乔治·加布里埃尔·斯托克斯Sir George Stokes, 1st Baronet

斯托克斯的父亲乔治·加布里埃尔·斯托克斯是斯莱戈郡斯克林教区的新教牧师。他的母亲伊丽莎白·霍顿是一位教会牧师的女儿，因此斯托克斯的成长环境非常宗教化。他是六个孩子中最小的，他的三个哥哥都成为了牧师。正如斯托克斯后来参加的剑桥教堂的牧师所写（见[18]）：-

尽管他在信仰和宗教同情心上从不狭隘，但他始终坚守从父亲那里学到的简单福音真理……

在[4]中，斯托克斯成长的环境被用比今天可能使用的更为生动的语言描述：-

斯克林教区长住宅的家庭生活非常幸福，孩子们在清新的海风中长大，体格健壮，思维活跃。为了满足这个大家庭的教育需求，需要极大的节约……

斯托克斯能够给予孩子们的不仅是宗教教育，还有更广泛的教育启蒙。特别是，由于曾在都柏林三一学院学习，他能够教斯托克斯拉丁语法。在上学之前，斯托克斯还由他父亲在斯克林教区的职员教导。1832年离开斯克林后，斯托克斯在都柏林上学。他在都柏林休姆街的R·H·沃尔牧师学校度过了三年，但他不是该校的寄宿生，这三年里他与叔叔John Stokes同住。事实上，家庭经济状况不允许他接受更昂贵的教育，但在这所学校[4]：-

他学习通常的学校课程，并因解决几何问题而引起了数学老师的注意。

正是在斯托克斯于都柏林度过的三年间，他的父亲去世了，这一事件正如人们所预料的那样，对这位年轻人产生了重大影响。

1835年，16岁的斯托克斯移居英格兰，进入布里斯托尔的布里斯托尔学院。斯托克斯在这所学院度过的两年，对他准备剑桥大学的学习至关重要。学院院长乔治·杰拉德博士是一位爱尔兰人，曾与斯托克斯的一位兄长William Stokes一同就读于剑桥大学。杰拉德博士本人是一位数学家，但斯托克斯在布里斯托尔学院的数学是由Francis Newman教授的（Francis Newman是弗瑞兹·约翰Henry Newman的兄弟，后者后来成为枢机主教马克斯·纽曼，并成为1833年创立的英格兰教会牛津运动的领袖）。显然，斯托克斯的数学天赋在布里斯托尔学院学习期间就已显露，因为他赢得了数学奖项，杰拉德博士写信给他（见[4]）：-

我已极力建议你的兄长让你进入三一学院，因为我确信，你极有可能在该学院获得研究员职位。

斯托克斯于1837年进入的并非三一学院，而是剑桥大学彭布罗克学院。关于他进入剑桥时的数学背景，存在一些细微的不一致。根据布里斯托尔学院的课程（据学院文献记载）（见[5]）：-

……学生应熟悉微分和积分，并进而学习静力学、动力学、conic sections以及艾萨克·牛顿的《原理》前三节……

然而，斯托克斯本人在1901年写道（例如见[4]）：-

1837年，我进入剑桥大学彭布罗克学院。那时，来上大学的男生一般不像现在这样在数学上已经读得那么深；我进学院时还没有开始学微分学，只是最近才读过解析截面。

在斯托克斯于剑桥的第二年，他开始接受威廉·霍普金斯的辅导，威廉·霍普金斯是剑桥著名的辅导教师，其作用比讲师更为重要。斯托克斯写道[4]：

在我第二年，我开始跟一位私人导师威廉·霍普金斯先生学习，他因有极多的学生在大学数学荣誉学位考试中获得高位而闻名……

威廉·霍普金斯对斯托克斯数学兴趣的方向产生了强烈影响。威廉·霍普金斯[5]：

……例如，他赞扬物理天文学和物理光学的研究，因为它们表明数学是‘人类可能借以认识到物质宇宙结构中如此多完美而美丽之物及其支配规律的唯一研究工具’。

1841年，斯托克斯在数学荣誉学位考试中以高级数学荣誉学位考试一等及格者（Wrangler）（最高一等学位）毕业，并且是第一位史密斯奖获得者。彭布罗克学院立即授予他研究员职位。他写道[4]：

