Bava Basra, Chapter 2, Mishnah 13. This Mishnah deals with tree branches that overhang into a neighbor's field: what is the halachah regarding them, and how far the owner of the field is permitted to cut them.
The Mishnah states: "Ilan shehu noteh lesedeh chaveiro - kotzetz melo hamardeia al gabei hamachareishah" - if a tree overhangs into another's field, one cuts it to the height of the ox-goad on top of the plow. When the tree's branches interfere with the neighbor's agricultural work, he is permitted to cut them, as they are in his way. But if they do not interfere at all - such as a branch that is very high above the field, which is not in anyone's way - he has no right to cut it.
"Melo hamardeia al gabei hamachareishah":
The mardeia is the ox-goad for the oxen. To goad means to urge and move forward, and the mardeia is intended to move the ox pulling the plow. This is a stick with a sharp point at its end, a sort of small metal spike, with which one pricks the animal when it is lazy and does not move, so that it will continue to move forward and plow.
The one plowing his field stands or sits at the back of the plow, holding the mardeia - the stick guiding the ox - vertically, since he is not aiming it at the animal the entire time. Thus, the highest point that needs clearance as the plow crosses the field is the top end of the mardeia. This is the measure given by the Mishnah: one cuts the tree to the full height of the mardeia as it is held on top of the plow, above the plowman's head. He is permitted to cut this amount, since the tree obstructs the way; beyond this - he is not permitted.
"Uvacharuv uvashikmah - keneged hamishkoles":
With a larger and thicker tree, possessing heavy branches, the halachah is different: it is permitted to cut everything that overhangs the property line. The reason for this is that these branches cast a shadow, thereby interfering with the sun reaching the field, the rain falling on it, and the formation of dew.
The meaning of the phrase "keneged hamishkoles" is opposite the plumb line and directly in line with it. A plumb line is a tool used in construction: a small lead weight tied to the end of a string. (The Latin word for lead is plumbum, which is where the English word plumber comes from - one who works with lead pipes, and also the symbol for lead on the periodic table: Pb. It has nothing to do with the plum fruit). The lead weight pulls the string straight down vertically, allowing one to see exactly where the property line runs. The application: one cuts along the property line vertically and straight up, removing the carob or sycamore branches overhanging it, because they cast too much shade which ruins the crops beneath them, or prevents rain and dew from reaching them.
Beis Hashelachin:
A beis hashelachin is a field that requires irrigation and additional water beyond rainwater. The owner of such a field desperately needs every drop of rain and every bit of moisture he can get. Therefore, he can argue against any branch overhanging his field: my field is not receiving the rain it needs, since even a single branch prevents some of the rain from reaching it; and the foliage also creates a sort of insulation, slightly warming the air above the field and reducing the dew that forms on it. Dew and rain are vital to it, and therefore no one else has any right to overhang even slightly above a field of this sort.
Therefore, we learned: "Beis hashelachin - kol ha'ilan keneged hamishkoles" - in an irrigated field, any tree is cut in line with the plumb line. This is not limited to a carob or sycamore, but rather any tree that overhangs the field reduces the water reaching and remaining in it, and the field owner is forced to make up the deficit by hauling buckets, and his field might even fail to grow properly. Therefore, nothing is permitted to overhang this field, and it is permitted to cut everything exactly along the property line - "keneged hamishkoles", directly in line with a plumb line.
The Opinion of Abba Shaul:
Abba Shaul adds and says: "Kol ilan srak - keneged hameshkoles" - any barren tree, according to the plummet. A barren tree is a tree that does not produce edible fruit, and in his opinion, it has no benefit that justifies its leaning over a neighbor's field, and therefore one cuts it all off straight up along the boundary line. If it is a fruit tree - it is understandable why its owner wants it to remain, and as long as the field is not an irrigated field, a branch is allowed to lean over it; but regarding a barren tree, which yields no edible fruit, Abba Shaul says that this should not be permitted at all.
In summary: The halachah is decided according to the Tanna Kamma and not according to Abba Shaul. The resulting rule is: one may not leave a branch leaning over a neighbor's field that causes him any disturbance; but in a place where there is no disturbance at all, and the branch is not in his way, the neighbor may not demand that it be cut down.