Yadayim, Chapter 3, Mishnah 1. Our tractate is devoted to the halachos of hands: how they contract tumah, how they are purified, and what they can render impure once they have become tamei. The premise underlying the whole discussion is a rabbinic one. Hands are busy, they touch what a person is not always watching, and so they are treated as suspect. When hands come into contact with a source of tumah, the Sages ruled that the hands themselves become impure to a certain degree, and that impurity is significant enough to invalidate terumah. Our chapter now opens by asking exactly which degree of impurity the hands acquire.
The case with which the Mishnah begins is a house that has been declared a bayis menuga, a house struck with the tzaraas of houses described in the Torah. Such a house conveys tumah to a person who enters it, and it conveys tumah to the garments he is wearing as well. But what if a person did not walk in? What if he only reached inside, so that his hands entered the house and the rest of him remained outside?
The Mishnah rules: "Hamachnis yadav l'vais hamenuga, yadav techilos, divrei Rebbi Akiva" - one who inserts his hands into a leprous house, his hands are techilos, that is, a rishon, a first degree of impurity. This is the position of Rebbi Akiva. "Vachachamim omrim, yadav shniyos" - and the Sages say that his hands are only shniyos, a second degree of impurity.
The Mishnah then broadens the case into a general principle, and the same two opinions repeat themselves. "Kol hametamei begadim b'sha'as maga'o metamei es hayadayim lihyos techilos, divrei Rebbi Akiva" - whatever conveys impurity to a person's garments at the moment he touches it likewise renders his hands a first degree of impurity, according to Rebbi Akiva. "Vachachamim omrim lihyos shniyos" - the Sages maintain that in all such cases the hands become only a second degree of impurity. Rebbi Akiva reasons that a source of tumah powerful enough to reach a person's clothing should certainly leave his hands with a full first-degree status, while the Sages hold that the rabbinic decree concerning hands never gave them more than the status of a sheini. The Mishnah records that the Sages and Rebbi Akiva pressed one another further on the point, each side testing whether the other's approach is consistent with the impurities we find elsewhere.
In practice the ruling is like the Chachamim: hands that have become tamei carry the level of a sheini. That is the assumption on which the rest of our chapter rests, and it carries real weight, since even a sheini is enough to disqualify terumah, though it lacks the potency of a rishon.