数学家传记
弗朗索瓦·阿拉戈是一位重要的法国数学家和政治家。他在光的微粒说方面做出了重要发现。
弗朗索瓦·阿拉戈的父亲是Bonaventure 阿拉戈,他是Estagel的市长,Estagel是佩皮尼昂西北约18公里处的一个小镇,他的母亲是Marie Roig。阿拉戈家族来自东比利牛斯,事实上阿拉戈这个名字与西班牙阿拉贡地区有西班牙联系,该地区相当接近。阿拉戈的父母有九个孩子,四个男孩和五个女孩。阿拉戈是男孩中最年长的,有兄弟Jean、Jacques和Étienne。Jean Arago(1788-1836)移民到北美并从事军事生涯;Jacques Étienne Victor Arago(1799-1855)参加了由Louis de Freycinet领导的l'Uranie航行,在太平洋进行磁学和海洋学研究;Étienne Vincent de 阿拉戈(1802-1892)是一位作家和剧作家。
阿拉戈家族参与政治,持有左翼共和主义观点,也有军事联系。起初阿拉戈表现出对军事生涯的兴趣,正是考虑到这一点,他在Perpignan市立学院接受教育,在那里他爱上了数学。1803年,他在Toulouse参加巴黎École Polytechnique的入学考试。他的考官是Louis Monge,加斯帕尔·蒙日的兄弟,当时是École Polytechnique的校长,阿拉戈在排名入学名单中被列为前五名学生之一。他于1803年进入École Polytechnique,并住在他父亲朋友拥有的一套巴黎公寓中。这位朋友将阿拉戈介绍给西莫恩·德尼·泊松,后者比阿拉戈大五岁,并在阿拉戈进入学校的前一年被任命为École Polytechnique的助理教授。阿拉戈和西莫恩·德尼·泊松成为朋友,并不真正像学生和老师那样相处。西莫恩·德尼·泊松经常在晚上到阿拉戈的公寓拜访他,两人会讨论政治和数学。尽管如我们所说,两人不像学生和老师,但西莫恩·德尼·泊松确实对他年轻的朋友产生了相当大的影响。尽管由世界上一些顶尖数学家授课,阿拉戈发现他们的教学能力远不及他们的研究能力。1805年,西莫恩·德尼·泊松能够给阿拉戈一项远比人们期望要求一个年轻学生承担的任务重要得多的任务。他要求阿拉戈帮助测量子午线。
让·巴蒂斯特·约瑟夫·德朗布尔和皮埃尔·梅尚在1792年至1798年间测量了从敦刻尔克到巴塞罗那的子午线。利用他们的数据确定了米的长度,但皮埃尔·梅尚仍然渴望获得更多数据。1801年9月,经度局要求派遣一支探险队将子午线测量延伸到巴塞罗那以南。皮埃尔·梅尚热衷于领导这次新的探险,并于1803年4月前往西班牙。他在6月沿乌惹内·查尔斯·卡塔兰海岸进行三角测量,到1804年1月他已穿越到伊维萨岛和马略卡岛。然而,他于1804年9月去世,任务未完成。皮埃尔·西蒙·拉普拉斯要求西莫恩·德尼·泊松寻找一个能继续这项工作的人,西莫恩·德尼·泊松推荐了他的年轻朋友阿拉戈。这项挑战令人生畏,阿拉戈花了一些时间才做出决定。然而,他最终决定接受这一享有盛誉的邀请,于1805年2月22日正式被提名,随后搬入巴黎天文台,那里将成为他的总部。让-巴蒂斯特·毕奥被指派为团队的第二名成员,两人花了大约十八个月学习必要的技术。事实上,他们被要求同时执行第二项科学任务,因为他们被要求使用摆来测量旅途中各个地点的重力,以便这些数据可用于更准确地估计地球的确切形状。
1806年9月3日,阿拉戈和让-巴蒂斯特·毕奥出发前往西班牙。他们继续了皮埃尔·梅尚在其最后一次探险中承担的任务,到1808年他们已在马略卡岛,这是一个重要地点,使得巴黎子午线可以延伸到巴塞罗那以南。他们在西班牙行动时正值极其困难的时期,因为他们是法国人。拿破仑在1807年将注意力转向西班牙和葡萄牙,并于1807年10月率军穿过西班牙进入葡萄牙。他们征服了葡萄牙并占领了西班牙的部分地区。1808年5月,拿破仑宣布其兄约瑟夫·波拿巴为西班牙统治者,独立战争由此开始。让-巴蒂斯特·毕奥和阿拉戈一定显得极其可疑;两个法国人带着精密测量仪器在西班牙领土上工作。让-巴蒂斯特·毕奥逃回法国,但阿拉戈留在马略卡岛,伪装成西班牙人,试图完成他记录在日志中的测量。然而,在加拉佐山顶点火相当可疑,因此他作为间谍被捕并投入监狱。
阿拉戈设法说服监狱指挥官他是一名科学家,而非间谍,指挥官同意给阿拉戈一个逃跑的机会。他于1808年7月29日这样做,仍然带着他珍贵的日志,设法找到一艘前往阿尔及尔的渔船,并登上了船。8月3日抵达阿尔及尔后,他去找法国领事,领事给了他一本伪造的奥地利护照,到8月16日他已在一艘前往马赛的船上。如果事情就此结束,这可能是一次非凡的冒险,但更多的戏剧性事件还在后头。阿拉戈乘坐的船在前往法国途中被一艘西班牙军舰捕获,他再次成为俘虏。阿拉戈被关押在罗塞斯的西班牙监狱,但仅过了很短一段时间,西班牙人决定将囚犯送往帕拉莫斯,因为法国军队正在西班牙推进。然而阿拉戈很幸运,被当局认出后获释,并于11月28日被送上另一艘前往马赛的船。