取得学位后，我继续留在学院居住并招收私人学生。我想我该尝试一下原创性研究了……

是威廉·霍普金斯建议斯托克斯从事流体动力学研究的，而这确实也是斯托克斯开始工作的领域。除了威廉·霍普金斯的建议之外，斯托克斯进入这一领域还受到乔治·格林近期工作的启发。斯托克斯在1842年和1843年发表了关于不可压缩流体运动的论文，特别是1842年的On the steady motion of incompressible fluids。完成这项研究后，斯托克斯发现让-马里·迪阿梅尔已经得到了类似的结果，但由于让-马里·迪阿梅尔一直在研究固体中的热分布，斯托克斯认定自己的结果是在足够不同的情形下得到的，足以证明他发表是正当的。

斯托克斯随后继续他的研究，考察他考虑运动流体内部摩擦的情形。在他推导出正确的运动方程后，斯托克斯发现他再次不是第一个得到这些方程的人，因为克洛德-路易·纳维、西莫恩·德尼·泊松和阿代马尔·巴雷·德·圣维南已经考虑过这个问题。事实上，这种结果重复并不完全是偶然，而是由于当时剑桥对大陆数学家工作的了解不足所致。斯托克斯再次认定他的结果是在足够不同的假设下得到的，足以证明发表是合理的，并于1845年发表了On the theories of the internal friction of fluids in motion。该工作还讨论了弹性固体的平衡和运动，斯托克斯使用连续性论证来证明弹性固体与黏性流体具有相同的运动方程是合理的。

也许，斯托克斯被公认为领先数学家的最重要事件，是他于1846年提交给英国协会 for the Advancement of Science的Report on recent researches in hydrodynamics。但流体研究肯定不是他此时作出重大贡献的唯一领域。1845年，斯托克斯发表了一篇关于光行差的重要著作，这是关于该主题的一系列重要著作中的第一部。他还利用关于流体中摆运动的工作来考虑地球上不同点重力的变化，并于1849年发表了一部具有重大意义的大地测量学著作On the variation of gravity at the surface of the earth。

1849年，斯托克斯被任命为剑桥的卢卡斯数学讲席教授。1851年，他当选为皇家学会会士，1852年被授予该学会的伦福德奖章，并于1854年被任命为该学会秘书。卢卡斯讲席的薪酬很低，因此斯托克斯需要赚取额外收入，他通过接受卢卡斯讲席之外的额外职位来做到这一点，即伦敦政府矿业学校的物理学教授。

斯托克斯关于摆体在流体中运动的工作，导致了1851年一篇关于流体动力学的基础性论文，当时他发表了他的黏性定律，描述了小球在黏性流体中的速度。他发表了若干关于光的波动理论的重要研究，例如1849年一篇关于衍射的论文。这篇论文在[14]中得到了详细讨论，作者们写道：-

……斯托克斯的结果与光的弹性理论相关，补充并扩展了若干问题，这些问题此前大多是在奥古斯丁·路易·柯西的著作中研究过的。斯托克斯解决衍射问题的方法与奥古斯丁·路易·柯西所采用的方法有相当大的不同，构成了对衍射现象数学理论进一步研究的基础。

斯托克斯在1852年命名并解释了荧光现象。他对这一现象的解释——该现象源于紫外光的吸收和蓝光的发射——基于一种弹性以太，它因被照亮的分子而振动。论文[12]对此作了详细讨论，而且特别有趣，因为作者充分利用了斯托克斯未发表的笔记本。

1854年，斯托克斯提出了对太阳光谱中夫琅禾费线的一种解释。他提出这些是由太阳外层中的原子吸收某些波长引起的。然而，当古斯塔夫·基尔霍夫后来发表这一解释时，斯托克斯否认有任何优先发现权。

