2) ONLY ROSH CHODESH IS DERIVED FROM YOM KIPPUR
OPINIONS: According to Rebbi Yehudah in the Mishnah (2a), the Se'irim offered in the Beis ha'Mikdash on Rosh Chodesh and on the Shalosh Regalim atone for a person who entered the Beis ha'Mikdash or ate Kodshim when he was Tamei, when that person did not know that he was Tamei at the beginning (when he became impure) or at the end (when he entered the Beis ha'Mikdash or ate Kodshim).

Rav Yehudah says in the name of Shmuel (9a) that Rebbi Yehudah derives his view from the verse, "And one male goat as a Chatas for Hash-m... shall be offered" (Bamidbar 28:15). The words "Chatas for Hash-m" imply a Chet (sin) that only Hash-m knows about; the person himself was totally unaware that he ever became Tamei. Since the verse is discussing the Sa'ir offered on Rosh Chodesh, it is clear that the Sa'ir of Rosh Chodesh and the Shalosh Regalim atones for this sin. Tana d'Vei Rebbi Yishmael taught that the Sa'ir does not atone for any other transgressions known only to Hash-m. This is derived from a comparison of the Sa'ir of Rosh Chodesh to the Sa'ir of Yom Kippur, both of which are brought at a fixed time. Just as the Korban of Yom Kippur provides atonement only for the Tum'ah of the Beis ha'Mikdash and Hekdesh, the Sa'ir of Rosh Chodesh atones only for this type of Tum'ah.

The Gemara proceeds to ask that since Rebbi Yehudah derives this law from a verse which discusses the Sa'ir of Rosh Chodesh, how does he know that the Sa'ir of the Regalim also provides this type of atonement?

The Gemara explains that the atonement of the Korban of the Regalim cannot be derived from the Korban of Rosh Chodesh through the teaching of Tana d'Vei Rebbi Yishmael (since both are brought at a fixed time), because the Korban of Rosh Chodesh is more frequent than the Korban of the Regalim, and thus it is able to atone even though one was unaware of the Tum'ah. The less-frequent Korbanos of the Regalim might not be able to achieve such atonement.

The atonement of the Korban of the Regalim also cannot be derive from the Korban of Yom Kippur (even though the former is more frequent), because the Sa'ir of Yom Kippur has a different advantage in that it atones for many sins, and thus it also can atone for Tum'ah of which one was totally unaware. The Sa'ir of the Regalim have no such advantage, and thus perhaps it cannot atone for such a sin.

The Gemara (beginning of 9b) asks that according to this reasoning (for why the atonement of the Sa'ir of the Regalim cannot be derived from the Sa'ir of Yom Kippur), how can the atonement of the Sa'ir of Rosh Chodesh be derived from Yom Kippur? The Sa'ir of Yom Kippur has the advantage that it atones for many sins, which the Sa'ir of Rosh Chodesh does not have! (See TOSFOS DH Ha Gamrinan.)

The Gemara answers that there is a difference between Rosh Chodesh and the Regalim. The Torah explicitly mentions atonement when it discusses Rosh Chodesh, and only a "Giluy Milsa" is needed (to limit the atonement) from Yom Kippur. In contrast, the entire atonement of the Sa'ir of the Regalim needs to be derived, and thus it cannot be derived from Yom Kippur.

What is the meaning of the Gemara's answer?

(a) RASHI (DH Hasam Kaparah) explains that atonement is written explicitly with regard to Rosh Chodesh. The verse states, "Chatas for Hash-m" (Vayikra 28:15), which teaches explicitly that the atonement is for an unknown sin. This implies that the atonement of the Sa'ir should be effective for all unknown sins. The Sa'ir's atonement is limited, however, by the derivation from Yom Kippur, which teaches that the Sa'ir of Rosh Chodesh atones only for Tum'ah of the Beis ha'Mikdash and Hekdesh, but not for other unknown transgressions (Rashi DH Giluy). Therefore, the derivation from Yom Kippur cannot be rejected on the grounds that Yom Kippur atones for many sins, since the only point of the derivation is to limit the atonement of Rosh Chodesh based on the limited atonement of the Sa'ir of Yom Kippur.

In contrast, the Torah writes with regard to the Sa'ir of the Regalim, "to atone" (Bamidbar 28:22, 28:30), but it gives no details about the sin for which the Sa'ir atones. One cannot derive from Yom Kippur that the Sa'ir of the Regalim atones for Tum'ah of the Beis ha'Mikdash and Hekdesh, a prohibition punishable with Kares, because Yom Kippur is different in that it atones for many sins. (The RITVA agrees with Rashi's explanation.)

(b) The RAMBAN explains that the verse of "Chatas for Hash-m" (Vayikra 28:15) stated with regard to Rosh Chodesh is apparently superfluous. Therefore, it may be used to teach the additional law that the Sa'ir of Rosh Chodesh atones for a sin that only Hash-m knows. If a Sa'ir offered on Yom Kippur, which generally atones for many sins, atones only for unknown sins of Tum'ah in the Beis ha'Mikdash and Hekdesh, then Rosh Chodesh certainly will atone only for such a sin. In contrast, there is no superfluous verse for Regalim. Therefore, one can derive only that the Sa'ir of the Regalim atones for the transgression of ordinary Mitzvos Aseh and Lo Ta'aseh, but not for Tum'ah of the Beis ha'Mikdash which is punishable with Kares.

(The NETZIV in HA'EMEK DAVAR (Bamidbar 28:15) suggests a different reason for why the Torah states "to atone for you" with regard to the Se'irim of Pesach, Shavuos, and Rosh Hashanah. He explains that those Se'irim also atone for transgressions committed by the public as a result of their merriment on Yom Tov. The Gemara in Kidushin (81a; see RASHI there DH Sakva) relates that when the men and women came together on Yom Tov to hear the Derashah, there often was inappropriate mingling. The Se'irim of the Regalim atoned for those sins. However, on Rosh Chodesh and Yom Kippur there was no merriment, and thus this Korban was not needed for that purpose. With regard to Sukos, the Netziv suggests that the merit of the Mitzvah of Sukah protected the people from sinning. The Torah therefore does not say "to atone for you" with regard to the Korbanos of Sukos.) (D. Bloom)