Ohalos, Chapter 15, Mishnah 8. This mishnah is built of two separate units. The first deals with a person standing in the open courtyard around which burial caves were hollowed out, and asks whether the rabbinic decree of four amos around a meis applies to him. The second deals with a beam that was pressed into service as a golel, the covering over a grave, and asks exactly which portions of that beam carry the tumah of a golel.
Chatzar hakever: the courtyard of the grave
The mishnah opens with the words "chatzar hakever," the courtyard of the grave. To picture it, one has to picture how burial was arranged in the times of the Mishnah. Meisim were not placed in the ground as we are used to; they were laid in caves dug out beneath the surface. In the center there was an open courtyard, and off that courtyard, on each of its four sides, a cave was hollowed out, so that the caves resembled rooms opening onto the courtyard. Into the walls of those caves they carved out niches, called kuchin, something like shelves, and each kuch held one meis. That whole arrangement, the open space in the middle ringed by the burial caves, is what the mishnah calls chatzar hakever.
Now comes the ruling: "ha'omeid besochah," one who stands inside this courtyard, is tahor. And this is a striking ruling, because it holds true even where he is standing within four amos of a meis lying in one of the caves.
Why should that be unexpected? Because Chazal enacted a gezeirah declaring tamei anyone who approaches to within four amos of a meis. This has nothing to do with touching, and nothing to do with overhanging: the gezeirah takes effect even where there was no contact of any kind and no ohel of any kind. Mere proximity within four amos is enough. The reason behind the enactment was to train people properly. Anyone eating terumah or kodashim has to eat them betaharah, and Chazal wanted such people conditioned to keep well away from a meis in the first place. When someone is positioned immediately beside a meis, there is a genuine risk that he will overhang it without paying attention, remain completely unaware of what happened, and then go eat terumah or kodashim in a state of tumah.
In the chatzar hakever, that risk is absent. The spot where he is standing is clearly demarcated as a separate location: the courtyard is here, and the caves are over there on the far side of walls. The mechitzos themselves broadcast the separation and keep him conscious of it. There is no plausible fear that he will overhang a meis inattentively, because he knows perfectly well that his place is the courtyard while the meisim rest inside the me'arah. Consequently, even when less than four amos separate him from a meis lying in the cave, his taharah is unaffected.
How large must the courtyard be?
This leniency depends on a condition concerning the courtyard's dimensions, and on that point Beis Shammai and Beis Hillel part ways. According to Beis Shammai, the courtyard must contain a space of four amos by four amos ("arba amos"). Beis Hillel accept a much more modest measure: four tefachim by four tefachim ("arba'ah tefachim").
What underlies their argument? Picture the man's predicament. He is in the courtyard with caves surrounding him, and clearly he has no plan to stay put indefinitely. Sooner or later he needs to leave, and leaving means pulling himself up over one of the outer walls of the caves. Pulling oneself up requires something to hold onto; no one walks vertically up a bare wall. That is exactly where the problem lies: as he feels around for a grip to hoist himself over the top, some part of his body could easily wind up inside a cave's mouth.
Beis Shammai maintain that in a courtyard measuring less than four amos square, there is virtually no way for him to climb out without his hand reaching into a cave's pesach. In their view, therefore, the halacha that one in the courtyard stays tahor applies only when the courtyard measures four amos by four amos. Beis Hillel counter that even a space four tefachim square leaves a person room enough to position himself while climbing out, without any part of him entering where the caves open.
In which circumstance could the courtyard be truly minuscule with all agreeing that he stays tahor? Where caves surround it on three sides only. Should one side be free of caves, his path out is unimpeded and the entire question never arises. All along, the sole difficulty had been that his only route out ran up past a burial cave.
To review this first half: there is a chatzar hakever, a courtyard with caves hollowed out on all four sides, each cave containing kuchin, niches in which meisim were laid. A person standing in that courtyard is tahor even if he is within four amos of a meis. Beis Shammai require the courtyard to measure four amos by four amos, so that he can get out without his hand landing in the pesach hame'arah as he climbs; Beis Hillel hold four tefachim by four tefachim is enough. And this minimum measure is demanded only where the courtyard is enclosed on four sides. If it is enclosed on only three and he has a clear exit, the concern falls away and the courtyard may be as small as it likes. (Those who have learned Maseches Bava Basra will recognize this sugya from there.)
A beam used as a golel
The second half of the mishnah speaks of a "korah," a beam, that is broader at one end and narrower at the other, "she'asah golel lakever," which was made into a golel for a grave.
What is a golel? Typically it was a sizable, wide stone laid across a grave to seal it from above. The term derives from the posuk that describes Yaakov Avinu at the well, "v'golelu es ha'even," that they would roll the stone away from the well's mouth. A stone positioned over an opening is accordingly called by this word, golel.
Halachically, a golel is metamei to anyone who touches it, bemaga, and to anyone who overhangs it, b'ohel. That is precisely what makes golel novel: stone by its nature is not mekabel tumah and can never become tamei itself, and yet this stone transmits tumah to whoever touches it or forms an ohel over it.
