The Ancient search for a Universal Standard of length 05/03/2014

AbstractThe Ancient search for a Universal Standard of lengthWhen 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 inMesopotamia 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 [email protected]

mailto:[email protected]


THE PENDULUM AND THE STANDARDS THAT MEASURED THE ANCIENT WORLDROLAND 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 betterThe 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) yearTiming 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 cmThe 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 Earth600 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 mmUsed 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 mmThis 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 BushelThe English Bushel was established as one Minoan Cubic Foot (27.983 liters)1/8 Bushel was established as the English Gallon1/64 Bushel was established as the English Pint1/64 Bushel filled with rain water was established as the Mercantile Pound1/60 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 FootThis 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 MileThe 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) = 1.01667The 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 feetIts 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 ConclusionThree 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]



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 beenfound. 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, andby inference the Pint and the London Quarter could bederived. Applying these formulas has led to this surprisingdiscovery.

The Assize established the Gallon at eight Tower Pounds ofcorn (grain) and the Bushel at 8 gallons or 64 Tower pounds.

A quick calculation of the size of a 64 pound cube of grain atthe standard specific gravity of 0.8 yields a cube 30.36 cm onedge. This is precisely the length of the foot used to buildthe Minoan palaces on Crete in the second millenniumBCE. A pint is defined as 1/8 of a gallon.

If this pint was filled with water it would weigh 1.25 TowerPounds or exactly one Scottish or English Mercantile Poundof 6750 grains. The accuracy of this calculation leads one toconsider the possibility that the Scottish Pound had beendefined in antiquity as 1/64 the weight of one Minoan cubicfoot of rain water.

The old saying “A pint’s a pound the world around” wouldhave been perfectly true and would tend to explain why eventoday the pint is divided into 16 “fluid” ounces.

The weight of 1/60 of this Minoan cubic foot of grain couldhave been used to established the weight of exactly one TroyPound. The accuracy of this calculation and its sexagesimalnature lends credence to this possibility.

That an ancient measurement developed in Crete could reachEngland should not be surprising since Cornwall suppliedlarge quantities of tin to the nations of the Mediterranean inthe Bronze Age. The Minoans were a sea-faring nation andtheir standard of measures can be found is such far awayplaces as Okinawa Japan.

Roland Boucher11 Deerspring Irvine, CA 92604email [email protected]

Appendix 2Developing standards to measure the Ancient World

Primary Standards of length, volume and weight weredeveloped in the ancient world probably as far back as thefourth millennium BCE. We believe they were derived fromthe length of a pendulum timed by a fraction of the dailyrotation 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 thelength 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 pendulumThis standard divided the day into 366 parts adjusting thelength 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 pendulumThis 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 usingcombinations 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 Boucher11 Deerspring Irvine, CA 92604email [email protected]

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http://www.metrum.org/measures/volumeweight_u.htm

http://www.metrum.org/measures/volumeweight_u.htm

http://en.wikipedia.org/wiki/Gravity_of_Earth

http://en.wikipedia.org/wiki/Gravity_of_Earth

http://home.online.no/~sigurdhu/Grid_1deg.htm

http://home.online.no/~sigurdhu/Grid_1deg.htm

http://www.dioi.org/kn/stade.pdf

http://www.dioi.org/kn/stade.pdf