Abstract. The Ancient search for a Universal Standard of length

Transcription

1 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.

2 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

3 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 ( 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.

4 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 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 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 rolandfly@sbcglobal.net

5 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 This longer period results in a cable length of very nearly 1/360 of a degree

6 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 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

7 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/ Celestial day one half the length of this pendulum was cm The length of a minoan cable was 366 x cm = meters Standard of length = Foot = 1/1000 Minoan Cable lengths ( mm) Standard of volume # 1 = Bushel = Volume of one cubic foot ( 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 ( 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 ( meters) Ten Minoan stadia of 6000 minoan feet = meters was 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 rolandfly@sbcgl

8 These three primary standards spread across the known world in Ancient times The Sumerian foot of mm The Zhou Dynasty in China circa 1100 BCE established that the Royal chi = mm. The town of Bordeaux in France established the Pied de Terre at mm The Egyptian foot of 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 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 ( 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)

9 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 mm and a foot of 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..

10 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/ Celestial day One half the length of this pendulum was cm The length of a Greek Cable = 360 x cm = 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 meters. The Parthenon in Athens Greece was measured at meters. an error of 2.67 cm. 100 Attic feet = meter s = arc seconds on Polar Circumference of the Earth. 10 Stadia = 6000 Attic feet = meters = 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

11 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 = meters = Roman Stadia = 625 new Roman feet. The Roman foot became 24/25 of a Greek attic foot = mm. The Roman mile became 5000 Roman feet = meters. 75 Roman miles became degrees on the Polar Circumference of the Earth. 27,000 Roman miles = 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

12 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 i rolandfly@sbcglobal.net