1) HOW TO BECOME A "ZAKEN MAMREI"
QUESTION: Rebbi Eliezer ben Yakov maintains that the procedure of Eglah Arufah requires the presence of the king, Kohen Gadol, and the Beis Din. The Gemara questions whether Rebbi Eliezer ben Yakov requires that the entire Sanhedrin leave the Lishkas ha'Gazis to be present at the site of the Eglah Arufah, or whether only three members (as Rebbi Yehudah rules) or five members (as Rebbi Shimon rules) of the Sanhedrin must be present.
Rav Yosef attempts to prove from a Beraisa that Rebbi Eliezer ben Yakov maintains that the entire Sanhedrin must be present at the site of the Eglah Arufah. The Beraisa discusses a Zaken Mamrei who meets the Sanhedrin outside of the Lishkas ha'Gazis, hears their ruling, and then returns to his own community and rules differently from the ruling of the Sanhedrin. How can the Beraisa say that the Zaken Mamrei hears a ruling from the Sanhedrin outside of the Lishkas ha'Gazis? The law requires that one-third of the members of the Sanhedrin always be present in the Lishkas ha'Gazis during court hours, as derived from the verse, "Al Yechsar ha'Mazeg" (Shir ha'Shirim 7:3). If only some of the members of the Sanhedrin leave the Lishkas ha'Gazis and the Zaken Mamrei meets them outside of the Lishkas ha'Gazis, he cannot be convicted for ruling differently from the Sanhedrin since the remaining members of the Sanhedrin might have agreed with him had they heard his ruling. It must be that the Beraisa is expressing the view of Rebbi Eliezer ben Yakov and maintains that the entire Sanhedrin is permitted to leave the Lishkas ha'Gazis under certain circumstances, such as in order to measure the distance in the case of an Eglah Arufah.
Why does the Gemara assume that a Zaken Mamrei cannot be convicted when he meets most of the Sanhedrin (two-thirds of its members) outside of the Lishkas ha'Gazis and they present him with a Halachic ruling? Even if the remaining members would have agreed with the Zaken Mamrei, their vote would have been overruled by the majority! Consequently, when the Zaken Mamrei rules differently from the majority of the Sanhedrin, his ruling is still contrary to the ruling of the entire Sanhedrin! (ARUCH LA'NER, Sanhedrin 14b)
ANSWER: The BE'ER SHEVA, MAHARIT (1:68), and HE'OROS B'MASECHES SOTAH answer that a Zaken Mamrei may be convicted only when he hears the entire Sanhedrin as a whole pass a ruling ("Ein Hamarah l'Chatza'in" -- it is not considered a Hamarah (rebellion) when one contradicts an incomplete Sanhedrin). Why, then, does the Gemara say that the reason he is not considered a Zaken Mamrei when he hears a ruling from some members of the Sanhedrin outside of the Lishkas ha'Gazis is that some of the remaining members might have agreed with him? The Gemara should say instead that the reason why he is not a Zaken Mamrei is that he did not contradict the entire assembly of the Sanhedrin!
The answer is that the Gemara is giving a logical reason for why a Zaken Mamrei must contradict the entire assembly of the Sanhedrin. If some members (even a minority) of the Sanhedrin are not present, the remaining opinions are not considered a reliable representation of the opinion of the entire Sanhedrin. Had they all been present, they would have discussed the matter between them and perhaps one of the members of the minority would have succeeded in convincing one of the members of the majority to agree with his opinion. Even if the Zaken Mamrei first hears a ruling from two-thirds of the Sanhedrin outside of the Lishkas ha'Gazis, and then he returns to the Lishkas ha'Gazis and hears the same ruling from the remaining members, he still cannot be convicted because had the entire Sanhedrin been together perhaps the group's discussion of other issues would have been taken into consideration and they would have come to a different conclusion.

45b----------------------------------------45b

2) THE PURPOSE OF THE PROCEDURE OF "EGLAH ARUFAH"
QUESTION: The Torah teaches that when a corpse is found between two cities (in Eretz Yisrael), the city nearer to the corpse must bring an Eglah Arufah. Why is that city responsible to bring an Eglah Arufah?
