Egypt

Origins

Origins

Refer to *Weights and Measures*, Flinders Petrie, Aris and Phillips, Ltd., Warminster, England,
1926. Some of these rods are now preserved in the Petrie Museum in London.

I do not discuss items insufficient to obtain information on measures. Thus missing item numbers.

All units are in English inches unless otherwise specified.

Petrie offers no information on hieroglyphic inscriptions useful to analysis.

Starting on page 38, Linear Measures, Section 87, Egyptian cubit rods.

**Item #1**

Square wood rod, 0.75 X 0.75, six palms. Petrie questioned if it were Roman. He measured both edges along scale. Excluding end-cap on each end of 0.20 left and 0.21 right. Palm 6 divided in one, one, and two digits.

Palm 1 |
Palm 2 |
Palm 3 |
Palm 4 |
Palm 5 |
Palm 6 |
Total |
Mean |
Median |

3.411 |
3.407 |
3.396 |
3.412 |
3.424 |
3.413 |
20.463 |
3.4105 |
3.4115 |

3.406 |
3.406 |
3.408 |
3.407 |
3.417 |
3.413 |
20.457 |
3.4095 |
3.4075 |

w (top) = 0.028 (0.71 mm)

w (bottom) = 0.011 (0.28 mm)

This difference illustrates the deficiency in the methods of Senigalleisi. Which edge should we use to judge the accuracy of the cutting? Senigalleisi does not tell us what edge, or perhaps average interval, he used. We obtain difference estimates of quality of the rods by the choice.

Although Petrie did not indicate digit divisions, calculated mean digit width at four digits per palm: 0.853.

Total scale length of 20.46 vs total rod length of 20.86. The first value is short the royal cubit length by 0.165 while the second is 0.235 over. These difference may again illustrate degradation from standards found in the Turin rods. Or it may illustrate a rod borrowed from other societies.

Note how this rod compares with the Bronze rod in the Turin Museum, and Scale D.

1. Square 0.75 X 0.75 vs 0.57 X 0.68

2. Wood versus bronze.

3. Total scale length of 20.46 vs Turin of 20.45

4. Mean palm lengths of 3.41 vs Turin of 3.41.

4. Six palms in both cases.

5. 0.853 digit length vs Turin 0.852.

This rod confirms 6-palm unit of measure of 3.41 as real, perhaps non-Egyptian, vs the usual 7-palm length of 2.95. A second example illustrating desire of Lepsius for six palm divisions. Uncertain why Petrie chose to classify it with Egyptian rods, except discovered in Egyptian context. This rod confirms proposal that Scale D of the Turin Bronze rod was one of several different scales then in use in Egypt, and shows that the Bronze rod was not a fake.

**Item #3:**

Flat slip of wood, broken, 0.5 X 0.3. Petrie questioned 12^{th} dynasty.
Rough cuts but useful to units of measure.

Digit 1 |
Digit 2 |
Digit 3 |
Digit 4 |
Digit 5 |
Digit 6 |
Digit 7 |
Total |
Mean |
Median |

0.850 |
1.230 |
1.070 |
1.100 |
0.860 |
1.080 |
1.000 |
7.19 |
1.027 |
1.075 |

w = 0.38 (9.65 mm)

Petrie assumed this was originally a rod with twenty decimal divisions, total length calculated from average and twenty units, to yield 20.54 length.

No palm divisions.

Note that mean digit length is close to 1.0 English inch, within 0.7 mm, but the great variations in the digit lengths make any conclusion uncertain. Compare with integral English inch units of Turin Specimen #1 and Bronze rod Scales B and C.

This could not have been a useful measuring
instrument. Hence, the value of the rod is highly questionable, except to
indicate that measurement standards had badly deteriorated, even by 2,000 BC if
12^{th} dynasty.

**Item #4:**

A round rod, 0.7 diameter, roughly cut. Divisions are highly irregular, varying between 0.58 to 0.93. Not useful for reaching conclusions regarding measures. Petrie gives 0.737 mean digit length, to provide a cubit rod of 20.6.

**Item #6:**

A thick bar of wood, 3.10 X 1.56, with fine and sharp cuts, 0.9 bevel face. This is a six-palm small rod.

Palm 1 |
Palm 2 |
Palm 3 |
Palm 4 |
Palm 5 |
Palm 6 |
Total |
Mean |
5P.Mean |
Median |

2.946 |
2.976 |
3.034 |
2.916 |
2.972 |
2.760 |
17.604 |
2.934 |
2.969 |
2.959 |

w = 0.274 with palm 6 (6.96 mm).

w = 0.118 without palm 6 (3.0 mm).

A cut 0.114 from left end would increase total length to 17.718. The sum of the last palm and the short cut would equal 2.874, still short of a mean palm. Since both ends are preserved, and since the last palm is short, one can question the purpose of both the first cut and the short palm. Mean and median of first five shown.

Theoretical ratio of 6/7 of royal cubit yields 17.68 inches.

Mean palm length multiplied by 7 would yield rod of 20.54. Provenance uncertain, but degradation of standards indicated.

**Section 88, Item #8:**

(Petrie classes this rod by itself.)

Rectangular wood 0.9 X 0.63, broken at palm 6, with bevel face, inscribed to Tuntankhamun and wife Onkhesamen.

