Machshirin, Chapter 1, Mishnah 3. This masechta deals with the laws of hechsher, the process by which liquid makes food susceptible to tumah. Two conditions must be met. First, the food has to become wet. Second, the wetting has to fit the words of the pasuk, "vekhi yutan mayim al zera," which teaches that the water must have come onto the food in a way that the owner wanted. Water that arrives entirely by chance, with nobody desiring it, does not create hechsher. Our mishnah presents a case where the wetting is one step removed from the person's action, and Beis Shammai and Beis Hillel argue about whether it still counts.
The Case
The mishnah's picture: "hamar'id es ha'ilan", a person gives a tree a shake so that its fruit will drop, "venafal al chaveiro", and what he dislodged comes down upon a second tree standing beside it. A parallel scenario is added, "o sukah", a bough that he shakes, "venaflah al chavertah", which then falls onto the bough next to it. "Vetachteihen", directly below that second tree or bough, there are "zra'im o yerakos mechubarim lakarka", seeds or greens still rooted in the soil, and these are damp.
So the fruit that the person shook loose did not travel directly to its destination. It struck a second tree or branch on the way, and only then came to rest on wet produce growing in the ground. The question is whether the moisture it picks up there is hechsher lekabel tumah.
The Machlokes
"Beis Shammai omrim": their ruling is that such moisture does count, it is "bekhi yutan". The man who set the first branch in motion understood full well that his fruit might come to rest exactly where it did. Since the result was something he could anticipate, halachah views the liquid the fruit encounters there as liquid he was content to have there, and the fruit can now receive tumah.
"Beis Hillel omrim" the opposite: "einan bekhi yutan". Their reasoning is that a second tree or bough came between the shaking and the landing. That intervening object severs the link joining what the man did to the wetting that followed, and once that chain is broken the moisture no longer carries the standing of water supplied willingly.
The Reasoning Behind Beis Hillel
"Amar Rabi Yehoshua": Rabi Yehoshua transmits a piece of reasoning that he received "mishum Abba Yosi", from Abba Yosi, who was known by the nickname "Chali Kufri" and is identified as "ish Tiv'on", a man of the town Tiv'on. His words are these: "Tmah atzmecha", be astonished at the very proposition, "im yesh mashkeh tamei baTorah", is there any liquid anywhere in the Torah that renders food able to contract tumah, "ad sheyiskaven veyitein", other than one that a person purposely applied? For, "shenemar", Scripture states "bekhi yutan mayim" upon seed, and the term yutan signifies an act of placing, something carried out on purpose.
This is an answer to Beis Shammai. Granted that the person knew such a thing might happen. Knowing that an outcome is possible is not the same as intending it. And the very proof that he did not intend it is that a second tree stood in the way and interfered. Hechsher requires that the water be placed with kavanah, or at least that the situation be treated as if the owner placed it with kavanah. Where another object interrupted between the person's act and the wetting, one can no longer describe him as having placed the water at all.
The upshot is that a case of this sort falls outside what the verse requires, and the fruit has not been rendered capable of contracting tumah.