Ohalos, Chapter 14, Mishnah 5. This chapter has been dealing with a ziz, a ledge or overhang that juts out from a wall, and with the question of when such a ledge is considered a proper ohel that spreads tumah beneath itself and blocks it from passing through. Our Mishnah takes the discussion one step further and presents a case of two such ledges, one directly above the other, and asks what happens when tumah is found underneath them, between them, or on top of them.
The case: two aligned zizin
The Mishnah opens: "Shnei zizin zeh al gabei zeh" - two overhangs protruding from a wall, one situated above the other, precisely aligned with each other. "V'yeish bahen poseiach tefach" - each one of these ledges measures a tefach by a tefach, which is the minimum size needed for something to function as an ohel. "U'veineihen poseiach tefach" - and there is the space of a tefach involved as well.
The Bartenura explains what that last phrase means in practice: the lower ledge is at least a tefach above the floor, and the upper ledge is at least a tefach above the lower one. So we have a tefach of open space between the ground and the first ziz, and another tefach of open space between the two zizin. And note carefully: according to the way the Bartenura understands the Mishnah, these ledges are protruding from a plain wall, not positioned above a doorway.
Tumah underneath the lower ziz
"Tumah tachteyan" - a k'zayis min hameis is on the ground below the bottom overhang. The ruling is "tachteyan tamei": the area under that ledge contracts tumah. Whatever has been placed above the ledge stays tahor, since the ziz, measuring a full tefach square, is itself an ohel that traps the tumah below it and prevents it from climbing higher. So a vessel resting on the ground under the overhang is tamei, while a vessel set on the surface of that very overhang is tahor.
Tumah between the two zizin
"Beineihen" - the tumah occupies the gap between the bottom overhang and the top one. In that case only the middle area contracts tumah. Keilim in that gap are tamei, but a vessel lying on the ground under the bottom ledge escapes, and so does a vessel placed on the surface of the top ledge. Each overhang measures a tefach square and each lines up exactly with the other, so each functions as a chatzitzah: the bottom one keeps the tumah from working its way down to the ground, and the top one keeps it from rising any further.
Tumah resting above the higher ledge
"Al gabeihen" - the tumah lies on the surface of the upper overhang. The ruling is "k'negdo ad l'raki'a tamei." Trace a vertical line from the tumah toward the heavens: whatever occupies that column contracts tumah, however great the distance, because nothing intervenes to stop it. Sideways the tumah does not travel, since no covering hovers over it to spread it out horizontally. Downward it cannot go either, for the top overhang, a complete tefach square, roofs the area beneath it and seals the tumah out. Consequently a vessel lying alongside the tumah on that upper surface stays tahor, and a vessel positioned in the space under that overhang stays tahor as well. Only what stands in the column directly over the tumah is tamei, at whatever height.
When the upper ziz extends a full tefach beyond the lower one
The Mishnah now changes the case: "hoyah ha'elyon odef al hatachton poseiach tefach." The two ledges are no longer aligned. The upper ledge covers the entire area of the lower one and then extends a full tefach further out beyond it.
Here the ruling is different. If there is tumah "tachteyan," beneath the lower ledge, "oy beineihen," or in the space between the two ledges, then both "tachteyan u'veineihen" are tamei: everything underneath the lower ledge and everything in the space between them becomes tamei.
What accounts for the difference? That projecting tefach. Imagine a person below raising his eyes: he takes in the bottom overhang, and past its edge he also takes in a full tefach of the top one. That exposed tefach of the upper ziz carries significance on its own, and it fuses the two areas into a single space in which the tumah intermingles. The upper overhang now serves as the dominant ohel, so all the room beneath it counts as one covered area, and tumah below climbs and diffuses throughout. A vessel on the top surface of the upper ledge, however, remains tahor, since that ledge stops the tumah from rising past it.
"Al gabeihen" - should the tumah be lying above the top overhang, nothing has changed from the earlier ruling: "k'negdo ad l'raki'a tamei." Trace a vertical line from the tumah upward to the heavens, and whatever sits in that column contracts tumah. Picture a laser aimed straight up from the place where the tumah rests: everything it strikes is tamei. Whatever lies off to either side, and whatever occupies the space below the overhang, stays tahor.
In short: since the upper ledge extends a full tefach past the lower one, it is the one roof we reckon with. It is as though that upper roof covers everything below it, both the space between the two ledges and the space beneath the lower one.
When the upper ziz extends less than a tefach
The Mishnah moves on to a further scenario: the top ziz is "odef" (projecting) past the bottom one, yet "pachos mitefach," its projection measuring under a tefach. A person below who lifts his gaze does see a strip of the top ledge reaching past the edge of the bottom one, but that strip falls short of a tefach. This case calls for finer distinctions.
