Ancient quest for universal measurement standards

Abstract
The Ancient search for a Universal Standard of length
When the French Academy of Science proposed a new Metric System in the
eighteenth century, they may not have realized that theirs was simply the latest
attempt in a centuries-old desire for a universal standard of measure.
This paper describes that quest, beginning with the Sumerians in
Mesopotamia over 5,000 years ago, who used a one-second pendulum to develop
all measurement of length, volume and weight. These ancient meters, liters, and
kilograms were exactly what the French were to propose in the eighteenth century.
This and four additional Standards of Length were used to measure most of the
Ancient World from China and Japan in the East to the British Isles in the West,
Each Standard could be reproduced with an accuracy of 1 mm or less, All were
logical variations of the original Sumerian design, and each succeeding standard
was more closely related to the polar circumference of the Earth.
A presentation given by Roland A. Boucher MS Yale 55, Retired at the
Eleventh Annual AIAA Southern California Aerospace Systems and Technology Conference 3 May 2014
Roland A Boucher 11 Deerspring Irvine, California 92604 email rolandfly@sbcglobal.net

THE PENDULUM AND THE STANDARDS THAT MEASURED THE ANCIENT WORLD
ROLAND A. BOUCHER
MS Yale 55, Retired, Orange County California Chapter Sigma Xi
THE STANDARDS THAT MEASURED THE ANCIENT WORLD
• All Standards were developed through use of a Pendulum
• The second two were direct variations of the original one second pendulum
• All pendulums were timed from astronomical observation
• Each could be reproduced with an accuracy of one mm or better
• These three and later variations measured most of the Ancient World
• Some were were developed to be related to the polar circumference of the Earth

The Original Standards for a Metric System in the 17th and 18th centuries
Standard of Time = Second (1/86,400 solar day)
Standard of length = Meter = length of one second pendulum (993.7 mm)
Standard of volume = Liter = Volume of 10 cm cube (981.2 cu cm)
Standard of weight = Kilogram = Weight of one liter of distilled water (981.2 gm)
Standard of distance = Kilometer = 1000 meters (993.7 meters)
The original definition for the Meter (993.7 mm) was the length of a one second pendulum,
when measured in the Earths gravitational field at 45 degrees North Latitude.
The Measurement Standards of Ancient Sumeria in 3000 BCE
Standard of Time = Gesh (1/360 solar day (240 modern seconds)
Standard of length = Step = length of a one second pendulum ( 994 mm)
Standard of volume = Sila = Volume of 1/10 Step cubed (982.11 cu cm)
Standard of weight = Mina = the weight of 1/2 Sila of distilled water (491 gm )
Standard of distance = Cable = 360 Steps or 1000 sudua or Feet) (357.8 meters)
Alternate standard of length = Sudua or Foot 1/1000 Cable (357.8 mm)
When studying the standards of measurement in Ancient Sumeria it became obvious
that they had invented the original metric system over 5000 years before the French proposed it.

The 994 mm Length of this Mesopotamian Standard can be Accurately Reproduced
Our first 994 mm experimental pendulum was constructed with a single 0.6 gram waxed Irish
linen string and a 267 gram spherical brass weight. The average period for 100 beats was found
to be 100.21 seconds. A second pendulum was constructed using the same string but with a
lighter 67 gram spherical weight. The period for 100 beats was now 100.00 seconds. The test
location was in the greater the Los Angeles area at 33 deg N latitude.
A ball bearing pivot was used
to suspend the pendulum.
A rubber band tensioner was used when
adjusting the length of the pendulum string.

