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The Pendulum and the Foot in Ancient Metrology
The Pendulum and the Foot in Ancient Metrology
The Pendulum and the Foot in Ancient Metrology
The Pendulum and the Foot in Ancient Metrology
The Pendulum and the Foot in Ancient Metrology
The Pendulum and the Foot in Ancient Metrology
The Pendulum and the Foot in Ancient Metrology
The Pendulum and the Foot in Ancient Metrology
The Pendulum and the Foot in Ancient Metrology
The Pendulum and the Foot in Ancient Metrology
The Pendulum and the Foot in Ancient Metrology
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The Pendulum and the Foot in Ancient Metrology

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An analysis of ancient standards of measurement which will show that only five basic standards were used to measure the ancient world from the Middle East to China and Japan in the East to Britain in …

An analysis of ancient standards of measurement which will show that only five basic standards were used to measure the ancient world from the Middle East to China and Japan in the East to Britain in the West. New data may extend this range to the new world.

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  • 1. The Pendulum and the Foot in Ancient Metrology Roland A. Boucher MS Yale 55, Retired, Orange County CA Chapter Sigma Xi Only Five Standards of Length Were Needed to Measure the Ancient World• All standards could be reproduced with an accuracy of one mm or less• All standards were logical variations of the original one second pendulum• All pendulums were timed from astronomical observation• These five standards were used to measure most of the Ancient World• All standards were developed through use of a Pendulum• All standards were related to the polar circumference of the Earth Roland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
  • 2. The Metric System and the Measurement Standards of Sumeria in 3000 BCEThe original definition for the Meter was the length of a one second pendulum, measured in the Earths gravitational field at 45degrees North Latitude. Its length was 993.7 mm in today’s metric system.When studying the standards of measurement in Ancient Sumeria it became obvious that they had invented the metric systemover 5000 years before the French proposed it. The standard length, the double “Cubit” or “Step”, was 994 mm. Their standardvolume was a cube 1/10 Step on edge (a Sumerian liter). Their standard of weight was this same volume of rain water. For shortlengths they divided their “STEP” into 60 parts. Long distances were measured in “Cables” of 360 Sumerian Steps of 994 mmeach which was also divided into 1000 Sumerian feet. The “Step” was defined as the length of a one-second pendulum just as theFrench were later to propose.Details of the Sumerian Measurement Standards of LengthThe Sumerian Double Cubit = 994 mm ( length of pendulum which beat 240 times in 1/360 solar day).The Sumerian Cable = 360 double Cubits = 357.84 meters which also defined 1000 Sumerian feet.The Sumerian foot = 357.84 mm. This Sumerian foot spread across the know world from France to China.In ancient China circa 1100 BCE the Zhou Dynasty established that the Royal chi = 358.2 mm.In ancient France the town of Bordeaux established the Pied de Terre at 357.2 mmRoland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
  • 3. 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 A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
  • 4. The Cable and the Foot can be related to the Polar Circumference of the Earth The Earth According to WGS 84:The average minute of latitude (nautical mile) = 1852.216 meters.The average degree of latitude = 111.13296 km.The Polar Circumference of the Earth = 40,007.863 km = 21,602.518 US ? nautical miles. The kingdom of Sumeria was aligned with the Tigris and Euphrates rivers in a north-south orientation. The elevation of the stars in the heavens would not go unnoticed nor would the fact that this elevation changed by one degree for every 310 cable lengths that the observer moved in a north-south direction. 310 Cable lengths = 310,000 Sumerian feet = 110930.4 meters.The Division of the Earth’s Circumference into Minutes and SecondsThe Polar circumference of the Earth = 60 x360 = 21600 minutes (one Geodetic nautical mile).The Polar circumference of the Earth = 6000 x 21600 = 129,600,000 seconds (100 Geodetic Feet). Therefore we find that 360 Cables = 360,000 Sumerian feet = 128.8224 km or 1.15917 degrees of latitude and 360x360 cables = 1296 x105 Sumerian feet = 1.15917 times the Polar Circumference of the Earth. Also 100 Sumerian feet = 1.159 arc seconds of the Polar Circumference of the Earth.The Sumerian pendulum was timed by the motion of the Sun. When the Egyptians and others used the motion of stars or theplanet Venus to time their pendulums, they took this opportunity to select an alternate division of the day to produce a standardof length more closely aligned to the division of the polar circumference into degrees, minutes and later into seconds of arc.Roland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
