1) THE "MIZBE'ACH" AND THE FIVE-TEFACH "AMAH"
OPINIONS: Rebbi Meir maintains that the Amah of five Tefachim (as opposed to the Amah of six Tefachim) is used in only four places. These four places are the base of the Mizbe'ach (Yesod), the raised walkway around the Mizbe'ach (Sovev), the four protruding cornerpieces on the top of the Mizbe'ach (Keren), and the incense altar (Mizbe'ach ha'Zahav).
The verse (Yechezkel 43:13) says that the width of the Keren is a "Zeres" (the span of a hand). How large is a "Zeres" and what dimension of the Keren does it describe?
(a) RASHI writes that a Zeres is half an Amah. Rashi points out that since the verse in Yechezkel refers to both the height and the width of the Keren when it says that the Keren is measured with the five-Tefach Amah (i.e., it was 5 x 5 Tefachim), it must be that there is also a large Zeres and a small Zeres, the large Zeres being half of a large Amah (three Tefachim) and the small Zeres being half of a small Amah (two and a half Tefachim). The verse means that the distance from the middle of the Keren to its edge is a small Zeres.
(b) The RAMBAM (Hilchos Beis ha'Bechirah 2:7) explains that the verse refers only to the height of the Keren. Its width is measured with the normal six-Tefach Amah. Accordingly, the Keren is six Tefachim wide and five Tefachim high. The distance from the center of the Keren to its edge is half of a normal six-Tefach Amah, which is one Zeres (three Tefachim). According to this understanding, there is no basis to assume that there are two different types of Zeres, a large and a small one.
(c) TOSFOS (21a) cites Rebbi Elazar ha'Kalir who says that a Zeres is a third of an Amah (two Tefachim). According to this definition, in what way is the Zeres related to the width of the Keren?
RAV GEDALYAH RABINOWITZ zt"l (of Manchester, author of GIDULEI HEKDESH) explains as follows. The RA'AVAD (Hilchos Beis ha'Bechirah 2:7) has difficulty with the measurements that the Gemara here presents for the various parts of the Mizbe'ach. If the Yesod and Sovev are only five Tefachim, then the Mizbe'ach, which we know is 32 by 32 Amos at its base, cannot measure 28 by 28 Amos at the outer edges of the Keranos, as the Mishnah says (Midos 3:1, see Menachos 97b). Rather, it must measure 28 Amos and 4 Tefachim by 28 Amos and 4 Tefachim (since the base and the walkway each are measured with five-Tefach Amos, while the rest of the Mizbe'ach is measured with six-Tefach Amos)!
The Ra'avad suggests that perhaps each Keren is situated two Tefachim away from the edge of the Mizbe'ach and not exactly at the edge. Accordingly, the distance from the outer edges of the Keranos indeed measures 28 by 28 Amos. Perhaps this, too, is what the verse means when it says, "From the side [of the Mizbe'ach] until the edge [of the Keren] was one Zeres," meaning two Tefachim! (-As heard from Rav Mordechai Rabin, shlit'a.)
2) "RUBO U'MAKPID CHOTZETZ"
OPINIONS: Rebbi Yitzchak says that mid'Oraisa, if the "majority of a person" is covered by an intervening substance, and that person is bothered by the presence of that substance on him, it serves as a Chatzitzah and invalidates his Tevilah. If the substance covers only a small part, or if it covers a majority but he does not care about it, mid'Oraisa the Tevilah is valid. The Rabanan, though, decreed the Tevilah invalid in all of these cases.
What type of Chatzitzah is the Gemara discussing?
(a) RASHI (DH Rubo) explains that the Torah law applies only to one's hair. If most of one's hair is covered by an intervening substance which disturbs him, mid'Oraisa the Tevilah is invalid. If his hair is covered by a substance which does not disturb him, then it is not a Chatzitzah unless it covers most of his hair. If, however, the intervening substance is on his body, the Tevilah is invalid mid'Oraisa even if it covers only a small part of his body.
(b) TOSFOS (DH Davar Torah) and other Rishonim explain that the Torah law refers to most of one's body. Only when a majority of one's body is covered by an intervening substance is the Tevilah invalid mid'Oraisa. Even if it covers all of one's hair, the Tevilah is valid mid'Oraisa.
The RITVA explains that perhaps Rashi agrees with Tosfos that "Rubo" applies to the body as well. Rashi, however, rules in accordance with the GE'ONIM (cited by the RAMBAM, Hilchos Mikva'os 2:15, who disagrees with the ruling of the Ge'onim). The Ge'onim maintain that we measure the proportion of hair that is covered and the proportion of the body that is covered individually. If most of the hair is covered, then even though the rest of the body is not covered, the substance is still considered a Chatzitzah mid'Oraisa. (See also Insights to Nidah 67:3.)