西蒙·纽康Simon Newcomb

西蒙·纽康的母亲是Emily Prince，新不伦瑞克一位地方法官的女儿。他的父亲弗瑞兹·约翰 Burton Newcomb是加拿大的一名校长。约翰在全国各地流动教书，特别是在新斯科舍和爱德华王子岛的不同村庄，而纽康除了从父亲那里之外没有接受过正规教育。尽管如此，他的父亲为他未来的学习提供了极好的基础。当他十六岁时，纽康在新不伦瑞克为一位名叫Foshay医生的草药师工作。他们达成协议，纽康将做五年学徒，在此期间Foshay将训练他使用草药治疗疾病。他做了两年学徒，但对Foshay不科学的方法越来越不满，意识到这个人是个骗子。他决定离开Foshay并撕毁他们的协议。

确实，他真的是走了出去，因为纽康步行了大约120英里到缅因州的Calais港，在那里他遇到了一位船长，船长同意带他去马萨诸塞州的拉斐尔·塞勒姆，条件是他愿意在船上做水手。大约1854年，他在塞勒姆与父亲团聚（John Newcomb早些时候已搬到美国），两人一起前往马里兰州。

到达马里兰州后，纽康从1854年到1856年教了两年书；第一年在肯特县Massey's Cross Roads的一所乡村学校，然后在南边不远的Sudlersville的一所学校教了一年。在业余时间，他学习了政治经济学和宗教等各种科目，但他最深入的研究是在数学和天文学方面。特别是，他在这时阅读了艾萨克·牛顿的Principia。1856年，他在华盛顿附近担任私人教师，并经常前往该市在图书馆学习数学。他能够从史密森尼学会的图书馆借到纳撒尼尔·鲍迪奇翻译的皮埃尔·西蒙·拉普拉斯的Mécanique céleste，但发现书中所包含的数学相当超出他当时的知识。

1857年，在⟦N1⟧的建议下，他在美国航海天文历办公室（当时位于马萨诸塞州剑桥）获得了一个职位。他必须承担的任务是编制用于海上导航的新天文表。在那里工作期间，他在哈佛大学劳伦斯科学学院学习，师从本杰明·皮尔斯，并于1858年毕业。在这个阶段，他把时间分配在哈佛和天文历办公室之间：在哈佛，虽然他没有正式注册，但开始进行研究；在天文历办公室，他继续从事计算工作。他最早的研究课题之一是考察小行星的轨道，试图了解它们起源的一些情况。

纽康来到美国时正值一个非常困难的时期，南方各州与北方各州之间的紧张关系不断加剧。1860年林肯当选总统后，南方各州开始脱离联邦。1861年4月战斗打响，美国海军中的几位数学教授感到自己无法再在这些军事职位上任职，于是辞职。1861年，纽康被任命为华盛顿海军天文台的数学教授和天文学家，以填补其中一次辞职造成的空缺。两年后，他与Mary Caroline Hassler结婚。

从1861年到1871年，他使用各种望远镜测定天体的位置，特别是使用一台26英寸折射望远镜——这是美国最大的此类望远镜，是在他的监督下建造的。他对行星和月球轨道背后的理论特别感兴趣，并试图通过计算其他天体引力引起的轨道摄动来改进对它们位置的预测。

当时已有的月球表是由Hansen编制的，而人们已经清楚地看到，月球正在偏离表中为它预测的位置。Hansen编制这些表时使用了可追溯到1750年的观测资料，但纽康认为使用更早的观测资料会很有价值。1870年他在巴黎观测日食时，发现他们自1672年以来就进行了高质量的观测，并且仍然保存着那些观测的数据。事实上，纽康在巴黎时正值一个非常困难的时期，因为在前一年遭到普鲁士人的羞辱之后，获胜的德国军队穿过了巴黎。法国首都迁往凡尔赛，但1871年3月26日，巴黎人选举产生了一个称为公社的委员会。5月21日政府军被派入，巷战持续了一周。天文台陷入了战斗之中，但对纽康来说幸运的是，他已在三周前危机不断加剧之际离开了这座城市。