斯托克斯的职业生涯在1857年确实走上了一条相当不同的路线，当时他从极为活跃的理论研究时期转入一个更多参与行政和实验工作的时期。当然，他1857年的婚姻与这一路线转变并非无关，尤其是因为它让我们得以一窥斯托克斯的个性，我们将考察这些事件。斯托克斯与玛丽·苏珊娜·罗宾逊订婚，她是爱尔兰阿马天文台天文学家的女儿。在[4]中给出了若干封斯托克斯写给玛丽·苏珊娜·罗宾逊的信。1857年1月21日，他写下了对她的感情：-

我能够被一种信念所打动，可以说是在数学上被打动，即相信某一条特定的道路是正确的；我确实相信上帝把这些观点放在我的心中，通过我里面已有的来补足那缺乏的。

三天后他写道，她阻止了他变成一个老单身汉：-

我觉得也许我和你结婚甚至会是我得救的转折点。

又过了三天，他写道：-

你说得完全对，最好不要一味沉思于自己的想法和感受，在一个家庭里这很容易，但你不知道完全独自生活是什么滋味。

1857年3月31日，他再次写信，用相当数学化的语言表达了他的感受：-

我也觉得我近来想得太多，但方式不同，我的脑子总在转发散级数、任意常数的不连续性……我常想，你若能让我不至于过分沉迷于这些事情，对我会有好处。

这些信显然没有表达出玛丽希望从中找到的爱意，当斯托克斯给她写了一封55页的信（这封信可能被有意销毁了），谈到他觉得自己对她负有责任时，她几乎在最后一刻取消了婚礼。收到她那封表明她不愿继续这桩婚事的信后，斯托克斯回复道：——

那么，即使现在你退缩也是对的，不必顾虑我会作为一个没有生气、没有欢愉、也没有家庭亲情温暖的思想机器走向坟墓。

婚礼还是举行了，斯托克斯确实告别了他那种紧张投入数学研究的生活。从上面这些引文或许可以看出，事实上斯托克斯正是在寻求生活中的这种改变，也许他寻求婚姻，部分原因就是想让这种生活方式的改变得以实现。

当时剑桥的会士必须未婚，因此1857年结婚时，斯托克斯不得不放弃他在彭布罗克学院的会士职位。不过，1862年规则修改后，已婚男子可以担任会士，他又得以重新获得彭布罗克学院的会士职位。斯托克斯自1854年获任命起担任皇家学会的秘书，直到1885年当选为该学会主席。他担任主席一职直到1890年。他还从1886年起担任维多利亚研究所所长，直到1903年去世。他还承担了其他一些行政事务。1859年，他曾写信给开尔文说：——

我现在又有一件事要忙了：我刚被任命为剑桥大学委员会的一名增补秘书。

彼得·格思里·泰特在他对英国科学组织方式的批评中提到了这一点[19]：-

像斯托克斯这样的天才被浪费在剑桥大学专员委员会秘书的苦差事上，或者矿业学校的讲师职位上，或者皇家学会秘书那种令人精疲力竭且报酬完全不足的工作上，这本身就是对现实状况多么深刻的评论。

斯托克斯于1893年从皇家学会获得了科普利奖章，并且在1902-3年担任彭布罗克学院院长时，获得了学院所能给予的最高荣誉。

斯托克斯的影响在Parkinson的[1]中得到了很好的总结：-

……斯托克斯对包括詹姆斯·克拉克·麦克斯韦在内的后续几代剑桥人产生了非常重要的塑造性影响。与乔治·格林（后者反过来又影响了他）一起，斯托克斯追随了法国人的工作，尤其是约瑟夫·拉格朗日、皮埃尔·西蒙·拉普拉斯、约瑟夫·傅里叶、西莫恩·德尼·泊松和奥古斯丁·路易·柯西。这一点在他关于光学和流体力学的理论研究中表现得最为明显；但也应当注意到，斯托克斯甚至在做本科生时就不断地进行实验。然而，他的兴趣和研究范围超出了物理学，因为他在化学和植物学方面的知识很广博，而且他在光学方面的工作常常把他带入这些领域。

他出版物清单中一个明显的遗漏是一部关于光的专著。这一遗漏部分是由于1857年之后他研究产出的变化，但也部分是由于他不愿报告一个正处于快速进展领域中的推测性想法。斯托克斯未能出版一部光学专著一事在[8]中有详细讨论。然而，他确实在1891-93年于阿伯丁大学的伯内特讲座中讲授了光学，这些讲座被出版了。

