Keilim, Chapter 27, Mishnah 3. The Mishnah here continues the discussion of the minimum measurements that a piece of material must have in order to be able to receive tumah. Each type of material has its own shiur: beged (woven cloth) needs three by three tefachim, sak (sackcloth) needs four by four, or (leather) needs five by five, and a mapatz (a coarse mat of woven reeds or similar) needs six by six. Our Mishnah asks a new question: what happens when a person produces a single piece of material by joining together two different kinds of material, so that neither one alone reaches its own shiur, but together they add up to the required size?
The cases that remain tahor
Three situations open the Mishnah. First, "ha'oseh shenayim min habeged": a person fashions a square of three by three tefachim, the shiur for cloth, but only two tefachim of it are genuine beged, and he fills out the missing tefach "min hasak", from sackcloth. Second, "sheloshah min hasak": he wants the four by four required for sak, he has three tefachim of sackcloth, and the last tefach he takes "min ha'or", from leather. Third, "arba'ah min ha'or": leather requires five by five, he has four tefachim of leather in hand, and he finishes off the piece with a single tefach "min hamapatz", from matting.
In all three of these cases the ruling is tahor. The combined piece cannot receive tumah at all. The reason is that in each case the material that was added is the weaker, less susceptible material, and a weaker material cannot complete the shiur of a material that is stronger than it. When we are measuring for cloth, the shiur of three by three must be filled by cloth itself; a tefach of sackcloth does not count toward it. The same is true of sackcloth completed by leather, and of leather completed by matting. The lesser material is treated as though it simply is not there, and what remains does not reach the necessary dimensions.
The cases that can become tamei
Now the Mishnah turns the pairings around. "Chamishah min hamapatz": the shiur of a mapatz is six by six, and here five of those tefachim are matting while the final tefach comes "min ha'or", from leather. Next, "arba'ah min ha'or": leather calls for five by five, four tefachim of it are leather, and the piece is rounded out by a tefach "min hasak", from sackcloth. Last, "sheloshah min hasak": sackcloth calls for four by four, three tefachim are sak, and the remaining tefach is "min habeged", woven cloth.
In all three of these cases the ruling is tamei. The piece can indeed receive tumah. Here the base material is present in almost its full shiur, one tefach short, and what completes it is a material that is stronger and more readily susceptible to tumah than the base. Since the added piece is of higher standing, its attachment is regarded as a genuine chibur, a real joining of the two materials, and the shiur is considered filled.
The general rule
Having set out the six cases, the Mishnah distills them into a formula, introducing it with the words "zeh hakelal", here is the governing principle. Whatever is attached, if it belongs to a category described as "hachamur mimenu", of stricter standing and more readily open to tumah than the material it was joined to, then once the two together fill the measurement demanded of the base material, the resulting piece is subject to tumah. Should the attached substance instead be "hakal mimenu", of a lighter standing and less open to tumah than the base, the piece stays tahor.
The lesson of the Mishnah is that a weaker material can never be recruited to fill out the shiur of something above it. In such a case we regard the addition as though it were absent, and since the measurement then falls short, the item has no way of receiving tumah. Only an addition from a material of greater standing counts, and then the piece is complete and susceptible like any other keli of its kind.