皮埃尔·梅尚Pierre Méchain

皮埃尔·梅尚的父母是梅尚-François 梅尚和Marie-Marguerite Roze。梅尚-François是一名专门涂抹天花板的泥水匠，家境并不富裕。梅尚出生于Loan，这是法国北部皮卡第地区的一座中世纪城镇。这座风景如画的古老城镇坐落在陡峭山丘的顶端，位于兰斯西北、巴黎东北。梅尚正是在Loan接受耶稣会士的教育；他年幼时的目标是成为建筑师，尽管他的主要爱好是天文。然而，他的数学才能很快被发现，有人建议他去巴黎的国立桥梁与道路学院学习。

1716年，桥梁与公路部队在巴黎成立；1747年，当梅尚还是个小孩时，它成为国立桥梁与道路学院。这是一所享有盛誉的机构，创办目的是培养土木工程师，其教师撰写的书籍成为材料力学、机械和水力学方面的标准著作。然而，在那里学习费用高昂，梅尚的父亲没有必要的财力来支持儿子。梅尚不得不中断学业，去给距巴黎约50公里的一户贵族家庭的两个小男孩当家庭教师。

他的家教职位使梅尚有了更稳固的经济基础，他得以攒下足够的钱购买一些优质天文仪器，从而能够追求自己的爱好。我们现在引用[2]中一则依据梅尚本人叙述的故事：-

……灾难降临。他的父亲输掉了一场使其元气大伤的诉讼，儿子……忠实地同意卖掉自己的仪器来偿还家庭债务。这次挫折后来证明是他第一次走运。他的仪器被Jérôme 拉朗德买下……

这个浪漫故事对让·巴蒂斯特·约瑟夫·德朗布尔来说可能并不真实，让·巴蒂斯特·约瑟夫·德朗布尔在十年间非常了解梅尚，他在梅尚去世多年后所写的梅尚传记中表示，没有证据支持这个故事。无论这个故事是否真实，毫无疑问的是，梅尚与拉朗德取得了联系，后者把自己《Traité d'astronomie》Ⓣ（天文学论著）第二版的校样寄给了他。梅尚在校样方面的帮助很快给拉朗德留下了深刻印象，他的热情和能力也是如此，因此，看到让他进入自己这一行业的好处后，他于1772年在凡尔赛的海军部制图部门为他安排了一个职位。这个职位薪水不高，而且至少在起初，梅尚不得不教数学来挣够维持生活的钱。

Gingerich 在1中写道：-

档案馆当时是政治庇护与阴谋的所在地，而梅尚卷入政治暗流之中，两次失去工作；但每次都因他作为地图绘制者的能力而复职。档案馆很快迁往巴黎，他在那里绘制了从佛兰德的尼乌波特到圣马洛的海岸线地图。

梅尚前往巴黎，在海军部制图局担任常任计算员，大约从1774年起居住在那里。他与在同一部门工作的Charles Messier成为朋友，两人在巴黎克吕尼府邸进行观测，拉朗德曾在25年前在此观测。1777年，梅尚与Barbe-Thérèse Marjou结婚，他是在凡尔赛工作时认识她的。他们有两个儿子，Jérôme-Isaac生于1780年，Augustin生于1784年，还有一个女儿。他们的长子以拉朗德命名，后者是他的教父。

从1780年到1790年的接下来十年里，梅尚进行了测量以制作地图，还从事天文学工作，尤其以发现彗星而闻名。其中一些地图是为军事目的制作的，比如他从1780年开始绘制的德国和意大利北部地图。另一些，比如1787年为确定英格兰格林尼治天文台与巴黎天文台之间的精确距离而进行的测量，则是一个国际项目的一部分。政府任命梅尚为专员，与阿德里安-马里·勒让德和让-多米尼克·德·卡西尼一起，对法国一侧进行三角测量。英国一侧将使用杰西·拉姆斯登的经纬仪进行测量，而法国则提议使用让-夏尔·德博尔达的重复圆环。[关于重复圆环的描述，见让-夏尔·德博尔达的传记。]让-多米尼克·德·卡西尼在梅尚作为助手的协助下，用让-夏尔·德博尔达的重复圆环在法国一侧进行了测量。起初，梅尚使用较旧的测量设备来核对让-多米尼克·德·卡西尼用重复圆环进行的测量，但后来在项目中，他接管了用重复圆环进行的测量。他很快赢得了最细心的观测者的声誉。