然而,事情并未如愿,因为阿拉戈再次未能到达祖国。一场风暴将船吹回北非海岸的布吉,他在那里被穆斯林捕获。在进一步的冒险中,他说服捕获者他愿意皈依伊斯兰教以获得优待,之后他被允许经陆路返回阿尔及尔,并于12月25日抵达那里。阿尔及尔的新地方领袖反对法国人,阿拉戈发现自己身陷囹圄,等待被运往流放地。然而法国领事再次救了他,1809年6月21日,阿拉戈第三次被送上前往马赛的船。这次他顺利到达目的地,1809年7月2日,他站在了法国的土地上。
带着记录测量的日志回到巴黎后,他被当作英雄对待。他成为巴黎综合理工学院的助理教授和科学院的成员。他在余下的职业生涯中还在巴黎天文台工作。1810年他在天文台进行的一项实验与光有关。他推理道,既然光通过棱镜折射的角度取决于棱镜外光速与棱镜内光速之比,那么他应该能够探测到光速的差异,这取决于地球朝向和远离光源的速度。
当然,我们现在从阿尔伯特·爱因斯坦中知道,这种推理是不正确的。阿拉戈大致知道速度应该是多少,因此他知道他所寻找的效应完全在他应该能够探测到的范围内。事实上,探测由于地球自转引起的速度差异应该是可能的。阿拉戈在1810年3月19日和27日对恒星进行了观测。他在地球朝向光源旋转时以及地球远离同一光源旋转时都进行了观测。令他惊讶的是,他没有探测到光速的任何差异。他在10月8日观测了同样的光源,当时地球的速度差异应该是地球轨道速度的两倍。他再次感到困惑,光速似乎不受观察者朝向或远离光源的速度影响。他于1810年12月10日向科学院展示了他的结果。阿拉戈如何解释这些令人困惑的结果?他提出光粒子以各种不同的速度传播,但人眼只对以某一特定速度传播的光敏感。这可以解释为什么速度似乎与观察者的速度无关。
阿拉戈于1811年与Lucie 乔治·卡里尔-Bescombes结婚;他们的一个儿子Alfred Arago(1816-92)成为美术督察,另一个儿子Emmanuel 阿拉戈与父亲一起在国民议会任职多年。1813年,阿拉戈开始讲授天文学普及讲座。他每年继续讲授这些讲座,直到1845年。他成为巴黎天文台台长。阿拉戈还以其他方式活跃。他多年担任科学院的秘书,并以此身份于1835年为Proceedings of the Academy of Sciences揭幕。
他积极为共和事业从事政治活动,除了科学职责外,还在政府中担任过多个政治职务。他的政治生涯始于1830年,当时他当选为东比利牛斯地区的议员。后来他担任巴黎的议员。在1848年革命后掌权的临时政府中,他于4月23日当选,并担任战争和海军部长。在担任这一政府职务期间,他推行了许多改革,包括在法国及其许多领地废除奴隶制。该政府在全法国确立了男性普选权,这是阿拉戈所倡导的事业。他于1848年5月10日当选为行政权力委员会成员,由于他获得的选票最多,被任命为委员会主席。我们还应该注意到,他利用自己的政治职位来推进科学,例如获得资金资助出版皮埃尔·德·费马和皮埃尔·西蒙·拉普拉斯的著作,支持铁路和电报的发展。他还能够为天文台获得最新天文仪器的资金,并能够为科学院获得财政支持。
阿拉戈于1811年在光的微粒理论方面做出了早期发现。与奥古斯丁·菲涅耳合作,他发现两束在垂直方向上偏振的光不会发生干涉,从而引出了光波的横向理论。他的光理论预测,光进入较密介质时速度应该减小。1838年,他描述了一个比较光在空气中和在水中或玻璃中速度的测试。然而实验的困难意味着阿拉戈直到1850年才有条件尝试他的实验。但到那时他的视力已经变差,因此实验的改进版本留给了其他人去完成。在阿拉戈去世之前,阿尔芒·斐索和莱昂·傅科取得了成功的结果。约瑟·伯特兰在阿拉戈的讣告中写道:-
阿拉戈对那个美丽的实验[由阿尔芒·斐索和莱昂·傅科完成]微笑,这个实验及其当之无愧的赞誉,唤起了他自己辉煌岁月的愉快回忆,那时他击败了皮埃尔·西蒙·拉普拉斯、西莫恩·德尼·泊松和让-巴蒂斯特·毕奥,赢得了在科学院中的位置。
1820年,丹麦物理学家H C Orsted产生了关于电和磁的实验结果。阿拉戈进行了这类进一步的实验,并展示了若干效应,这些效应后来使麦可·法拉第将它们解释为感应。看来阿拉戈是第一个构造电磁铁的人。
阿拉戈与让-巴蒂斯特·毕奥合作,对地球上的弧长进行了测量,这导致了长度米制的标准化。我们在上面描述了他去南方进行测量的冒险经历,但后来,在1821年,两人将他们的结果扩展到北方,在苏格兰爱丁堡附近的Leith以及设得兰群岛使用摆测量重力。
他建议他的学生于尔班·勒维耶研究天王星轨道的不规则性,在海王星被发现后,参与了关于命名该行星的争论,并与约翰·柯西·亚当斯就优先权发生争执。尽管许多人批评阿拉戈在这场争论中的角色,特别是他努力将新行星命名为于尔班·勒维耶,但人们不得不感到,他为自己按照他的建议做出发现的学生辩护是做对了。
阿拉戈的其他贡献包括光的偏振研究、太阳日冕和色球层的考察,以及行星直径的测量。他还研究了声速。
