数学家传记
约翰·柯西·亚当斯是一位天文学家和数学家,他是第一个预测天王星之外行星位置的人。
约翰·柯西·亚当斯的父母是Tabitha Knill Grylls和Thomas Adams。这个家庭很贫穷,Thomas是佃农,而Tabitha也来自一个农耕家庭。Thomas和Tabitha在康沃尔郡Launceston附近务农,弗瑞兹·约翰,父母七个孩子中的长子,就出生在Lidcott农场。亚当斯以他母亲的舅舅约翰 亚当斯命名。这种情况特别合适,因为约翰 亚当斯为Tabitha提供了一些教育,她继承了他的图书馆,其中包括几本天文学书籍。正是这个图书馆,特别是其中的天文学书籍,激发了约翰成长过程中的兴趣。Hutchins写道[3]:-
亚当斯在一个虔诚的卫斯理宗家庭中长大,继承了他母亲良好的听力和对音乐的热爱。
约翰在Laneast附近的乡村学校上学,在那里学习希腊语和代数,直到十二岁时,他去了Devonport的一所私立学校,这所学校由他的表兄Revd 约翰 亚当斯 Grylls开办。他还曾在Saltash和Landulph的学校就读。在Devonport学校,他继续学习古典文学,展现出极大的数学才能,并因精确数值计算的卓越能力而闻名。正是在这一时期,他首次对天文学产生兴趣,1835年,在Landulph时,他观测到了爱德蒙·哈雷的彗星。他计算出1836年将在Lidcot可见一次太阳日环食,并前往那里进行观测。然而,他的数学技能是自学的,因为他在学校很少学到这方面的知识。他会去Devonport机械学院,在那里查阅有关数学和天文学的文章。
亚当斯在剑桥大学圣约翰学院接受教育,但这只有通过一些偶然的情况才成为可能。他的母亲在1836年收到了一小笔遗产,亚当斯在1837年做家教赚钱,然后他获得了圣约翰学院的奖学金。这些资金来源使他能够接受大学教育,但经济上很困难。他于1839年10月开始本科数学课程,四年后以Senior Wrangler(一等第一名)毕业,相当了不起的是,他每年都获得希腊语圣经考试的第一名。在1843年的数学荣誉学位考试中,据说他的分数是第二名的一倍,如果属实,这是一项令人难以置信的成就。同样在1843年,他成为第一位史密斯奖获得者,并成为圣约翰学院的会士。然而,他并没有把所有时间都花在研究上,因为他辅导本科生,以便赚钱寄回家帮助弟弟的教育。我们应该注意到,在他的三个兄弟中,Thomas Adams成为传教士,George Adams成为农民,而William Grylls 亚当斯成为伦敦国王学院的自然哲学和天文学教授,并当选为皇家学会会士。
1841年7月3日,还在读本科时,亚当斯记下他已决定研究:-
……天王星运动的不规则性……以查明它们是否可归因于其外侧一颗未被发现的行星的作用。
1845年9月,亚当斯向剑桥天文台台长James Challis提供了关于新行星位置的准确信息。Challis给格林尼治皇家天文学家乔治·比德尔·艾里写了一封介绍信给亚当斯。亚当斯在10月两次拜访格林尼治,试图见到乔治·比德尔·艾里,但他没有预约,因此未能成功。他确实留下了给出他预测位置的数据,乔治·比德尔·艾里收到了这些数据,并给亚当斯写了一封信,提出了他认为至关重要的问题。亚当斯觉得乔治·比德尔·艾里的问题微不足道,因此没有回复。剑桥天文台没有采取行动。拉尔夫·艾伦·桑普森写道[6]:-
詹姆斯·惠特布雷德·李·格莱舍在[9]中报告说,亚当斯说他期望乔治·比德尔·艾里会有:-
……在他的通信者中传播我的结果。
詹姆斯·惠特布雷德·李·格莱舍总结[9]:-
作为大学[Challis]的教授,他不应该允许一位年轻的Senior Wrangler,由于谦虚、缺乏自信或缺乏经验,对自己如此不公。
1845年11月,亚当斯当选为皇家天文学会会士,并非凭借他对那颗仍未被发现的新行星的预测,而是凭借他的论文Elements of the comet Faye,Challis在文中报道说:-
……[亚当斯]表明,这颗彗星也许在其当前轨道上运行的时间并不长,而且,如同1770年那颗彗星的情形一样,我们应归功于木星的作用,才使它有了现在的这次出现。
于尔班·勒维耶的预测于1846年6月发表,而亚当斯的预测当时仍只有Challis和乔治·比德尔·艾里知道。尽管这一已发表的预测与亚当斯的预测接近,他仍未就自己的优先权提出任何主张。奇怪的是,乔治·比德尔·艾里写信给于尔班·勒维耶,提出了他曾向亚当斯提出的同一个问题,但仍未提及亚当斯的预测(事实上,亚当斯的名字也未被提及)。正是于尔班·勒维耶的预测导致了1846年9月23日Galle在柏林天文台发现海王星。
Hutchins在[3]中写道:-
亚当斯在其大学里备受推崇,被视为自艾萨克·牛顿以来最具想象力的英国数学头脑和计算能力的人。他从未说过一句反对Challis或乔治·比德尔·艾里的话,而这种缄默以及他温和的性格使他深受许多人喜爱。
