Niddah, Chapter 2, Mishnah 5. This mishnah falls into two halves. It first lays down a wide, reassuring rule about the standing of Jewish women, and it then picks up the thread of this chapter's earlier discussion about examination cloths and the women who work with taharos, a matter on which Beis Shammai and Beis Hillel divide.
A woman's assumed status
The opening words are "Kol hanashim bechezkas taharah leva'aleihen": every woman is held to be in a state of taharah so far as her husband is concerned. The default reading of reality is that she is tehorah and therefore permitted to him, and that default holds firm unless she herself says something to the contrary, or unless some evidence overturns it.
The mishnah applies this at once to a concrete situation: "Haba'im min haderech, nesheihem lahem bechezkas taharah". A man who arrives back home after travelling out of town may lean on this default and treat his wife as tehorah and permitted to him. He is under no obligation to greet her with an inquiry about whether she is tehorah or tmei'ah. So long as she has not told him that matters stand differently, the chazakah, the settled presumption, decides the case.
How many cloths does one night require?
Now the mishnah turns back to the women mentioned earlier in the perek: those who deal with taharos, objects that have to be maintained in a condition of ritual purity. Because of the heightened care expected of them, such a woman checks herself with a cloth, a bedikah, both prior to relations and afterwards. What the two houses argue over is how that duty plays out across an entire night.
Beis Shammai rule that she needs two cloths "al kol tashmish vetashmish", on each and every occasion of relations: one used beforehand and one used afterwards, every single time. She may not designate a single cloth to serve for the night as a whole; every instance calls for checks of its own, both prior and subsequent.
Beis Shammai then present a second option: "o teshamesh le'or haneir", or she may conduct herself by lamplight. That is, one cloth is able to do duty for the whole night, provided that each check, the one done before and the one done after, is inspected under the light of a lamp. What lies behind this? Blood from an earlier check could be rubbed off without her noticing, leaving her with no dependable evidence of what had appeared on the cloth. Every inspection must therefore be read clearly, so that its findings are firmly established; and if the cloth proves to be clean, it may be pressed into service again.
"Beis Hillel omrim: dayah bishnei eidim kol halaylah": Beis Hillel maintain that two cloths cover the night in its entirety, one employed when the night begins, serving both husband and wife, and a second employed as the night draws to a close, again for both of them. In their view, no individual act of relations requires a cloth dedicated to it alone.
The mishnah thus travels from the general rule to its particular application. In principle, a woman carries the status of taharah and is permitted to her husband, so that a man coming home from the road need not open with questions. In practice, among those women who handle taharos and consequently examine themselves before and after, the houses of Shammai and Hillel dispute whether each act calls for a fresh pair of cloths, or whether two cloths, one when the night opens and one when it finishes, are sufficient.