Useful Measurements by Edwin Danson, C & C Technologies
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Surveying technical Useful measurements by Edwin Danson, C & C Technologies This article explores briefly La Caillé’s meridian arc and explains the strange distorting anomaly that suggested a prolate form for the Earth in the southern hemisphere, and concludes with the scientific works of Mason and Dixon in South Africa. he scientific quest to discover Caillé, travelled to Cape Town on a the son of a destitute member of the size and shape of the Earth mission to observe navigation stars, the household of the duchess of Tcan be dated to the intellectual lunar motion and to replicate, in the Vendôme. Through the patronage of studies of Sir Isaac Newton, published southern hemisphere, the meridian the duke of Bourbon, La Caillé studied in Philosophiæ Naturalis Principia arc work that his colleagues had theology at the Collège de Lisieux Mathematica, and the first modern achieved in the north. in Paris. Despite a Jesuit education, meridian arc measured by Jean in the Age of Enlightenment it was Ten years later, two Englishmen, one practical philosophy (science), Picard in 16691. In the following astronomer and one land surveyor, particularly mathematics and seventy years, various measuring landed in Cape Town to observe the astronomy, which attracted the campaigns were undertaken by the Transit of Venus of 1761 and to add young La Caillé. In 1738, he joined French Académie Royale de Science, more stellar positions for the Nautical the French coast survey and the culminating in the two most ambitious Almanac. These two were Charles following year he was engaged to and extraordinary meridian arcs of assist in the re-measurement of the Mason and Jeremiah Dixon whose Lapland (1736) and Peru (1735 to French meridian arc. Elected the fame lives on in the Mason-Dixon 1743). These two latter effectively set Académie Royale des Sciences, he Line. the shape of the Earth as an oblate progressed swiftly becoming professor spheroid; however, all observations A gravitational discordance of mathematics at the Collège to date had been in the Northern Mazarin (now L’Institut de France), Hemisphere. In 1751, the French Nicolas Louis de La Caillé (1713-1762) Paris, where he built an astronomical academician Nicolas Louis de La was born at Rumigny, near Rheims, observatory. Organisation Principle Year Work Method Conclusion Académie Royale de Jean Picard Meridian arc – Paris Spherical 1669 Triangulation Science (1620-1682) to Amiens (oblate) Principia: oblate Intellect 1669 shape of the Sir Isaac Newton and Picard’s Oblate (published 1684) Earth, attraction of measurements mountains Gravity Académie Royale de Jean Picard & Jean Astronomical 1672 observations, Oblate Science Richter regulator, quadrants Cayenne Charles-Nicolas Gravity Académie Royale de Astronomical Varin and Louis des 1681 observations Gorée, Oblate Science regulator, quadrants Hayes Senegal Quadrants, Meridian arc Académie Royale de Jean-Dominique triangulation, 1683 Dunkerque to Prolate Sciences Cassini astronomical Perpignon regulator Pierre Louis Moreau Quadrants, Académie Royale de de Maupertuis 1736 Lapland arc triangulation, zenith Oblate Science (1698-1759) sector Charles-Marie de la Quadrants, Académie Royale de Condamine & Pierre 1735-43 Peru arc triangulation, zenith Oblate Sciences Bouguer sector Table 1: Earth measurements for size and form 1669-1743 1 Eratosthenes of Cyrene measured a size of the Earth in C5th BC, Snellius and others explicated his methods to measure a size; none were "scientific" in the sense of that of the Enlightenist movement. PositionIT – March 2010 23 SURVEYING technical La Caillé and other academicians had for some years lobbied the council of the Académie to sponsor an expedition to South Africa to observe the positions of southern "navigational stars" for the académie’s catalogue and to determine the solar parallax with simultaneous observations in Paris and Berlin. La Caillé was awarded the task. His remit was to make stellar, solar observations and lunar observations, the latter for the lunar distance method for finding longitude. The site for the observations was to be the Dutch colony at Cape Town where, additionally, La Caillé would determine the precise latitude and longitude relative to the meridian of the Paris Observatory. In this exercise, the observations, using the occultation of Jupiter’s moons, were to coincide with similar observations by Jérôme Lalande (1732-1807) at the observatory in Berlin. It was for all these purposes, Fig. 1: Nicolas Louis de La Caillé (1713-1762). (Public domain.) and not for measuring a meridian arc, that La Caillé was given charge of the expedition: the Earth measuring would have to fit in with the astronomy. La Caillé set off for the Cape of Good Hope in 1750. On arrival at Cape Town, La Caillé’s first task was to ingratiate himself with Hans Tulbagh, the Dutch governor of the province. With Tulbagh’s assistance, La