斯托克斯的数学和物理论文出版了五卷，其中前三卷由斯托克斯自己编辑，分别于1880年、1883年和1891年出版。最后两卷由约瑟夫·拉莫尔编辑，工作于1905年完成。

这些关于斯托克斯在[3]中性格的评论很有趣：-

从1887年到1892年，他是剑桥大学的议员之一。尽管——或许是因为——他渊博精深的知识和卓越的能力，他很少在下议院发言，但人们总是专注地倾听他的讲话。在私人生活中，他的简朴和谦逊与他的巨大成就一样引人注目。

George Stokes' father, Gabriel Stokes, was the Protestant minister of the parish of Skreen in County Sligo. His mother, Elizabeth Haughton, was the daughter of a minister of the church, so George Stokes' upbringing was a very religious one. He was the youngest of six children and every one of his three older brothers went on to become a priest. As the priest of the church in Cambridge which Stokes later attended wrote (see [18]):-

Though he was never narrow in his faith and religious sympathies, he always held fast by the simple evangelical truths he learnt from his father...

In [4] the atmosphere in which George grew up is described in words which are more colourful than those which might be used today:-

The home-life in the Rectory at Skreen was very happy, and the children grew up in the fresh sea-air with well-knit frames and active minds. Great economy was required to meet the educational needs of the large family...

It was not only religious teaching, but a wider introduction to education, which Gabriel Stokes was able to give his children. In particular, having studied at Trinity College Dublin, he was able to teach George Latin grammar. Before going to school George was also taught by the clerk in his father's parish in Skreen. Leaving Skreen in 1832, George attended school in Dublin. He spent three years at the Rev R H Wall's school in Hume Street, Dublin, but he was not a boarder at the school, living for these three years with his uncle John Stokes. In fact the family finances would not have allowed him a more expensive education, but at this school [4]:-

He pursued the usual school studies, and attracted the attention of the mathematical master by his solution of geometrical problems.

It was during George's three years in Dublin that his father died and this event had, as one would expect, a major effect on the young man.

In 1835, at the age of 16, George Stokes moved to England and entered Bristol College in Bristol. The two years which Stokes spent in Bristol at this College were important ones in preparing him for his studies at Cambridge. The Principal of the College, Dr Jerrard, was an Irishman who had attended Cambridge University with William Stokes, one of George's elder brothers. Dr Jerrard was himself a mathematician but Stokes was taught mathematics at Bristol College by Francis Newman (who was the brother of John Henry Newman, later Cardinal Newman, who became the leader of the Oxford Movement in the Church of England which was founded in 1833). Clearly Stokes talent for mathematics was shown during his studies at Bristol College, for he won mathematics prizes and Dr Jerrard wrote to him (see [4]):-

I have strongly advised your brother to enter you at Trinity, as I feel convinced that you will in all human probability succeed in obtaining a Fellowship at that College.

It was not Trinity, rather Pembroke College, Cambridge, which Stokes entered in 1837. There are slight inconsistencies in what his mathematical background was on entering Cambridge. In the course at Bristol College (according to the College literature) (see [5]):-

... a student was to become acquainted with the differential and integral calculus and to go on to statics, dynamics, conic sections and the first three sections of Newton's "Principia"...

However, Stokes himself wrote in 1901 (see for example [4]):-

I entered Pembroke College, Cambridge in 1837. In those days boys coming to the University had not in general read so far in mathematics as is the custom at present; and I had not begun the differential calculus when I entered the College, and had only recently read analytical sections.

In Stokes' second year at Cambridge he began to be coached by William Hopkins, a famous Cambridge coach who played a more important role than the lecturers. Stokes wrote [4]:-

In my second year I began to read with a private tutor, Mr Hopkins, who was celebrated for the very large number of his pupils gaining high places in the University examinations for mathematical honours...

Hopkins was to exert a strong influence on the direction of Stokes' mathematical interests. Hopkins [5]:-

... praised the study of physical astronomy and physical optics, for example, because they revealed mathematics to be 'the only instrument of investigation by which man could possibly have attained to a knowledge of so much of what is perfect and beautiful in the structure of the material universe, and the laws that govern it'.

