We now move to Mishnah 3, which deals with a similar situation: long cords attached to an object, and the question of how far along the cord it is still considered joined to the object - so that if the object becomes tamei, the cord becomes tamei along with it. Here the discussion concerns a lead weight, lead being a metal that is susceptible to tumah, which serves as the weight of a plumb line.
The instrument and its purpose:
Builders use this weight to determine whether the walls they have put up are straight: they hang the lead weight on a cord, let it down, and from this they know whether the wall is straight or not. This instrument - the long cord with the lead weight at its lower end - is called in Hebrew an anach: a weight, usually made of lead or another heavy metal, together with a cord attached to it.
The Mishnah clarifies up to what point along the cord, measured from the weight, the cord is susceptible to tumah. A cord on its own is not susceptible to tumah at all; but once it is attached to a metal weight that is susceptible to tumah, then whatever is attached to something tamei is itself tamei, and the cord becomes tamei.
The measurements of attachment according to the various trades:
This depends on the type of weighted cord, on the plumb line being used, and on the work for which it serves:
"Chut hamishkoles" - the ordinary, average cord, the standard one made for laymen and not for professional craftsmen who construct buildings: twelve tefachim along the cord are considered attached to the weight.
"Shel charashin" - professional craftsmen need a longer cord, since they build taller buildings or taller structures: eighteen tefachim from the weight and inward are susceptible to tumah, that is, they are considered attached to it, and if the weight is tamei, they are tamei as well.
"Shel binyan" - the plumb line of the builder who constructs three story houses and towers: fifty amos along the cord are considered attached to the weight.
"Yoser mikan... af al pi she'rotzeh l'kayem - tahor":
Suppose the ordinary weighted cord is longer than twelve tefachim, or the craftsman's weighted cord is longer than eighteen tefachim, or the builder's cord extends more than fifty amos from the weight - "yoser mikan". And even "im rotzeh l'kayem", meaning even if he wants it that length and wishes it to be longer than the usual standard - nevertheless it is tahor.
That portion which goes beyond the established limits - the twelve tefachim of the ordinary weight, the eighteen of the craftsmen's, and the fifty amos of the builder's - is tahor. And not only is it not considered attached, so that if the metal weight became tamei the extra cord beyond the limit does not become tamei with it, but it is not susceptible to tumah at all: it is simply a cord, and a cord is not susceptible to tumah.
"Shel sayadin v'shel tzayarin - kol shehu":
The cord used as a plumb line by those who plaster buildings, and likewise by the painters who paint and sketch designs on the sides of buildings - they too need this instrument, and for them the measure is any length at all: even an extremely long cord is still considered attached to the weight.
The Tiferes Yisrael explains the reason: architects and carpenters, when they check a wall with a plumb line to see whether it is straight, are not checking the entire wall but only the section they have just finished working on, and therefore there is a limit to the length of cord that is considered attached to the weight. Plasterers and painters, however, must deal with the whole picture: they have to make sure that the entire wall of a forty story building is straight, that the plaster was applied properly and that the pictures are painted properly. Therefore there is no fixed measure, and everything depends on the height of the wall.
And with that we have completed Mishnah 3 of chapter 29.