Royal Astronomical Society在亚当斯和于尔班·勒维耶的问题上处境困难。在1846年11月14日的会议上,除了来自乔治·比德尔·艾里和Challis的、解释他们关于亚当斯预测之行动的信件外,还宣读了一篇来自亚当斯的论文,题为Explanation of the observed irregularities in the motion of Uranus。桑普森在[6]中写道:-
没有一句抱怨、怨恨或遗憾的话。几乎没有一句涉及个人的话,只有一个宽宏大量的段落把全部荣誉让给了于尔班·勒维耶。
亚当斯亲自出席了会议,据说他[6]:-
……表现得像个害羞的男孩。
他的论文于1847年1月发表。你可以在THIS LINK读到这篇论文。
然而在此之后,Royal Astronomical Society陷入了谁应获得其金质奖章这一无法解决的问题。他们的规定只允许颁发一枚奖章,因此经过多次争论,两人都未因发现海王星而获得金质奖章。不过,亚当斯因关于月球近地点和加速度的工作于1866年被授予金质奖章。
1852年,Adam在圣约翰学院的会士职位结束,因此他实际上失业了,尽管他继续进行研究。然而,1853年2月,他被选为剑桥大学彭布罗克学院的会士,并恢复了教学。除了其他职位外,他一直持有这个会士职位直到去世。亚当斯于1857年10月成为圣安德鲁斯大学的钦定数学教授。这个讲席的任期很短,因为1859年3月,他接替乔治·皮科克成为剑桥大学的洛恩德天文学与几何学教授,并担任该职位超过32年。他于1861年成为剑桥天文台台长,但为他的任命谈判了相当不寻常的条件。天文台资金不足,Challis曾努力为其争取支持。最终,在1858年12月,Challis与Anne Sheepshanks安排,让她为纪念她的兄弟而捐款。Challis和乔治·加布里埃尔·斯托克斯联系亚当斯,请他接任台长职位,以替代希望离开该职位的Challis。亚当斯对理论工作感兴趣,而不是观测,因此他提出了条件,即他不必进行观测或处理数据。如果发现工作以任何方式干扰他的研究,他可以辞去该职位。所有这一切之所以可能,是因为Sheepshanks的捐款使得能够雇用一名高级助理来承担观测工作。
1862年10月,亚当斯遇到了来自都柏林的伊丽莎白·布鲁斯,她是乔治·加布里埃尔·斯托克斯妻子的朋友。12月,当亚当斯前往爱尔兰向马克里天文台台长安德鲁·格雷厄姆提供高级助理职位时,他们再次相遇。亚当斯向伊丽莎白求婚,他们于1863年5月2日结婚。
亚当斯对天文学还做出了许多其他贡献,尤其是他对狮子座流星雨的研究。他在1864年正确预测了流星雨将在1866年11月出现。计算轨道是一项极其困难的任务,因为必须考虑行星摄动的影响。1867年3月,他表明流星雨的轨道与坦普尔彗星的轨道非常相似。他能够正确地得出结论:流星雨与那颗彗星有关。纽沃尔在[6]中写道:-
就这样确立了彗星与流星之间的密切关系。
亚当斯在描述月球运动这一复杂问题上花费了大量精力,给出了一个比皮埃尔·西蒙·拉普拉斯的理论更为精确的理论。他在1851年当选为皇家天文学会主席时开始了这项工作,并于1853年向皇家学会提交了一篇论文,其中他指出皮埃尔·西蒙·拉普拉斯从他的方程中省略了一些不可忽略的项。他对皮埃尔·西蒙·拉普拉斯工作的修正将观测轨道与预测轨道之间的差异减少了一半。现在已知这一误差是由于月球对地球的潮汐拖曳导致地球自转减慢所致。公平地说,法国人看到亚当斯修正皮埃尔·西蒙·拉普拉斯并不高兴,尤其是因为几年前当他们看到他试图贬低于尔班·勒维耶的荣耀时,他们曾愤怒地作出反应。
亚当斯还研究了地磁,确定了地球上每一点的高斯磁常数,并绘制了等磁变线地图,这些地图在他去世后出版。他还给出了木星卫星位置的表格,花费大量时间编制艾萨克·牛顿论文的目录,并将莱昂哈德·欧拉常数计算到236位小数。他总共写了约50篇论文,其中十一篇是关于纯数学的,但正是他对完美的执着使他未能发表更多。詹姆斯·惠特布雷德·李·格莱舍写道[9]:-
四十五年来,他[强大的]头脑一直专注于主要与天文学相关的数学研究[但由于他]对完美的天生渴望[他发表得很少]。
然而,亚当斯最为人所铭记的是他作为海王星共同发现者的角色。我们现在回到这个话题,因为当研究亚当斯的性格时,他在这一发现中的角色与于尔班·勒维耶的角色之间的差异就更加清楚了。剑桥的一位本科同学几乎不记得亚当斯,并这样描述他:-
一个相当矮小的男人,走路很快,穿着一件褪色的深绿色外套。
亚当斯一向一丝不苟,以为学生构造数学问题而闻名,这些问题因其优美而受到所有人的赞赏(也许正在考试的学生除外!)。他是一个学识渊博的人,研究历史、文学、生物学和地质学。他对政治有着浓厚的兴趣,并且深受普法战争的影响,据[11]说:-
……他几乎无法工作或入睡。
他从不夸耀自己的成就,事实上他拒绝了1847年授予他的爵士爵位。不过,他确实接受了牛津、都柏林、爱丁堡和博洛尼亚授予的荣誉学位。他当选为皇家学会、St Petersburg Academy和科学院的成员。
发现海王星之后,亚当斯于1847年6月在牛津首次会见了于尔班·勒维耶。根据[9]的记载:-
他没有发出任何抱怨,也没有声称自己拥有优先权,于尔班·勒维耶是最热忱的仰慕者。
