The PENDULUM AND THREE STANDARDS THAT MEASURED THE

ANCIENT WORLD-

A STORY OF REDISCOVERY

ROLAND A. BOUCHER

MS Yale 55, Retired

Sigma Xi Orange County Chapter

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REDISCOVERY

The Rediscovery of the Ancient Methods used to establish Standards of Length,

Volume and Weight

In the past 150 years many of these Standards have been studied and recorded

The studies showed their world wide use and developed ratios which linked a number of them

No Basis or Formula for their development was proposed

This Presentation will propose just such a Rule or Formula

It will prove beyond any reasonable doubt that such a formula did exist and provide examples

from throughout the Ancient World from Cornwall in the West to Okinawa in the East

THE PENDULUM AND THREE STANDARDS THAT MEASURED THE ANCIENT WORLD

Ancient Civilizations kept accurate records of the motion of the sun, the stars, and the planets in the sky- and probably used a pendulum to divide time (degrees) into 60 parts

Two types of numbers or values which all civilizations could agree upon: Length of the day from noon to noon or from midnight to midnight Number of days in the calendar, solar, or celestial year.

I propose that each civilization used the length of a pendulum to develop their standards of length and that these pendulums were adjusted to swing anumber of periods equal to the number of days in a year during the time ittook the sun (stars) to move that same fraction of a day.

For example:Sumerian calendar had a a year of 360 days- Their Standard Pendulum swung 1/3 of 360 complete swings during a period of 1/360 of a solar day

NOTE: A strict application of the rule would have resulted in a very short pendulum, by increasing the period it was much easier to obtain an accurate result

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SUMMARY of FINDINGS

All three Standards were developed through use of a Pendulum

The first was nearly identical to the original Metric System proposed in 1723

The second and third were logical variations of the first

All pendulums were timed from astronomical observation

Each could be reproduced with an accuracy of one mm or better

Some were developed to be related to the polar circumference of the Earth

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The Original French Proposal 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)

Its obvious that the standards of measurement in the original Metric System were invented over 5000 years earlier in Ancient Sumeria

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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 Length of this Mesopotamian Standard can be Accurately Reproduced

The sumerian year had 360 days with 5 off for celebrationTheir 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 limitedAll 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 wellThe 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 day by 365.25Timing a pendulum 1/366 day with Venus in opposition divides the day by 365.25

This longer period results in a cable length of more nearly equal to 1/360 of a degree

The Sumerian system was great but everything can be made better

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

The length of the Egyptian djser (foot) was = 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

The Measurement Standards of Ancient Egypt circa 3000 BCE

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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 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

The length of a Minoan Foot was 303.6/1000 meters= 303.6 mm Standard of volume # 1 “Amphora“ (Bushel) = Volume of one cubic foot = 27.984 liters Standard of volume # 2 “Pint” = 1/64 “Bushel” = 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 = weight of a “Pint” of rain water = 437.2 grams Standard of distance ? The Stadia of 600 feet = 182.16 meters

Ten of these Minoan stadia was equal to 1821.60 meters or 1.653 percent less than the Geodetic Nautical Mile. and did not require the creation of an auxiliary standard like the Reman

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Looking to Venus -- The Minoan Standards of Length

These three primary standards spread across the known world

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 was established as one Minoan Cubic Foot (27.983 liters)1/64 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)

If the original Sumerian pendulum had been timed through 360 beats instead of 240 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 lengths it became the Doric Foot (322 mm) in Greece. With a cable of 366 lengths it became the Luwain pous (323 mm) in Anatolia.

The British Furlong, Foot, and 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 or (304.8 mm) and the British Statute Mile to be exactly 8 Furlongs or 5280 feet..

The Curious Case of the Chinese Market Foot and the British Furlong

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The Egyptians had aligned the Great Pyramid to the North Star within 1/30 degree therefore they could have calculated the Polar Circumference of the Earth with an error of 0.1 percent.

The Minoan, foot, stadia, and nautical mile were about 1.67 percent too short. A simple correction in the ratio of of (366/360) was introduced to remove this error.

The length of 100 of these new “Attic” feet was 30.861 meters

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 Standard Was Almost a Perfect Fit to the Polar Circumference of the Earth

The French who proposed the meter 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 water.

The Final Solution, The Attic Foot

The Greek “Attic” Stadia was Adopted by the Roman Empire as a 625 Foot Roman Stadia

The Roman Stadia of 625 new Roman feet = 185.166 metersThe new Roman foot = 296.266 mm.The new Roman mile of 5000 Roman feet = 1481.330 meters.27,000 new Roman miles was 12 km short of the the Polar Circumference of the Earth.

Note: The Romans use of the ratio of 24/25 in developing their new foot would lead to other cultures throughout Europe adopting this ratio to other standard feet as well. The resulting confusion and profusion of European Standards provided a strong impetus for reform.

The Roman Empire and 24/25 of the Near Perfect Solution

3000 BCE Sumeria uses a pendulum to develop a sexagesimal version of the Metric system Sumeria develops the foot as decimal division of the 360 meter cable This standard can be found as far away as China and France

3000 BCE Egypt develops similar system dividing the celestial day by 366 Egypt develops the Reman, Cubit, and Royal Cubit based on its 16 digit Foot This standard is carried by Phoenician traders throughout the Mediterranean

2500 BCE The Minoans develop a similar system using Venus to time their pendulum These standards establish the early English pint and Winchester bushel These standards establish the Trojan and English Mercantile Pounds These standards spread from Cornwall England to Okinawa Japan

500 ?BCE The Greeks Attic foot lengthens the Minoan foot by the ratio 366/360 This establishes the Polar Circumference of the earth at 216,000 attic stadia 300? BCE Rome adopted the Greek Stadia of 600 feet as Roman stadia of 625 Roman feet This establishes the Polar Circumference of the earth at 27,000 Roman mile

Note: There is some evidence that both the Minoan and Attic standards may have reached the new world

Chronology

CONCLUSION

Ancient Standards were based on a Pendulum

All were accurate to fractions of a mm

Each could be reproduced over great distances

The Attic foot was 366/360 Minoan feetIt divided the Polar Circumference of the earth into 216,000 Stadia

The Roman Foot was 24/25 Attic feet

CONCLUSION

The Magna Carta of 1215 immortalized the Minoan foot and its bushel, pint and pound.

This bushel also established the Troy Pound which is still in use today

Appendix 1

The Lost Winchester BushelAnd 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 Boucher11 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 to time 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 pendulumThis 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 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 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 Boucher11 Deerspring Irvine, CA 92604 email rolandfly@sbcglobal.net

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Roland A Boucher 11 Deerspring Irvine, California 92604 rolandfly@sbcglobal.net