让-夏尔·德博尔达的重复圆仪图片见THIS LINK。

梅尚在彗星方面的工作在1781年变得极为重要，那一年他发现了两颗彗星。与他所有的彗星发现一样，也与许多其他人发现的彗星一样，他计算了它们的轨道。事实上，正是他根据1532年和1661年所作的观测计算两颗彗星轨道的工作，使他当选为Académie des Sciences会士。梅尚关于这些彗星的论文被提交给科学院，参加1782年的大奖评选，在论文中他出人意料地表明，它们并不是同一颗彗星的两次出现，而确实是不同的彗星。他的论文赢得了该奖，这反过来又是他当选科学院院士的主要原因。他继续发现彗星，并在寻找彗星的过程中发现了29个星云，这些星云将被添加到Messier的星表中。

1785年，梅尚被问及是否愿意接任天文年历Connaissance des temps的编辑工作。他接受了，并一直出版到1794年，共出了七卷，之后曾较早担任编辑的拉朗德第二次接任。度量衡委员会由Académie des Sciences于1790年设立，成员包括尼古拉·德·孔多塞、Lavoisier、皮埃尔·西蒙·拉普拉斯和阿德里安-马里·勒让德，目的是引入统一的度量体系。该委员会于1791年3月19日向国民议会报告，提议一米应为从北极到赤道距离的一千万分之一。决定使用三角测量法，并用让-夏尔·德博尔达重复圆环进行瞄准，测量敦刻尔克与巴塞罗那之间那段子午线。这段子午线被分为两个不相等的部分：敦刻尔克到Rodez，以及Rodez到巴塞罗那。北段要长得多，因为它在1740年已由塞萨尔-弗朗索瓦·卡西尼·图里精确测量过。让·巴蒂斯特·约瑟夫·德朗布尔负责敦刻尔克到Rodez的部分，梅尚负责Rodez到巴塞罗那的部分，其中大部分此前未曾测量过。

梅尚于1792年6月28日离开巴黎，前往巴塞罗那开始测量。夏季，他在加泰罗尼亚设立站点作为三角测量点；秋季，他使用让-夏尔·德博尔达重复圆环对这些站点进行精确瞄准。随后，他在冬季几个月前往巴塞罗那，对其纬度进行精确测量。西班牙当局予以合作，他获准使用俯瞰城市的Mont-Jouy山顶城堡。他在三个月内对恒星进行了大量观测，以得出精确的纬度结果。梅尚对精度极为执着，正如我们很快将看到的，这些测量将给他余生带来痛苦。

1793年3月法国与西班牙之间爆发战争时，梅尚不得不离开因军事目的而被征用的Mont-Jouy。那年5月，他的一位朋友带他参观一座新的液压泵站时，他险些丧命。为了救那位被机器缠住的朋友，他被一根杠杆击中，多处骨折。过了几个月，他才完全恢复右臂的功能，但到了9月，一旦恢复得足够好，他就开始对比利牛斯山脉的山峰进行三角测量。冬季回到巴塞罗那后，由于战争，他无法返回Mont-Jouy，但在他所住的旅店里进行了纬度测量。到1794年3月，梅尚发现他从旅店进行的纬度测量与从Mont-Jouy进行的测量不一致，但他无法返回城堡进行进一步测量。他没有把这一误差告诉任何人。

在这个阶段，他听从了西班牙朋友的建议，前往意大利。他在热那亚住了一年，在那里得知子午线项目被取消。然而在1795年4月，项目重新启动，梅尚被告知返回巴黎。他拒绝了，因为担心自己的生命安全，他知道其他科学家已被送上断头台，于是转而乘船前往马赛。他在那里待到8月底，然后前往佩皮尼昂继续他的测量工作。然而此时他已不愿继续，受到恶劣天气的阻碍，继续拒绝返回巴黎与正在测量北段的让·巴蒂斯特·约瑟夫·德朗布尔会面，两年间几乎一事无成。尽管让·巴蒂斯特·约瑟夫·德朗布尔将他收集的所有数据都寄给了他，梅尚却拒绝让任何人查看他的数据。他担心一旦返回巴黎、数据被审查，自己的错误就会暴露。他开始修改数据，不是改变平均值，而只是减小与平均值之间的偏差。

梅尚所承受的痛苦源于他有着极高的标准，他相信让-夏尔·德博尔达重复圆能够达到几乎任何所需的精度。他所不理解的是误差理论背后的统计学，而这在当时自然尚未发展出来。只有误差是随机的，进行越来越多的测量才会带来更高的精度。仪器中的任何偏差都会产生系统误差，这种误差会出现在所有观测中。他为那些根本不是他的过错造成的偏差而自责。

