Pierre François-André Méchain


Born: 16 August 1744 in Laon, France
Died: 20 September 1804 in Castellón de la Plana, Spain

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Pierre Méchain's parents were Pierre-François Méchain and Marie-Marguerite Roze. Pierre-François, a plasterer who specialised in plastering ceilings, was a man of modest means. Pierre was born in Loan, a medieval town in the Picardy region of northern France. The picturesque old town, situated on the summit of a scarped hill, lies northwest of Reims and northeast of Paris. It was in Loan that Pierre was educated by the Jesuits and as a young boy his aim was to become an architect, although his main hobby was astronomy. His ability at mathematics was soon spotted, however, and he was advised to study at the École Nationale des Ponts et Chaussées in Paris.

In 1716 the Bridge and Highway Corps had been founded in Paris and, in 1747 when Méchain was still a small child, it became the École Nationale des Ponts et Chaussées. It was a prestigious institution founded to train civil engineers and its teachers wrote books that became standard works on the mechanics of materials, machines, and hydraulics. Studying there was, however, expensive and Méchain's father did not have the necessary resources to be able to support his son. Méchain had to interrupt his studies and take on the role of tutor to two young boys from a noble family some 50 km from Paris.

His tutoring position put Méchain on a firmer financial footing and he was able to save enough to buy some good quality astronomical instruments so that he could pursue his hobby. We now quote a story from [2] which is based on Méchain's own account:-

... calamity struck. His father lost a crippling lawsuit, and the son ... loyally agreed to sell his instruments to pay off the family debt. This setback proved his first stroke of fortune. His instruments were purchased by Jérôme Lalande ...

This romantic story may not be true for Delambre, who knew Méchain very well over a period of ten years, stated in his biography of Méchain, written many years after his death, that there was no evidence to support the story. Whether the story is true or not, what is undoubtedly the case is that Méchain made contact with Lalande who sent him proofs of the second edition of his Traité d'astronomie. Méchain's assistance with the proofs soon impressed Lalande, as did his enthusiasm and abilities, so, seeing the benefits of having him enter his profession, he arranged a position for him in the cartography department in the Depôt de la Marine in Versailles in 1772. The position was not well paid and, certainly at first, Méchain had to tutor mathematics to make enough money to live on.

Gingerich writes in [1]:-

The archives were then a seat of political patronage and intrigue, and, caught in the political crosscurrents, Méchain twice lost his job; but each time he was reinstated because of his competence as a map-maker. The archives were soon transferred to Paris, and there he drew up the maps of the shoreline from Nieuwpoort in Flanders to Saint-Malo.

Méchain went to Paris in the permanent position of calculator in the Depôt de la Marine, living there from around 1774. He became friendly with Charles Messier who worked in the same department and the two observed from the Hotel de Cluny in Paris where Lalande had observed 25 years earlier. In 1777 Méchain married Barbe-Thérèse Marjou, whom he met while working in Versaille. They had two sons, Jérôme-Isaac born 1780 and Augustin born 1784, and a daughter. Their eldest son was named after Lalande who was his godfather.

For the next ten years from 1780 to 1790 Méchain undertook surveys to produce maps and also worked in astronomy where he is particularly famed as a discoverer of comets. Some of the maps were produced for military purposes like those of Germany and north Italy which he worked on from 1780. Others, like that carried out in 1787 to find the precise distance between the Greenwich observatory in England and the Paris observatory, were part of an international project. The Government appointed Méchain as a commissioner, along with Legendre and Dominique Cassini, to triangulate the French side. The English part would be surveyed using Ramsden's theodolite while the French proposed using Borda's repeating circle. [See Borda's biography for a description of the repeating circle.] Dominique Cassini, with Méchain as his assistant, made the measurements with Borda's repeating circle on the French side. Initially Méchain used older surveying equipment to check Dominique Cassini's measurements with the repeating circle, but later in the project he took over measurements with the repeating circle. He soon gained a reputation as the most careful of observers.

