Mikvaos 10:8-Niddah 1:1

Mikvaos 10:8

If a person ate ritually-unclean food or drank ritually-unclean liquid and then immersed in a mikvah, after which he regurgitated the unclean food or drink, they are still unclean because they weren’t purified in his body. If someone drank ritually-unclean water and immersed, after which he regurgitated it, it is clean because it was purified in his body. If someone swallowed a ritually-clean ring and then went into a corpse’s tent, was twice sprinkled with purification water and immersed, after which he regurgitated the ring, it retains its status quo (i.e., of ritual purity). If one swallowed a ritually-unclean ring, he may immerse himself and eat trumah; if he regurgitated it, the ring is unclean and it renders him unclean. If an arrow is stuck in someone, it is an interposition so long as it remains visible; if it’s not visible, he may immerse and eat trumah.

Niddah 1:1

Shammai says regarding all women that their time is sufficient (i.e., if they see uterine blood, they are impure as of its discovery); Hillel says from one exam to the next (i.e., they assume the blood came after their last exam) even after several days. The Sages say that the halacha is like neither of these authorities. Rather, a 24-hour period of time reduces the period from one exam to the next and from one exam to the next reduces a 24-hour time period. If a woman has a regular cycle, then her time (i.e., of discovering blood) is sufficient. If a woman uses examination cloths before and after intimacy, it’s like an exam and it reduces both a 24-hour period of time and the time from one exam to the next.