  • 5. Looking to the Stars -- The Egyptian Standards of LengthThe Sun subtends an angle of nearly 1/2 degrees in the sky while the stars are mere pinpoints of light.Although the stars provide a more accurate reference with which to time a standards pendulum, they rotate through theheavens at a faster rate than the Sun, arriving nearly 4 minutes (one Gesh) earlier each night.Accordingly the Egyptians divided the day into 366 parts and timed their pendulum through 366 beats in this time.Details of Egyptian Measurement StandardsThe Egyptian pendulum length = 409.84 mm (The pendulum beat 366 times in 1/366 star day).The length of the Egyptian Cable = 366 x2 Pendulum lengths = 1000 Egyptian feet = 300 meters.The Egyptian foot = 300 mm. This standard Egyptian foot spread across the Mediterranean and was established as thePhoenician foot = 300 mm; Fuss of the Canton of Aargau = 300 mm; Reichsfuss of Baden in Germany = 300 mm.Additional Egyptian Standards of LengthThe length of the Reman = 375 mm ( 20 Digits of 18.75 mm each or 20/16 of an Egyptian foot).The length of the Standard Cubit = 450 mm (24 Digits of 18.75 mm each or 24/16 of an Egyptian foot).The length of the Royal Cubit = 525* mm (28 Digits of 18.75 mm each or 28/16 of an Egyptian foot)(*28.28 Digits).The New Standards are a Much Better Fit to the Polar Circumference of the EarthOne Egyptian mile = 5000 Reman = 1875 meters = 1.0123 arc minutes on the Polar Circumference of the Earth.21,600 Egyptian miles = 40,500 km, just 1.23 percent larger than the Polar Circumference of the Earth.100 Egyptian feet = 30 meters or 0.97213 arc-seconds on the Polar Circumference of the Earth. Roland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
  • 6. Looking to Venus -- The Minoan Standards of LengthThe Planet Venus is closer to the Sun than the Earth and orbits it in 244 days. By viewing Venus when it is in opposition itsmotion cancels out some of the apparent motion caused by spinning Earth. The result is a division of the day which is close to1/365.25 day when timed through 1/366 of the Earth’s circumference thus adding approximately one second to the periodwhich would have been provided by a star as a reference.Details of Minoan Measurement StandardsThe Minoan Pendulum length = 414.75 mm ( pendulum which beat 366 times in 1/366 Venus day).The length of the Minoan Cable = 366 x 2 pendulum lengths = 1000 Minoan feet = 303.6 meters.The Minoan foot = 303.6 mm This standard Minoan foot spread to both Europe and Japan. It was established as theJapanese Shaku = 303.0 mm; Stadtschuh = 304.0 mm in the Canton of Basel ; Fuss = 303.0 mm in Linz Austria.This New standard was a Better Fit Without the Need to Introduce an Auxiliary LengthTherefore we find that 360 Cables = 360,000 Minoan feet = 109.296 km or 0.98347 degrees of latitude,and 360x360 cables = 1296 x105 Minoan feet = 0.98347 times the Polar Circumference of the Earth.Also 100 Minoan feet = 0.98347 arc seconds of the Polar Circumference of the Earth.One Minoan mile of 6000 feet = 1821.60 meters or 30.6 meters short of the Geodetic Nautical Mile.This is an error of only 1.653 percent short of the actual value and was achieved almost 4000 year ago. Roland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
  • 7. Looking to Venus and the 360 degree circle -- The Final SolutionThe final solution came about by combining the time period of the Minoan Venus timing method with a return to the originalSumerian 360 beats. The new cable was made up of 360 x 2 pendulum lengths. We shall call this new standard the ‘Greek“Attic” foot.Details of Greek “Attic” Measurement StandardThe Greek “Attic” Pendulum length = 428.61 mm (Pendulum which beat 360 times in 1/366 Venus day).The length of the Attic Cable = 360 x 2 Pendulum lengths = 1000 Attic feet = 308.6 meters.The Greek Attic foot = 308.6 mm.The most outstanding example of this standard is found in the 100 foot width of the Parthenon in Athens Greece.This cable is essentially 1/6 of a nautical mile with the length of 360 cables equal to one degree in latitude.The Greeks created the Stadia of 600 Attic feet making the length of 600 Stadia equal to one degree in latitude.The New Standards Were Almost Perfect Fits to the Polar Circumference of the Earth100 Greek Attic feet = 30.86 meters = 0.999667 arc seconds of the Polar Circumference of the Earth.1 Stadia = 600 Attic feet = 185.160 meters = 0.099967 arc minutes in the Polar Circumference of the Earth.600 Stadia = 36x105 feet = 111.096 km = 0.999667 degrees in the Polar Circumference of the Earth.Note: The WGS 84 gives the length of one average second of arc at 30.87027 meters. The 100 foot wide Parthenon was measured at 30.897 meters. an error of 2.67 cm. Roland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
