Kelim, Chapter Three, Mishnah Four
1) If a jar was about to be cracked but was strengthened with cattle dung, although the potsherds would fall apart were the dung to be removed, it is unclean, because the designation of vessel never ceased to apply.
2) If it was broken and some of its pieces were stuck together again, or if he brought other pieces of clay from elsewhere, and it was also lined with cattle dung, even though the potsherds hold together when the dung is removed, it is clean, because the designation of vessel ceased to apply.
3) If it contained one potsherd that could hold a quarter of a log, all its parts contract impurity by contact, but that potsherd contracts impurity through its air-space.
Section one: The jar was about to fall apart, but dung was applied to the outside as glue and the pieces were held together. Although the jar would fall apart were the dung removed, it is still susceptible to impurity because the jar never broke, and therefore never lost its designation as a vessel.
Section two: In this case the jar actually broke, thereby ceasing to be a vessel. Although it has been repaired, the jar can no longer receive impurity, because once a vessel has been completely broken (and not just pierced) it can no longer receive impurity.
Section three: If one potsherd was large enough to hold a quarter of a log, then if a defiling agent touches the inside of the jar, the entire jar is impure, even if it touched a different potsherd. Since one potsherd was large enough to be considered a “vessel” the entire repaired vessel can still be defiled.
The large potsherd can become impure even through something defiling entering its airspace. So if a piece of something impure enters the airspace opposite that piece, then the entire jar is impure. But if something impure enters the airspace opposite the other potsherds, nothing is impure.