In 1841 Stokes graduated as Senior Wrangler (the top First Class degree) in the Mathematical Tripos and he was the first Smith's prizeman. Pembroke College immediately gave him a Fellowship. He wrote [4]:-

After taking my degree I continued to reside in College and took private pupils. I thought I would try my hand at original research....

It was William Hopkins who advised Stokes to undertake research into hydrodynamics and indeed this was the area in which Stokes began to work. In addition to Hopkins's advice, Stokes was also inspired to enter this field by the recent work of George Green. Stokes published papers on the motion of incompressible fluids in 1842 and 1843, in particular On the steady motion of incompressible fluids in 1842. After completing this research Stokes discovered that Duhamel had already obtained similar results but, since Duhamel had been working on the distribution of heat in solids, Stokes decided that his results were obtained in a sufficiently different situation to justify him publishing.

Stokes then continued his investigations, looking at the situation where he took into account internal friction in fluids in motion. After he had deduced the correct equations of motion Stokes discovered that again he was not the first to obtain the equations since Navier, Poisson and Saint-Venant had already considered the problem. In fact this duplication of results was not entirely an accident, but was rather brought about by the lack of knowledge of the work of continental mathematicians at Cambridge at that time. Again Stokes decided that his results were obtained with sufficiently different assumptions to justify publication and he published On the theories of the internal friction of fluids in motion in 1845. The work also discussed the equilibrium and motion of elastic solids and Stokes used a continuity argument to justify the same equation of motion for elastic solids as for viscous fluids.

Perhaps the most important event in the recognition of Stokes as a leading mathematician was his Report on recent researches in hydrodynamics presented to the British Association for the Advancement of Science in 1846. But a study of fluids was certainly not the only area in which he was making major contributions at this time. In 1845 Stokes had published an important work on the aberration of light, the first of a number of important works on this topic. He also used his work on the motion of pendulums in fluids to consider the variation of gravity at different points on the earth, publishing a work on geodesy of major importance On the variation of gravity at the surface of the earth in 1849.

In 1849 Stokes was appointed Lucasian Professor of Mathematics at Cambridge. In 1851 he was elected to the Royal Society, awarded the Rumford medal of that Society in 1852, and he was appointed secretary of the Society in 1854. The Lucasian chair paid very poorly so Stokes needed to earn additional money and he did this by accepting an additional position to the Lucasian chair, namely that of Professor of Physics at the Government School of Mines in London.

Stokes' work on the motion of pendulums in fluids led to a fundamental paper on hydrodynamics in 1851 when he published his law of viscosity, describing the velocity of a small sphere through a viscous fluid. He published several important investigations concerning the wave theory of light, such as a paper on diffraction in 1849. This paper is discussed in detail in [14] in which the authors write:-

...the results of Stokes are related to the elastic theory of light, and supplement and expand a number of questions, previously studied for the most part in the works of A Cauchy. Stokes's methods for solving diffraction problems, differing considerably from the methods employed by Cauchy, form the basis of the further studies of the mathematical theory of the phenomenon of diffraction.

Stokes named and explained the phenomenon of fluorescence in 1852. His interpretation of this phenomenon, which results from absorption of ultraviolet light and emission of blue light, is based on an elastic aether which vibrates as a consequence of the illuminated molecules. The paper [12] discusses this in detail and is particularly interesting since the author makes full use of Stokes' unpublished notebooks.

In 1854 Stokes theorised an explanation of the Fraunhofer lines in the solar spectrum. He suggested these were caused by atoms in the outer layers of the Sun absorbing certain wavelengths. However when Kirchhoff later published this explanation, Stokes disclaimed any prior discovery.

Stokes' career certainly took a rather different tack in 1857 when he moved from his highly active theoretical research period into one where he became more involved with administration and experimental work. Certainly his marriage in 1857 was not unconnected with the change in tack and, particularly since it gives us an insight into Stokes' personality, we shall look at the events. Stokes became engaged to marry Mary Susanna Robinson, the daughter of the astronomer at Armagh Observatory in Ireland. In [4] a number of letters from Stokes to Mary Susanna Robinson are given. On 21 January 1857 he wrote of his feelings for her:-

I was capable of being moved, mathematically, as it were, by the belief that a particular course was right; and I do believe that God put these views in my mind, working by means of that which was in me to supply that which was wanting.