纽康能够研究1750年以前的观测数据，他发现Hansen的表在1750年以前的时期存在严重误差。由于他在这段时期对月球运动以及天王星和海王星位置的研究工作，他于1874年被授予皇家天文学会金质奖章。此时他已作为天文学家享有极高的声誉，因此，1875年他被授予哈佛学院天文台台长一职。然而他拒绝了，因为尽管他在观测天文学方面取得了成就，他真正热爱的却是计算以及发展数学理论来解释观测数据。

1877年，纽康成为美国航海天文历办公室主任（此时该办公室位于华盛顿），这确实给了他一个强调计算而非观测的职位。随后他开始了自己最重要的工作，用他自己的话说，这给了[3]：-

……根据现有最佳数据系统地确定天文学常数，重新研究天体运动理论，并编制用于构建星历表以及这些结果的其他应用的表格、公式和规则。

他承担这项工作的原因是：-

……外国和各机构的天文学家在工作中所使用的基本数据各不相同，由此产生的混乱遍及整个精确天文学体系。

他还在3中解释了他如何着手实现这些目标：-

我所规划的工作方案，作为其中一个分支，涉及讨论自1750年以来世界主要天文台对太阳、月球和行星位置以及顺便对明亮恒星所作的一切有价值的观测。几乎可以说，这涉及在十年或十五年的时间内，重复过去一个多世纪中世界天文学工作的重要部分。……这项工作的其他分支是……计算各行星彼此之间摄动的公式。

纽康于1884年被任命为约翰威廉·霍普金斯大学数学和天文学教授，担任此职位至1893年。在1885年至1900年的大部分时间里，他是American Journal of Mathematics的编辑。他还是美国天文学会的创始成员和第一任主席（1899-1905）。他于1897年至1898年担任美国数学会主席。

尽管纽康的大部分工作是在数学天文学领域，但他的一些论文是纯理论的。他写了一篇论文，展示了一颗行星的坐标如何可以用三角级数来表示。皮埃尔·西蒙·拉普拉斯曾设计了一种涉及余弦级数的方法，用于计算其他行星对一颗行星产生的摄动力。级数中的系数被称为“皮埃尔·西蒙·拉普拉斯系数”，但该方法的缺点是它只适用于圆轨道。纽康展示了如何通过引入作用于皮埃尔·西蒙·拉普拉斯系数的微分算子，将皮埃尔·西蒙·拉普拉斯的级数推广到椭圆轨道的情形，从而给出摄动函数。这些微分算子后来被称为“纽康算子”。他还撰写了关于non-euclidean geometry和阿瑟·凯莱的文章，在评论他的一个定理时说：-

... from the boldness of the conception and beauty of the result a very remarkable one, and constitutes an important addition to theoretical dynamics。

纽康在其助手乔治·威廉·希尔的帮助下，计算了天文常数的值，这些值都是对先前公认值的重大改进。在1896年于巴黎达成的一项相当引人注目的国际协议中，决定世界上每个国家的历表都应使用纽康对这些常数的取值。达成该协议的巴黎会议还交给纽康一项任务：完成一份亮星位置和运动的星表，并计算一个新的岁差值。由于纽康在一年后达到了强制退休年龄，这项任务变得更加困难，但已作出安排以使工作得以完成，并给了他一个顾问角色。卡内基研究所为他继续研究月球轨道理论提供了资助。

然而，纽康做出重大贡献的领域并不仅限于数学和天文学。自从在美国开始学习以来，他就对政治经济学感兴趣，并撰写了关于该主题的文章和书籍。他在该主题上的主要著作是教科书Principles of political economy（1885年）。约翰·梅纳德·凯恩斯将这部著作描述为：-

