[Avodah] Shiur of an Etzbah(finger)

[Micha Berger]

On Sun, Feb 10, 2013 at 10:37:22PM +0200, R Michael Elkohen wrote:
: With regard to various halakhic rulings we are told that things need to
: be the width of a finger? What are the various opinions regarding that.

Wouldn't you just use 1/24 of your favorite shitah for ammah?

1 amaah = 6 tefachim
1 tefach = 4 etzba'os

Since I do not know what ROY holds WRT the ammah, I can't answer what
he would say is an etzbah.

BTW, according to Y-mi Shabbos 8:1 (vilna 54b) and Sheqalim 3:2 (vilna
13b, bavli 9a), a revi'is is
    2 x 2 x 1-5/6 cubic etzba'os

According to the Bavli Pesachim 109a, though, a revi'is is
    2 x 2 x 2.7 cubic etzba'os

Tosafos (Pesachim 109a "revi'is") offers two possible solutions, both of
which justify the Bavli by saying the Y-mi is describing a cylinder in a
way that is an over-estimate lehachmir. Of course, given the much bigger
machloqesin over liquid measures compared to those over linear lengths,
this isn't going to help much.

The answers, just for tangential discussion:

1- The Y-mi is describing a cylinder of radius 2 etba'os and a height
of 1-5/6 etzba'os -- but all their etzba'os are those of Tzipori. The
Bavli is describing a block in etzba'os Midbarios. A Tzipori ammah
(and thus etzbah) are 1-1/6 the size of the Midbari ones.

So the Y-mi comes to
    pi * (2 * 1-1/6) ^2 * (1.6 * 1-1/6) = appx 11.4 etzbaos ^3
in Midbari etzbaos, compared to the bavli's
    2 x 2 x 2.7 = 10.8 etzba'os midbarios

2- The Y-mi is describing a cylinder that can encompass a 2x2 etzba
square, ie the radius is sqrt(2) etzba'os -- albeit all etzba'os
are Midbarios. On Eruvin 76b we see Chazal estimated that a circle is
1-1/2 times the area of the inscribed square, and by that estimate
we would get
   2 * 2 * 1-5/6 * 3/2 = 11 etzba'os



Tir'u baTov!
-Micha

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