Caillé built a wooden astronomical observatory on Cape Town’s Strand Straat and began his long program of observations. In August 1752, toward the end of his second southern winter, he took some time out from astronomy to travel north on a field trip to scout the country and locate the sites for his meridian arc observations. At Klipfontein, in a barren valley among the mountains north of Piquetberg, he chose a farm that he judged to be at an adequate distance from the observatory in Cape Town; this would be his northernmost point providing a distance from Cape Town Fig. 2: Left – La Caillé’s triangulation scheme Right: La Caillé’s sextant (Paris Observatory). of about 1,5 degrees of latitude. An 8-mile-long baseline was measured across the Darling Flats, about 40 miles Cape Town to the farm at Klipfontein. he could see south to Cape Town and due north of Cape Town, using 4 toise His scheme was, by the standards of north to Klipfontein, about 38 miles (approximately 25 feet, 7,6 m) wooden meridian arcs, a simple one. From the distant. rods supported on stands. By early terminals of the baseline, he observed spring 1753, La Caillé was ready to the angles to Kapokberg and Riebeek Using a large iron quadrant, La Caillé start measuring the angles in the chain Casteel, high upon the mountains to determined the latitude on Strand of triangles linking his observatory in the east. From Kapokberg and Riebeek, Straat and at Klipfontein. When he 24 PositionIT – March 2010 SURVEYING technical calculated the meridian distance between the two extremes of the triangulation scheme he received a nasty shock. According to his colleague Pierre Bouguer’s figure of the Earth, at the latitude of the Cape the distance of 1 degree of latitude should have been 57 037 toises. Instead, La Caillé found from his calculations that his distance was 430 pieds (131 m) short. Every observation and every calculation was rechecked but there was no mistake, the distance was definitely short of what it was supposed to be. It was from these diligent observations and scrupulous mathematics that La Caillé was forced to conclude that the Earth in the southern hemisphere, at least at the latitude of the Cape, had the form of a prolate spheroid; according to him, the Earth was pear-shaped. The Earth measuring apart, La Caillé’s time in Cape Town was extremely fruitful. He had observed nearly 10 000 new stars, named fourteen new constellations, made some valuable observations of the lunar motion and had determined the latitude of the Cape. He was the most prolific astronomer of all time. A natural recluse, his fame on returning the Paris in 1756 was too much and he withdrew into the sanctuary of his Mazarin college. The excessive work and long nights brought on an attack of gout – he died on 21 March 1762. He was just 49 years old. Jérôme Lalande wrote of him that, in the short time allotted to him, "He had made more observations and calculations than all the astronomers of his time put together." Nicolas de La Caillé died never knowing that his observations and calculations for the Cape meridian arc were in fact flawless. The reasons for the unwelcome discovery that the Earth looked like a pear were soon to be uncovered. In 1792, the results of Reuben Burrow’s meridian and latitude arcs in Bengal were published posthumously by his lifelong friend, Isaac Dalby2. Although observed in the northern hemisphere, the conclusion by Dalby was "it seems extremely probable, that the meridians are not elliptical in low latitudes; but that the Earth (as M. Bouguer supposed) is flatter in a north and south direction… And were we certain how far M. de la Caille’s degree at the Cape of Good Hope is erroneous… it might serve to show if the variation from an ellipsoid is greater, or extends farther on the south side of the equator, than on the north." In 1798, Ordnance Survey Director General William Mudge determined the length of a degree of longitude in southern England between Dunnose Point and Beachy Head, Sussex. The longitude between the two points, when computed, exhibited a similar anomaly as that observed in South Africa. Mudge’s conclusion was that "the attraction of mountains" or, as there were no mountains in southern England, local subterranean causes were to blame that "may perhaps affect the direction of gravity". Mudge could make the claim because, in 1774, Astronomer Royal Nevil Maskelyne had proven that the gravitational effect of mountains affected the direction of the vertical. In the twenty years after the Schiehallion experiment, evidence was 2 Mathematician to William Roy and for the embryonic Ordnance Survey. PositionIT – March 2010 25 SURVEYING technical building to suggest that it wasn’t just mountains that affected the plumb bob; "The figure of the Earth is not a solid formed by the revolution of an ellipse on its axis; and the agreement or disagreement of the measures of degrees with one another, is not to be judged of by their agreement or disagreement with this hypothesis.