……那些原创性著作之一，一个未被过多正统内容所扭曲的新鲜科学头脑，能够不时在像经济学这样一门半成形的学科中产生这样的著作。

在[5]中，描述了纽康在学术主题之外的兴趣：-

他能流利地说法语和德语，并且对意大利语和瑞典语也懂得足够多，足以在这些国家舒适地旅行。他从小习惯长距离步行，一生都继续这种锻炼方式，每天在办公时间结束到晚餐之间步行数英里。星期天步行的时间要长得多。在国外期间，没有什么比去瑞士的徒步旅行更让他高兴的了。即使到了七十岁，他还爬上了马特洪峰一侧高处的木屋，这对一个他这个年纪的人来说几乎是前所未有的壮举。他热爱旅行。……他充满乐趣，喜欢在孩子们年幼时和他们嬉戏打闹。他广泛阅读历史和其他文学作品，能一页又一页地背诵诗歌。他热爱艺术……他还是一位国际象棋高手……

我们还应补充一点，他是一位通俗天文学书籍的作者，如Popular astronomy（1878年）、Astronomy for schools and colleges（1880年）、Elements of astronomy（1890年）、The stars（1901年）、Astronomy for everyone（1903年）和Spherical astronomy（1906年）。他还写了一部科幻小说His wisdom the defender，于1900年出版。

纽康获得了许多荣誉，事实上，在[5]中列出这些荣誉几乎需要两页。在这些荣誉中，他于1877年当选为皇家学会会士，并于1890年获得其科普利奖章。他当选为世界上大多数主要科学学会的荣誉会员，并因其工作获得了许多奖项和奖金。这些包括上文提到的1874年来自皇家天文学会的金奖，以及1878年来自哈勒姆科学院的克里斯蒂安·惠更斯奖章。法国于1893年授予他荣誉军团骑士称号。太平洋天文学会于1898年授予他布鲁斯奖章（这是该奖章的首次颁发）。引文记录道：-

……无可置疑的事实是，自本杰明·富兰克林以来，他比任何其他美国人做得都多，使美国科学在全世界受到尊重和尊敬。

1908年9月，他的健康状况开始恶化，被诊断出患有膀胱癌。意识到自己时日无多，他将最后几个月投入到完成关于The Motion of the Moon的主要著作中，并在去世前不久完成了这部著作[1]：-

纽康以军礼安葬于阿灵顿国家公墓；塔夫脱总统和几个外国政府的代表出席了葬礼。

Simon Newcomb's mother was Emily Prince, the daughter of a New Brunswick magistrate. His father, John Burton Newcomb, was a school master in Canada. John moved around teaching in different parts of the country, particularly in different villages in Nova Scotia and Prince Edward Island, and Simon received no formal education other than from his father. Nevertheless his father provided him with an excellent foundation for his future studies. When he was sixteen years old Simon took a job with a herbalist, called Dr Foshay, in New Brunswick. They entered an agreement that Newcomb would serve a five year apprenticeship during which time Foshay would train him in using herbs to treat illnesses. For two years he was an apprentice but became increasingly unhappy about Foshay's unscientific approach, realising that the man was a charlatan. He made the decision to walk out on Foshay and break their agreement.

Indeed he did literally walk out, for Newcomb walked about 120 miles to the port of Calais in Maine where he met the captain of a ship who agreed to take him to Salem in Massachusetts if he was prepared to work as a sailor on board ship. In about 1854 he joined his father in Salem (John Newcomb had moved earlier to the United States), and the two journeyed together to Maryland.

After arriving in Maryland, Newcomb taught for two years from 1854 to 1856; for the first year in a country school in Massey's Cross Roads, Kent County, then for a year at a school not far south in Sudlersville. In his spare time he studied a variety of subjects such as political economy and religion, but his deepest studies were made in mathematics and astronomy. In particular he read Newton's Principia at this time. In 1856 he took up a position as a private tutor close to Washington and he often travelled to that city to study mathematics in the libraries there. He was able to borrow a copy of Bowditch's translation of Laplace's Mécanique céleste from the library of the Smithsonian Institution but found that the mathematics which the book contained was rather beyond his current knowledge.

