Ohalos, Chapter 10, Mishnah 7. Here the Mishnah places an earthenware pot in the doorway of a house and asks how tumah travels: does the pot join the ohel of the house, does it seal the tumah off, or does the tumah simply rise and descend in a straight line?
Picture the setup. A pot made of cheres is resting partly on the askufa, the step that sits just in front of the entrance, and partly in the doorway itself. The crucial detail is the pot's shape: it is broad at its base and narrows toward its top, something like an ice cream cone turned upside down, with the mouth of the pot at the wide lower end. Because of that shape, the pot can be positioned so that its opening lies entirely outside the line of the doorway (if you stood on the roof and looked straight down, you would see the whole mouth of the pot), while the body of the pot, which widens as it descends, extends a full tefach into the house.
Reading the Mishnah's wording
The Mishnah opens with "haysa netunah betzad ha'askufa": the kedeira has been set down alongside the step at the entrance, within the opening itself. Its exact placement is then defined: "she'im talah hi nogaas bamashkof poseach tefach", that is, were one to raise it straight upward, it would meet the mashkof (the lintel spanning the top of the entrance) with a tefach of it falling on the inner side. Stretch a string, or shine a laser beam, vertically up from the vessel: the mouth in its entirety still lands beyond the house, yet a tefach of the vessel's breadth lands within.
First case: the kedeira stands directly on the floor
In this opening case the vessel is resting flat on the ground of the entrance. Nobody is actually raising it; the raising was invoked only as a way of mapping out where it sits. The halachah reads: "tumah tachteah", should tumah be located below the vessel, "betocha", within it, "oy al gaba", or hovering over it, then "tumah bokaas ve'olah, bokaas veyoredes". The tumah breaks through in a vertical column upward, defiling whatever stands in that column, and it breaks through downward in exactly the same way. Sideways it does not travel at all, since nothing here forms an ohel that could carry it outward.
Second case: the kedeira is held a tefach above the floor
"Haysa gevohah min ha'aretz tefach": the vessel now stands at least a tefach clear of the ground. Should tumah be found below it, the halachah declares the space beneath and the house alike tamei: keilim positioned under the vessel contract tumah, and so do keilim standing anywhere indoors.
The reason is that the gap of a tefach under the vessel constitutes an ohel in its own right. Lie down there in your imagination and look up: the underside of the kedeira serves as your ceiling. Because a tefach of that ceiling extends over the threshold and into the house, this miniature ohel merges with the ohel of the dwelling; the two are reckoned as one, and mimeila everything beneath the vessel and everything indoors is included in it.
Nevertheless the Mishnah adds: "tocha vegaba tahor". The contents of the vessel, and objects lying on its outer surface, escape tumah, because the kedeira itself halts the tumah's advance. This parallels the earlier ruling about a vessel that generates an ohel: once there is a tefach of airspace below it, we invoke gud asik and treat the vessel as though its walls continued upward as far as the lintel. A keli that is tahor and that thereby unites with the wall or the roof is competent to act as a barrier, so its interior and its top remain unaffected.
The picture changes when the tumah is "betocha", inside the vessel, or "oy al gaba", suspended over it. Then "hakol tamei", nothing is spared. The tumah drives upward and downward along its column; descending, it defiles the kedeira, and it carries on into the tefach of air below, which qualifies as an ohel, and out of there into the house, since a tefach of the vessel's width lies over the threshold and the space below is one continuous ohel. The kedeira is of no assistance now, having been rendered tamei by the tumah in it or above it. A keli that is tamei is not regarded as an extension of the house's walls; gud asik is simply unavailable for it. With nothing sealing the tumah off, it fills the ohel below, that ohel is continuous with the interior, and the entire house becomes tamei.
Third case: the kedeira sits nearer the outside
The final case: the vessel is once again elevated a tefach and still lies within the entrance, but it has been shifted somewhat outward. "She'im talah eina nogaas bamashkof poseach tefach": raise it upward and it would not reach the lintel with a tefach on the inner side. "Oy medubekes bamashkof": alternatively it is pressed flush against the lintel, so that raising it would leave it wholly beyond the upper frame. Whatever part of it does fall under the lintel measures less than a tefach.
The ruling is "tumah tachteah, ein tamei ela tachteah". True, a tefach of airspace exists below the vessel and does form an ohel, but the tumah is confined to that space alone. Since not even a tefach of the kedeira reaches over the threshold, nothing links the ohel below it to the ohel of the dwelling, and consequently keilim indoors stay tahor. Keilim inside the vessel or on top of it are likewise unaffected, for the vessel bars the tumah from rising. Gud asik applies in this case too: raise the vessel upward in your mind and it comes to rest against the outer surface of the doorframe. Being tahor, and uniting once so extended with the side of the ohel, it functions as a chatzitza and detains the tumah.
The three cases together
Our Mishnah deals with a kedeira lying in the entrance of a house, placed so that raising it vertically would leave its entire mouth beyond the doorway (the vessel being narrow above), while a tefach of its breadth, down where it widens out, would come to lie over the inner side.
- Standing on the ground: tumah below, within or over the vessel breaks through vertically, up and down, and goes nowhere else. No ohel exists here to draw it to the sides.
- Elevated a tefach, tumah below: keilim under the vessel and keilim indoors all become tamei, since a tefach of the vessel overhangs the inner side, so that the ohel created beneath it merges with the ohel of the dwelling into one. Its contents and whatever rests on it remain tahor: the vessel is tahor, so we extend it upward as far as the lintel and it shuts the tumah out.
- Elevated a tefach, tumah within it or over it: nothing is spared. The tumah comes down, defiles the vessel, presses on into the ohel beneath it, and that ohel opens toward the interior. A tamei vessel is no longer eligible for gud asik to unite it with wall or roof, and it cannot serve as a chatzitza.
- Shifted outward, so that raising it would leave under a tefach on the inner side, or so that it sits tight against the mashkof with no part of it indoors at all: tumah below it does create an ohel in the raised tefach, so the space underneath is tamei, but that ohel has no link to the house's ohel, and the dwelling stays tahor.
Everything in this Mishnah hinges on two measurements: is the vessel elevated a tefach, so as to generate an ohel below itself, and does a tefach of the vessel extend over the inner side of the entrance, welding that ohel to the one belonging to the dwelling? A third principle joins these two: a vessel that is tahor may be projected upward by gud asik and thereby block the tumah, whereas a vessel that has itself contracted tumah forfeits that capacity.