Mikvaos, Chapter 10, Mishnah 6. This mishnah continues the discussion of hashaka, the arrangement by which water in one place is brought into contact with water in another place so that the two are treated as a single body of water.
There are two distinct applications of hashaka in the laws of a mikveh. The first is used to solve a problem of mayim she'uvim, drawn water. Drawn water on its own is not valid for a mikveh, but if it is made to touch a valid mikveh of rainwater containing forty se'ah, the entire amount takes on the status of mikveh water. The second application, which is the subject of our mishnah, deals with mayim temei'im, water that has become tamei. As long as such water is placed in contact with a mikveh of mayim tehorim, the tamei water becomes tahor.
The dispute of Beis Shammai and Beis Hillel
The mishnah opens: "Beis Shammai omrim ein matbilin chamin b'tzonen v'lo tzonen b'chamin." When the mishnah uses the word matbilin here, it does not mean literal immersion of an object; it refers to performing hashaka. Beis Shammai holds that hot water which is tamei cannot be joined by hashaka to cold water, and cold water which is tamei cannot be joined by hashaka to hot water. Hot water and cold water are regarded as two different kinds of water, and since there is no compatibility between them, the contact does not create a single body of water and the hashaka will not be effective to render the tamei water tahor.
The mishnah applies the same reasoning to a second pair: "lo yafim b'ra'im v'lo ra'im b'yafim." Good water, meaning sweet water, cannot be joined by hashaka to bad water, meaning bitter water, and bitter water cannot be joined to sweet water. Here too Beis Shammai considers them two separate categories of water, so hashaka cannot draw taharah from the one to the other.
The opposing view is stated in a single word: "matbilin." Beis Hillel rule that the hashaka does work. In their understanding, variations of temperature or of flavor do not divide water into separate species; hot or cold, sweet or bitter, it is all water in the end, and contact between the two bodies unites them.
A vessel filled with other liquids
The mishnah now turns to a related case: "kli shehu malei mashkin v'hitvilo, k'ilu lo taval." A vessel filled with liquids other than water was immersed in a mikveh. Since hashaka does not exist for other liquids, the liquids inside the vessel are never joined to the mikveh water at all. They therefore remain in place as a chatzitza, a barrier separating the mikveh water from the vessel itself, and the immersion accomplishes nothing.
"Malei mei raglayim, ro'in osam k'ilu hein mayim." If the vessel is full of urine, the halachah is different. Urine is essentially water that has become discolored, and so we view it as though it were water. Hashaka is therefore feasible in such a case, and the immersion is effective.
A vessel filled with mei chatas
"Malei mei chatas": and what if the vessel is filled with mei chatas, the spring water into which the eifer, the ash of the Parah Adumah, has been placed? One might have assumed that since this too is fundamentally a water solution, it would join with the mikveh. The halachah says otherwise. Given the special standing and unique character of mei chatas, it retains its own identity and functions as a chatzitza, so it does not merge with the water of the mikveh.
A condition follows: "ad sheyirbu hamayim al mei chatas." Should plain water be poured in until it outnumbers the mei chatas inside the vessel, the mei chatas is nullified within the larger quantity. Once that happens, the immersion serves as a valid hashaka, and the liquid in the vessel attains taharah.
Rebbi Yosei rules more stringently, holding that mei chatas is never subject to nullification at all: "Rebbi Yosei omeir, afilu kli machzik kor v'ein bo ela revi'is, k'ilu lo taval." Take a vessel whose capacity is a kor, which is thirty se'ah, holding no more than a revi'is of mei chatas. Even so, the tevilah counts for nothing. No hashaka links the contents to the mikveh, and the tumah remains upon them.