Mikvaot, Chapter Three, Mishnah One
1) Rabbi Yose says: two mikvehs neither of which contains forty seahs and a log and a half [of drawn water] fell into this one and a log and a half into this one, and then they are mixed together, they remain valid, since they had never been called as invalid.
a) But if there is a mikveh holding less than forty seahs, and three logs [of drawn water] fell into it, and it was then divided into two, it is invalid, since it had already been called invalid.
2) Rabbi Joshua declares it valid, for Rabbi Joshua used to say: any mikveh containing less than forty seahs into which three logs [of drawn water] fell and from which a kortov was withdrawn becomes valid, since the three logs have also been diminished.
3) But the sages say: it always remains invalid until the amount of its former contents and a little more are removed.
Section one: According to Rabbi Yose, if the mikveh was never declared invalid because a full three logs of drawn water fell in at one time, then it remains valid even if it turns out that there are three logs of drawn water in it. This is what occurs in the first scenario. The opposite is true in the second scenario. Even though the mikveh was split into two and now in each mikveh there are less than three logs of drawn water, since it was originally declared invalid, both mikvaot remain invalid.
Section two: Rabbi Joshua says that both mikvaot are valid because neither mikveh now contains three logs of drawn water. This matches his general opinion that a mikveh into which exactly three logs of drawn water have been put can be made valid by removal of even a kortov, 1/64 of a log of water. Since this tiny bit of water will have some drawn water mixed in with it, there will now be less than three logs of drawn water in the mikveh. Therefore it is valid.
Section three: The other sages disagree with Rabbi Joshua. They hold that once a mikveh is disqualified because it has three logs of drawn water it cannot be made valid until an amount equal to and a little bit more than its original contents (the amount that was in it before the three logs were put in) is removed.