R. Yosi bei R. Bun: R. Shimon ben Lakish was once passing a Beis Midrash and he heard the voices inside reciting the following Pasuk (Divrei Hayamim 1, 29, 21), "And they brought [Shelamim] sacrifices to Hash-m and they brought Olah offerings to Hash-m on the next day''.

He said: One who pauses (between 'and they brought sacrifices to Hashem' [meaning that day] and 'and they brought Olah offerings to Hash-m on the next day') follows to opinion of Beis Shamai (that only Shelamim offerings can be brought on Yom Tov but not Olah offerings). One who does not pause (meaning that all of the sacrifices were brought the next day) can also follow the opinion of Beis Hillel.

Question: It is understandable why they did not bring Olah offerings on Yom Tov, but why would they delay bringing the Shelamim offerings until the next day? Even Beis Shamai allows them to be brought on Yom Tov!

Answer (R. Yosi bei R. Bun): King Dovid died on Shavuos and all of Israel was mourning his death and could not bring sacrifices; they therefore brought the sacrifices the next day.

There was a story of Hillel the Elder who brought an Olah offering to the Temple courtyard on Yom Tov and performed on it Semicha. The students of Shamai gathered around him to protest (as they held that one may not bring Olah offerings on Yom Tov. It appears that they did not see Hillel perform Semichah, or they would have protested that as well.)

Hillel began to shake its tail (appearing that he wished to show them that it was female, as an Olah cannot be female. He did this in order to keep the peace.) He said to them - Look, it is female, and I brought it as a Shelamim (which you permit on Yom Tov)! He distracted them with conversation and they left (without discovering that it was an Olah).

Later on, Beis Shamai had the upper hand over Beis Hillel and wished to establish the Halacha like themselves. (Note: See Chazon Yechezkel on Tosefta Chagigah 2, 6 who explains that they had the upper hand because they claimed that Hillel had retracted. They proved this from the way he replied to the students in the story above.) Amongst them was Baba ben Buti who was one of the students of Beis Shamai but he knew that the Halachah follows Beis Hillel.

Once, he entered the Temple courtyard and found it to be almost empty (people were not bringing Olah offerings because Beis Shamai had pressured the people to follow their ruling). He said - those people who emptied the House of H-shem should have their houses empty. (He was angered that they had convinced the people to follow this Halachah, because he knew that the Halachah followed Beis Hillel that it was permitted to bring Olah offerings on Yom Tov.)

What did he do? He ordered 3000 superior quality sheep to be brought to the Temple. He checked them for blemishes and stood them on the Temple Mount. He said to the people - Listen, my brothers, House of Israel; whoever wishes to bring an Olah offering should do so and perform Semichah. Whoever wishes to bring a Shelamim offering should do so and perform Semichah!

It was at that time that the Halachah was established like Beis Hillel, and nobody questioned it at all.

R. Yitschak bar Elazar: When a cup is heated from cold, a basket of firewood is required; when it is already partially heated, a small amount of wood will prevent it from cooling down.

Another parable - A coal that does not burn at the beginning needs a lot of firewood as it will cool down rather than burn. (Similarly, because Hillel was silent at the beginning, great efforts were needed to overturn Beis Shamai's ruling later on.)

There was another story with one of the students of Hillel who brought his Olah to the Temple courtyard and performed Semichah. One of the students of Shamai saw him and said, "What is this Semichah?!'' (How can you transgress the ruling of Beis Shamai?)

He replied - "What is this silence?!'' (It would have been better if you would have remained silent!)

The student of Shamai was silenced with this rebuke and he left (and the Halachah was established like Beis Hillel).