Where the tumah rests "tachteyan," below the bottom overhang, the ruling is "tachteyan u'veineihen tamei": vessels in the space below contract tumah, and so do vessels lying in the gap above the bottom ledge, between the two overhangs. Although the strip jutting past the lower ledge falls short of a tefach, we nonetheless treat the two areas as blending together, and tumah situated below is not halted by the bottom ledge but ascends to the one above it.
A second scenario now arises: "beineihen," the tumah is situated in the gap separating the two ledges, "oy" it rests on the ground "tachas hamoisar," that is, not below the bottom overhang but below the strip of the upper one that reaches past it. Put differently: aim the laser upward from the spot where the tumah lies, and it never touches the bottom ledge at all; it strikes only the underside of the top one. Regarding this scenario the Mishnah records a machlokes.
Rabi Eliezer omer: "tachteyan u'veineihen tamei." Whatever is underneath and whatever is in between become tamei. In his view, the fact that the upper ledge protrudes at all, even by less than a tefach, is enough for it to take the tumah that is beneath it, whether in the middle space or on the floor beyond the lower ledge, and carry it downward and throughout.
Rabi Yehoshua omer: in this case, "beineihen v'tachas hamoisar tamei," whatever is in the space between the two ledges, and whatever lies on the ground directly beneath the protruding portion, is tamei, since the upper ledge is an ohel covering it. "V'tachteyan tahor" - but a keli underneath the lower ledge remains tahor. Since the upper ledge does not extend a full tefach past the lower one, the tumah does not travel from under the upper ledge into the space beneath the lower one. If the tumah is directly beneath the lower ledge, ain hachi nami, everything becomes tamei. But if the tumah rests above the lower ledge, or off to the side on the floor where a straight line upward misses the lower ledge entirely, it does not affect keilim standing beneath the lower ledge.
The lomdus behind Rabi Yehoshua
The mefarshim explain the reasoning. Since the upper ledge does not have a full tefach of its own protruding past the lower one, it lacks independent chashivus. The lower ledge is the ikar, the primary ohel, and the upper ledge is no more than a tafel, a secondary addition to it.
Rabi Yehoshua's position is that in any such arrangement, a principal ohel with a modest projection contributed by something else, tumah lodged beneath the principal ohel does spread outward into that subordinate piece as well. That is why tumah under the bottom ledge renders the gap between the two ledges tamei. But tumah lodged only beneath the tafel, the subordinate covering, whether it sits in the gap (which only the upper ledge roofs) or on the ground past the point where the bottom ledge terminates, will not cross over into the domain of the ikar. Tumah beneath the primary covering reaches the secondary one; tumah beneath the secondary stays where it is and never reaches the primary.
All of this applies only because the upper ledge does not extend a full tefach. Once it does extend a tefach, it is no longer a secondary ohel at all; it becomes the main ohel itself, and everything beneath it is one space.
Reviewing the cases
Case one: two ledges, one above the other, exactly aligned, each a tefach by a tefach, with a tefach of space between the floor and the lower one and a tefach between the two ledges. Tumah underneath renders only what is underneath tamei, and a keli in the middle space is tahor. Tumah in the middle space renders only what is in the middle space tamei. Each ledge is an independent ohel: the lower one blocks tumah from rising, and when the tumah is in the middle, the lower one blocks it from descending while the upper one blocks it from ascending. Tumah on top of the upper ledge is tamei in a straight line upward, but a keli to the side stays tahor, since there is no ohel above the tumah to spread it.
Case two: the upper ledge is not aligned with the lower one but extends a full tefach beyond it, a poseiach tefach. It is a solid ohel in its own right, it overrides the lower ledge and becomes the main ohel. Therefore tumah beneath the lower ledge or in the space between them makes everything underneath and everything in between tamei. Tumah on top is unaffected by the protrusion: there is no ohel above it, so only the straight line upward is tamei.
Case three: the top overhang reaches past the bottom one, yet its projection measures under a tefach. A person below who looks upward sees the bottom ledge plus a narrow band of the top one, narrower than a tefach. Should the tumah lie beneath the bottom ledge, everything below and everything in the gap is tamei, and here there is no dispute, since even so small a projection suffices to blend the two areas. The argument concerns tumah that sits in the gap between the ledges, or on the ground directly under that narrow band alone, so that a line rising from the tumah bypasses the bottom ledge and reaches only the strip of the upper one. Rabi Eliezer rules that both the space below and the space between are tamei, because the top ledge still unites the areas. Rabi Yehoshua rules that keilim between the two ledges, and keilim on the ground straight below the projecting band, are tamei, while keilim beneath the bottom ledge stay tahor. Because the top ledge lacks a full tefach of projection, it counts merely as a subordinate covering while the bottom one is the principal ohel, and tumah under the principal covering carries over to the subordinate one, but not the reverse.