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
The Metric System and the Measurement Standards of Sumeria in 3000 BCE The original definition for the Meter was the length of a one second pendulum, measured in the Earths gravitational field at 45 degrees 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 system over 5000 years before the French proposed it. The standard length, the double “Cubit” or “Step”, was 994 mm. Their standard volume was a cube 1/10 Step on edge (a Sumerian liter). Their standard of weight was this same volume of rain water. For short lengths they divided their “STEP” into 60 parts. Long distances were measured in “Cables” of 360 Sumerian Steps of 994 mm each which was also divided into 1000 Sumerian feet. The “Step” was defined as the length of a one-second pendulum just as the French were later to propose. Details of the Sumerian Measurement Standards of Length The 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 mm Roland A Boucher A member of the Orange County Ca Chapter of Sigma Xi email rolandfly@sbcglobal.net
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
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 Seconds The 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 x10 5 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 the planet Venus to time their pendulums, they took this opportunity to select an alternate division of the day to produce a standard of 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
Looking to the Stars -- The Egyptian Standards of Length The 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 the heavens 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 Standards The 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 the Phoenician foot = 300 mm; Fuss of the Canton of Aargau = 300 mm; Reichsfuss of Baden in Germany = 300 mm. Additional Egyptian Standards of Length The 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 Earth One 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
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. The result is a division of the day which is close to 1/365.25 day when timed through 1/366 of the Earth’s circumference thus adding approximately one second to the period which would have been provided by a star as a reference. Details of Minoan Measurement Standards The 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 the Japanese 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 Length Therefore we find that 360 Cables = 360,000 Minoan feet = 109.296 km or 0.98347 degrees of latitude, and 360x360 cables = 1296 x10 5 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
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