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Home , Jean Picard, Jeremiah Dixon, Pierre Bouguer

Surveying technical Useful measurements by Edwin Danson, C & C Technologies

This article explores briefly La Caillé’s and explains the strange distorting anomaly that suggested a prolate form for the 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 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 , 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 . 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 , which attracted the campaigns were undertaken by the 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 ), 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 (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.

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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 . The site for the observations was to be the Dutch colony at Cape Town where, additionally, La Caillé would determine the precise and longitude relative to the meridian of the . In this exercise, the observations, using the occultation of Jupiter’s , 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 (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

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calculated the meridian distance between the two extremes of the triangulation scheme he received a nasty shock. According to his colleague Pierre Bouguer’s , 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 ; 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 , than on the north."

In 1798, Ordnance Survey Director General William Mudge determined the length of a degree of longitude in southern 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 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.

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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. To attempt to judge of them in that manner, may be offering violence to nature, and may be only trying to reconcile her phenomena with out conjectural or arbitrary theories."

In 1802, Mudge measured a long meridian arc by triangulation from Dunnose Point on the Isle of Wight to Clifton, . The results were disturbing: whereas the lengths Fig. 3: Cape Town, ca. 1759. of the degrees should have been getting longer towards the north, they appeared to be getting shorter. "These inconstancies," wrote Mudge, "are very striking when it is considered that, on the supposition of the Earth being compressed at the poles, the degrees of the meridian must go on increasing at a uniform rate, each degree exceeding that immediately to the south of it by about twenty fathoms..." Mudge was certain that it was gravity anomalies, and not a prolate Earth, causing the plumb-line to be "drawn towards the south at all the stations, and that by attractive forces".

The effects that caused La Caillé’s anomaly in South Africa were finally resolved in 1820 when George Everest (1790-1866) on recuperation leave from India, inspected the Cape region Fig. 4: Cape Town 1760 (J de Groot). on the recommendation of his superior, George Lambton. Everest concluded (1733-1779), a land surveyor from that the problem was the attraction following year. The primary objective County Durham. For St Helena, the of mountains or, as he put it, "a was to determine the solar parallax and observer was to be the Reverend Nevil gravitational discordance” caused by astronomical distances. The secondary Maskelyne (1732-1811). the considerable mass of Piquetberg objectives for the observers were and Table Mountain. In the event, to make stellar observations for the In stark contrast to these days of the arc was totally re-measured in nautical almanac, observe the motions suspicion and nationalistic aspirations, the 1840s by Sir Thomas MacLear, of the and to determine precise where the crowns of France and HM astronomer at the Cape. MacLear latitudes and . England were enjoying the Seven Years confirmed Everest’s hypothesis when The distant locations selected by the War, when their "armies and navies he discovered a deflection in the ferociously fought one another", the society for the observations were to vertical of some eight seconds of Royal Society and Académie Royale include Fort Nelson, Hudson's Bay, arc caused by the attractions of the des Sciences continued their close and Madras, Newfoundland, St Helena and Cape’s mountainous terrain. There friendly relationship. It is therefore Bencoolen, Sumatra. It was to be an was, after all, no error in old La Caillé’s unfortunate that Mason and Dixon had international effort, with astronomers measurements. hardly begun their long sea voyage on from across Europe and Asia taking HMS Seahorse to Sumatra when they The Transit of Venus part. were attacked by the French frigate In 1760, the Royal Society of The observer selected for Bencoolen L’Grand. Forced to return to Plymouth decided to send out teams to observe was the Greenwich Observatory for repairs and further delayed by bad the Transit of Venus across the face of assistant, (1728-1786) weather, Dixon wrote to the Royal the predicted to occur in June the assisted by Jeremiah Dixon Society suggesting they diverted to