The Sumerian system was great but everything can be made better
The sumerian year had 360 days with 5 off for celebration
Their pendulum swung 1/3 this number of Periods during 1/360 solar day
The sun subtends and angle of about 1/2 degree - high accuracy would be limited
All standards except the foot were organized in a sexagesimal fashion
There are 366 days in a celestial (star) year
Timing a pendulum the same way with a star is accurate but the pendulum is very short
Timing a pendulum 1/2 this number of Beats during 1/366 celestial day works well
The new standard length would be 1/2 the length of this 162 cm long pendulum
This new length is still not closely related to the polar circumference of the earth
How to divide the polar circumference of the Earth
Timing a pendulum 1/366 day with Venus in opposition divides the day by 365.25
This longer period results in a cable length of very nearly 1/360 of a degree

The Measurement Standards of Ancient Egypt circa 3000 BCE
The Egyptian pendulum swung 366/2 of Beats during 1/366 Celestial day
one half the length of this pendulum was 82 cm
The length of the Egyptian cable was 366 x 82 cm = 300 meters
Standard of length # 1 = djser (foot) = (366 pendulum lengths)/1000 (300 mm)
Standard of length # 2 = Reman = 20/16 djser (375 mm)
Standard of length # 3 = Cubit = 24/16 djser (450 mm)
Standard of length # 4 = Royal Cubit = 28/16 djser (525 mm)
Standard of volume = Khar = Volume of 36/34 cubic Cubits (96.5 liters)
Standard of weight = deben = weight of 1/1000 cubic Cubits of distilled water (91 gm )
Standard of distance = Stade = 500 Reman (187.5 m)
10 Stade was 1.0123 minutes of arc on the Polar Circumference of the Earth
600 x 360 Stade was 1.23 percent larger that the Polar Circumference of the Earth

Looking to Venus -- The Minoan Standards of Length
The Planet Venus is closer to the Sun than the Earth and orbits it in 244 days. By viewing
Venus when it is in opposition its motion cancels out some of the apparent motion caused by
spinning Earth.. This adds one second to the period which would be provided by a star.
The Minoan pendulum swung 366/2 of Beats during 1/365.25 Celestial day
one half the length of this pendulum was 82.95 cm
The length of a minoan cable was 366 x 82.95 cm = 303.6 meters
Standard of length = Foot = 1/1000 Minoan Cable lengths ( 303.6 mm)
Standard of volume # 1 = “Bushel” = Volume of one cubic foot (27.984 liters)
Standard of volume # 2 = “Gallon” = 1/8 “Bushel” (3.498 liters)
Standard of volume # 3 = “Pint” = 1/8 “Gallon” (437.2 cu cm)
Standard of weight # 1 = Troy Pound = weight of 1/60 “Bushel” of grain (373.12 grams)
Standard of weight # 2 = Mercantile Pound = of one “Pint” of rain water (437.2 grams)
Standard of distance = Stadia = 600 Steps or nearly 1/600 degree (182.16 meters)
Ten Minoan stadia of 6000 minoan feet = 1821.60 meters was 1.653 percent less than the Geodetic Nautical Mile.
This accuracy did not require the creation of an auxiliary standard like the Reman

These three primary standards spread across the known world in Ancient times
The Sumerian foot of 357.8 mm
The Zhou Dynasty in China circa 1100 BCE established that the Royal chi = 358.2 mm.
The town of Bordeaux in France established the Pied de Terre at 357.2 mm
The Egyptian foot of 300.0 mm
Used by the Phoenicians and early Romans it was used throughout the Mediterranean.
Found as the Fuss of the Canton of Aargau and the Reichsfuss of Baden in Germany
The Minoan foot of 303.6 mm
This foot was established as the Shaku (303.0 mm) in ancient Okinawa, Japan And in Europe
as the Stadtschuh (304.0 mm ) in the Canton of Basel and the Fuss (303.0 mm) in Linz Austria.
This Foot was immortalized in the Magna Carta of 1215 with the English Bushel
The English Bushel was established as one Minoan Cubic Foot (27.983 liters)
1/8 Bushel was established as the English Gallon
1/64 Bushel was established as the English Pint
1/64 Bushel filled with rain water was established as the Mercantile Pound
1/60 Bushel filled with grain was established as the Troy Pound
The Japanese in Ancient Okinawa adopted the 1/100 Troy pound as the momme (3.75 grams)
and established the sho (1.804 liters) as a unit of volume equal to four Troy Pounds of rice
(There is evidence that the Minoan pendulum length can also be found in construction of the stonehenge)