1851年12月2日,法国发生政变,路易-拿破仑·波拿巴掌握绝对权力并解散国民议会。整整一年后,他成为皇帝,称拿破仑三世。各领域的领导人被要求宣誓效忠,阿拉戈担任两个这样的职位,即天文台台长和科学院秘书。阿拉戈,一位坚定的共和主义者,拒绝宣誓效忠。他留在巴黎天文台,拿破仑二世已将其更名为帝国天文台。阿拉戈请求科学院替换他担任秘书,不是因为拿破仑三世的问题,而是因为他觉得自己的健康正在衰退,特别是他的视力现在非常微弱,他无法正常履行职责。他患有组织间液体积聚、糖尿病和肾脏炎症。
1853年8月22日,阿拉戈最后一次参加科学院,然后,尽管有健康问题,他还是踏上了前往鲁西永地区家人的艰难旅程。在就各种事项给他们建议后,他回到巴黎,不久后去世。他被安葬在巴黎的拉雪兹神父公墓。
阿拉戈于1825年荣获皇家学会科普利奖章,1850年荣获伦福德奖章。月球和火星上的陨石坑都以他的名字命名,海王星的一个环也是如此。Academy of Sciences于1893年设立了阿拉戈奖章。
François Arago's father was Bonaventure Arago, who was the mayor of Estagel which is a small town about 18 km north west of Perpignan, and his mother was Marie Roig. The Arago family came from the eastern Pyrenees, and in fact the name Arago has Spanish connections with the Aragon region of Spain which is quite close by. François' parents had nine children, four boys and five girls. François was the eldest of the boys, having brothers Jean, Jacques, and Étienne. Jean Arago (1788-1836) emigrated to North America and had a military career; Jacques Étienne Victor Arago (1799-1855) took part in the voyage of l'Uranie led by Louis de Freycinet to conduct magnetic and oceanographic researches in the Pacific; and Étienne Vincent de Arago (1802-1892) was an author and dramatist.
The Arago family were involved in politics, having leftist republican views, and also had military connections. At first François Arago showed an interest in a military career and it was with this in mind that he was educated at the Municipal College of Perpignan where he came to love mathematics. In 1803 he was examined at Toulouse for admission to the École Polytechnique in Paris. His examiner was Louis Monge, the brother of Gaspard Monge who was at the time director of the École Polytechnique, and Arago was placed as one of the top five students in the ranked entrance list. He entered the École Polytechnique in 1803 and took up lodgings in a Paris apartment owned by a friend of his father. This friend introduced Arago to Poisson who was five years older than Arago and had been appointed at an assistant professor at the École Polytechnique in the year before Arago entered the school. Arago and Poisson