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Mason and Dixon either took with them three nights observing the passage of a portable observing house or had one Procyon, Regulus, Castor and Pollux fabricated. The structure was circular, across the meridian that the regulator 6,5 feet across and the walls 5,5 feet was losing of 1 sidereal second a day. high. Above this was a movable conical The equipment set up, adjusted and roof of boards with an opening of 3 feet calibrated, Mason and Dixon were all covered by a flap. While the building set to make the important observations was being erected, a temporary of the Transit of Venus. On 18 June place (perhaps in Widow Xieman’s they had a practice run, observing house) was chosen for housing the an eclipse of the moon. The day of all-important astronomical regulator. the Transit, 5 June, the sun rose in The regulator, made by the London a thick haze and their spirits fell. firm of Ellicott, served two functions: As the haze cleared so a dark cloud first, it provided a sidereal time signal intervened. Eventually, they got their and second, because the length of the first sighting of Venus as it passed in was fixed at Greenwich, any front of the Sun’s disk. There were a few more heart-stopping moments variations in the strength of gravity but all was well and they were able to would affect the rate of the . This measure the angular distance between latter was the means by which gravity the Sun's northern limb and Venus's was measured in the latter years of the southern limb. In all, they successfully Fig. 5: John Bird’s quadrant (Science Museum, eighteenth century. London). made eighteen measurements and The observatory complete, the determined the apparent diameters of regulator was moved into the building the Sun and Venus; the Sun 31' 33,3", and strapped firmly to a stout timber the Levant or Black Sea because it was Venus 59,6". They also were successful post. Then the optical instruments were in timing the internal and external now impossible to reach Bencoolen installed. These included a quadrant of contact of Venus as it departed from before the date of the Transit. The one foot radius made by John Bird, two the Sun’s disk. society however thought the proposal reflecting telescopes made by James scandalous and made it clear to Mason Short magnifying 120 times and fitted The Transit observations were made and Dixon that it was either Sumatra or with micrometers. independently by Dixon and Mason a court of law. using the reflecting telescopes with The first astronomical task was to their micrometer adjustment. "When I Fortunately, the commander of establish the local meridian and this saw the planet first," wrote Mason, "its Seahorse, Captain Smith, not a man to Mason did by equal altitudes of stars periphery, and that of the Sun’s, were using the Bird quadrant. While the be bullied by a bunch of land-lubbing in a great tremor; but this vanished, as quadrant was, for its time and size, academics, decided that, Bencoolen the Sun rose, and became well defined. a precise instrument, it was capable being out of the question (in fact it had Four minutes before the internal of direct reading to little better than already fallen to the French) he would contact, the Sun’s disk was entirely hid a quarter minute. However, equal make for Cape Town. by cloud, for about one minute." These altitudes do not depend on precise few words were all Mason wrote of the Arriving at the Dutch colony on 27 April measurement; rather on precise event; he was a man of economy but 1761, a temporary observatory was replication and this the quadrant possessed of a deep soul. with its rotating vertical axis did well. established. The site of the observatory The process was simple if somewhat is a little contentious. Mason makes The Transit over for the time being, laborious. It must be recalled that no mention of its location in his Mason and Dixon spent the rest of the regulator was keeping at the rate June and on into late September, seminal paper of the Transit. However, of sidereal time (time as measured measuring the meridian passages of it is known that the same site was by the stars). Now, local sidereal navigational stars and calibrating the used by Captain James Cook and his time is the of a star regulator by occultations of Jupiter’s astronomer, William Wales (1734-1798) on the meridian, i.e. the instant it moons, the time honoured means when they called at Cape Town in crosses the meridian from east to of deriving precise time – the stellar west. By observing a star rising east 1772. Wales noted in his journal, "Went precursor of Harrison’s remarkable of the meridian and noting the time with Capt Cook to the Governor and clockwork chronometer. Thus was the by the regulator, and keeping the obtained leave to carry on shore and longitude and the latitude of Cape Town vertical angle fixed, the star was erect my observatory and instruments. determined with great precision for the tracked westwards until it set across Also agreed with the Widow Xieman for the horizontal wires of the quadrant first time. the use of the ground whereon they and the time again noted. The mean On 28 September 1761, they packed stood before, and where Messieurs of the times was the instant of the away their instruments and "put them Mason and Dixon observed." The Cook mid-heaven, the meridian crossing on board the Mercury. Capt Harold Society states that "the transit was point. In order that time was accurately sailed for St Helena." successfully observed from Concordia determined, it was critical that the Gardens, a social club that used to be "going" of the regulator had to be On St Helena, Nevil Maskelyne, the behind St Mary's Cathedral in Cape known, i.e. the rate at which it lost man who would one day be Astronomer Town." or gained. Mason determined from Royal and whose legacy to navigation

