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.
|A loom (Wikimedia Commons)|
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
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
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.]