Science Tech

Mapping: In Praise of the Triangle

"At the heart of the survey was the calculation of distances and directions using the method of triangulation."
By Suvrat Kher


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Jerry Brotton in his book A History Of The World In 12 Maps writes about France’s National Map Project. Begun around the 1670s upon the establishment of the Academie de Sciences and the Paris Observatory, and headed by the astronomer Cassini I, it first attempted to create an accurate geodetic survey of France using the latest surveying instruments. At the heart of the survey was the calculation of distances and directions using the method of triangulation. Latitude was calculated using a quadrant that measured the altitude of celestial bodies. Then, using a measuring stick, a baseline of a known length was established. A third point on the landscape was sighted. The angles between the three control points were measured. Using trigonometric tables the lengths of the remaining two sides of the triangle could be calculated.

I liked this passage:

“In 1744 the survey was finally completed. Its geometers had completed an extraordinary 800 principal triangles and nineteen base lines. Cassini III had always envisaged printing regional maps as they were produced, and by 1744 the map was published in eighteen sheets. Its new map of France, on an approximately small scale of 1:1,800,000, shows the country represented as a network of triangles, with virtually no expression of the land’s physical contours, and with large areas such as the Pyrenees, the Jura and the Alps left blank. It was a geometrical skeleton,a series of points,lines and triangles following coasts, valleys and plains in connecting key locations from which observations were carried out. Over it all lay the triangle, the new immutable symbol of rational, verifiable scientific method. On Cassini III’s map the triangle almost takes on its own physical reality, a sign of the triumph of the immutable laws of geometry and mathematics over the vast, messy chaos of the terrestrial world. The Babylonians and the Greeks had revered the circle, the Chinese celebrated the square, the French now showed that it was the application of the triangle that would ultimately conquer the earth.”

Cassini III was the grandson of Giovanni Domenico Cassini (Cassini I). The directorship of the Paris Observatory remained in the Cassini family over four generations.

This surveying method was quickly adopted and adapted by others. The Ordnance Survey began mapping the British Isles using this method in the late 1700’s.  William Lambton took the Ordnance Surveys acquired expertise and began the Great Trigonometrical Survey of India in the year 1800, a feat that took nearly 50 years to complete. John Keay’s book The Great Arc details that mammoth effort.


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The author, Suvrat Kher, is a Sedimentary Geologist and Science Writer. His work focuses on the geosciences, biological evolution and environmental issues.
This article was originally published on Suvrat’s personal blog, Rapid Uplift.

Tweet at Suvrat: @RapidUplift




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