Palm 1 |
Palm 2 |
Palm 3 |
Palm 4 |
Palm 5 |
Palm 6 |
Total |
Mean |
Median |

2.811 |
2.973 |
2.885 |
3.062 |
3.000 |
3.035 |
17.766 |
2.961 |
2.987 |

2.846 |
2.962 |
2.865 |
3.051 |
3.010 |
3.060 |
17.794 |
2.966 |
2.986 |

w (top) = 0.251 (6.37 mm)

w (bottom) = 0.215 (5.46 mm)

One can see the poor quality of the rod from these w values.

Divisions from the left are palm, two halves, palm, half and two digits, palm, palm, one lost.

Extrapolated length 20.77. This would make a rod similar in length (20.81) to the hinged wood rod of Kha.

Mean palm length near 3.0 English inches, within 1 mm. Another example of integral English inch measure.

Petrie then lists Assyrian and Jewish cubits, Section 89:

**Item #9:**

Rectangular wood rod, 0.6 X 0.75 divided into 6 palms, end palm divided into four digits.

Palm 1 |
Palm 2 |
Palm 3 |
Palm 4 |
Palm 5 |
Palm 6 |
Total |
Mean |
Median |

3.518 |
3.502 |
3.507 |
3.555 |
3.498 |
3.466 |
21.046 |
3.5077 |
3.5045 |

w = 0.089 (2.26 mm)

Note how this rod compares with Item #1 above at palm length of 3.41 and the Turin Bronze rod Scale D at palm length of 3.41. This could mean that all were of non-Egyptian origin. A further demonstration that Turin Bronze rod was not a fake.

Another example of divisions close to English units of measure. 3.508 mean palm length is 0.17 mm from 3.500. If of Assyrian or Jewish origin, (Petrie does not say), it would again show how close foreign cubit rods were to Egyptian. Difference from royal cubit is 0.42. Another example of degradation from standards.

**Item #10:**

Rectangular wood rod, 0.5 X 1.05, Ptolemaic, third, fifth and sixth palms divided into digits, fourth digit of palm six into two halves.

Palm 1 |
Palm 2 |
Palm 3 |
Palm 4 |
Palm 5 |
Palm 6 |
Total |
Mean |
Median |

3.614 |
3.566 |
3.592 |
3.572 |
3.464 |
3.674 |
21.482 |
3.580 |
3.582 |

w = 0.21 (5.33 mm)

These palm lengths are the greatest of the rods thus far considered, and further support for the possibility of non-Egyptian origin. Total length over the royal cubit by 0.857.

**Item #11:**

Rectangular wood rod, 0.6 X 0.85, six palms on narrow side.

Palm 1 |
Palm 2 |
Palm 3 |
Palm 4 |
Palm 5 |
Palm 6 |
Total |
Mean |
Median |

3.44 |
3.51 |
3.65 |
3.56 |
3.5 |
3.41 |
21.07 |
3.511 |
3.505 |

w = 0.24 (6.1 mm)

This rod again has palm length indicative of non-Egyptian origins that may have later become part of the Egyptian culture. Or degradation of standard royal cubit borrowed by other societies. Difference from royal cubit of +0.445. Compare with similar Item #9 in interval and total lengths.

**Item #12:**

Rectangular beveled wood rod, broken, 1.25 X 0.6, six palms, palm four divided into halves.

Palm 1 |
Palm 2 |
Palm 3 |
Palm 4 |
Palm 5 |
Palm 6 |
Total |
Mean |
Median |

3.02 |
3.1 |
3.06 |
2.91 |
broken |
broken |
12.09 |
3.0225 |
3.04 |

Because of the damaged state I do not attempt to assess the resolution of the inscribed lines.

Note that the palm mean lengths on this rod are very nearly 3.0 English inches, within 0.57 mm.

Remaining rods of Petrie's list are too rough, not adequate to study of measures.

Petrie, Section 92, cites a very fine stone standard, 26.9 X 12.75 X 2.3 to 3.0 thick, upper surface finely smoothed, with inscribed palm lines across the breadth, Mean range error of straightness and parallelism of 0.007 inches. The mean distance of the palms between lines is 3.829, mean difference of 0.006.

This standard stone greatly exceeds mean palm length of any item thus far considered. Again we might question the devolution of measurement standards with time.

None of the cubit rods in Petrie's list compare with the fine tolerance displayed in this standard.

Petrie then lists broken or irregular rods with various digits and lengths.

Illustration | # of digits | Rod Length | Mean digit length |
---|---|---|---|

A |
6 | 4.35 - 4.4 | 0.738 |

B |
8 | 5.8 - 5.9 | 0.731 |

C |
10 | 7.3 - 7.4 | 0.735 |

D |
12-13 | 8.7 - 9.6 | 0.725-0.738 |

E |
15 | 10.9 - 11.1 | 0.733 |

F |
18 | 13.1 - 13.3 | 0.733 |

G | 19 | 13.9 - 14.0 | 0.734 |

H |
22-2 | 15.2 - 16.2 | 0.691-0.704 |

Note how these digit lengths all are near the royal cubit ideal of 0.737.

In the next section I shall offer a general discussion and assessment.

**Next - Part IV - Cubit Rods Assessment**