1) JUDGING KINGS FIRST
QUESTION: The Gemara explains that when the people of the world are judged on Rosh Hashanah, each person passes before Hash-m to be judged one at a time. He does not judge them all at the same moment.
Similarly, the Gemara in Avodah Zarah (2b) says that when Hash-m judges nations, the kings (i.e., the more important nations) are judged before the others for two reasons. The first reason is that it is not respectful to the more important nations to make them wait to be judged. The second reason is that they should not be judged after Hash-m has reviewed the sins of all the others, because then Hash-m's wrath is kindled and the judgment is more severe. The Gemara implies that when Hash-m judges the nations, He judges one nation after the other, and He does not judge them all at the same moment.
How are these statements to be reconciled with the Gemara here which says that the deeds of the entire world are scrutinized in a single act of scrutiny ("v'Chulan Niskarin b'Sekirah Achas")? (See MAHARSHA here, MAHARAL in Chidushei Agados to Rosh Hashanah 8a, and BEN YEHOYADA to Rosh Hashanah 16a.)
ANSWERS:
(a) The CHIDA (in PESACH EINAYIM to Rosh Hashanah 16a) answers in the name of RAV YOSEF KARO (the Beis Yosef) that although everyone else is judged at the same time, the king is an exception and is judged separately.
The Chida points out, however, that this answer is not consistent with the Gemara's explanation that it is not proper for the king to wait while the others are judged. If Hash-m judges more than one person or nation at the same time, then He could judge the king at the same time as the others so that the king would not have to wait.
(b) The Chida answers further in the name of Rav Yosef Karo that Hash-m reviews everyone's actions at the same moment. However, he passes judgment for each person individually.
The Chida asks that this answer is not consistent with the other explanation that the Gemara in Avodah Zarah gives for why precedence in judgment is given to a king. The Gemara says that the reason why the king is judged first is so that his judgment will come before Hash-m's anger is aroused when He reviews the deeds of all the other people. However, if Hash-m has already reviewed the deeds of all of the other people and now is judging each one individually, then His anger has already been aroused and it will not help to judge the king first.
The answer to this question may depend on the reason why Hash-m does not pass judgment on the people at the same moment that He reviews their deeds. The answer might be that Hash-m allows the people, after their deeds have been reviewed, to have time to defend themselves, as the Gemara in Avodah Zarah mentions. If, during that time, they repent or accept upon themselves His justice, then their punishment will be mitigated. Accordingly, Hash-m's anger is aroused only at the time that the sentence is passed when He sees that the people did not repent or accept His justice.
(c) Why indeed is it necessary for Hash-m to review the actions of the entire world in a single moment? Perhaps the reason is as the RAMBAM writes (in Hilchos Teshuvah 3:2): judgment is passed not only on individuals but also on entire nations, and also on the entire world as a single entity. If the sins of the world outweigh the Mitzvos of the world, then the world will be destroyed, as occurred in the times of Noach (as the verse states, "Ki Rabah Ra'as ha'Adam ba'Aretz" (Bereishis 6:5), which may be translated as, "The evil of mankind has become the majority (outnumbering the good deeds of mankind)"). In order to judge the world as a whole, Hash-m must review the actions of the entire world at the same moment, for the world is considered a single entity when it is being judged.
According to this understanding, perhaps the Gemara refers to two different judgments. The judgment in which people pass before Hash-m one at a time is the judgment of the individual. The judgment for which the king is not made to wait is his judgment as an individual. Similarly, when Hash-m judges nations, the nation that is most honorable is judged before the others. When the Gemara here says that Hash-m reviews the actions of the entire world at one moment, it refers to the judgment that Hash-m passes upon the entire world as a whole. (See also Insights to Avodah Zarah 2:2.) (M. Kornfeld)
2) THE MESSENGERS OF THE NEW MONTH
QUESTIONS: The Mishnah states that Sheluchim, messengers, are sent out to the Diaspora to announce the declaration of the new month. They are sent for six specific months of the year (months for which it is necessary to know the exact date of Rosh Chodesh in order to observe the festival on the proper day). One of the months in which the Sheluchim go out is Elul. They inform the people of the exact date of Rosh Chodesh so that the people will know when to observe Rosh Hashanah.
