Ohalos, Chapter 12, Mishnah 5. Our mishnah places us in the middle of a building project. Imagine a home under construction, with a residence planned above the ground level as well, be'ezras Hashem. The outer walls have already gone up, yet inside almost nothing is finished. Step in, stand on the lower level, and turn your eyes upward. What is there? Beams, running across from one wall to the wall facing it. In time, boards and plaster will be spread over them and they will become the ceiling of the lower level, which is simultaneously the floor of the story above. At the moment, however, the boards and the plaster are still stacked outdoors, not yet put to use. Nothing is there but the naked beams.
One detail is essential: each of these beams is a tefach wide. A tefach is the minimum measure that qualifies something as an ohel. That means every single beam, in and of itself, functions as a tent over whatever lies directly beneath it.
The Words of the Mishnah
Here is the language of the mishnah: "koros habayis veha'aliyah", that is, the beams belonging to the lower level and those belonging to the story overhead. The term bayis designates the ground level, while aliyah points to the level built on top of it. Both rows of beams are already set in place, and each row is meant to become a ceiling in due course. At this moment, though, "she'ein aleihen maazivah": no plaster surfacing lies over them yet. The Bartenura spells out what is missing, namely the tit and the tzerorois, the lime together with the small stones that get laid over beams to produce a completed ceiling. Neither row has received them, not the one below and not the one above.
So the picture is two rows of beams, one row above the other, "vehein mechuvanos", and they are precisely aligned. Each beam is a tefach wide, and every lower beam has an upper beam directly over it. Every gap has a gap above it as well. Standing on the ground floor and looking straight up, you can see clear through to the sky.
Case One: Aligned Beams
The mishnah proceeds to map out the possible locations of tumah. "Tumah tachas achas meihen": the tumah is situated on the ground level, directly under a beam of the lower row. Concerning this the halacha is "tachtav tamei", meaning that the area sheltered by that beam contracts tumah. A keili lying on the ground level under the identical beam that covers a kezayis of a meis becomes tamei. Even though a beam is a slender thing, it measures a full tefach across, which is enough to make it an ohel in its own right. The result is that the tumah and the keili are housed together under one tent.
The mishnah turns to a second location: "bein hatachtoinah le'elyoinah", where the tumah sits in the gap separating a beam of the lower row from the beam of the upper row positioned right over it. Let us picture this precisely. You are standing on the ground level with your gaze turned up. First you make out the lower row of beams, the ones that will later hold the plaster forming the ceiling of the ground level and the floor of the story above. Because nothing has been surfaced yet, your eye continues past them to the higher row, the beams that will eventually carry the ceiling of the second story. Both rows are laid along the same line, with each upper beam positioned squarely over its counterpart below. The tumah now occupies the open air between a beam of the lower row and its partner above. Here the mishnah states "beineihen tamei": a keili situated in that identical airspace becomes tamei, for the beam overhead acts as one ohel covering both the keili and the tumah that rests on the beam below. That, however, is the limit. A keili positioned under the lower beam, or one sitting on the surface of the upper beam, stays tahor, since these beams are mafsik and hold the tumah back.
And if the piece of the meis is "al gabei ha'elyoinah", resting on top of the upper beam, the beam that will become the ceiling and roof of the upper story? Then "kenegdo ad haraki'a tamei", everything directly above it is tamei, straight up to the sky. The tumah does not descend, because that beam is an ohel and blocks it from coming down. And it does not spread sideways, since spreading sideways would require a shared roof overhead, and at this stage there is none. The beams themselves are the only covering the house has. A roof will be built one day, but it does not exist yet. So the tumah travels straight upward and no further: a keili in the space between the two rows of beams, or a keili down on the ground floor, is tahor.
Case Two: Beams Not Aligned
The mishnah goes on: "hoyu ha'elyoinois kevein hatachtoinois". Until now the two rows corresponded to each other exactly. Now the arrangement is purposely staggered, with each upper beam positioned over an opening in the row below. Previously, had you stood upon a beam of the lower row and raised your hand straight overhead, you would have touched the beam above you. That is no longer so. Standing on a lower beam here and reaching upward, your hand passes through the open air separating two of the upper beams. Should the upper beams be lowered, they would not come to rest on the beams below them; they would settle exactly into the openings that separate them.
The visual difference is striking. In the first case, looking up from the ground you would see beams, and between the beams, sky. In this case, looking up from the ground you never see the sky at all: either your eye meets a lower beam, or, peering through a gap between the lower beams, it meets an upper beam. That is what "hoyu ha'elyoinois kevein hatachtoinois" means, the upper beams line up with the empty spaces of the lower row. And note that not only are the beams a tefach wide; the avir, the airspace between them, is also a tefach.
The halacha here is "tumah tachas achas meihen, tachas kulan tamei". Wherever the tumah is found underneath a beam, whether that beam belongs to the higher row or the lower one, the tumah extends beneath every beam in the structure. In halachic terms the whole assembly counts as a single unbroken ceiling containing no gaps at all. The principle at work is gud achis: we treat the upper beams as though they were brought down to fill the openings of the row below, fitting together like the pieces of a puzzle. Others describe it through gud asik, viewing the lower beams as raised up to close the openings in the row above. The conclusion is the same by either route: al pi halacha the covering is fully closed. In practice there is a single solid roof here, and therefore the tumah spreads out under all of the beams.
What if the piece of the meis is "al gabeihen", lying on the upper surface of a beam? Then "kenegdo ad haraki'a tamei". The tumah ascends in a straight column, without spreading to either side and without penetrating downward. The same applies whether the tumah is set on a beam of the higher row or on a beam of the row that divides the two stories. Since it is positioned above an ohel and not underneath one, its only path is upward.
Reviewing the Mishnah
Our mishnah deals with the beams of a house running from wall to wall, awaiting the plaster that will turn them into ceilings: one row between the ground floor and the upper story, and one row above the upper story that will eventually also serve as the roof. As of now there is no plaster at all.
- When the rows are aligned, beam directly beneath beam and airspace directly beneath airspace, tumah affects only what shares its own beam. Tumah on the ground floor renders tamei only a keili under that same beam on the ground floor. Tumah in the space between the two rows renders tamei only what lies in that space, since the tumah rises, meets the tefach wide beam above, and that beam becomes the ohel over everything under it, but only under it, with no sideways spread. Tumah on top of the highest beam rises straight up and does not descend.
- When the rows are not aligned, beam beneath airspace, tumah beneath any beam renders everything tamei, because we view either the upper beams as coming down or the lower beams as going up, so that the covering counts as sealed. Any tumah underneath is then like tumah under a single ohel spanning the house, and it spreads from side to side. Tumah resting on top of a beam, however, rises straight up, and a keili beneath that beam stays tahor.