became friends, not really behaving as student and teacher. Poisson would frequently visit Arago in his apartment in the evenings and the two would discuss politics and mathematics. Although, as we have said, the two were not like student and teacher, nevertheless Poisson did influence his younger friend very considerably. Despite being taught by some of the leading mathematicians in the world, Arago did not find their abilities to teach come anywhere close to their abilities for research. In 1805 Poisson was able to offer Arago a task of far more importance than one would have expected a young student to be asked to undertake. He asked Arago to help in measuring the meridian.
Delambre and Méchain measured the meridian from Dunkerque (Dunkirk) to Barcelona between 1792 and 1798. Using their data the length of the metre was set but Méchain had remained keen to obtain more data. In September 1801 the Bureau des longitudes requested that an expedition be sent to extend the meridian measurements south of Barcelona. Méchain was keen to lead this new expedition and in April of 1803 he left for Spain. He triangulated down the Catalan coast in June, and by January of 1804 he had crossed to Ibiza and Mallorca (Majorca). However he died in September of 1804 with the task incomplete. Laplace asked Poisson to find someone who would continue the work, and Poisson proposed his young friend Arago. The challenge was a daunting one, and Arago took some time to make a decision. However he finally decided that he would accept the prestigious offer, was nominated formally on 22 February 1805 and then moved into the Paris Observatory which would become his headquarters. Biot was assigned to become the second member of the team and the pair spent about eighteen months learning the necessary techniques. In fact they were asked to carry out a second scientific task at the same time for they were asked to use a pendulum to measure the force of gravity at the various locations on their travels so that the data might be used for a more accurate estimate of the exact shape of the Earth.
