Eruvin, Chapter 1, Mishnah 9. In the previous Mishnah we learned that in order to turn an area into a private domain and permit carrying there on Shabbos, at least a majority of its perimeter must consist of solid partition.
The assumption behind the law, and the law of lavud:
This rule was stated on the assumption that the openings are three handbreadths or more apart from one another. But when the gap between the solid sections of the partition is less than three handbreadths, the law of lavud applies: the gap is considered a continuous partition, and it is not viewed as open at all. This brings us to the ruling of our Mishnah, which deals with horizontal partitions that join together to form a partition, even though most of it is open, because they are within three handbreadths of one another.
The words of the Mishnah:
"Makifin sheloshah chavalim zeh lema'alah mizeh vezeh lema'alah mizeh" - one may surround an area with three ropes, one above the other.
"Uvilvad shelo yehei bein chevel lachavero sheloshah tefachim" - provided that there is not a gap of three handbreadths or more between the ropes. Since the ropes are within three handbreadths of one another, the space between them is treated as though it were sealed.
"Shiur chavalim ve'ovyan yeser al tefach, kedei sheyehei hakol asarah tefachim" - the thickness of the ropes must be slightly more than a handbreadth, so that the total comes to the measure of ten handbreadths.
The calculation in practice:
One stretches a rope on stakes slightly less than three handbreadths above the ground, a second rope slightly less than three handbreadths above it, and a third rope slightly less than three handbreadths above the second. The result is three gaps, each of them less than three handbreadths, coming to less than nine handbreadths in all. When the thickness of the three ropes is added to that, amounting to a handbreadth and a bit more, we arrive at a full partition of ten handbreadths.
Even though most of the area serving to create the partition is open, since all the parts are within three handbreadths of one another, the whole is viewed as sealed, by force of the principle called lavud.
In summary: In this Mishnah we learned that horizontal partitions, three ropes surrounding an area one above the other, join together to form a valid partition of ten handbreadths, provided that there are not three handbreadths between one rope and the next and that the thickness of the ropes exceeds a handbreadth. Even though most of the perimeter is open, the law of lavud views gaps of less than three handbreadths as a continuous, sealed partition.