Pesachim, Chapter 3, Mishnah 2. This Mishnah addresses the question: at what point is a piece of dough considered nullified to the vessel in which it sits, and when is it not nullified to it?
Dough in the cracks of a kneading trough:
The Mishnah opens: "Batzek shebesidkei areivah" - a piece of dough lodged in the crack of a kneading trough. When is it considered part of the trough, with no obligation to remove it as chametz?
"Im yesh kezayis bemakom echad" - if there is the measure of a kezayis in one spot, "chayav leva'er": one is obligated to dig it out and remove it.
"Ve'im lo" - if there is not a kezayis in one spot, "batel bemi'uto": it is nullified because of its small size, it counts as part of the vessel, and it is treated as though it does not exist at all.
The Gemara qualifies this statement: it applies specifically when the dough is attached to the trough in a crack in a way that it is "asuy lechazek" - it is placed there in order to strengthen the trough. In such a case we assume a person will leave it where it is, and it becomes part of the trough. But if it is not there to strengthen the trough, then even though it is less than a kezayis, one is still obligated to get rid of it, since a person does not leave it there, and therefore it is not nullified to the trough.
"Vechein le'inyan hatumah":
The Mishnah continues: "Vechein le'inyan hatumah". The same rule applies with regard to tumah that touched the trough not directly, but by way of the piece of dough - for example, a sheretz, a dead mouse, that touched the piece of dough:
In a case where one is obligated to remove the dough: the dough is considered separate and is not nullified to the trough. Therefore, if the sheretz touched it, this is not like touching the trough, and the trough is not tamei, because there is a chatzitzah - the piece of dough interposes between the tumah and the trough, since it is not considered part of it.
In a case where one is not obligated to get rid of it: the dough is nullified, and it is placed there, as explained, in order to strengthen the kneading trough and the like. Therefore, if the sheretz touched that part of the trough which is the dough, this is like touching the rest of the trough, and the trough is tamei.
During the rest of the year - the test of particularity:
Now the Mishnah turns to a case that is not on Pesach but during the rest of the year, when chametz is not a factor, and the matter depends on the question of particularity: does a person mind the piece of dough that is sitting there?
"Im makpid alav" - if he intends to remove the piece of dough, then it interposes between the sheretz and the trough. And even if it is less than a kezayis, since he does not intend to leave it there, the sheretz touching the dough is not like touching the trough. The same is true on Pesach when it is less than a kezayis: if he minds it, it is a chatzitzah.
"Im rotzeh bekiyumo" - if he wants it to remain there and he does not mind it, "harei hu ka'areivah": it has the status of the trough itself, and therefore the sheretz touching the dough is like touching the trough.
Batzek hacheresh:
Now the Mishnah turns to a different case: a piece of dough about which it is not known whether it became chametz or not. The matter is unclear, and its appearance shows no sign of leavening. Such dough is called "batzek hacheresh", after a deaf mute, who has no way of informing us that the dough has become chametz, and it displays none of the usual signs of leavening.
The Mishnah says: "Im yesh kayotzei bo shechimeitz" - if there is another piece of dough that was kneaded at the same time and has begun to leaven, "harei zeh asur": the batzek hacheresh is forbidden as well, and we assume that it too became chametz.
And if there is no other dough to compare it to, the Gemara there gives us the familiar measure: leavening occurs within the amount of time it takes a person to walk a mil, two thousand amos, which in our practical terms is eighteen minutes.
In summary: in this Mishnah we learned the parameters of dough being nullified to a vessel - a kezayis in one spot must be removed, while less than that is nullified because of its small size, provided that it sits in a crack and serves to strengthen the vessel; the implication for tumah, that dough which is not nullified interposes between the sheretz and the trough, while dough which is nullified has the status of the trough; the test of particularity during the rest of the year - "makpid alav" as opposed to "rotzeh bekiyumo"; and the law of batzek hacheresh, that if there is comparable dough that became chametz it is forbidden, and if there is none, the measure is the time it takes to walk a mil.