A number of sources imply that it is assumed that the unknown killer came from the city nearest to where the corpse was found. The purpose of the Eglah Arufah procedure is to determine the identity of the killer; when the Beis Din of the city publicizes the killing through the procedure of Eglah Arufah, the people hear about it and if anyone has any information about the identity of the killer, he will come forth and inform Beis Din (see RABEINU BACHYE to Devarim 21:1, and TARGUM YONASAN to Devarim 21:8). This is evident from the Gemara in Bava Basra (23b) which attempts to prove from the laws of Eglah Arufah that in the case of a doubt with two opposing factors to resolve the doubt, a factor of "Rov" (majority) versus a factor of "Karov" (physical proximity), the factor of "Karov" is considered a stronger proof than "Rov." That is why the Eglah Arufah is brought from the nearest city; its proximity "proves" that the killer came from that city.
According to this understanding of the purpose of the procedure of Eglah Arufah, what is the meaning of the Gemara here that says that if the nearest city has no Beis Din, that city is ignored and the Sanhedrin instead measures to the closest city that has a Beis Din? If the killer is assumed to have come from the nearest city, what is gained by bypassing that city and measuring to a farther city that has a Beis Din? The killer did not come from that city! (TOSFOS to Bava Basra 23b, DH bed'Leika)
ANSWER: Perhaps it is assumed that the residents of cities without a Beis Din frequent the cities which have a Beis Din, and therefore they also hear the talk of the town of the larger city. Consequently, the identity of the killer will be revealed when the elders of the larger city bring the Eglah Arufah. (If members of the city without a Beis Din would bring the Eglah Arufah, the rest of the city might not hear about it, since it was not done by Beis Din and thus was not publicized well.)
According to this explanation, perhaps when the nearest city to the corpse has no Beis Din, the Sanhedrin does not measure to the city with a Beis Din which is nearest to the corpse, since that Beis Din might not be the one that serves the people of the city nearest to the corpse. Rather, they measure to the city with a Beis Din which is nearest to the city nearest to the corpse.
3) IS A "NACHAL" THAT IS NOT "EISAN" VALID FOR THE "EGLAH ARUFAH"?
QUESTION: The Mishnah states that although the Eglah Arufah must be brought in Nachal Eisan (Devarim 21:4; see following Insight), if it is brought in a Nachal that is not "Eisan" it is still valid. RASHI explains that if the Nachal is not "Eisan" it nevertheless is valid (that is, the quality of "Eisan" is not Me'akev) because the Torah does not say that it is Me'akev.
Why should the Torah need to say that the quality of "Eisan" is Me'akev in order for it to be Me'akev? Whenever the Torah commands that a procedure be performed in a certain way, if one does not perform the procedure in the specified manner it should not be valid. (KEREN ORAH; see Insights to Sotah 16:1.)
ANSWERS:
(a) REBBI AKIVA EIGER cites the Sifri which infers that "Eisan" is not Me'akev from the fact that the Torah refers to the Nachal later (in verses 4 and 6) as simply "Nachal" and not "Nachal Eisan."
Why, though, should the Torah need to repeat the word "Eisan"? The Torah omits a word when the point can be understood without the extra word.
Perhaps Rashi means that the Mitzvah of Eglah Arufah is in the category of Kodshim, since the verse uses the term "Kaparah" (Devarim 21:8) with regard to the Eglah Arufah as it uses the term with regard to Kodshim (Rashi 47a, DH Kiprah; Kidushin 57a). A general rule states that in all areas of Kodshim, the procedure written in the Torah is Me'akev only when the verse repeats it with in an additional verse (see Insights to Sotah 16:1). Since Eglah Arufah is considered like Kodshim, and since the Torah writes only once that the Eglah Arufah must be brought to Nachal Eisan, "Eisan" is not Me'akev. (The MALBIM cites the VILNA GA'ON's Girsa of the Sifrei which reads, "Shanah Alav ha'Kasuv l'Akev.")
(b) The RAMBAM (in Perush ha'Mishnayos) explains the Mishnah differently. He explains that "Eisan" can mean "strong" and describes the force of the stream, or it can mean "great" and describes the amount of water in the stream. The Mishnah teaches that there must be a forceful flow of water in the stream in order to be valid for use with the Eglah Arufah, and it does not need a large quantity of water. The Rambam (in Mishnah Torah) indeed implies that if the stream is not strong it is not valid for Eglah Arufah (unlike Rashi), while nowhere does he mention that the Nachal is valid if it is not "Eisan."