On 3 September 1806 Arago and Biot set out for Spain. They continued the task which Méchain had been undertaking on his final expedition and by 1808 they were on Mallorca, an important point which allowed the Paris meridian to be continued south of Barcelona. They had been operating in Spain at an extremely difficult time, given that they were French. Napoleon had turned his attention towards Spain and Portugal in 1807 and marched his armies through Spain to Portugal in October 1807. They conquered Portugal and occupied parts of Spain. In May 1808 Napoleon declared his brother Joseph Bonaparte as Spanish ruler and the War of Independence began. Biot and Arago must have looked extremely suspicious; two Frenchmen with sophisticated measuring instruments working on Spanish territory. Biot fled back to France but Arago remained on Mallorca, disguised as a Spaniard, trying to complete his measurements which he had recorded in a logbook. However lighting of fires on the top of Mount Galatzo was pretty suspicious so he was arrested as a spy and put in prison.
Arago managed to persuade the commander of the prison that he was a scientist, not a spy, and the commander agreed to give Arago a chance to escape. He did so on 29 July 1808 and, still carrying his precious logbook, managed to find a fishing boat heading for Algiers, which he boarded. Reaching Algiers on 3 August he went to the French consul who supplied him with a forged Austrian passport and by 16 August he was on a boat heading to Marseille. This might have been a remarkable adventure had it ended at that point, but more drama was to come. The boat on which Arago was sailing was captured while on its way to France by a Spanish warship and he was back in captivity again. Arago was held in a Spanish prison in Roses but after only a short spell the Spanish decided to send their prisoners to Palamos since the French armies were advancing through Spain. However Arago was lucky and, having been recognised by the authorities, was released an put on another boat for Marseille on 28 November.
It was not to be, however, for again Arago failed to reach his homeland. A storm blew the boat back to Bougie on the north African coast where he was captured by Moslems. After further adventures during which he persuaded his captors that he wished to convert to Islam to obtain favourable treatment, he was allowed to return to Algiers which he did overland, arriving there on 25 December. A new local leader in Algiers was opposed to the French and Arago found himself in prison waiting to be shipped off to a penal colony. However the French consul again came to his rescue and, on 21 June 1809, Arago was put, for the third time, on a ship bound for Marseille. This time he reached his destination without mishap and on 2 July 1809 he was standing on French soil.
Arriving back in Paris with his logbook containing the measurements he was treated as a hero. He became an assistant professor at the École Polytechnique and a member of the Academy of Sciences. He also worked at the Paris Observatory for the rest of his career. One experiment which he carried out at the Observatory in 1810 concerned light. He reasoned that since light was refracted by a prism through an angle depending on the ratio of the velocity of light outside the prism to that inside it, then he should be able to detect differences in the velocity of light depending on the speed of the Earth towards and away from the source.
Of course we now know, from Einstein, that this reasoning is incorrect. Arago knew roughly what the velocities should be, so he knew that the effect he was looking for was well within what he should be able to detect. In fact detecting the differences in velocities due to the rotation of the Earth should have been possible. Arago made observations of stars on 19 and 27 March 1810. He made observations when the Earth was rotating towards the sources and also when it was rotating away from the same sources. To his surprise he did not detect any differences in the velocity of light. He observed the same sources on 8 October when the Earth when the difference in velocity should have been twice the Earth's orbital velocity. Again he was puzzled that the velocity of light seemed unaffected by the velocity of the observer towards or away from the source. He presented his results to the Academy of Sciences on 10 December 1810. How did Arago explain the puzzling results? He suggested that light particles travel at a variety of different velocities but the human eye of only sensitive to light travelling at one particular velocity. This would explain why the velocity appeared independent of the velocity of the observer.
Arago married Lucie Carrier-Bescombes in 1811; one of their sons, Alfred Arago (1816-92), became an Inspector of Fine Arts, another son Emmanuel Arago served with his father on the National Assembly for many years. In 1813 Arago began to give popular lectures on astronomy. He continued to give these lectures every year until 1845. He became Director of the Paris Observatory. Arago was also active in other ways. He served for many years as secretary of the Academy of Sciences and in this capacity he inaugurated the Proceedings of the Academy of Sciences in 1835.