In 1857, at the suggestion of the director to the Smithsonian Institution, he obtained a position in the American Nautical Almanac Office (situated in Cambridge, Massachusetts, at that time). The task which he had to undertake was producing new astronomical tables to be used for navigation at sea. While working there, he studied at the Lawrence Scientific School of Harvard University, working under Benjamin Peirce, and graduated in 1858. At this stage he divided his time between Harvard, where although not formally enrolled he began to undertake research, and the Almanac Office where he continued his computational work. One of his first research topics was to examine the orbits of the asteroids in an attempt to learn something of their origin.

Newcomb had arrived in the United States at a very difficult time with tensions rising between the southern and northern states. When Lincoln was elected president in 1860, the southern states began to leave the Union. Fighting began in April 1861 and several professors of mathematics in the United States Navy felt they could no longer serve in these military posts and resigned. In 1861 Newcomb was appointed as professor of mathematics and astronomer at the Naval Observatory at Washington to fill a vacancy created by one of these resignations. Two years later he married Mary Caroline Hassler.

He spent the years from 1861 to 1871 determining the positions of celestial objects using various telescopes but in particular a 26-inch refractor telescope, the largest such telescope in the United States, which had been built under his supervision. He became particularly interested in the theory behind the orbits of the planets and the moon, and looked to improve their predicted positions by calculating the perturbations in their orbits caused by the gravitational attraction of other bodies.

The tables for the moon which existed at this time had been compiled by Hansen, and it had become clear that the moon was deviating from the position predicted for it in the tables. Hansen had used observations dating back to 1750 in order to compile the tables but Newcomb felt that using older observations would be valuable. When he was in Paris to observe a solar eclipse in 1870, he discovered they had made high quality observations since 1672 and still held the data from those observations. In fact Newcomb was in Paris at a very difficult period for, following humiliation by the Prussians in the previous year, the victorious German armies marched through Paris. The French capital moved to Versailles but on 26 March 1871 the Parisians elected a council called the Commune. The Government forces were sent in on 21 May and street fighting lasted for a week. The Observatory was caught in the midst of the fighting but, fortunately for Newcomb, he had been able to leave the city three weeks earlier in the midst of the mounting crisis.

Once Newcomb was able to study the pre-1750 observational data, he discovered that Hansen's tables were badly in error for the period before 1750. For his work during this period on the moon's motion, and also on the positions of Uranus and Neptune, he was awarded the Gold Medal of the Royal Astronomical Society in 1874. By now he had a very high reputation as an astronomer and, as a consequence, he was offered the post of Director of the Harvard College Observatory in 1875. He declined, however, since despite his achievements in observational astronomy his real love was in computation and developing mathematical theories to explain the observational data.

In 1877 Newcomb became director of the American Nautical Almanac Office (by this time in Washington) and this did indeed give him a position where the emphasis was on computation rather than observation. He then started his most important work which, in his own words, gave [3]:-

... a systematic determination of the constants of astronomy from the best existing data, a reinvestigation of the theories of the celestial motions, and the preparation of tables, formulae, and precepts for the construction of ephemerides, and for other applications of the same results.

The reason he undertook this work was because of the:-

... confusion which pervaded the whole system of exact astronomy, arising from the diversity of the fundamental data made use of by the astronomers of foreign countries and various institutions in their work.

He also explained in [3] how he went about achieving these aims:-

The programme of work which I mapped out involved, as one branch of it, a discussion of all the observations of value on the positions of the sun, moon, and planets, and incidentally on the bright fixed stars, made by the leading observatories of the world since 1750. One might almost say it involved repeating, in a space of ten or fifteen years, an important part of the world's work in astronomy for more than a century past. ... The other branches of the work were ... the computation of the formulae for the perturbation of the various planets by each other.

Newcomb was appointed professor of mathematics and astronomy at Johns Hopkins University in 1884, holding this position until 1893. He was an editor of the American Journal of Mathematics for most of the period from 1885 to 1900. He was also a founding member and first president (1899-1905) of the American Astronomical Society. He served as president of the American Mathematical Society from 1897 to 1898.