1868年,于尔班·勒维耶因其关于水星、金星、地球和火星的理论而被授予皇家天文学会的金质奖章。亚当斯作为该学会的主席,在1876年于尔班·勒维耶因其关于木星、土星、天王星和海王星的理论再次获得金质奖章时发表了颁奖致辞。然而,这一次,于尔班·勒维耶生病了,无法亲自出席。
亚当斯在科学之外的兴趣由Hutchins [3]描述如下:-
亚当斯婚姻幸福,极其虔诚,喜欢社交拜访、留客住宿、娱乐、音乐、跳舞、聚会、每天长时间散步、槌球、草地滚球和惠斯特。他对当时流行的催眠术和神秘学也有兴趣。他是一位藏书家,晚上不社交时就读书。至少从1860年到1889年,他参加The Family的每周聚会,这是一个大学用餐俱乐部。他大量参与学院和大学的事务。
1889年10月,亚当斯因胃出血而病重。他康复了,但疾病复发,这种循环重复了好几次,直到1891年6月。从这时起,显然不会再有康复。他在剑桥天文台去世。
上面的肖像是在他位于圣安德鲁斯时由先驱摄影师约翰 Adamson拍摄的。
John Couch Adams's parents were Tabitha Knill Grylls and Thomas Adams. The family was a poor one with Thomas being a tenant farmer while Tabitha also came from a farming family. Thomas and Tabitha farmed near Launceston, Cornwall, and it was on Lidcott farm that John, the eldest of his parents seven children, was born. John Couch Adams was named after his mother's uncle, John Couch. It is particularly fitting that this should be the case since John Couch provided some education for Tabitha who inherited his library which included several astronomy books. It was this library, particularly the astronomy books in it, which fired John's interest as he grew up. Hutchins writes [3]:-
Adams was brought up in a close Wesleyan family and had his mother's good ear and love of music.
John attended the nearby village school at Laneast, where he studied Greek and algebra, until he was twelve years old when he went to a private school at Devonport run by his cousin the Revd John Couch Grylls. He also attended schools at Saltash and Landulph. At the Devonport school he continued his studies of classics, showed great mathematical ability and became known for his considerable abilities for accurate numerical calculations. It was during this period that he first became interested in astronomy and in 1835, while at Landulph, he observed Halley's comet. He worked out that an annular eclipse of the Sun would be visible in Lidcot in 1836, and he was there to make the observations. His mathematical skills were, however, self-taught for he learnt little of the topic at school. He would go to the Devonport Mechanics' Institute where he looked up articles on mathematics and astronomy.
