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.
Roland A Boucher
11 Deerspring Irvine, California 92604
email [email protected]
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
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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
Roland A Boucher
11 Deerspring Irvine, California 92604
email [email protected]
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) (994 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.
Roland A Boucher
11 Deerspring Irvine, California 92604
email [email protected]
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.
Roland A Boucher
11 Deerspring Irvine, California 92604
email [email protected]
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
Roland A Boucher
11 Deerspring Irvine, California 92604
email [email protected]
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
Roland A Boucher
11 Deerspring Irvine, California 92604
email [email protected]
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
Roland A Boucher
11 Deerspring Irvine, California 92604
email rolandfly@sbcgl
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)
Roland A Boucher
11 Deerspring Irvine, California 92604
email [email protected]
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
as well as 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..
Roland A Boucher
11 Deerspring Irvine, California 92604
email [email protected]
Mixing and matching to the Final Solution
Sometime in the mid second or early first millennium the Greek “Attic” foot was developed.
It was truly a “Measure of the Earth” combining the Minoan system with the 360 day year
The Greek Attic pendulum swung 360/2 of Beats during 1/365.25 Celestial day
One half the length of this pendulum was 85.72 cm
The length of a Greek Cable = 360 x 85.72 cm = 308.6 meters
This New Standards Was Almost a Perfect Fit to the Polar Circumference of the Earth
The WGS 84 gives the length of one average second of arc at 30.87027 meters.
The Parthenon in Athens Greece was measured at 30.897 meters. an error of 2.67 cm.
100 Attic feet = 30.86 meter s = 0.999667 arc seconds on Polar Circumference of the Earth.
10 Stadia = 6000 Attic feet = 1851.60 meters = 0.999667 arc minutes of Polar Circumference
An outstanding example of this standard is the 100 ft width of the Parthenon in Athens Greece.
The Roman Empire immortalized this standard by adopting the 600 foot Greek Stadia at
625 Roman feet. They would spread this Stadia throughout the then known Western World
Roland A Boucher
11 Deerspring Irvine, California 92604
email [email protected]
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 became 0.999667 degrees on the Polar Circumference of the Earth.
27,000 Roman miles = 0.999667 times the the Polar Circumference of the Earth.
Roman Navigators could determine their latitude with an error of only 3.3 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.
The length of each side was 1/100 seconds of arc on the Polar Circumference of the Earth
Roland A Boucher
11 Deerspring Irvine, California 92604
email [email protected]
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 [email protected]