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A History of Measurement
2007-10-11

A History of Measurement Under the Roman Empire, Rome became the center of the western world. All roads led to Rome and all distances were measured from Rome. The distances were based upon one-thousand Roman paces of the Roman soldier. A Roman pace is equal to two of our steps and very near 64 inches. The Latin for thousand is mille from which we derived the word mile. Each Roman road had occasional small oblisk statues placed to indicate the distance from Rome much as Mexico today does from Mexico City. Hence, statute miles.

The first paths for ships were called Porotan Charts. These were lines drawn across the Mediterranean between the coastal ports. Where many of these lines crossed the map makers would draw wind roses. The wind rose initially varied but settled on the eight points. The predecessor to the compass rose and our eight wind direction terms.

Thales of Miletus (640-546 BC) made a projection (use of shadows) of the region where he lived. Hipparchus in the 2nd century B.C had used sterographic (showing heights) and orthographic projections (perspective). Eratosthenes in 3rd century B.C. calculated the size of the earth circumference to be 24,000 miles. He developed a 16 point wind rose and use of `degree". He also wrote a description of the known world.

Ptolemy, a 2nd century Greek, made a world map and made a world size error when he calculated size of world's circumference to be only 18,000 miles. Eratosthenes' calculations had been lost to the western world with the destruction of the libraries of Egypt. Copies of scrolls from Eratosthenes were discoverd in Constantinople by Polish researchers but it was over a hundred years before application was applied to nautical navigation. This corrected size of the world was drawn on navigational charts in 1669 by Jean Picard.

Ptolemy used the first conic projection plane map with the top as north. This made possible drawing of rhumb (one direction) lines from point to point on the globe. He devised the 60 minute and 60 second divisions of the 360 degrees in a circle. A mile at sea, on this world of Ptolemy, was essentially equal to a mile on the land. The length of a statute mile was 1000 (mille, from the Latin) Roman paces. A Roman pace is two of our steps.

A 1466 Chart of Nicolaus Germanus divided the degree into 60 equal spaces called miles. This was based upon an earth of 18,000 mile circumference and gave us a nautical mile the same length as a Roman statute mile. Other cartographers including Hipparchus and Mercator gave us a world with an overlying grid with numerical markings of longitude and latitude. Gerardus Mercator (Gerhard Kremer), Flemish, in 1569 drew world globe map with 180 degrees E/W longitude 0 to 90 N/S latitude. He made errors which were corrected by Edward Wright who published the computations required as "Meridional Parts" and made this knowledge universal. In combination, we now had a world which could be mapped in degrees of longitude and latitude. Each degree of longitude had divisions of 60 miles equal to a statute mile and each mile was again divided into 60 units called minutes and each minute was again divided into 60 units called seconds.

This was the kind of map and scale used by Columbus. The navigators of his time had not the timing device to make possible the exact determination of longitude. The best 15th Century data available to Columbus came from Ptolemy. The error by Ptolemy directly resulted in Columbus' declaring that he had reached and was exploring India. Columbus thought he had sailed through enough degrees of longitude to have reached India. He may well have, had the world been 18,000 statute miles in circumference.

When the world was computed to be 24,000 statute miles in circumference all the degrees and their divisions were longer and did not conform. More accurate computation of the world's circumference kept changing and finally came to 24,902 statute miles. The circumference of the earth has always been measured as 21,600 nautical miles (360 degrees X 60 nautical miles per degree). However, the individual nautical mile has ballooned by nearly a third through this recalculation of the earth's size. For many of the same reasons the U. S. has failed to convert to metric, later cartographers decided to use statute miles for land and the expanded nautical mile at sea.

Now we can see the background for the difference between nautical and statute miles and Columbus' reasoning. We have Columbus sailing around an earth at least 1/3 larger than he was led to believe. Based on available knowledge Columbus was quite justified to assume that he had actually reached and explored India.

For the navigator, it is very important that distance only be measured along the lines of longitude which has evenly spaced tick arks throughout. The elongated orange peel appearance of the region between lines of longitude means that various latitude lines will have tick marks at differing intervals although always 60 ticks per degree. Only at the Equator do the tick marks correspond to the size of those along the lines of longitude.

Johann Henrich Lambert from Alsace devised the lambert conformal conic projection in which the line you draw is the way you go. This is the charting used on aircraft. As with any flat map of a round surface it has areas of inaccuracy which increase in one direction or another. Errors exist along the top, bottom, and center parts of such a map.

A sphere cut by a plane always makes a circle. The sectional chart used in flying is drawn from such a plane. The globe for a specific chart area is given a cone for a hat. Then a plane is cut through the cone and the globe at right angles to the vertical axis of the cone. The lines of latitude and longitude are projected onto the plane as are the lines making the map. Sectionals are most inaccurate (stretched) in the six inches at the top and bottom. The center ten inches of the sectional for 5 inches up to five inches down from center is somewhat contracted in size.

Its About Time... The next major step in aviation measurement came from the Greeks about 2500 years ago. The Greeks sought rules for the way number-ideas seemed to work. They applied a reasoning process to build on known facts to reach a conclusion. They knew it as deduction. Some flyers call it, albeit incorrectly, the origin of the term Dead Reckoning. Actually it is a deductive system of navigation. The first ship's time was kept with sand glass and the speed was determined by counting oar strokes during a sand glass sequence. Distance over water could be deduced by the number of strokes in a given time period.

A sailing ship's speed over a nautical a mile was, historically, measured by means of a knotted (knots) rope tied to a log. A sand filled timing glass would be used to measure the time from leaving the log dead (much as a dead man might appear) in the water (dead reckoning) and the number of evenly spaced knots passed along the rope. All of this would be recorded in the logbook.

I contend that dead reckoning is a not a corruption of deduced reckoning, the term derived from the navigational practice of starting from a point (Buoy) that was dead in the water. From this point the direction and time would be used to deduce location along the route as it crossed longitudinal lines.

Since the chronometer was yet to be invented, sailors had no way to determine longitude except by this dead reckoning. Within crude limits, speed and compass indications could be used to determine estimated distance and estimated longitude. Magellan in 1519 had access to charts, globe, theodolites, quadrants, compasses, magnetic needles, hour glasses, and timepieces. He was unable to determine exact longitude.

By the 18th Century a chronometer (first weighed over 36 pounds) was used to get longitude. A chronometer differs from a clock or watch because it has a temperature adjustment for greater accuracy. Captain Cook in 1768 had three such clocks for his voyage. In 1779 he sailed with 4 chronometers and a nautical almanac which enabled him to determine longitude. The very first effort to make a calculator was financed by the British to make the making of the nautical almanac easier. The original design was completed in 1991 and found to work accurately. Interesting to speculate where the world would be had it been completed in the 1700s.

This ability was treated as a military secret by England to the extent that Mr. Harrison was a very old man before his family was rewarded by the English government. This single invention enabled England to become the master of the world seas for several hundred years. Knowledge is power. If you have not yet read a small pocketbook "Longitude", you should.

Written by Gene Whitt

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