The Curious Case of the Chinese Market Foot and the Anglo-Saxon Furlong
If the original Sumerian pendulum had been timed through 360 beats instead of 240, or if the
Greek Attic pendulum had been timed using the Sun rather than the planet Venus, a pendulum
length of 883.6 mm and a foot of 318.08 mm would result.
The Chinese Market Foot
This Foot was adopted as the Shin Ch’ih (318 mm) by the Zhou Dynasty in China.
It also became the standard foot in the cities of Bern and Innsbruck Austria. With a cable of 365
or 366 lengths it became the Doric Foot (322 mm) in Greece, and the Luwain pous (323 mm) in
Anatolia.
The British Furlong, Foot, Mile, and Nautical Mile
The Doric Foot may have taken a curious part in the development of the modern British Foot.
The length of the Anglo-Saxon Furlong (201.2 meters) is approximately 625 Doric feet. This
Furlong was the standard for land measurement in early England.
In 1592 Queen Elizabeth 1st declared the British Foot to be 1/660 of a Furlong (304.8 mm)
and the British Statute Mile to be exactly 8 Furlongs or 5280 feet..

The Final Solution, The Attic Foot
The Minoan foot,stdia and nuatical mile were about 1.67 percent too short. A simple correction in the ratio of (366/360) was
introduced to remove this error. The correction was accomplished by swinging the pendulum one half of 360 (instead of 366)
times in the minoan period then multiplyng the length by 360 ( instead of 366) to develop the new cable and foot.
The correction was (366/360)squared x (360/366) = (366/360) = 1.01667
The length of this new “Attic” foot was 308.61 mm
The WGS 84 gives the length of one nautical mile (arc minute) at 1852.216 meters.
10 Stadia or 6000 Attic feet was 1851.66 meters, an error of only 56 cm
This New Standards Was Almost a Perfect Fit to the Polar Circumference of the Earth
The width of the Parthenon in Athens Greece is reported to be 100 Attic feet
Its width has been was measured at 30.897 meters yeilding an error of only + 2.67 cm.
The Roman Empire immortalized this foot by adopting the 600 foot Greek Stadia as the
Roman Stadia of 625 feet . This standard would spread throughout the Western World

The Roman Empire and 24/25 of the Near Perfect Solution
The Greek “Attic” Stadia was Adopted by the Roman Empire as a 625 Foot Roman Stadia
The Greek Attic Stadia = 185.16 meters = Roman Stadia = 625 new Roman feet.
The Roman foot became 24/25 of a Greek attic foot = 296.2 mm.
The Roman mile became 5000 Roman feet = 1481.280 meters.
75 Roman miles was only 33 meter short of a degree on the Polar Circumference of the Earth.
27,000 Roman miles was only 12 km short of the Polar Circumference of the Earth.
Roman Navigators could determine their latitude with an error of only 3 km
Note: The Romans used the ratio of the 24/25 in developing their new foot. This would lead to
other cultures throughout Europe adopting it to other standard feet as well. The resulting
confusion and profusion of European Standards provided a strong impetus for reform.
The French who led the revolt were unaware that they already had an earth centered standard
in their Livre (pound) which was simply the weight of 1/60 of an attic cubic foot of rain water.
Its width was 1/100 Arc seconds on the Polar Circumference of the Earth

In Conclusion
Three Standards and Their Variations Were Used to Measure the Ancient World
All Standards were developed through use of a Pendulum
All Pendulums were timed from astronomical observations
The second two were logical variations of the original one second pendulum
The Minoan Standard was related to the Polar Circumference of the Earth
These three and subsequent variations measured much of the Ancient world
The Greek variation measured the polar circumference of the Earth to 0.033%
The Romans spread their standard of 24/25 Greek feet throughout Europe and the middle east.
This ratio was misapplied to other standards obscuring the true nature of the Greek and Roman standards
I hope that you will join me in the search for other examples of these precise standards
Note: There is some evidence that the both the Minoan and Greek standards may have reached the new world
Roland A Boucher 11 Deerspring Irvine, California 92604 i email rolandfly@sbcglobal.net

