Keilim, Chapter 19, Mishnah 2. This chapter is devoted to the bed and the ropes woven through it, and to determining which parts count as one keli together with the bed for the laws of tumah. A bed in those days was built as a wooden frame: two boards at the short ends, at the head and at the foot, joined by two long boards along the sides, the whole thing resting on four legs. Ropes were then threaded back and forth across the frame, in both directions, forming the mesh on which the bedding rested. Such a rope becomes part of the bed as soon as three of its rows have been threaded through the frame, and once that happens its full length is treated as belonging to the bed.
A rope that had to be lengthened
The case before us begins after those three rows have already been woven, and then the weaver discovers that his rope will run out before the mesh of the bed is finished. To gain more length, he knots a second rope onto the end of the first. So at this moment a portion of the original rope is woven into the frame, while the remainder of it, along with the whole of the newly attached rope, is still dangling free. Now the bed contracts tumah. Since the first rope already has its three woven rows, its entire length is tamei along with the bed itself.
The question is what happens to a person who touches one rope or the other: "Vehanogea min hakesher velifnim, tamei." One who touches from the knot that joins the two ropes and inward, that is, anywhere along the first rope, becomes tamei, because that rope is considered part of the bed.
Then the Mishnah adds the second half of the ruling: "Min hakesher velachutz, tahor." Touching outward from that knot, that is, touching the added rope at any point along it, leaves a person tahor. The second rope is indeed fastened to the first, but it has never been woven into the bed at all. A knot tying it to a rope of the bed does not turn it into a piece of the keli, and so the bed's tumah does not extend to it.