We now turn to Maseches Beitzah, chapter 5, mishnah 3. From this point until the end of the chapter, which is also the end of the maseches, the mishnayos deal with the laws of techum on Yom Tov.
"HaBeheimah v'haKeilim k'raglei haBe'alim":
An animal and utensils, as far as the techum within which they may be taken, follow the feet of their owners. If the owners made an eiruv techumin, the animal and utensils are drawn along with that eiruv as well; and if they did not, their techum is determined by the city in which the owners are located. The rule in short: wherever the owners are permitted to go, they may also take their animal and their utensils.
"HaMoser beheimto l'vno o l'ro'eh":
What is the law when, on Yom Tov itself, the identity of the person responsible for the animal changes, and the owner hands it over to his son or to a shepherd? The mishnah rules: "Harei eilu k'raglei haBe'alim" - since at the onset of Yom Tov the animal was in the owners' possession and under their control, its techum is determined by the owners. Even if the son or the shepherd has a different techum from theirs, the animal does not follow him, even though he is the one who now controls it, because the techum was already fixed at the onset of Yom Tov.
The Gemara clarifies that regarding a shepherd, this applies specifically when there is more than one shepherd in the city. But if the city has only a single shepherd, there is already an assumption at the onset of Yom Tov that the shepherd will come and take the animal during Yom Tov, and therefore the animal's techum is determined by the techum of the shepherd.
"Keilim hameyuchadin l'echad min ha'achim shebabayis":
The mishnah deals with a group of brothers living in one house who own various items. Here the mishnah distinguishes between two situations:
"Keilim hameyuchadin l'echad min ha'achim shebabayis - harei eilu k'raglav" - utensils or garments designated for one particular brother have their techum determined by the techum of that brother. And if another brother borrowed his coat from him, he may take it only as far as the place to which the brother who owns it was permitted to go.
"V'she'einan meyuchadin - harei eilu k'makom shehol'chin" - utensils that are not designated for one brother are considered, as it were, the joint property of them all, and their techum is determined by the lowest common denominator: only the places to which all of them are permitted to go. If the brothers' techumin differ from one another, the permission is limited to the techum shared by all of them. Therefore, if one of them made an eiruv techumin and the others did not, the utensils may be taken only within the area of overlap between the techum of the brothers who did not make an eiruv and the techum of the brother who did.
In summary: in this mishnah we learned that an animal and utensils follow the feet of their owners, and that even if the animal was handed over on Yom Tov to a son or to a shepherd, its techum remains that of the owners, except in the case where there is only one shepherd in the city. We also learned the distinction between utensils designated for one of the brothers, which follow his feet, and utensils that are not designated, whose movement is limited to the techum shared by all the brothers.
As the chapter continues, we will go on dealing with the laws of techum on Yom Tov.