Here is a picture of the Borda repeating circle.

Méchain's work on comets became of major importance in 1781 when he discovered two comets in the same year. As with all his comet discoveries, and with many comets discovered by others, he calculated their orbits. In fact it was his work in calculating the orbits of two comets from observations which had been made in 1532 and 1661 that led to his election to the Académie des Sciences. Méchain's memoir on these comets was presented to the Academy for the Grand Prix of 1782 and in it he showed, unexpectedly, that they were not two appearances of the same comet but indeed different comets. His memoir won the prize which in turn was the main reason for his election to the Academy. He continued to discover comets, and while searching for them, he discovered 29 nebulae which would be added to Messier's catalogue.

In 1785 Méchain was asked if he would take over the editorship of the astronomical almanac Connaissance des temps. This he did and produced seven volumes up to 1794 when Lalande, who had been the editor earlier, took over of a second time. The Commission of Weights and Measures, which had as its members Condorcet, Lavoisier, Laplace and Legendre, was set up by the Académie des Sciences in 1790 to bring in a uniform system of measurement. It reported to the National Assembly on the 19 March 1791 with the proposal that one metre should be one ten millionth of the distance from the North Pole to the equator. It was decided to measure, using the method of triangulation with sightings made with the Borda repeating circle, that part of the meridian between Dunkerque and Barcelona. This was divided into two unequal parts, Dunkerque to Rodez and Rodez to Barcelona. The northern part was much the longer since it had been accurately measured by Cassini de Thury in 1740. Delambre was given charge of the Dunkerque to Rodez sector and Méchain the Rodez to Barcelona sector much of which had not been previously surveyed.

Méchain left Paris on 28 June 1792 and travelled to Barcelona to begin his survey. During the summer he set up stations in Catalonia to act as triangulation points and in the autumn he used the Borda repeating circle to take accurate sightings of these stations. He then went to Barcelona for the winter months to take accurate measurements of its latitude. The Spanish authorities were cooperative and he was allowed to use the castle on the top of Mont-Jouy overlooking the city. He made a large number of observations of the stars over a period of three months to give a precise result for the latitude. Méchain was fanatical about accuracy and, as we shall soon see, these measurements would cause him anguish for the rest of his life.

When war broke out between France and Spain in March 1793, Méchain had to leave Mont-Jouy which was required for military purposes. In May of that year he was nearly killed when being shown a new hydraulic pumping station by one of his friends. In saving his friend, who had become tangled in the machinery, he was struck by a lever and suffered several broken bones. It was months before he fully regained the use of his right arm but, in September, once he had recovered sufficiently, he began triangulating the peaks of the Pyrénées. Back in Barcelona for the winter he could not return to Mont-Jouy because of the war but made latitude measurements from the inn he was living in. By March of 1794 Méchain had discovered that the latitude measurements he had taken from the inn did not agree with those from Mont-Jouy, yet he could not return to the castle to take further measurements. He did not inform anyone of the error.

At this stage he took the advice of his Spanish friends and went to Italy. He lived for a year in Genoa and while there he learnt of the cancellation of the meridian project. However in April 1795 the project was restarted and Méchain was told to return to Paris. He refused, fearing for his life since he knew that other scientists had gone to the guillotine, and instead sailed to Marseille. He remained there until late August when he went to Perpignan to resume his measurements. However he was now reluctant to proceed, was hampered by bad weather, continued to refuse to return to Paris to meet with Delambre who was triangulating the northern sector, and achieved almost nothing for two years. Although Delambre sent him all the data that he was collecting, Méchain refused to let anyone see his data. He feared that his error would be discovered if he returned to Paris and his data was examined. He began to alter his data, not so as the average was changed, but just so that the deviation from the average was reduced.