  • 8. The Roman Empire and the Spread of 24/25 of the Near Perfect SolutionThe Greek “Attic” Stadia was Adopted by the Roman Empire as a 625 Foot Roman StadiaThe Greek Attic Stadia = 185.16 meters = Roman Stadia = 625 new Roman feet.The Roman foot = 24/25 Greek attic feet = 296.2 mm.The Roman mile = 5000 feet = 1481.280 meters.75 Roman miles = 375000 feet = 111.096 km = 0.999667 degrees in the Polar Circumference of the Earth.360x75 roman miles = 39,994.56 km = 0.999667 times the the Polar Circumference of the Earth. Roman Navigators could determine their position with an error of only 3.3 km when calculating their latitude.Note: The use of 625 feet in the Roman Stadia would later lead to an Anglo-Saxon Furlong of 625 Doric feet which wouldthen be defined as consisting of 600 Anglo-Saxon feet. Roland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
  • 9. The Curious Case of the Chinese Market Foot and the British FurlongIf the original Sumerian pendulum had been timed through 360 beats instead of 240, or if the Greek Attic pendulum had beentimed using the Sun rather than the planet Venus, a pendulum length of 441.8 mm and a cable length of 318.08 meters wouldresult.The Chinese Market FootThis pendulum length, which may not be related to the Earth’s circumference, appears to have been used to created the ChineseMarket Foot or Shin Ch’ih (318 mm) which was adopted by the Zhou Dynasty in China. It also became the standard foot in thecities 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 MileIt appears that the Doric Foot may have taken a curious part in the development of the modern British Foot. The length of theFurlong (201.2 meters), an early Anglo-Saxon land measurement, is 625 Doric feet. This Furlong became the standard for landmeasurement in early England. In 1592 Queen Elizabeth the First created the British Statute Mile while maintaining the exactlength of the Furlong. She declared the new British Foot to be 1/660 of a Furlong (304.8 mm) and the British Mile to be 8Furlongs or 5280 feet. Later the British Admiralty would declare the Admiralty Mile (nautical mile) to be 6080 British feet. Roland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
  • 10. In Conclusion These Five Standards of Length Were Used to Measure the Ancient World• All Standards were developed through use of a Pendulum• All Standards could be reproduced with an accuracy of one mm or less• All Standards were logical variations of the original one second pendulum• All Pendulums were timed from astronomical observation• These five Standards were used to measure most of the Ancient world• All Standards were related to the polar circumference of the Earth• The final Standard measured the polar circumference of the Earth to 0.033% Note: There is evidence that the both the Minoan and Greek standards may have reached the new world. Roland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
  • 11. References1 Robson, E 2008. Mathematics in Ancient Iraq, Princeton University Press 2008 Table A.3, 2942 Margenau, Watson & Montgomery. Physics Principles and Applications, New York McGraw-Hill 1949. 178-1803 Bronwell, A. Advanced Mathematics in Physics and Engineering, New York McGraw-Hill 1953. 137-1394 Janhke E, & Emde F. Table of Functions, New York Dover Publications Fourth Edition 1945 Table V. Complete elliptical integrals 855 WGS 84 Gravity of Earth http://en.wikipedia.org/wiki/Gravity_of_Earth6 Earth according to WGS 84 http://home.online.no/~sigurdhu/Grid_1deg.htm7 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. 20079 Petrie, Sir W.M.F. Inductive Metrology London,H. Saunders, 1877 section 21- 3910 Graham, J. W. The Palaces of Crete Princeton University Press 1962. 22411 United Nations. Department of Economic and Social Affairs. World Weights and Measures Handbook of statistics series M 21 English Rev 1 6212 Knight C. & Butler A., Civilization One, Watkins Publishing London 2004. 18,3013 Kollerstrom, N. Greek Foot The Acropolis Width and Ancient Geodesy http://www.dioi.org/kn/stade.pdf) 200514 P. Guilhiermoz Bibliothèque de lécole des chartes De léquivalence des anciennes mesures. A propos dune publication récente Volume 74 27815 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. 10116 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 Roland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net

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