Adams was educated at St John's College, Cambridge but this was only made possible by a number of fortuitous circumstances. His mother received a small inheritance in 1836, Adams earned money as a tutor in 1837, and he then won a scholarship to St John's College. These sources of money made a university education for him possible but financially difficult. He began his undergraduate mathematics course in October 1839 and graduated as Senior Wrangler (ranked top of the First Class) four years later having, rather remarkably, won the first prize in Greek testament every year. In the Mathematical Tripos examinations of 1843 he is said to have been awarded double the marks of the Second Wrangler which, if true, is an incredible achievement. Also in 1843 he became first Smith's Prizeman and he became a Fellow of St John's College. He did not spend all his time on research, however, for he tutored undergraduates so that he might earn money to send home to help with his brother's education. We should note that of his three brothers, Thomas Adams became a missionary, George Adams became a farmer, while William Grylls Adams became professor of natural philosophy and astronomy at King's College, London, and was elected a Fellow of the Royal Society.
On 3 July 1841, while still an undergraduate, Adams made a note that he had decided to investigate:-
... the irregularities of the motion of Uranus...in order to find out whether they may be attributed to the action of an undiscovered planet beyond it.
In September 1845 Adams gave accurate information on the position of the new planet to James Challis, director of the Cambridge Observatory. Challis gave Adams a letter of introduction to Airy, the Astronomer Royal at Greenwich. Adams twice called at Greenwich during October attempting to see Airy, but he had not made an appointment and was unsuccessful. He did leave the data giving his predicted position which Airy received and sent a letter to Adams with what he considered a vital question. Adams felt that Airy's question was trivial and so did not reply. Action was not taken by the Cambridge Observatory. Sampson writes [6]:-
Glaisher, in [9], reports that Adams said that he expected Airy would have:-
... communicated my results among his correspondents.
As professor in the University [Challis] should not have allowed a young Senior Wrangler, through modesty or diffidence or inexperience, to do such injustice to himself.
In November 1845 Adams was elected a Fellow of the Royal Astronomical Society, not on the strength of his predictions for the new planet which remained unknown, but rather for his paper Elements of the comet Faye in which, Challis reported:-
... [Adams] suggests that the comet may, perhaps, not have been moving long in its present orbit, and that, as in the case of the comet of 1770, we are indebted to the action of Jupiter for its present apparition.
Urbain Le Verrier's prediction was published in June 1846 while Adams' prediction was still only known to Challis and Airy. Despite this published prediction being close to that of Adams, he still made no claim regarding his precedence. Strangely, Airy wrote to Le Verrier with the same question he had posed to Adams, but still did not mention Adams' prediction (in fact Adams' name was not mentioned). It was Le Verrier's prediction which led to the discovery of Neptune on 23 September 1846 by Galle at the Berlin Observatory.
Hutchins writes in [3]:-
Adams was lionized in his university, perceived as having the most imaginative English mathematical mind and power of calculation since Newton. He never uttered a word against Challis or Airy, and that reticence and his genial nature endeared him to many.
The Royal Astronomical Society was in a difficult position over Adams and Le Verrier. At its meeting on 14 November 1846, as well as communications from Airy and Challis explaining their actions regarding Adams' prediction, a paper from Adams was read entitled Explanation of the observed irregularities in the motion of Uranus. Sampson writes in [6]:-
There is not a phrase of complaint, bitterness, or regret. There is hardly a personal word at all. except one generous passage conceding the whole glory to Le Verrier.
Adams attended the meeting in person and is said to have [6]:-
... behaved like a bashful boy.
His paper was published in January 1847. You can read this paper at THIS LINK.
However following this the Royal Astronomical Society plunged itself into the impossible question of who should receive their Gold Medal. Their rules only allowed one medal to be awarded so after many arguments neither received a Gold Medal for the discovery of Neptune. Adams was, however, awarded the Gold Medal in 1866 for his work on the lunar perigee and acceleration.
In 1852 Adam's fellowship at St John's College ended so he effectively became unemployed although he continued his research. However in February 1853 he was elected to a fellowship at Pembroke College, Cambridge, and resumed teaching. He was to hold this Fellowship, in addition to other posts, until his death. Adams became Regius Professor of Mathematics at St Andrews in October 1857. It was a short tenure of the chair for, in March 1859, he succeeded Peacock as Lowndean Professor of Astronomy and Geometry at Cambridge and held the post for over 32 years. He became director of the Cambridge Observatory in 1861 but negotiated rather unusual conditions for his appointment. The Observatory was poorly funded and Challis had tried hard to obtain support for it. Eventually, in December 1858, Challis arranged with Anne Sheepshanks that she make a donation in memory of her brother. Challis and Stokes approached Adams to take on the directorship in place of Challis who wished to leave the post. Adams was interested in theoretical work, not in observing, so he made conditions that he would not have to observe or process data. He could resign the position if he found that the work in any way interfered with his research. All this was possible since the Sheepshanks donation enabled a senior assistant to be employed to undertake observational work.
