Journal of Geomancy vol. 2 no. 3, April 1978

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IDEAL UNITS: THE CUBIT

BY Hermon Gaylord Wood.

This is an excerpt from the extremely rare book IDEAL METROLOGY, which was privately published by H.G. Wood at Dorchester, Mass., U.S.A. in 1908. 

In the Egyptian department of the Museum of Fine Arts, Boston, there is a scribe’s palette, received from Memphis and believed to be four thousand years old.  It is a rare antique of great metrological value.  It is of wood, fifteen inches in length, an inch and a half wide and three-fourths of an inch thick.  The right-hand end has three cups incised on the broad face, to hold colors for the artist’s use; the edges of the cups show much wear by the brush.  In the middle of the stick there is a deep undercut for brushes.  On the narrow side six transverse lines are scored at irregular intervals, which mark important sections of the ancient Egyptian cubit. 

This cubit rod played an important part in ancient Egyptian architecture.  Its total length in English inches was 20·625.  Mr. Petrie, in Pyramids of Gizeh, confirms this measure as the result of his examination of many monuments and cubit rods.  He says ” On the whole we may take 20·62 ± ·01 as the original value; the digit (a subdivision of the cubit) is ·727 ± ·002; in some Egyptian cubits a decimal division is found as in other countries; the cubit and the digit have no integral relation, the connection of 28 digits with the cubit being certainly inexact”.  (Page 181).  This is the testimony of an expert whose experience and accuracy command the highest respect. 

In the ancient treatment of geometric forms the conversion of a circle into a square of equal area, or of equal perimeter, was accomplished with remarkable accuracy: this could not have been done without a unit of measure.  The peculiar division of the cubit in two unequal parts served this purpose.  The right-hand division, 17·52 inches, comprised 24 digits; the left-hand, 3·1 inches, had four subdivisions with a total length of 4·25 digits; hence the whole cubit was 28·25 digits, equal to 20·625 inches; this gave ·73 inch for the length of a digit.  Mr. Petrie gives ·727 ± ·002 as the result of his measurements of many cubit rods.  The ancient Roman cubitus was 17·52 and its digitus was ·73.  The Egyptian cubit of the Turin museum is 20·611 inches, that of the Louvre is 20·595; in both of these the left-hand division of four parts is greater than four digits of the right-hand division.  It is therefore an error to reckon the whole cubit at 28 {58} digits.  It has 28 subdivisions, but its length is more than 28 digits. 

No doubt the singular left-hand appendage of four subdivisions served some purpose in Egyptian metrology.  What was that?  Three of its subdivisions had a total length of 3·1875 digits; adding to this 19 digits of the right-hand part of the cubit, we have 22·1875 digits, which is the side of a square whose perimeter is equal to the circumference of the circle described on a diameter of one cubit, 28:25 digits.  This geometric device gives the value of Pi, correctly to six decimal places, 3·141592+. 

Again, the circumference of a circle being 28·25 digits, its area is equal to the square whose diagonal is 11·27 digits, or closely approximate to 4·25 + 7 = 11·25 digits. 

Again, at the 15th digit on the cubic rod there is a line scored across its face; the remaining 9 of the 24 digits is the diameter of the circle whose circumference is one cubit, 28·25 digits.  All of these geometric coincidences are integrally correct.  The problem of squaring the circle appears to have been practically solved four thousand years ago.  From these observations the geometric purpose of the short appendage at the left hand of the cubit is evident. 

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The cubit held a prominent place in Hebrew metrology.  It was the basis of a system of weights and measures unsurpassed in the extent and harmony of its correlations.  Temples and altars were measured by the cubit unit.  The oil and flour for religious uses were measured by the log, which was 43·2 cubic digits according to the famous Rabbi Maimonides, that is, one-third of 129·6, the circumference by inches of the circle whose radius is one cubit, 20·625 inches, or 28·25 digits. 

The religious tenacity of the Hebrew people served to protect the integrity of their metrology.  Cubit, span, handbreadth, digit, log, quab, omer, hin, seah, bath and cor were not forgotten in their broken civilization.  These measures were so identified with their religious obligations that such a misfortune was well nigh impossible.  Commercial relations led to the introduction of their metrology to European nations.  The 24 digit rule of 17·52 inches reappears in the Russian Verschok of 1·75 inches.  One-tenth of the Hebrew reed of 6 cubits, 123·75 inches, is seen in the foot rules of Denmark 12·36, Norway 12·35, and Prussia 12·36.  A dozen cubit rules appear of about 18 inches, probably derived from the 24 digit rule of 17·52 inches, or from the measure of six handbreadths of 3·1 inches.  The Greek Foot, 12·13, is one sixth of 100 digits of ·728 inches.  The Roman foot, 11·65, is 16 digits of ·728 inches.  Austria’s foot rule, 12·44, appears to be four handbreadths of 3·1 inches.  Thus there seems to be good foundation for believing that the old European systems of Metrology were derived from the cubit of Egypt, which was the cubit of Noah, Moses and Ezekiel. 

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The origin of the British inch is unknown, but its close relation to the Hebrew cubit is remarkable, for the diameter of a circle being 20 cubits, the measure of the Most Holy in Solomon’s Temple, its circumference is 1296 in. which is just 120 Gudea rules.  The Gudea rule, 10·8 in., was the ancient standard of lineal measures in Babylonia, where Hebrews were in captivity many years.  There is a tradition that after the captivity some Hebrews settled in England, as they did in European countries.  The Comacine architects were familiar with the number 1296, since it often appears by inch measures in the cathedral plans.  The circumference of Stonehenge by the inch is equal to the number of days in 10 years.  Whether this unit be of Egyptian, Babylonian, Hebrew, Italian, Roman or Druidic origin its identity of measurement is preserved almost if not altogether without fault, and, not less remarkable than this, is its beautiful correlation with the harmony of Nature and the most ancient and modern divisions of time and the circle; the foot of 12 inches was a natural sequence, one-half of the number of aliquot digits in the cubit of Egypt.