they maintain that one may not make Pasei Bira'os nowadays. When the Gemara says that Pasei Bira'os are not permissible in Chutz la'Aretz because there are no Yeshivos there, it means that when the Rabanan originally permitted the construction of Pasei Bira'os, they did not permit it in Chutz la'Aretz because there were no people traveling to and from Yeshivos. Since the original enactment did not apply to Chutz la'Aretz, regardless of what happens in later times it remains prohibited to use Pasei Bira'os in Chutz la'Aretz. This also seems to be the ruling of the SHULCHAN ARUCH, who omits all of the laws of Pasei Bira'os.