Machshirin, Chapter 2, Mishnah 4. This chapter takes up waters whose status is doubtful, including water that a person has already used and discarded and which therefore carries a presumption of tumah. Our mishnah presents a case where such used water becomes mixed with fresh rainwater, and it teaches both the rule that decides the mixture and the practical way to tell which water predominates.
The case
The mishnah opens with two workers. "Hatorei es gago": a man was coating his roof with tar, and the accepted method was to pour water across the fresh surface afterward so that it would spread out evenly and lie flat. Alongside him the mishnah sets "hamachabes es ksusav," someone laundering his garments. The water in each of these jobs is treated as tamei from the outset, because nobody takes care to protect such water, and no one intends to drink it.
"Veyardu lahem geshamim": rain then fell upon that water. Rainwater is tahor, and now the two waters have run together into a single mixture.
Following the majority
The deciding factor is which water makes up the bulk of the mixture. Where the used water is the larger part, the mishnah rules "tamei," and everything is tamei. Where the fresh rainwater is the larger part, it rules "tahor," and everything is tahor. And when neither side is larger, "mechtzah lemechtzah, tamei": an exact split leaves the mixture tamei, since the tumah is there and no majority of tahor water stands against it to cancel it.
How do you tell which is the majority?
Practically speaking, one measures by watching the flow. Compare how thickly the water is running off now with how it ran before the rain began. If the stream became considerably heavier once the rain started, one may assume that most of what is flowing is rainwater. If the flow is roughly as it was, it is assumed to be the same water as before, and it is tamei.
Rabbi Yehuda proposes a different gauge. He does not measure the width of the stream at all; he counts how often the water drips. The mishnah records his test in three words, "im hosif halenatef," meaning: did the dripping become more frequent? Water that had been dripping slowly, and after the rainfall began to drip at a noticeably quicker pace, may be credited entirely to the rain. Should the drops keep falling at their earlier pace, we treat the water as unchanged from before, and it remains tamei.
The halachah is not paskened according to Rabbi Yehuda; we go by the volume of the flow rather than by the count of the drops.
The mishnah thus gives us a rule and a ruler: the rule is that a mixture of tamei and tahor water follows its majority, with an even split leaving the tumah in place, and the ruler is the ordinary observation of how the water is running off the roof.