The agony that Méchain suffered was because he had extremely high standards and he believed that the Borda repeating circle could attain essentially any desired accuracy. What he did not understand was the statistics underlying the theory of error, something which of course had not been developed at this time. Taking more and more measurements would only lead to greater accuracy if the errors were random. Any bias in the instrument would produce a systematic error which would be present in all observations. He blamed himself for discrepancies which were in no way his fault.

In January 1798 the Académie des Sciences set up an international conference to take place in September of that year to give an international standing to the new value of the metre which the Delambre-Méchain survey had still to finalise. Yet by May Méchain still was making no progress and Delambre and Borda arranged for Méchain's wife to travel from Paris to join her husband and ensure that he finish his task. When Méchain met his wife in Rodez in July it was the first time they had seen each other for six years. She returned to Paris unable to convince Méchain to complete his task. Delambre went to help Méchain who by this time had suffered a nervous breakdown. They completed the triangulations by November 1798. Méchain wanted to return to Barcelona to take further readings but he was persuaded to return to Paris [1]:-

Faced with the choice of returning to Paris and the warm welcome of his colleagues, or remaining forever an expatriate, Méchain reluctantly came back to Paris. There he was less than cooperative in presenting his observations to the commissioners charged with setting up the decimal metric system.

It may have been the promise that he would be made director of the Paris observatory which tempted Méchain back to Paris. Certainly he was elected to this position shortly after his return and made temporary director of the Bureau de Longitudes. This put him in a good position to get a project approved to extend the measurement of the meridian line to the Balearic Islands. He argued that accuracy would be improved by measuring the longer line, but his real reason was that the extension would make the latitude measurements at Barcelona which so tormented him, unnecessary. In his request to Napoleon for permission, however, he stressed the strategic position of the Balearic Islands, and how his mission could improve French relations with Spain. Napoleon, after taking advice from Delambre and Laplace, approved the mission.

Méchain left Paris on 26 April 1803 for Spain. When he arrived in Barcelona, however, he discovered that the Spanish were opposed to his mission and he was offered no passport to the Balearic Islands. He spent time measuring triangles on the Spanish coast down to Montsia, then an epidemic of yellow fever struck. Another problem was that he failed to be able to see Ibiza from Montsia and one had to be able to see his Montsia station from there to complete his triangles. In January 1804 he managed to get a passport and a ship to take him to Ibiza. Despite what the Spanish had told him he could not see his Montsia station and he wrote to Delambre (see for example [2]):-

Hell and all the plagues it spews upon the earth - storms, wars, pestilence and dark intrigues - have all been unleashed against me. What demon still awaits me? But vain exhortation will solve nothing, nor complete my task.

On the advice of Delambre he returned to the Spanish coast to triangulate down to Valencia. However, he developed a fever and died from malaria about 10 days later. Delambre wrote a fine eulogy for Méchain describing his meridian measurements [2]:-

Never did he consider these observations, the most exact ever achieved in this domain and conducted with unsurpassed certainty and precision, never did he consider them sufficiently perfected ...

However, when he worked on Méchain's data for his Base du système métrique he discovered that Méchain had changed his readings to make them appear more precise than they were. We explained above how a lack of understanding of the theory of errors in Méchain's time led him to down this path since he blamed himself for the discrepancies. Delambre did not want confidence in the metric system destroyed and a public announcement that Méchain had altered his data might well have had this result. He was too honest a scientist to pretend discrepancies were not there, so he treated Méchain's results as important scientific discoveries rather than as errors. The more sensitive personal letters and the evidence that Méchain had fiddled the results and lied to his colleagues were sealed in the archives of the Paris observatory. We should make it clear however that Delambre wanted to preserve Méchain's high reputation which, in Delambre's words [2]:-

... [he] rightly enjoyed for the care he put into all his observations and calculations.

Article by: J J O'Connor and E F Robertson


List of References (3 books/articles)

A Poster of Pierre Méchain

Mathematicians born in the same country

Cross-references in MacTutor

  1. History Topics: The history of measurement

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