Keilim, Chapter 18, Mishnah 1. Before entering the words of the Mishnah, we need one basic rule of tumah in wooden vessels. A wooden vessel whose capacity reaches forty se'ah of liquid is not subject to tumah at all. The reason is bound up in a principle: only a vessel that can be carried both when it is empty and when it is full is included in the laws of tumah. A container that holds forty se'ah is simply not that kind of object. Once it is filled, it is far too heavy to be picked up and moved, and any attempt to do so would tear it apart. Such a large wooden container is therefore outside the category of a vessel that can contract tumah.
Given that rule, everything depends on how the forty se'ah is calculated. Our Mishnah takes up exactly that question with regard to a wooden cart: which of its parts are counted into the volume, and which are left out?
The dispute of Beit Shammai and Beit Hillel
The Mishnah opens: "Hashidah", a wooden cart. "Beit Shammai omrim, nimdedet mibifnim." Beit Shammai hold that the cart is measured from within. Only the inner airspace, the hollow that actually receives what is placed inside, is counted toward the forty se'ah. The wood of the walls and the wood of the floor are not added into the reckoning.
"Uveit Hillel omrim, nimdedet mibachutz." Beit Hillel disagree and measure the cart from the outside, meaning that the thickness of the walls and of the floor is included along with the inner space. If the cart taken together in that fuller way amounts to forty se'ah, it has no capacity to become tamei.
What both houses exclude
There is a point on which the two houses stand together: "Modim eilu va'eilu", both of them agree. What they agree about is that two features of the cart stay out of the reckoning entirely: the legs' thickness, "ovi haraglayim", and the thickness of the rims running around the top, "ovi lizbezin". Even Beit Hillel, generous enough to fold the wood of the walls and floor into the volume, draw the line here. Legs and rims may be physically attached, yet they are not regarded as part of the cart's body proper, and what is not part of the body does not enter the measurement.
Rebbi Yose: there is no dispute at all
The Mishnah now brings tana'im who read the earlier houses differently and maintain that Beit Shammai and Beit Hillel are not divided here at all.
"Rebbi Yose omer": in his reading, the houses are "modim", in agreement, that the wood of the legs and the wood of the rims do enter the count toward forty se'ah. And if even those peripheral parts are counted, then kal vachomer the cart's own walls and floor are certainly counted. There is one thing that neither house includes, and about it the Mishnah says "uveineihem eino nimdad": the hollow area enclosed between the legs, the open region underneath the cart's floor, is left out of the measurement.
Rebbi Shimon Shezuri: it depends on the height of the legs
The last opinion in the Mishnah works from the same starting point as Rebbi Yose, that legs and rims are counted by both houses, but it refuses to rule in one sweep about the region underneath the cart. There, it says, one must distinguish, and the distinction turns on how far the legs lift the cart off the ground.
"Rebbi Shimon Shezuri omer", and he draws his line at a tefach: "im hayu haraglayim gevohot tefach, ein beineihen nimdad". Where the legs raise the cart a full tefach, the region enclosed beneath it contributes nothing to the forty se'ah. "Ve'im lav, beineihen nimdad": should the legs stand lower than a tefach, that region is added to the total. Halachah does not treat so slight a clearance as genuine open space; it is looked upon as if it were packed solid. A cart lifted less than a tefach above the floor is thus reckoned as though the thin layer down to the ground were part of its own bulk, and that bulk is included in its volume.
So the whole question of this Mishnah is one of measurement, and the stakes are considerable: whether the legs, the rims and the space beneath the cart are folded into the count determines whether this wooden cart reaches forty se'ah and stands beyond the reach of tumah, or falls short of that volume and remains a vessel like any other.