Related for Beitzah 40:9

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."

One must not work for the food of the Gentiles or for the fodder of the dogs on the holiday. An incident is told about Shimon of Timnah who did not go to the house of study on the night of the holiday came. At the early in the morning R. Yehuda ben Baba met him. He said to him: Why didn't you come to the house of study last night? He said to him: A duty has come upon me, and I have fulfilled it. A band of Gentiles came into the city. I feared they would harm the residents. So, we slaughtered a calf and gave it to them to eat! He said to him: I should be surprised if your reward were not outweighed by your damage. Didn't they say: One must not work for the food of the Gentiles or for the fodder of the dogs on the holiday?!