RASHI comments that due to the arrival of the Sheluchim, "the people in the Golah know to make Rosh Hashanah thirty days after the start of Elul, because Elul is usually not Me'ubar (30 days long). Even though it is possible that Beis Din will make Elul a 30-day month, we follow the majority of years (in which Elul is 29 days long), and therefore they observe the thirtieth day after Rosh Chodesh Elul as Rosh Hashanah."
There are a number of difficulties with Rashi's explanation.
(a) Why does Rashi say that the people in the "Golah" need Sheluchim in order to know when Elul began so that they will observe Rosh Hashanah on the thirtieth day of Elul? Even in Eretz Yisrael, the people outside of Yerushalayim need to know when Elul began so that they will know when to observe Rosh Hashanah. (RASHASH)
(b) Rashi implies that the people in the Golah observe only one day of Rosh Hashanah because they rely on a Rov (that in most years, Elul has only 29 days). However, the Gemara in numerous places (see Beitzah 6a) says that the people in Chutz la'Aretz observe two days of Rosh Hashanah out of doubt. Why does Rashi say that they observe only one day?
(c) According to Rashi, the people in the Golah know when the first of Tishrei is because they know (due to the Sheluchim) when the first day of Elul occurred, and they may assume that Elul is 29 days long. Accordingly, they should also know when the tenth of Tishrei (Yom Kippur) occurs and when the fifteenth of Tishrei (Sukos) occurs. Why, then, is there a need for Sheluchim to go out to inform them of the exact date of Rosh Chodesh Tishrei?
ANSWERS:
(a) Perhaps Rashi understands that in Eretz Yisrael (outside of Yerushalayim), even though the people do not know exactly when Rosh Chodesh Tishrei occurs and therefore need to know when Rosh Chodesh Elul was, they do not need Sheluchim to inform them. Word about when Rosh Chodesh Elul was established spreads through the country quickly. Sheluchim are needed only for those in the Golah.
(Although the RAN and BARTENURA quote the words of Rashi as they appear in our text with the word "ba'Golah," in the words of Rashi on the Rif and as quoted by the SHITAS RIVAV, the word "ba'Golah" is omitted. According to that Girsa, this question is no question at all.)
(b) When Rashi says that they observe one day of Rosh Hashanah in the Golah, he apparently is bothered by the question of the RITVA. The Ritva asks that if the people in the Golah must observe two days of Rosh Hashanah out of doubt about how many days were in the month of Elul (29 or 30), of what benefit are the Sheluchim of Rosh Chodesh Elul? (This is also the question of the LECHEM MISHNEH in Hilchos Kidush ha'Chodesh 3:9.) The benefit of the Sheluchim cannot be that without them the people would have to observe three days of Rosh Hashanah, because the Rabanan never required any festival to be observed for three days out of doubt. What benefit do the Sheluchim provide if either with or without them the people must observe two days of Rosh Hashanah in the Golah out of doubt? To answer this question, Rashi explains that the Sheluchim enable the people to observe only one day of Rosh Hashanah, and thus they benefit by not having to observe two days.
When the Gemara says, in a number of places, that the people in Chutz la'Aretz observe two days of Rosh Hashanah, it refers to when there are no Sheluchim and the people do not know when Rosh Chodesh Elul was established.
Other Rishonim disagree with Rashi (see TOSFOS DH v'Al). They assert that the people in the Golah observe two days even when Sheluchim are sent to them from Yerushalayim. Accordingly, the benefit of sending out Sheluchim is so that the people need not observe three days of Rosh Hashanah. Even though they would not be required to observe three days of Rosh Hashanah even without the Sheluchim (since they may assume that Beis Din does not establish three, 29-day months in a row), nevertheless it is preferable to have certainty about when Rosh Hashanah occurs and not to be in doubt. Therefore, Sheluchim are sent to confirm when Beis Din indeed declared the new month of Elul. The Sheluchim inform the people that they may observe two days of Rosh Hashanah and that there is no doubt at all about three days. (RITVA)
(c) Rashi (DH v'Al Tishrei) explains that the Sheluchim of Tishrei are sent only to inform the people that they acted correctly and should have no feelings of guilt on Yom Kippur. Even without Sheluchim, however, the people's observance of the tenth day of Tishrei according to their count from the beginning of Elul is the correct day of Yom Kippur.

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