Appendix 1
The Lost Winchester Bushel
And the origin of the Troy and Scottish (mercantile) Pounds
The volume of the long lost Winchester Bushel has been
found. It is exactly a one foot cube.
This ancient foot was used to build the Minoan palaces on
Crete in the second millennium BCE. Its cube may well have
been the origin of both the Troy system of weights and the
Scottish (mercantile) pound of medieval England.
Let me explain.
During the tenth century, the capital city of the English King
Edgar was at Winchester and, at his direction, standards of
measurement were instituted. Following the Norman
Conquest, the King Edgar physical standards
(prototypes)were removed to London. Later in 1215 the
Magna Carta established the London Quarter of eight bushels
as the standard of volume for all of England. This bushel was
called the Winchester Bushel.
In 1266, after the original standards were lost, King Henry
III issued the “Assize of Bread and Ale” which established a
formula by which the volume of the Bushel, the Gallon, and
by inference the Pint and the London Quarter could be
derived. Applying these formulas has led to this surprising
discovery.
The Assize established the Gallon at eight Tower Pounds of
corn (grain) and the Bushel at 8 gallons or 64 Tower pounds.
A quick calculation of the size of a 64 pound cube of grain at
the standard specific gravity of 0.8 yields a cube 30.36 cm on
edge. This is precisely the length of the foot used to build
the Minoan palaces on Crete in the second millennium
BCE. A pint is defined as 1/8 of a gallon.
If this pint was filled with water it would weigh 1.25 Tower
Pounds or exactly one Scottish or English Mercantile Pound
of 6750 grains. The accuracy of this calculation leads one to
consider the possibility that the Scottish Pound had been
defined in antiquity as 1/64 the weight of one Minoan cubic
foot of rain water.
The old saying “A pint’s a pound the world around” would
have been perfectly true and would tend to explain why even
today the pint is divided into 16 “fluid” ounces.
The weight of 1/60 of this Minoan cubic foot of grain could
have been used to established the weight of exactly one Troy
Pound. The accuracy of this calculation and its sexagesimal
nature lends credence to this possibility.
That an ancient measurement developed in Crete could reach
England should not be surprising since Cornwall supplied
large quantities of tin to the nations of the Mediterranean in
the Bronze Age. The Minoans were a sea-faring nation and
their standard of measures can be found is such far away
places as Okinawa Japan.
Roland Boucher
11 Deerspring Irvine, CA 92604
email rolandfly@sbcglobal.net

