Mikvaos, Chapter 1, Mishnah 5. The opening chapter of Maseches Mikvaos works its way through the grades of gathered water, from the lowest and weakest kind up to the highest. The mishnayos just before ours dealt with a pit of water whose standing came into question: a droplet of tamei water made its way in, and from that moment the water is under suspicion of tumah. Our mishnah picks up exactly where that leaves off and asks the obvious follow-up question.
The mishnah opens: "Mei'eimasai taharasan?" From when do these waters return to being tahor? In other words, water that fell under suspicion because a drop of tamei water entered it does not have to stay that way forever. Fresh rain will come down and pour into the pit. The question is how much fresh water is needed, and what it has to accomplish, before we can once again relate to the water in the pit as tahor.
Beis Shammai: two conditions
Beis Shammai: two conditions
Beis Shammai, whose ruling is stated first as the Tanna Kamma, demands that two things happen: "misheyirbu veyishtofu." To begin with, the newly arrived rainwater must outweigh in quantity whatever water was already standing in the pit. Beyond that, the inflow must arrive with enough force that it drives the older water out, so that the pit fills to the brim and its contents spill over the edge and drain away. Taharah is restored only when both of these have taken place. Such is the ruling of Beis Shammai.
Beis Hillel and Rebbi Shimon
Beis Hillel disagree: "she'rabu aleihem af al pi shelo shotfu." It is enough that the fresh rainwater which came in is now the majority, even if the water never overflowed the edges of the pit. For Beis Hillel, the first of Beis Shammai's two conditions carries the day on its own.
Rebbi Shimon says the reverse: "shotfu af al pi shelo rabu." If the incoming water swept the pit's water over the sides, that suffices to be metaher the water even though the new water never became the majority. Rebbi Shimon's position turns out to be the most lenient of the three, going further even than the shitah of Beis Hillel.
What this water may be used for
The mishnah ends by identifying the uses to which water of this level may be put. It is "kesheirim l'challah v'litol meihen l'yadayim": one may use it to work a dough from which challah will later be taken, and one may pour it over the hands for netilas yadayim, an obligation instituted by the Rabbanan, both when washing before eating chulin and when washing for terumah. Herein lies the usefulness of water in this category. Immersing in it will not accomplish anything, since it lacks the standing required for a tevilah; for pouring over the hands, however, it serves without any difficulty.