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and geodetic surveying is incalculable, Mason and Dixon eventually arrived . Mason in particular, stands out was not a happy astronomer. His home to England in February 1762; in surveying history as a remarkable Transit of Venus had been nothing each £230 the richer. Within eighteen figure, mostly lost to time until recently short of disaster. The weather had months they were off again, this time when his achievements once more been cloudy throughout and his to America and their most notable broached the light of day. zenith sector’s (a large instrument achievement: the establishment of He was but one of the hundreds for determining precise latitudes by the famous Mason-Dixon Line. From that led us from the darkness into zenith distances) had developed a November 1763 to September 1768, enlightenment. Mason, a devout fault in its plummet. This, as it turned they ran the "impossible" border Protestant and Dixon, a lapsed Quaker, out, was fortuitous, for it encouraged dividing from what is now were men of their time as was the Maskelyne to devise a far more precise Delaware; a line of constant latitude arrangement; one that enabled him separating from Maryland remarkable Jesuit Abbe La Caillé – to measure the insidious attraction of and Virginia (as it was), some 300 km clever, resourceful, adventurous and mountains (deviation of the vertical) where the greatest deviation observed brave. and win the Royal Society’s prestigious by RTK GPS is no more than 30 m. Not Astronomy has moved on since the Copley Medal in so doing. But that is content with such remarkable feats, days of charting navigational stars another story told elsewhere. they then measured 100 odd kilometres and tracking the motions of the moon, with rods and chains for America’s As soon as Mason and Dixon arrived, probing so deep into space and time first meridian arc; the one included by Maskelyne recruited them to his that the common mind is numbed by George Airy in the determination of his extracurricular activities; measuring the enormity of the universe in which Figure of the Earth. And the regulator the rise of the Atlantic tide and yet we dwell. Our tiny dot of a world, they used was, of course, their trusty more gravity observations. To this end, a dust mote lost in the vastness of Shelton from South Africa. Jeremiah Dixon was sent back to Cape the cosmos, has been measured and Town with the Greenwich Observatory’s In 1769, the next and final Transit of charted, mapped and drilled to such an regulator, a superb piece made by the Venus for a hundred years occurred. extent that it seems hardly necessary celebrated John Shelton, to make more Jeremiah Dixon, now as accomplished to keep up the work. Yet the work is gravity observations. The story of the an astronomer as he was land surveyor, just as important today as it ever was. Shelton regulator, now on display in teamed up with William Bayly to make No longer do we measure long meridian the Museum of Scotland, Edinburgh, the observations in northern Norway. arcs with great swaths of triangles, is quite incredible – Maskelyne took Charles Mason was despatched to we just press a button and voila! it to Barbados in 1763 and Jamaica County Donegal in Ireland. His return perfection, or not, as the case maybe. in 1764 when testing John Harrison’s trip across the Irish Sea, in an open chronometer. Later it was employed boat, with a horse, was the prelude Acknowledgements by Maskelyne on the mountain to another adventure, this time in This paper was presented at Hydro9 Schiehallion where its precision enabled Scotland. and is published here with permission. the Astronomer Royal to measure the Perhaps the nicest thing written deflection of the vertical. about the Cape Town observations References appeared in the first issue of the [1] E Danson: Drawing the Line: How Mason Nautical Almanac in 1767, where and Dixon Surveyed the Most Famous Maskelyne stated that the "latitude Border in America, John Wiley & Sons, New York, 2000. and longitude of Cape Town are given [2] E Danson: Weighing the World: The as found by Mason and Dixon in 1761. Quest to Measure the Earth, 2nd Edition, It is probable that the situation of few Oxford University Press, New York, 2009. places is better determined." [3] J Donald Fernie: Transits, Travels and Tribulations II, American Scientist vol Conclusions 85, 1997. [4] D Howse: Nevil Maskelyne: The It is not surprising that Cape Town, Seaman's Astronomer, London 1989 its position at the foot of Africa and [5] C Mason and J Dixon: Observations enjoying a climate many would envy, Made at the Cape of Good Hope; By Mr. became a magnate for astronomers and Charles Mason and Mr. Dixon; Reduced geodesists. The holding of Hydro 09 is to Apparent Time by Mr. Mason. With an Appendix. Phil. Trans. 1761-1762 52, pp a further testimony to the excellence 378-394. of the place, perhaps in this instance [6] Monthly Notes of the Astronomical reflecting more its hospitality than the Society of South Africa, November , pp. light of stars. 99-102, 1951. [7] JR Smith: The Meridian Arc Measure The work of La Caillé and later, Mason in Peru, 1735-1745, (Surveying and and Dixon, marked the early years Mapping the Americas, Federation of the development of that special International de Geophysique thinking and scientific observation of Convention, Washington DC 2002) the Earth that today we lump together Contact Edwin Danson, under the rather dull epithet of C & C Technologies, [email protected]

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