Eruvin, Chapter 7, Mishnah 1. This Mishnah and those that follow it deal with two courtyards adjacent to one another that have an opening between them, and with the questions: under what conditions may they make a joint eruv and under what conditions may they not, and when are they required to make a joint eruv and when are they not.
The text of the Mishnah:
"Chalon shebein shtei chatzeirot" - a wall separates the two courtyards, and there is a window set into the wall. In such a case the halachah depends on two conditions:
"Arba'ah al arba'ah" - the size of the window is four handbreadths by four handbreadths.
"Betoch asarah" - the opening of the window is within ten handbreadths of the ground. The Gemara clarifies that it is enough that part of the window is within ten handbreadths of the ground.
When these two conditions are met, the Mishnah rules: "Me'arvin shnayim, ve'im ratzu me'arvin echad" - the residents of the two courtyards may make two separate eruvin, one in each courtyard, and they are not obligated to join together; and if they wish, they may make a single eruv for both.
The reason is this: a window measuring four handbreadths by four handbreadths that is within ten handbreadths of the ground is passable, and the residents of the courtyards can easily pass through it from one courtyard to the other. Since it is passable, it is considered an opening, and therefore they are permitted to make a joint eruv. Had there been no opening or any means of passage from one to the other, they could not have made a joint eruv at all and would have been required to make two separate eruvin; but when there is something resembling an opening, the choice is theirs - to make a joint eruv, or to make two separate eruvin and not join together.
A window that is not of the required size:
If the window is smaller than four handbreadths by four handbreadths, or if it is higher than ten handbreadths from the ground - even if it does measure four by four - it is not considered a place through which one can pass from one courtyard to the other. Therefore the Mishnah rules: "Me'arvin shnayim ve'ein me'arvin echad" - they may make only two separate eruvin, and they cannot make a single eruv, since they are two entirely separate areas.
A window between two houses:
The Gemara clarifies that in contrast to two courtyards, which are a more public place, if there were two houses with a window open between them measuring four by four, even if it is higher than ten handbreadths, they may make a joint eruv. The reason: in houses, which are not a public place, the members of the household can easily bring chairs, steps or some other object and set them beside the wall. Therefore the presence of a wall ten handbreadths high between the two houses does not prevent passage between them, and that ten handbreadth wall no longer has the status of ten handbreadths that separate. For this reason, in the case of two houses adjacent to one another, they may make a joint eruv if they wish to do so.
In summary: a window between two courtyards that measures four handbreadths by four handbreadths and is within ten handbreadths of the ground is considered an opening, and therefore "me'arvin shnayim, ve'im ratzu me'arvin echad." If the window was smaller than the required size, or higher than ten handbreadths - "me'arvin shnayim ve'ein me'arvin echad." And in the case of two houses, even a window higher than ten handbreadths permits a joint eruv, because passage there is easy and they are not a public place.
In the coming Mishnayos we will continue to deal with the conditions for joining two courtyards together and with the ways in which they are separated from one another.