Related for Chagigah 2:10

They may not expound upon the subject of forbidden relations before three but they may expound before two, and they may not expound concerning the Work of Creation before two but they may expound before one (Chag. 2:1). They may not expound on the [Work of] the Chariot before one unless he is wise and understands of his own accord. A story of R. Yochanan ben Zakkai who was riding on his donkey and Rabbi Ele'azar ben Arakh was riding behind him. He said to him: "Rabbi, teach me one chapter concerning the Work of the Chariot. He said to him: "No. Have I not said to you from the beginning that one does not teach concerning the [Work of] the Chariot before one unless he is wise and understands of his own accord?" He said to him: "Now give me permission to expound before you." He said to him: "Speak!" Rabbi Ele'azar ben Arakh began to expound on the Work of the Chariot. Rabbi Yochanan ben Zakkai alighted from his donkey and wrapped himself in his tallit and the two of them sat on an outcropping of rock under an olive tree and he presented the subject before him. Rabbi Yochanan stood up and kissed him and said: "Blessed is Adonai, God of Israel, who gave a son to Abraham our father that knows and understands how to expound on the glory of our Father in Heaven!" There are those suited to expound and who are not suited to fulfill, those who are suited to fulfill and who are not suited to expound. Ele'azar ben Arakh is suited to expound and to fulfill. Happy is Abraham our father, that Ele'azar ben Arakh, who came forth from your loins, knows and understands well enough to expound on the glory of our Father in heaven!" Rabbi Yosi bar R. Yehuda says: "Rabbi Yehoshua expounded before R. Yochanan ben Zakkai, Rabbi Akiva expounded before Rabbi Yehoshua and Chananiah ben Chachinai expounded before Rabbi Akiva."

In their days (i.e., the days of the pairs), they only argued about the laying of hands (i.e., whether the owner of a peace offering must lean his hands against the animal before it is sacrificed, see Chag. 2:2). There were five pairs. Three of the first pairs said not to lay on hands and two of the last pairs said to lay on hands. Three were Nesi'im (princes) and two (of them) were the heads of courts, the words of R. Meir. R. Judah said Simon ben Shetah was Nasi (prince) and Judah ben Tabbai the head of the court. Said R. Yose: Originally there were no arguments in Israel. Rather, a 71 member court sat in the chamber of hewn stone (the Sanhedrin) and other courts of 23 existed in the cities of Erez Yisrael. And two courts of 3 apiece were in Jerusalem, one on the Temple Mount and one in Chayil. When one of them was necessary [a person] goes to the court in his city. No court (in his city)--[the person] goes to the court near his city. If they heard, they say to him; if not, he and their most distinguished member go to the court on the Temple Mount. If they heard, they say to him; if not, he and their most distinguished member go to the court in Hayil. If they heard they say to him; if not these and these arrive at the court in the chamber of hewn stone (And the court of the chamber of hewn stone even though it is 71, it can never have less than 23. If one of them needs to leave, he sees if there will be 23 he may leave; if not, he may not leave until there are 23. They would sit from the offering of the morning sacrifice until the offering of the afternoon sacrifice. And on Sabbaths and Festivals they would enter the Beit Midrash on the Temple Mount.) If they heard they say to them, and if not, they establish a quorum and take a roll. If the majority says impure it is impure. If the majority says pure it is pure. From there the Halakhah (law) goes out widespread in Israel. When there increased the students of Shammai and Hillel who did not properly apprentice, conflict increased in Israel and it became as though there were two Torahs (Sanh. 88b:7). And for there they would sit and inspect. Whoever was wise and humble and abundant and sin-fearing and mature and getting along with other people they make him a judge in his city. After being made a judge in his city they could elevate and set him on the Temple Mount and from there they could elevate and seat him in Chayil and from there they can elevate and seat him in the chamber of hewn stone and from there they sit and inspect the lineages of the priests and levites. A priest in whom has been found a blemish wears black and wraps in black, exits and leaves. One in whom not a blemish is found wears white and wraps in white, enters and serves with his brothers the priests. They would make a holiday that not a blemish was found among the children of Aaron. And he would bring a tenth of an Eifah of his own flour and do the service with his own hands even though it is not his priestly shift. A high priest and a regular priest who served before bringing their tenth of an Eifah their service is acceptable.

What is the "laying of hands" that Beit Shammai disagreed about? They say, "There is no laying of the hands on festivals, and [as to] peace offerings, he brings them and lays hands on them on the evening before the festival." [And] Beit Hillel says, "They bring peace offerings and burnt offerings and lay their hands on them [on the day of the festival]" (Chag. 2:2-3). Said Beit Hillel to Beit Shammai, "Since at a time that you do not permit commoners (non-priests) to perform [laying of the hands], you permit it to be performed for the Most High, thus, at a time that you do permit commoners to perform [laying of the hands], is is not logical that you should [certainly] permit it [to be performed] for the Most High?" Beit Shammai said to them, "Vows and freewill offerings are proof, since they are permitted to be performed by commoners but are not permitted for the Most High." Beit Hillel said to them, "No. If you are speaking of vows and freewill offerings, which do not have a fixed time, what would you say regarding festival offerings, which do have a fixed time?" Beit Shammai said to them, "However, there are instances that a festival offering has no fixed time, since if [one did not bring a festival offering] on the first Yom Tov of the festival, he [nonetheless] may celebrate the whole festival and on the last day [he brings it]." Abba Shaul would state a different version [of this exchange] in the name of Beit Hillel: "Since at a time when your stove is closed down, the stove of your Master is open, then at a time that your stove is open, would not the stove of your Master also be open?" Another version: "It is in order that your table not be full, while the table of your Master is empty."

There is a greater stringency with regards to consecrated food [of sacrifices] and Terumah than with regards to the [waters of] purification [containing the ashes of the red heifer], since everyone is believed regarding [the purity status of the waters of] purification, but not everyone is believed as to [the purity status of] consecrated foods or Terumah. There is greater stringency with regards to the [waters of] purification, which is that one who is pure [with respect to the waters of purification] is impure with respect to consecrated food and Terumah, and there is no than with the purity of consecrated food and Terumah. There is a "counting" with respect to consecrated food and Terumah (i.e., 3rd- and 4th- level impurity, see Minchat Yitzchak), but there is no "counting" as to the [waters of] purification. A mourner is forbidden [to partake] in tithes but permitted [to partake] in Terumah and in [the purification rite involving] the red heifer. A tevul yom (i.e., one who has immersed but remains impure until sunset) is forbidden in Terumah but permitted in tithes and in the red heifer. One who lacks atonement (i.e., who has not yet brought a sacrifice) is forbidden in the red heifer but permitted in tithes and in Terumah.