Appendix 2
Developing standards to measure the Ancient World
Primary Standards of length, volume and weight were
developed in the ancient world probably as far back as the
fourth millennium BCE. We believe they were derived from
the length of a pendulum timed by a fraction of the daily
rotation of the earth. They each used either the sun, the
stars,or the planet Venus to divide the day. Examples of each
can be found throughout the Ancient world from England in
the west to Japan in the East. There is also some evidence
that some versions may be found in the western hemisphere.
Developing a standard using the sun and a pendulum.
This standard divided the day into 360 parts adjusting the
length of a pendulum so that it would swing 1/3 that number
of times in that period. This 2 second pendulum was nearly
one meter long being only 0.6 % short of today’s standard.
The standards of volume and weight were correspondingly
very nearly one liter and one kilogram. The standard length
was divided in two to form a length called the cubit, and was
multiplied by 360 to form a standard of distance
measurement of 1000 feet or about a third of a kilometer.
Developing a standard using a star to time a pendulum
This standard divided the day into 366 parts adjusting the
length of a pendulum so that it would swing 1/2 this number
of times in that period. One half the length of this pendulum
was multiplied by 366 and divided by 1000 to develop a
standard Foot which was multiplied by 1.5 to create the
cubit.The volume of a Cubic Cubit was divided by 200 to
provide the standard of volume. The weight of rain water
contained in a cube 1/10 cubit on edge became the standard
of weight
Six of the 1000 foot lengths was nearly 1/60 of a degree on
the polar circumference of the earth. It was about 24/25 of
today’s value derived from satellite data.
Developing a standard using Venus to time a pendulum
This standard divided the daily rotation of Venus in the sky
by 366 parts adjusting the length of a pendulum so that it
would swing 1/2 this number of times in that period. One
half the length of this pendulum was multiplied by 366 and
divided by 1000 to develop the standard Foot. This foot was
used to develop both standards of volume and weight. The
volume of a cubes of one, on half, and one quarter Foot
(pint) became the standards of volume, The weight of rain
water contained in a one quarter foot cube (pint) became the
standard pound. Six of the 1000 foot lengths was very nearly
1/60 of a degree on the polar circumference of the earth. It
was about 1 percent shorter than today’s value derived from
satellite data
These three standards as well as additional standards using
combinations of these numbers spread throughout the
ancient world. Examples of the first can be found in
Mesopotamia, China, and France. Examples of the second
can be found in Egypt, Phoenicia, and early Rome,
Examples of the third can be found in Crete, on Okinawa in
Japan, and in medieval England where the standards of
volume and weight are immortalized in the Magna Carta of
1215.
Roland Boucher
11 Deerspring Irvine, CA 92604
email rolandfly@sbcglobal.net

References
1 Livio C. Stecchini. A History of Measures. http://www.metrum.org/measures/volumeweight_u.htm Part V: Mesopotamian Measures, Units of length, section 1.0
2 Margenau, Watson & Montgomery. Physics Principles and Applications, New York McGraw-Hill 1949. 178-180
3 Bronwell, A. Advanced Mathematics in Physics and Engineering, New York McGraw-Hill 1953. 137-139
4 Janhke E, & Emde F. Table of Functions, New York Dover Publications Fourth Edition 1945 Table V. Complete elliptical integrals 85
5 WGS 84 Gravity of Earth http://en.wikipedia.org/wiki/Gravity_of_Earth
6 Earth according to WGS 84 http://home.online.no/~sigurdhu/Grid_1deg.htm
7 Berriman, A.E Historical Metrology, New York ,E.P. Dutton & CO 1953.
8 Katz, Victor J. (editor), Imhausen, Annette et.al. The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook,
Princeton University Press. 2007
9 Petrie, Sir W.M.F. Inductive Metrology London,H. Saunders, 1877 section 21- 39
10 Graham, J. W. The Palaces of Crete Princeton University Press 1962. 224
11 United Nations. Department of Economic and Social Affairs. World Weights and Measures Handbook of statistics series M 21 English Rev 1 62
12 Knight C. & Butler A., Civilization One, Watkins Publishing London 2004. 18,30
13 Kollerstrom, N. Greek Foot The Acropolis Width and Ancient Geodesy http://www.dioi.org/kn/stade.pdf) 2005
14 P. Guilhiermoz Bibliothèque de l'école des chartes De l'équivalence des anciennes mesures. A propos d'une publication récente Volume 74 278
15 Noback, Christian, Friedrich Eduard (1851) (in German). Vollständiges taschenbuch der Münz-, Maass- und Gewichts-Verhältnisse etc.
aller Länder und Handelsplätze[Comprehensive pocketbook of money, weights and measures for all counties and trading centres].
I. Leipzig: F. А. Вrockhaus. Retrieved October 24, 2011. 101
16 Niemann, Friedrich (1830) Vollständiges Handbuch der Münzen, Masse, und Gewichte aller Länder der Erde fur Kaufleute, Banquiers . in alphabetischer
Ordnung.
Quedlinburg und Leipzig, G. Basse. 102

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