Tuesday, January 8, 2013

Design of the Paroches

SUMMARY The design of the Paroches curtain is described in the Mishnah in Shekalim and from here such details as the diameters of its various threads can be determined.

Interior of the Sanctuary looking west.
Paroches is in the background.
In the Second Temple there were three large  Paroches curtains: one at the opening of the Antechamber and two which hung in the Sanctuary and divided the Holy from the Holy of Holies. These curtains measured 20 amos wide by 40 amos tall (30 x 60 feet). The Mishnah (Shekalim 8:5) states that the Paroches of the Temple was woven upon seventy-two heddle shafts. The heddles of a loom are those devices which raise and lower the warp threads to allow the shuttle holding the woof thread to pass from one side of the fabric to the other. See item "f" in the diagram below.
A loom (Wikimedia Commons)
Tiferes Yisrael (Boaz 2 ad loc.) demonstrates that the 72 heddle shafts mentioned in the Mishnah could not have accounted for the full 20-amah width of the Paroches. Instead, he concludes that the Paroches was woven in sections which required 72 heddle shafts each and these sections were then sewn together to form the full Paroches.

The Mishnah (ibid.) also records the thickness of the Paroches as one handbreadth (3 inches). In order to create a fabric which is one handbreadth thick the warp cords must be 1/3 of a handbreadth thick and the woof cords, which were normally twice the diameter of the warp threads, would be 2/3 of a handbreadth (Tiferes Yisrael loc. cit.). Since each section used 72 heddles, and each heddle held one cord, this means that the sections were 24 handbreadths wide. [72 cords x 1/3 handbreadth per cord = 24 handbreadths.] 24 handbreadths is equal to 4 amos (6 handbreadths per amah), so five sections would be needed to produce a width of 20 amos. This means that the Paroches had a total of 360 warp cords [5 sections x 72 cords per section = 360 cords] along its 20-amah width.

Diameter of the Strings in the Warp Cords

Each warp cord was comprised of 24 smaller strings dyed with different colors, as follows: 6 strings of techeiles, 6 of argaman, 6 of tolaas shani, and 6 of sheiss. Since the diameter of the warp cords is given as 1/3 of a handbreadth, it is possible to estimate the diameter of the 24 smaller strings making up that cord.

In a cross-section of a cord made of smaller strings let the cord have radius R and area A such that

A = πR2

Let the strings have radius r and area a such that

a = πr2

Cross-section of a thicker cord
made of smaller strings
The total area of the cross-section of the cord is approximately equal to the sum of the areas of the smaller strings. This is only an estimate since the cord is not perfectly round in cross-section and this calculation also does not take into account the airspaces between the strings:

A = Na

where N is the number of strings in the cord.


πR2 = Nπr2

r = R / √N

d = 2r = 2R / √N

In the case of the warp cords of the Paroches:

R = 1/6 handbreadth
N = 24

Thus the diameter of each string is 0.068 handbreadths (0.14 inches).

Diameter of the Threads

The Mishnah (ibid.) states that there were a total of 820,000 threads used in the warp. To account for this number Tiferes Yisrael understands that the dyed strings which made up the warp cords were themselves made of many smaller threads. According to his arrangement, if the 360 warp cords were made of 24 dyed strings each then there were a total of 8640 dyed strings. [360 x 24 = 8640] Dividing 820,000 threads among 8640 strings gives approximately 95 threads per string. Using the same estimation from above:

d = 2R / √N

R = 0.034 handbreadths
N = 95

Thus the diameter of each thread is 0.0070 handbreadths (0.021 inches). [Common yarn diameters range from approximately 0.004 to 0.031 inches.]

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