He was active politically for the republican cause and filled several political roles in government in addition to his scientific duties. His political career began in 1830 when he was elected as a deputy from the Pyrénées-Orientales region. Later he served as a deputy from Paris. In the provisional government which took power after the 1848 Revolution he was elected on 23 April and he served as minister of war and the navy. He introduced many reforms while holding this government position including the abolition of slavery throughout France and its many possessions. This government established universal manhood suffrage in France, a cause championed by Arago. He was elected to the Executive Power Commission on 10 May 1848, being named as president of the Commission since he was elected with the largest number of votes. We should also note that he used his political positions to advance science, such as obtaining money to fund the publication of the works of Fermat and Laplace, supporting the development of railways and of the telegraph. He was also able to get funding for the latest astronomical instruments for the Observatory and able to gain financial support for the Academy of Sciences.
Arago made early discoveries on the corpuscular theory of light in 1811. Working with Fresnel he discovered that two beams of light polarised in perpendicular directions do not interfere, leading to the transverse theory of light waves. His theory of light predicted that the velocity of light should decrease as it passes into a denser medium. In 1838 he described a test to compare the velocity of light in air and in water or glass. However difficulties with the experiment meant that Arago was not in a position to try his experiment until 1850. By this time however his sight had become poor, so it was left to others to carry out a refined version of the experiment. Successful results were obtained by Fizeau and Léon Foucault before Arago died. Bertrand, in his obituary of Arago, wrote:-
Arago smiled at the beautiful experiment [of Fizeau and Foucault] which, with its well deserved praise, brought back pleasant memories of his own glory days when he beat Laplace, Poisson, and Biot, to gain his place in the Academy of Sciences.
In 1820 the Danish physicist H C Orsted produced experimental results on electricity and magnetism. Arago carried out further experiments of this type and demonstrated several effects which led Faraday later to explain them as induction. It appears that Arago was the first person to construct an electromagnet.
Working with Biot, Arago made measurements of arc length on the Earth which led to the standardisation of the metric system of lengths. We described above the adventures he had in taking readings in the south, but later, in 1821, the two extended their results to the north making measurements of the force of gravity using a pendulum in Scotland at Leith, near Edinburgh, and in the Shetland Islands.
He suggested that his student Le Verrier investigate irregularities in Uranus's orbit and, after Neptune was discovered, participated in the argument regarding naming the planet and disputed with Adams regarding priority. Although many have criticised Arago for his part in this dispute, particularly for his efforts to get the new planet named Le Verrier, one has to feel that he did the right thing in championing his own student who had made the discovery following his advice.
Other contributions made by Arago include work on the polarization of light, investigations of the solar corona and chromosphere, and measurements of the diameters of the planets. He also worked on the velocity of sound.
On 2 December 1851 there was a coup d'état in France with Louis-Napoleon Bonaparte assuming absolute power and dissolving the National Assembly. Exactly one year later he became Emperor taking the title Napoleon III. Leaders in various field were required to swear allegiance and Arago held two such positions, as Director of the Observatory and as secretary of the Academy of Sciences. Arago, a staunch republican, refused to swear allegiance. He remained at the Paris Observatory, which Napoleon II had renamed the Imperial Observatory. Arago requested that the Academy of Sciences replace him as Secretary, not because of the problems with Napoleon III, but rather because he felt that his health was failing, in particular his eyesight was by now very weak, and he could not properly carry out his duties. He was suffering from a build-up of fluid between his tissues, diabetes, and inflammation of the kidneys.
On 22 August 1853 Arago attended the Academy of Sciences for the final time then, despite his health problems, he set out on the difficult journey to his family in the Roussillon region. After giving them advice on a wide range of matters he returned to Paris where he died shortly after. He was buried in the Père Lachaise cemetery in Paris.
Arago was honoured with the award of the Royal Society Copley Medal in 1825 and the Rumford Medal in 1850. Craters on both the Moon and Mars have been named after him, as has a ring of Neptune. The Academy of Sciences inaugurated the Arago Medal in 1893.
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