Case one: the broad end at the bottom
Our mishnah discusses a case in which the golel is this beam. It was placed as the covering above the grave, and the mishnah addresses two orientations: "bein omedes," standing erect, the way matzeivos are set up in Chutz La'aretz, and "bein mutah al tzidah," laid flat on its side, as matzeivos are placed in Eretz Yisroel. The halacha in both orientations is identical: "ein tamei ela k'neged hapesach," tumah attaches solely to the stretch of beam facing the opening.
The picture is this. Since the beam is broader at the bottom and narrower at the top, the central part of the broad lower end covers the grave, but the beam juts out to either side, and those projecting portions are not over the grave at all. The mishnah teaches that touching or overhanging the golel does indeed make a person tamei, but only in the section that lies over the grave. The projecting parts at the bottom, which extend past the opening on either side, do not convey tumah.
Case two: the broad end on top
The mishnah continues with the reverse arrangement: "asah roshah golel lakever." The mishnah refers to the narrow end as the head of the beam, and here that narrow end was made the covering over the grave. Now the beam sits at the bottom with its width fitting exactly over the opening, projecting nowhere; it is at the top that it broadens out and juts past on both sides, like a tree, narrow below and wider above.
The mishnah rules "ein tamei ela ad arba'ah tefachim." If a person touches the wide portions which are now up above, but which in practice are not situated over the grave, he is tahor. And even where he touches the part that is genuinely over the meis, over the pesach of the grave, he becomes tamei only within four tefachim measured up from the ground, from the grave itself. Above four tefachim he does not become tamei. When? "U'vizman she'asid legodzo," when his intention is to lop off the upper part of the beam and put it to use elsewhere. Since he plans to cut it away, that upper portion is not truly designated to remain here as part of the grave, and we treat it as though it were already severed. Only the lowest four tefachim, which will remain in place no matter what, are permanently part of the kever, and there he becomes tamei in all cases.
And what about the mishnah's first case, with the wide end below? The meforshim (see Tosafos Yom Tov) hold that precisely the same din applies there. Where he means to saw off the upper section, tumah comes only from contact with the lower stretch standing above the opening, and no higher than four tefachim. The meforshim also address why the mishnah preferred to spread the material across two different cases. Fundamentally, the mishnah is delivering two independent halachos by means of two orientations of the golel. Placing the wide end below teaches that only the central stretch is metamei, and not the sections flanking the grave. Placing the wide end above teaches an additional halacha: where cutting is intended, even the stretch directly above the grave is metamei no higher than four tefachim off the ground. And that second halacha applies to either orientation, wide end up or wide end down, whenever cutting is intended.
Rabbi Yehuda's dissent
All this is the view of the Tanna Kamma. "Rabbi Yehuda omer": his position is that intending to remove the upper section changes nothing, since "kulo chibur," the beam is viewed as a single connected whole, and its entire length holds the status of golel. So long as no actual severing has taken place, even what stands higher than four tefachim carries the din of golel, and tumah passes to whoever makes contact with it or overhangs it.
As the Tiferes Yisroel and the Mishnah Achronah explain here, a far broader question stands behind this exchange: when a person intends to cut something, is it already viewed as cut before any cutting has occurred? The Tanna Kamma treats it as cut; Rabbi Yehuda does not.
To review the second half: a golel is the covering of a grave, and even when it is stone, one who touches it or overhangs it becomes tamei. Here the covering is a wooden beam. In the mishnah's first case it is broader below and narrower above, and the mishnah teaches that one is tamei only by touching the portion that lies over the grave; touching the lower projections that extend past the opening leaves him tahor. This applies whether the beam stands upright or lies on its side. In the second case, with the broad end above, the mishnah adds a further halacha (which is really true in both cases): if he intends to cut the beam, one becomes tamei only by touching the lower part, within four tefachim of the grave. That is the Tanna Kamma's view, for although the cutting has not yet been done, the intention to cut removes the upper section from the status of golel for this grave. Rabbi Yehuda counters that intentions do not help; until he actually cuts, the entire beam is a golel, and any part of it above the opening conveys tumah.
Two closing points
Tosafos Yom Tov notes that should the grave be unusually narrow for some reason, such that the flanking sections would fail to stand above the grave's opening even had the beam not widened at all, the din is unchanged and whoever touches them stays tahor. The mishnah is merely portraying the typical case, in which a beam of even width would normally span the opening. The governing rule is that anything not positioned above the pesach transmits no tumah.
The same underlying question, whether an item a person plans to cut is regarded as already cut, comes up in the halachos of toiveling a keili. Take a pot fitted with an exceptionally long handle. The handle is awkward to use, and the owner has decided to shorten it. At this moment he is immersing the pot. Does the section he means to remove require immersion too, given that it is not genuinely slated to stay part of the keili? The Tanna Kamma says no, because removal is intended. Rabbi Yehuda replies that intentions notwithstanding, so long as nothing has actually been cut, immersing this keili obligates immersing all of it, handle and all.