Although most of Newcomb's work was in mathematical astronomy, some of his papers were purely theoretical. He wrote a paper showing how the coordinates of a planet might be represented by trigonometric series. Laplace had devised a method involving cosine series for computing the perturbing force on a planet caused by other planets. The coefficients in the series were known as 'Laplace coefficients' but the drawback of the method was that it only worked for circular orbits. Newcomb showed how to extend Laplace's series to give a perturbing function in the case of elliptical orbits by introducing differential operators which act on the Laplace coefficients. These differential operators became known as 'Newcomb operators'. He also wrote on non-euclidean geometry and Cayley commented on one of his theorems saying:-

... from the boldness of the conception and beauty of the result a very remarkable one, and constitutes an important addition to theoretical dynamics.

Newcomb, helped by his assistant Hill, computed values for the astronomical constants which were all major improvements on the previous accepted values. In a rather remarkable international agreement in Paris in 1896, it was decided that the ephemerides of every country in the world should use Newcomb's values for these constants. The Paris conference at which the agreement was reached also gave Newcomb the task of completing a catalogue of the positions and motions of the bright stars and also with computing a new value for precession. This task was made rather more difficult since Newcomb reached compulsory retiring age one year later, but arrangements were made to allow for the work to be completed, and he was given a consulting role. The Carnegie Institution provided financial support for him to continue working on his theory of the moon's orbit.

It was not only in mathematics and astronomy, however, that Newcomb made major contributions. He had been interested in political economy since he began his studies in the United States and he wrote articles and books on the topic. His major work on this topic is the textbook Principles of political economy (1885). Keynes described this work as:-

... one of those original works which a fresh scientific mind, not perverted by having read too much of the orthodox stuff, is able to produce from time to time in a half-formed subject like economics.

In [5] Newcomb's interests outside academic topics are described:-

He spoke French and German fluently and knew sufficient of the languages of Italy and Sweden to be able to travel in these countries with comfort. Accustomed from childhood to long walks he continued this form of exercise throughout his life, walking daily several miles between the close of office hours and dinner. On Sundays the walks were much longer. Nothing delighted him more than his walking trips to Switzerland while he was abroad. Even when he was seventy years old he climbed to the chalet high up the side of the Matterhorn, a feat almost unprecedented for a man of his age. He was a lover of travel. .. he was full of fun and loved to romp with his children, when they were young. He read history and other literature extensively and could recite page after page of poetry. He delighted in art... he was an expert chess player...

We should add to this that he was a writer of popular astronomy books such as Popular astronomy (1878), Astronomy for schools and colleges (1880), Elements of astronomy (1890), The stars (1901), Astronomy for everyone (1903), and Spherical astronomy (1906). He also wrote a science fiction novel His wisdom the defender published in 1900.

Newcomb received many honours, in fact it requires almost two pages in [5] to list them. Among these honours, he was elected a Fellow of the Royal Society in 1877 and he received its Copley Medal in 1890. He was elected an honorary member of most of the major scientific societies of the world and received many awards and prizes for his work. These included the Gold Medal from the Royal Astronomical Society in 1874 as mentioned above, and the Huygens Medal from the Haarlem Academy of Sciences in 1878. France made him chevalier of the Légion d'Honneur in 1893. The Astronomy Society of the Pacific awarded him the Bruce Medal in 1898 (the first time the Medal was awarded). The citation records:-

... the undoubted fact, that he has done more than any other American since Franklin to make American science respected and honoured throughout the entire world.

In September 1908 his health began to deteriorate and he was diagnosed with cancer of the bladder. Realising that he had not long to live he devoted his last months to completing his major work on The Motion of the Moon which he completed shortly before his death [1]:-

Newcomb was buried with military honours in Arlington National Cemetery; President Taft and the representatives of several foreign governments attended the funeral.