In October 1862 Adams met Elizabeth Bruce, from Dublin, who was a friend of Stokes's wife. They met again in December when Adams went to Ireland to offer the senior assistant position to Andrew Graham, director of Markree observatory. Adams proposed marriage to Elizabeth and they were married on 2 May 1863.
Adams's made many other contributions to astronomy, notably his studies of the Leonid meteor shower. He predicted correctly in 1864 that the meteor shower would occur in November 1866. Calculating the orbit was an extremely difficult task since the effect of planetary perturbations had to be taken into account. In March 1867 he showed that the orbit of the meteor shower was very similar to that of Tempel's comet. He was able to correctly conclude that the meteor shower was associated with that comet. Newall writes in [6]:-
And thus was established the close relation between comets and meteors.
Adams spent much effort on the complex problem of a description of the motion of the Moon, giving a theory which was more accurate than that of Laplace. He began this work in 1851 when elected as President of the Royal Astronomical Society and he presented a paper to the Royal Society in 1853 in which he showed that Laplace had omitted terms from his equations which were not negligible. His corrections to Laplace's work reduced by half the discrepancy between the observed orbit and the predicted one. The error is now known to be due to the tidal drag of the moon on the Earth which is slowing down the Earth's rotation. It is fair to say that the French were not pleased to see Adams correcting Laplace, particularly since they had reacted angrily a few years earlier when they saw him as attempting to detract from Le Verrier's glory.
Adams also studied terrestrial magnetism, determined the Gaussian magnetic constants at every point on the Earth and produced maps with contour lines of equal magnetic variation which were published after his death. He also gave tables of the positions of the moons of Jupiter, spent much time on a catalogue of Newton's papers, and calculated Euler's constant to 236 decimal places. In all he wrote about 50 papers, of which eleven were on pure mathematics, but it was his passion for perfection which prevented him publishing much more. Glaisher writes [9]:-
For forty-five years his [powerful] mind was constantly directed to mathematical research relating principally to astronomy [but because of his] innate craving for perfection [he published little].
Adams will be best remembered, however, for his role as the co-discoverer of Neptune. We return to this topic now since the difference between his role in that discovery and that of Le Verrier is more clearly understood when Adams's character is studied. A fellow undergraduate at Cambridge could hardly remember Adams and described him as:-
A rather small man, who walked quickly, and wore a faded coat of dark green.
Always meticulous, Adams had a reputation for constructing mathematical questions for his students which were admired by all for their beauty (except perhaps the students being examined!). He was a man of great learning studying history, literature, biology and geology. He had a keen interest in politics and he was so affected by the Franco-Prussian war that, according to [11]:-
... he could scarcely work or sleep.
He never boasted of his achievements and in fact he refused a knighthood which was offered to him in 1847. He did, however, accept honorary degrees from Oxford, Dublin, Edinburgh, and Bologna. He was elected to the Royal Society, the St Petersburg Academy, and to the Academy of Sciences.
After the discovery of Neptune, Adams first met Le Verrier in Oxford in June 1847. According to [9]:-
He uttered no complaint, he laid no claim to priority, Le Verrier had no warmer admirer.
In 1868 Le Verrier was presented with the Gold Medal of the Royal Astronomical Society for his theories of Mercury, Venus, Earth and Mars. Adams, as President of the Society, gave the address when Le Verrier received the Gold Medal again in 1876 for his theories of Jupiter, Saturn, Uranus and Neptune. However, on this occasion, Le Verrier was ill and could not attend in person.
Adams' interests outside science are described by Hutchins [3]:-
Adams was happily married, profoundly devout, and enjoyed social visits, house guests, entertaining, music, dancing, parties, long daily walks, croquet, bowls, and whist. He shared contemporary interests in mesmerism and the occult. A bibliophile, when not socializing in the evenings he read. He attended the weekly meetings of The Family, a university dining club, at least from 1860 to 1889. He was much involved in college and university business.
In October 1889 Adams became seriously ill with a stomach haemorrhage. He recovered but the illness recurred and this cycle repeated itself several times until June 1891. From this time on it was clear that no recovery would occur. He died in the Cambridge Observatory.
The portrait above was taken when he was in St Andrews by the pioneer photographer John Adamson.
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