1798年1月，Académie des Sciences安排了一次国际会议，于当年9月举行，以赋予米的新值国际地位，而让·巴蒂斯特·约瑟夫·德朗布尔-梅尚测量尚未最终确定。然而到那时May Méchain仍无进展，让·巴蒂斯特·约瑟夫·德朗布尔和让-夏尔·德博尔达安排梅尚的妻子从巴黎前往与丈夫会合，确保他完成任务。当梅尚7月在罗德兹见到妻子时，这是他们六年来第一次见面。她返回巴黎，未能说服梅尚完成任务。让·巴蒂斯特·约瑟夫·德朗布尔前去帮助梅尚，后者此时已遭受神经崩溃。他们在1798年11月完成了三角测量。梅尚想返回巴塞罗那进行进一步读数，但被说服返回巴黎[1]：-

面对返回巴黎并受到同事热烈欢迎，或永远留在异国的选择，梅尚不情愿地回到了巴黎。在那里，他在向负责建立十进制公制系统的委员们提交观测结果时并不太合作。

可能是被任命为巴黎天文台台长的承诺诱使梅尚回到巴黎。确实，他回来后不久就被选为此职位，并被任命为经度局的临时局长。这使他处于有利地位，能够获得一个项目的批准，将子午线测量延伸至巴利阿里群岛。他辩称，测量更长的线会提高精度，但他的真正原因是，这一延伸将使巴塞罗那的纬度测量变得不必要，而这些测量如此折磨他。然而，在他向拿破仑请求许可时，他强调了巴利阿里群岛的战略位置，以及他的任务如何能改善法国与西班牙的关系。拿破仑在听取让·巴蒂斯特·约瑟夫·德朗布尔和皮埃尔·西蒙·拉普拉斯的建议后，批准了这项任务。

梅尚于1803年4月26日离开巴黎前往西班牙。然而，当他抵达巴塞罗那时，他发现西班牙人反对他的任务，并且没有给他前往巴利阿里群岛的护照。他花时间在西班牙海岸测量三角形，一直测到蒙特西亚，随后黄热病疫情爆发。另一个问题是，他无法从蒙特西亚看到伊维萨岛，而为了完成他的三角形测量，必须能从那里看到他的蒙特西亚测站。1804年1月，他设法获得了护照和一艘船，将他送往伊维萨岛。尽管西班牙人告诉过他，他还是无法看到他的蒙特西亚测站，于是他写信给让·巴蒂斯特·约瑟夫·德朗布尔（例如参见[2]）：-

地狱以及它向人间喷吐的所有瘟疫——风暴、战争、瘟疫和黑暗的阴谋——都已向我袭来。还有什么恶魔在等着我？但徒劳的劝诫解决不了任何问题，也无法完成我的任务。

在让·巴蒂斯特·约瑟夫·德朗布尔的建议下，他返回西班牙海岸，进行三角测量直到瓦伦西亚。然而，他发烧了，大约10天后死于疟疾。让·巴蒂斯特·约瑟夫·德朗布尔为梅尚写了一篇精彩的悼词，描述了他的子午线测量[2]：-

他从未认为这些观测——该领域有史以来最精确、以无与伦比的确定性和精确度进行的观测——从未认为它们足够完善……

然而，当他在为他的Base du système métrique处理梅尚的数据时，他发现梅尚修改了自己的读数，使它们看起来比实际更精确。我们在上文解释了，在梅尚的时代，对误差理论缺乏理解如何导致他走上这条路，因为他将差异归咎于自己。让·巴蒂斯特·约瑟夫·德朗布尔不想让人们对公制系统的信心被摧毁，而公开宣布梅尚篡改了数据很可能导致这一结果。他是一位过于诚实的科学家，不会假装差异不存在，因此他将梅尚的结果视为重要的科学发现，而非错误。那些更敏感的个人信件以及梅尚篡改结果并欺骗同事的证据被密封在巴黎天文台的档案中。然而，我们应该明确指出，让·巴蒂斯特·约瑟夫·德朗布尔希望维护梅尚的崇高声誉，用让·巴蒂斯特·约瑟夫·德朗布尔的话来说[2]：-

……[他]因其对所有观测和计算所投入的细心而理应享有的声誉。

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.

A picture of the Borda repeating circle is at THIS LINK.

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.