A body measure made official

A cubit began as the length of a forearm, from elbow to fingertip. Every early civilisation that built in stone had some version of it. Egypt made it official: the royal cubit (meh nesut) was longer than the common forearm and fixed by master rods, and it was divided into seven palms of four fingers each, twenty-eight fingers in all. A shorter “small cubit” of six palms was also used.

Four rods in public collections

The surviving rods can be checked by anyone: the major museums publish their records online. Four well-documented examples:

The figure used in this book: 523.5 mm

This book, and the workshop of sacredcubit.com and tensorcoil.com, use 523.5 mm for one royal cubit. The value is taken from the published literature, as the lower bound of the measured range of surviving royal cubit rods (523.5–529.2 mm) in Lepsius 1865, Clagett 1999 and Arnold 1991, and it is used as a single engineering constant for cutting wire. It is not a new measurement by the author: the author has not measured the Turin rod or any other rod in person.

cubit = 0.5235               # m, the value used in this book
print(f"palm  = {cubit/7*1000:.2f} mm, finger = {cubit/28*1000:.2f} mm")
lo, hi = 0.5235, 0.5292      # range of royal cubit rods (m)
print(f"spread of rods: {(hi-lo)*1000:.1f} mm = {(hi-lo)/lo*100:.2f} %")
museum_cm = {"Turin 6347": 52.5, "Turin S. 8647": 52.4, "Louvre N 1538": 52.3, "BM EA 23078": 52.5}
for name, cm in museum_cm.items():
    print(f"{name:14s} {cm*10:6.1f} mm  ({(cm*10 - 523.5)/523.5*100:+.2f} % from 523.5)")
# palm  = 74.79 mm, finger = 18.70 mm
# spread of rods: 5.7 mm = 1.09 %
# Turin 6347      525.0 mm  (+0.29 % from 523.5)
# Turin S. 8647   524.0 mm  (+0.10 % from 523.5)
# Louvre N 1538   523.0 mm  (-0.10 % from 523.5)
# BM EA 23078     525.0 mm  (+0.29 % from 523.5)

What 0.3% means for the physics

In Chapter 2 the cubit becomes a resonator, and its resonant frequency is inversely proportional to its length. A difference of 0.3% in length therefore moves the resonance by 0.3%: about 0.4 MHz at 136 MHz, or half a hertz at 164 Hz. Both are smaller than the effect of the wire’s thickness, the room’s temperature or the way a ring is mounted for measurement. The choice between 523 and 525 mm is historically interesting; for the measurements in this book it is almost irrelevant.

Claims about the cubit

Many claims about the cubit circulate: that it encodes $\pi$ or the golden ratio, that it is a fraction of the Earth’s circumference, that it was chosen for its “resonance”. Some of these are arithmetic coincidences that appear with almost any length if one is free to choose the formula; some are historical questions that Egyptologists have studied in detail.

Summary

• The royal cubit was a fixed standard of seven palms and twenty-eight fingers, kept by master rods.
• Four well-documented rods in Turin, Paris and London are recorded at 52.3 to 52.5 cm; surveys of all surviving rods give about 523.5 to 529.2 mm.
• This book uses 523.5 mm, the lower bound of the published range, as an engineering constant; it is not a new measurement by the author.
• A 0.3% difference in length moves a resonance by 0.3%, less than other practical effects.