The Gemara (Eruvin 58a) mentions that Rabbi Yehoshua ben Chananyah says it would have been best to measure Techum Shabbos using a 50 Amah long iron chain, since it does not stretch. Thereafter no mention (a flaxen rope is used in practice) - I believe wisely as the science just does not add up.
We are dealing with a chain of 50 Amah x 68 cm long or thereabouts whose weight is limited to the maximum that two men can comfortably carry and manipulate. This maximizes at 90 Kg so we have a chain measuring 34 metres long by 90 Kg which at first calculation tells us that as a single wire of wrought iron [they did not have steel at the time of the Gemara] with a specific gravity of say 7.5 (pure iron is 7.81) equates to a volume of 14,000 cm3.
Thus we now have a single wire with a cross sectional area of 4.5 cm2. Once we convert that into a chain we widen the choice of wire diameter because of the links, but the mass has to remain similar because it is still held by the same two men. So we can end up with a wire /link diameter 2 - 5 mm [rough approximations]!!
However this is where it all falls apart:
1) Eulers theorem DOES obtain - as a guide - that anything long and thin bends in the middle, and this chain is almost 100 feet long.
2) We now look at the tensile strength/elasticity of this material - say 10 tonnes per square inch . Sorry to mix dimensions, but basically the effort required by the two surveyors to hold the chain straight will lead to if not breaking the chain (for the thinnest wires used in the equation), to stretching it.
3) We also have to figure in coefficient of thermal expansion which has a value.
4) And just to be more difficult I think the overall weight of 90 Kg is altogether too generous!
In my mind is the image of a picture-frame brass/chrome plated hanging chain. Although its SG maybe about 9/10 - it will weigh about 1/2 lbs per foot, and will stretch like toffee when effort is made to hold straight to measure horizontally!
Best, Kalman Bookman
1) First, let me point out that according to the Me'iri it would seem that the measuring can indeed be done with iron chains even l'Halachah. None of the other Poskim accept his ruling, though.
2) With regard to whether iron chains could be used in practice - we find in a number of places that metal chains were indeed preferred over fiber ropes for obtaining accurate measurements of land.
The Mishnah in Kelim 14:3 refers to "Shalsheles Shel Meshuchos," a measurer's chain. The Bartenura explains that chains were commonly used to measure land rather than ropes since a rope can be stretched unevenly, making for unfair apportionment of land. Similarly, we find in Bava Metzia 61b that a rope stretches differently in the rainy season than in the sunny season, and the Rambam (Hilchos Geneivah 8:3) recommends using iron chains to avoid this problem.
3) As for how iron chains could be lifted by the Techum-measurers - the Rambam writes in Hilchos Kelim 9:14 that when iron ropes were used to apportion land, pegs were affixed to the ground and the chains were stretched between the pegs. In my opinion, if Techum Shabbat would have been measured with iron chains the same method would have been applied and it would not be necessary to lift the chains. The reasons given for holding the measuring tool near the heart only apply to ropes (which must be held off the ground in order to stretch them to their utmost), not to chains. This would allow for a much more weighty chain.
4) In addition, had the Rabanan required iron chains, it would have been permissible to use much shorter chains. With ropes, we must minimize the amount of individual measurings in order to minimize the inaccuracies that are introduced by each stretch of the rope. But with iron chains, there is no such need.
In short, Rebbi Yehoshua ben Chananyah commented that it would be best to use iron chains because of the inherent inaccuracy of rope measurements, as mentioned above. However the Rabanan were lenient when it came to measuring the Techum (perhaps even if Techumim are mid'Oraisa - see Pri Megadim in Mishbetzos Zahavm OC 399:1) and they allowed the use of the less accurate rope measurements, finding an Asmachta to support this (see Tosfos Yomtov Eruvin 5:4). Because of a fiber rope's inherent inaccuracy, Chazal instituted ways to get the most accurate measurement from the ropes. That is why one uses a 50-Amah rope, holds it near the heart and stretches it with all of his might (as stated in Tosefta 4:13).
5) The Rashash in Kelim 14:3 (cited by Tosfot Anshei Shem) questions the Bartenura's contention that the accepted practice was to measure with chains from our Gemara, which says "Shel Pishtan l'Medidah."
However, Rabeinu Chananel explains that when the Gemara says 'l'Medidah" it is referring specifically to measuring Techum Shabbos. As we have explained, this was a leniency instituted for Techum measurements. Measurements for commercial purposes were usually done with metal chains stretched along the ground, as we have explained.
Best regards,
Dovid Bloom, Kollel Iyun Hadaf
I found an explanation in the Mesivta edition of the Gemara that relates to the difficulty involving the very heavy iron chains.
1. This is based on what is written by Rav Yakov Emden (the Ya'avetz), printed at the back of most editions of the Gemara.
The Ya'avetz writes that the Gemara does not actually mean that the chains are made out of rings, but rather the Gemara is referring to bars of iron.
2. The Mesivta edition, in Yalkut Bi'urim on page 58a (#16), writes that since iron chains are so heavy, it would not be possible for two men to carry them around, and they would break in the middle. Therefore, the Ya'avetz prefers to say that we are referring to iron bars, which are somewhat lighter than chains. Even though the Rambam (Hilchos Kelim 14:3) writes that they used to measure land using chains, this was possible only because the chains were less than 50 Amos long.
Kol Tuv,
Dovid Bloom