Taharos, Chapter 8, Mishnah 3. This chapter continues to work out the practical rules of when we may assume that keilim have stayed tahor and when we must suspect that an am ha'aretz, or simply an unknown passerby, has handled them. Our Mishnah takes up three situations: an object that was lost and found again, keilim spread out in a public or private place, and a bucket that fell into the cistern of an am ha'aretz.
Lost by day, found by day
"Hame'abed beyom umatza beyom": one who loses an object during the daytime and finds it again that same day. The ruling is tahor. The reasoning is simple and human: an object lying in the open during daylight hours would have been noticed. Had anyone come upon it, he would have picked it up and taken it home with him. Since it is still lying exactly where it fell, we may assume that nobody came near it at all, and it therefore retains its taharah.
When the night intervenes
Three variations follow, and all of them end the same way. "Beyom umatza balailah": it slipped away in daylight but was recovered after dark. "Balailah umatza beyom": it went missing at night and was found once the sun was up. And "beyom umatza beyom shele'acharav": it disappeared on one day and surfaced only the next, a full day later. Each of these cases is ruled tamei. Once darkness enters the story, the earlier logic collapses. In the dark a passerby may bump the item with his foot or brush past it without ever realizing that something worth taking home is lying there. We can no longer maintain that whoever made contact would certainly have carried it off, and so the concern that someone touched it and conveyed tumah becomes a genuine one.
The Mishnah then formulates the governing rule. It opens with the words "Zeh hakelal", and the deciding factor it names is whether nighttime elapsed while the item lay unattended: "kol she'avar alav halailah o miktzaso, tamei". If a whole night went by, or even a fraction of one, the object is treated as tamei.
Keilim spread out
"Hashotei'ach keilim birshus harabbim, tehorin." One who spreads out his garments, presumably to dry them, in a public domain: they remain tahor. "Birshus hayachid, temei'in": if he spread them out in a private domain, they are tamei. This follows the standard pattern of these halachos regarding what we suspect in a place where an unseen person may have gone about his business undisturbed.
"Ve'im hayah meshamran, tehorin." If he was standing there watching over them, they are tahor. That is self evident: nothing could have happened to them without his knowing.
"Naflu vehalach lehavi'an, temei'in." But if the garments fell and he walked off to retrieve them, they are tamei. Once they were out of his field of vision, he was no longer truly guarding them, and the protection of shemirah is gone.
The bucket in the cistern of an am ha'aretz
"Nafal delyo lesoch boro shel am ha'aretz": a man's bucket dropped into a cistern belonging to an am ha'aretz. Then, "vehalach lehavi bameh ya'alenu": he walked away to fetch some implement, a rope perhaps, with which to draw it back up. The verdict is tamei. The Mishnah gives the reason, "mipnei shehunach birshus am ha'aretz sha'ah achas", since the bucket sat for a stretch of time inside an am ha'aretz's reshus.
What is more, the tumah assigned here is that of a meis, so the vessel requires the full seven day process of taharah. Consider how sweeping this ruling is: the am ha'aretz never laid a finger on the bucket resting in his water pit. Even so, the chachamim refused to sort keilim into categories once they have been left behind on an am ha'aretz's property, and pronounced every one of them tamei.
Three cases, one thread running through them: taharah is preserved where we can reasonably reconstruct that no one had access, and it is lost the moment we can no longer account for what happened to our keilim.