Three days later he wrote that she had stopped him becoming an old bachelor:-

I feel that perhaps my marriage with you would be even the turning-point of my salvation.

A further three days later he wrote:-

You are quite right in saying that it is well not to go brooding over one's own thoughts and feelings, and in a family that is easy, but you don't know what it is to live utterly alone.

On the 31 March 1857 he wrote again expressing his feelings in rather mathematical terms:-

I too feel that I have been thinking too much of late, but in a different way, my head running on divergent series, the discontinuity of arbitrary constants, ... I often thought that you would do me good by keeping me from being too engrossed by those things.

These letters clearly did not express the love that Mary hoped to find in them and when Stokes wrote her a 55 page letter (which was possibly deliberately destroyed) about the duty he felt towards her, she came close to calling off the wedding at the last moment. On receiving her letter showing that she was unhappy to go ahead with the marriage Stokes replied:-

Then it is right that you should even now draw back, nor heed though I should go to the grave a thinking machine unenlivened and uncheered and unwarmed by the happiness of domestic affection.

The marriage did go ahead and Stokes certainly turned away from his life of intense mathematical research. It may appear from the above quotations that in fact Stokes was really looking for this change in his life and perhaps he sought marriage partly so that this change in his life-style could come about.

At that time Fellows at Cambridge had to be unmarried, and so on his marriage in 1857 Stokes had to give up his fellowship at Pembroke College. However, a change in the rules in 1862 allowed married men to hold fellowships and he was able to take up the fellowship at Pembroke again. Stokes continued as secretary of the Royal Society from his appointment in 1854 until 1885 when he was elected President of the Society. He held the position of President until 1890. He was also president of the Victoria Institute from 1886 until his death in 1903. There were other administrative tasks which he undertook. In 1859 he had written to Thomson saying:-

I have another iron in the fire now: I have just been appointed an additional secretary of the Cambridge University Commission.

P G Tait mentioned this in his criticism of the way that science was organised in Britain [19]:-

What a comment on things as they are is furnished by the spectacle of genius like that of Stokes' wasted on the drudgery of Secretary to the Commissioners for the University of Cambridge; or of a Lecturer in the School of Mines; or the exhausting labour and totally inadequate remuneration of a Secretary to the Royal Society.

Stokes received the Copley medal from the Royal Society in 1893 and he was given the highest possible honour by his College when he served as Master of Pembroke College in 1902-3.

Stokes' influence is summed up well by Parkinson in [1]:-

... Stokes was a very important formative influence on subsequent generations of Cambridge men, including Maxwell. With Green, who in turn had influenced him, Stokes followed the work of the French, especially Lagrange, Laplace, Fourier, Poisson, and Cauchy. This is seen most clearly in his theoretical studies in optics and hydrodynamics; but it should also be noted that Stokes, even as an undergraduate, experimented incessantly. Yet his interests and investigations extended beyond physics, for his knowledge of chemistry and botany was extensive, and often his work in optics drew him into those fields.

One notable omission from his publication list was a treatise on light. This omission was in part due to the change in his research output after 1857 but it was also partly due to not wishing to report upon speculative ideas in a field which was in a rapid state of progress. Stokes' failure to publish a treatise on optics is discussed in detail in [8]. However, he did lecture on optics in his Burnett lectures at the University of Aberdeen in 1891-93 and these lectures were published.

Stokes' mathematical and physical papers were published in five volumes, the first three of which Stokes edited himself in 1880, 1883 and 1891. The last two were edited by Sir Joseph Larmor with the work being completed in 1905.

These comments about Stokes' character in [3] are interesting:-

From 1887 to 1892 he was one of the members of Parliament for Cambridge University. In spite, or perhaps because of, his great and profound knowledge and remarkable ability, he rarely spoke in the House of Commons, but was always listened to with attention. In private life his simplicity and modesty were as conspicuous as his great attainments.