Mikvaos, Chapter 10, Mishnah 5. This chapter deals with the halachos of chatzitzah and with how much of an object must enter the water of the mikveh. Our Mishnah takes up a specific question about yados hakeilim, the handles of vessels: what happens when a handle is longer than it needs to be and the owner plans to trim it down? The underlying issue is whether something that is omeid liktzotz, standing to be cut off, is already regarded as if it were not there, or whether it is still a full part of the keli that requires tevilah along with the rest.
A handle that will be shortened
"Kol yados hakeilim", every handle that is joined onto a keli, "shehein aruchin", that runs longer than it needs to be, "ve'asid lekatztzan", where the owner means to trim it back to the size he wants. In such a case, "matbilan ad mekom hamidah": the tevilah reaches only as far as the mark where he intends to cut, and whatever extends beyond that mark never needs to touch the water at all.
"Rebbi Yehudah omer", Rebbi Yehudah disagrees: "ad sheyatbil es kulo". In his view the future intention to cut does not remove the handle from the keli, and the entire handle must be submerged for the tevilah to be valid.
The chain of a bucket
The Mishnah applies the same kind of measurement to a chain. "Shalsheles deli gadol", the chain of a large bucket, is counted as part of the keli up to "arba tefachim", four tefachim. "Veshel katan", the chain of a small bucket, which must be lowered further down into the water in order to draw, is counted for "asarah", ten tefachim; that much of it must be submerged.
And if the chain is longer than that measurement, the halacha is "matbilan ad mekom hamidah": one submerges it only up to the shiur that the Tanna has just given us, and no further.
"Rebbi Tarfon omer", Rebbi Tarfon adds a qualification: "ad sheyatbil es kol hataba'os". Suppose the measurement of four tefachim or ten tefachim ends in the middle of one of the links. One cannot toivel half a ring; the whole link in which the shiur ends must be brought into the water.
A rope tied to a basket
The Mishnah finishes with a chatzitzah case involving a chevel, a rope. "Chevel shehu kashur bekupah", where a rope has been tied onto a basket, "eino chibur": the tie does not make the two into one object, so at the time of tevilah the rope interposes. The exception is "ela im kein tafar", where he stitched the rope on, and the stitching demonstrates a permanent bond. Sewn on in that way, the rope counts as a piece of the basket, and there is no chatzitzah.
A question to consider
A question emerges from this Mishnah, and it touches the wider debate about whether keilim are subject to a din of beis hastarim, concealed spots that the water need not physically reach. Even according to the view that keilim carry no such requirement, we are still left with a difficulty: when a portion of the keli stays above the surface, in what sense has the keli as a whole experienced a ma'aseh tevilah? That upper portion was never mukaf, encircled, by the water of the mikveh.
Several terutzim have been proposed. Both the Chazon Ish (Mikvaos, siman 10, os 1) and the Avi Ezri (Hilchos Mikvaos, perek 2, halacha 15, os 2) deal with the matter, and they are worth studying inside.