Eruvin, Chapter 7, Mishnah 3. This mishnah too continues to discuss the things that separate between two courtyards, and now we will deal with a separation that is not built upward but rather dug downward - a trench.
"Charitz sheben shtei chatzeiros":
The mishnah opens: "Charitz sheben shtei chatzeiros amok asarah v'rachav arba'ah" - a trench located between two courtyards, ten handbreadths deep and four handbreadths wide. Such a trench functions exactly as a wall ten handbreadths high functions: it constitutes a partition separating between the two courtyards.
Why a width of four handbreadths is required here:
In the previous mishnah we mentioned that a partition need not be four handbreadths wide, and the width of four was mentioned there in that case of a wall for a different halachic reason - because the top of the wall is considered a domain in its own right, an area of its own. But with a trench the law is different: if it is not four handbreadths wide, it is not considered a partition at all, since when it is less than four handbreadths people step across it easily, and it does not provide a partition. Once, however, it is four handbreadths wide and ten deep, it is a partition between the two, and therefore "me'arvin shnayim v'ein me'arvin echad" - they must make two separate eruvin, and they are not permitted to make one joint eruv.
A trench that has been filled in:
From here the mishnah discusses what happens when the trench becomes filled with objects. At what point is the filling considered to nullify the existence of the trench, so that it appears permanently filled and no longer has the status of a partition?
"Afilu malei kash o teven" - even if the trench is full of various kinds of straw, it is still considered a partition, because this filling is not destined to remain in place. It is the way of people to remove it, and they do not leave it there, but rather take it for animal feed and the like - and even on Shabbos they may take it. Therefore the filling does not nullify the partition.
"Malei afar o tzeroros" - if the trench became filled with earth or stones, since it is the way of people to leave them there, and they certainly cannot move them on Shabbos, the law is "me'arvin echad v'ein me'arvin shnayim". It is as though the trench does not exist and there is no wall here at all, and since there is no wall, the two courtyards are considered one courtyard, and they must make one joint eruv, and they cannot make two separate eruvin.
In summary: in this mishnah we learned that a trench ten handbreadths deep and four wide constitutes a partition between two courtyards, and therefore they make two eruvin and do not make one; and if it is less than four handbreadths it is not a partition at all, since people step across it. We also learned the distinction between a temporary filling, such as straw and stubble, which does not nullify the partition, and a permanent filling, such as earth and stones, which nullifies the trench and unites the two courtyards into a single eruv.