[glenc (Glen)]

Diameter of the Earth
With his star catalogue completed, Lacaille turned his attention to measuring an arc of the meridian, to determine the shape of the Earth. Between September 9 and October 23, 1752, Lacaille measured an arc 135.8 km long with the southern end at his Cape Town observatory and the northern end at Klipfontein (the modern town of Aurora). This involved measuring the angles in two large triangles and two small triangles and also measuring the altitude of stars from the two ends of the arc.
(Aurora. https://maps.app.goo.gl/wf6RL6jn7QTiHN5B8)

Lacaille took two friends, two wagons, one drawn by six horses and the other by ten oxen, and eight slaves with him. From Klipfontein on September 24, he measured the angles to two signal fires on two mountains, Riebeek Kasteel and Kapokberg. On October 14, from Riebeek Kasteel Mountain, he measured the angle to a fire at Klipfontein and also the angle to his observatory at Cape Town. On October 16, Lacaille made similar measurements from Kapokberg Mountain to Klipfontein and Cape Town. Between October 17 and 21, he measured a base line 12.6 km long across flat ground just north of Kapokberg using pine rods 5.85 m long. He also measured the angles from the eastern and western ends of this line to the Kapokberg and Riebeek Kasteel mountains.

By measuring the angular altitude of stars he calculated that the celestial angle between Cape Town and Klipfontein was 1d 13’17.3” and this meant that one degree equalled 111.165 km. Klipfontein was 5.1 km east of the meridian line through Cape Town.

When Lacaille arrived back at Cape Town, he discovered that the arc was not in accordance with northern hemisphere measurements. His measurements incorrectly indicated that the Earth is pear-shaped. He decided there was no error in the six angles of the two large triangles, so he suspected an error in the base line. He remeasured it on November 3 with a chord 58.5 m long but found no error.

However his problem primarily arose from the mountain’s effect on his plumb line, as first suggested by the surveyor Colonel Sir George Everest. Everest arrived “at an estimate that the sums of the deviations of the plumb-line at Lacaille’s two stations must be 8.99” due to the presence of Table Mountain, Devil’s Peak and Lion’s Head. Lacaille’s meridian length was also later (1841) confirmed to be in error when Maclear from the Royal Observatory at the Cape found a difference of 36 m in the 135.8 km arc from Cape Town to Klipfontein. “He thus verifies Everest’s total effect of the plumb line deviations but attributes the greater part to the close mountains at Klipfontein not to Table Mountain.” Modern measurements give the Earth’s circumference as 40,007.863 km, making one latitude degree equal to 111.133 km.

Longitude at Sea
Another of Lacaille’s goals was to determine longitude at sea using the moon’s motion through the stars. Sailing ships leaving coastal waters needed to navigate in open oceans. This (as already mentioned) prompted the British to offer £20,000 for an accurate method for measuring longitude at sea. Several people suggested using the moon’s motion through the stars, including Sieur de St. Pierre (1674), Bouguer and Halley. Lacaille adapted Halley’s suggestion for finding longitude using the moon’s position with respect to bright stars. “The moon makes a circuit of the sky with respect to the star background on average every 27.322 days.” This can be used to “establish the longitude with an uncertainty equal to the rotation of the Earth in two minutes, that is, half a degree or roughly 30 nautical miles (55 km) on the equator.” There were two major problems: neither the star positions nor the motion of the moon were known with sufficient precision to make the method workable. Two more complications had to be considered: the moon’s position varies depending on the observer’s location on earth and the moon’s position varies depending on its distance from the earth. Lacaille studied refraction, made star catalogues and observed the moon’s orbit in an attempt to solve these problems. He used a graphical method to make it easier for ship’s captains to calculate their longitude.

In 1761, just one year before Lacaille died, John Harrison introduced the marine chronometer which he developed over many decades and this gradually made the lunar method of determining longitude obsolete. With this invention, longitude could be accurately measured at sea, and Harrison eventually received the £20,000 prize money. However the high cost of chronometers meant the lunar method of determining longitude was still used for many years. In the late 1700s, marine chronometers cost £70–£150.

Cartography, mapping
Lacaille left Cape Town on March 8, 1753 and arrived at Mauritius on April 18, 1753. While on the voyage he tested his new method for determining longitude at sea, using the distance of stars from the moon. During the next nine months he made an accurate map of the coastline of Mauritius. On January 16, 1754 Lacaille sailed to the nearby island of Réunion where he made longitude and latitude determinations from January 17 until February 27, 1754. On his return voyage to France, Lacaille visited Ascension Island (St Helena) from April 15 to 20, 1754. This was the place where Halley made his star catalogue in 1677. Lacaille arrived back in L’Orient, France on June 4, 1754.

LACAILLE’S WORK BACK IN FRANCE

The next few years were spent working with his observations from the Cape and in revising his textbooks on mathematics, astronomy and optics. “In 1759 he wrote up his graphical method for the determination of the longitude at sea, by the method of ‘lunars,’ that is the position of the moon with respect to certain bright stars.”

In February 1762 Lacaille had a recurrence of an illness which he experienced at the Cape. On March 19 he was bled by a physician but died on March 21, 1762 aged 49, probably as a result of the bleeding. He was buried at the Collège Mazarin in Paris, but his remains were later moved. Lacaille is honoured by a monument at Rumigny, by a plaque in Cape Town and by a bas-relief bust at Curepipe in Mauritius.

James Dunlop made the second catalogue of southern star clusters and nebulae from Parramatta, NSW in 1826 and John Herschel made the third catalogue from Cape Town between 1834 and 1838.