Taharos, Chapter 10, Mishnah 2. We are in the final chapter of Taharos, which deals with the olive press and its workers, the badadim. These men are typically amei ha'aretz who immerse and purify themselves specifically for the sake of this work, since the owner wants his oil produced in taharah. The recurring question of the chapter is how much we may rely on them, and this mishnah presents three practical scenarios.
The first: "Habadadim shehayu nichnasin veyotze'in", the olive press workers were going in and out of the press, "umashkin temei'in betoch beis habad", and there were tamei liquids lying on the floor. The workers are walking barefoot through the press, and their feet may well pass through those liquids on the way to the olives. The mishnah gives us the measure: "im yesh bein hamashkin lezeisim kedei sheyingvu es ragleihem ba'aretz, harei eilu tehorin." If the distance between the puddle of tamei liquid and the olives is great enough that their feet would dry off along the way as they walk on the ground, the olives remain tahor. If the distance is shorter than that, the olives are tamei.
The logic behind this measure is worth spelling out. A person's feet are not among the limbs that contract tumah from tamei liquids; that halachah applies to hands, which become tamei upon contact with such liquids. Feet do not. (Shoes are a different matter, since a shoe itself is a vessel that can become tamei, so this whole leniency is speaking of bare feet.) The concern here, then, is not the foot itself becoming tamei, but the tamei liquid being carried along on a wet foot and reaching the olives. Once the walk to the olives is long enough for the feet to dry, nothing tamei arrives with them, and the olives stay tahor.
The second scenario: olive press workers and grape pickers before whom a source of tumah was set down. "Ne'emanin lomar lo naganu", they are believed when they say, "We did not touch it." Even though these are amei ha'aretz, for the purposes of their work we accept their word about the tumah lying in front of them.
"Vechein hatinokos shebeineihem", and the same applies to the small children among them, the youngsters the workers bring along to the press. These children are themselves presumed tamei, since their mothers, who are niddos, hold and carry them. Regarding the placement of this clause there are two readings: some understand "and likewise the children among them" as belonging to the previous statement, that the children too are believed when they say they did not touch the tumah, and some read it as the introduction to what follows. Either way, both halachos stand.
The third scenario: "yotze'in chutz lefesach beis habad ufonin le'achorei hagader, vehen tehorin." They step out past the entrance of the olive press and turn aside behind the fence, and they remain tahor. The reason they have gone out is to relieve themselves, and since they are still in the immediate vicinity of the press, we do not suspect them of having picked up tumah in the meantime.
But how far does "the immediate vicinity" extend? The mishnah asks: "Ad kamah yarchiku veyihyu tehorin?" How far may they go and still be tahor? And it answers: "ad kedei sheyir'u osan", as far as they can still be seen. So long as they remain within range of sight, we know they have not gotten into anything, and they retain their taharah. Once they pass out of view, we can no longer vouch for them, and we suspect that they have become tamei.
Three rulings, then, all built on the same practical realism: measure the walk from the puddle to the olives, accept the worker's word about what he did not touch, and keep an eye on him when he steps outside.