爱德蒙·哈雷Edmond Halley

哈雷（或Edmund）爱德蒙·哈雷的父亲也叫哈雷（或Edmund）哈雷。他来自德比郡的一个家庭，是伦敦一位富有的肥皂制造商，当时肥皂的使用正在整个欧洲传播。关于哈雷出生的日期和年份都存在一些混淆。日期的混淆仅仅是由于历法的变化（按他当时的历法是10月29日）。年份的混淆较难确定，但我们给出1656年，哈雷自己声称这是他出生的年份。

哈雷的父亲在伦敦大火中损失惨重，那一年哈雷十岁。他的父亲仍能负担得起儿子接受良好教育，哈雷在圣保罗学校上学之前，在家中接受私人辅导。正是在圣保罗学校，哈雷充分展现了他的才华，[16]：-

……在古典学和数学方面同样出色，[他]十五岁时升为学校的队长，制作日晷，观测variation of the compass的变化，并如此仔细地研究天空，以至于地球仪制作者莫克森评论说‘如果地球仪上有一颗星移位了，他马上就能发现’。

哈雷于1673年进入牛津大学王后学院，当时他十七岁，已经是一位专业的天文学家，拥有父亲为他购买的精良仪器收藏。他于1675年开始与约翰·佛兰斯蒂德合作，后者是皇家天文学家，在牛津和格林尼治协助他进行观测。约翰·佛兰斯蒂德在1675年发表于Philosophical Transactions of the Royal Society的一篇论文中评论道：-

哈雷，一位来自牛津的才华横溢的年轻人，出席了这些观测，并仔细协助了许多观测。

哈雷在牛津进行了重要观测，包括1676年6月11日月球掩火星的掩星，他将其发表在Philosophical Transactions of the Royal Society上。关于哈雷的本科生涯发生了什么，情况有点不清楚，但可以肯定的是，他于1676年放弃学业，并于当年11月航行到南半球的圣赫勒拿岛。最可能的解释是，随着1675年格林尼治皇家天文台的启用，约翰·佛兰斯蒂德承担了绘制北半球恒星图的任务，而哈雷决定通过承担南半球的类似任务来补充这一计划。

这样的任务没有财政支持是无法进行的，事实上哈雷从父亲那里获得了这样的支持，还从不少于国王查理二世那里获得了支持，国王提供了一封信，要求东印度公司将哈雷和一位同事带到圣赫勒拿岛（英国统治下的最南端领土）。其他重要人物也支持这一冒险，包括威廉·布朗克，他是皇家学会的主席，以及约纳斯·摩尔，他曾在皇家天文台的建立中发挥了重要作用。

圣赫勒拿岛的天气对天文观测来说不如哈雷所期望的那么好，但尽管如此，他在岛上逗留的十八个月里，还是编目了341颗南半球恒星，并发现了一个半人马座的星团。在航行期间[16]：-

……他改进了六分仪，收集了许多与海洋和大气有关的宝贵事实，注意到了摆锤的赤道减速现象，并于1677年11月7日在圣赫勒拿岛首次完整观测到了水星的中天。

他提出利用水星凌日（甚至更好的金星凌日）来确定太阳的距离，从而利用约翰内斯·开普勒第三定律确定太阳系的尺度。哈雷于1678年返回英格兰，并出版了他的南半球恒星目录。尽管没有从牛津大学毕业，他却发现自己拥有了顶尖天文学家之一的声誉。荣誉很快接踵而至。1678年12月3日，他成为牛津大学的毕业生，没有参加学位考试，学位是根据国王查理二世的命令授予的。他还在1678年11月30日当选为皇家学会会员，年仅22岁，成为其有史以来最年轻的会士之一。

1679年，Royal Society派哈雷前往但泽，仲裁罗伯特·胡克与赫维留之间的争端。罗伯特·胡克声称赫维留没有使用望远镜瞄准器进行的观测不可能准确。赫维留当时68岁，发现派来评判他的是一个23岁的年轻人，一定有些沮丧。然而，哈雷是[1]：-

……一个极具天生外交才能的人……

在检查了赫维留两个月来所做的观测后，他宣布这些观测是准确的。

哈雷如此迅速地获得的名声与认可，丝毫没有让他得到约翰·佛兰斯蒂德的喜爱；尽管约翰·佛兰斯蒂德在学生时代曾赞扬过哈雷，但很快就转而反对他。与皇家天文官为敌，对一位年轻天文学家来说并非最好的推荐，即使他像哈雷那样著名，也很快会付出代价。

哈雷在这一阶段没有寻求教职，宁愿自由旅行和从事研究而不受约束。1680年，他与校友Robert Nelson一起开始了欧洲之旅。哈雷在加来附近观测到一颗彗星，并前往巴黎，在那里与乔凡尼·多美尼科·卡西尼一起做了进一步观测，试图确定其轨道。1681年的大部分时间，哈雷是在意大利度过的。次年回到英格兰后，哈雷与Mary Tooke结婚，而他的父亲也再婚了（哈雷的母亲已于十年前去世）。

婚姻不仅给哈雷带来了经济责任，而且他父亲的婚姻似乎完全是一场灾难，其后果是来自父亲的资助很快枯竭。进一步的个人问题接踵而至，因为1684年3月他的父亲失踪了，五周后被发现已经死亡。哈雷不得不管理父亲的个人遗产，并卷入了家庭、财产和法律事务，这些在[12]中有详细描述。

就在父亲失踪前不久，哈雷参与了一项激动人心的研究。他证明了约翰内斯·开普勒第三定律蕴含平方反比吸引定律，并于1684年1月24日在皇家学会的一次会议上展示了结果。随后，克里斯托弗·雷恩、罗伯特·胡克和哈雷讨论了能否证明平方反比定律蕴含行星的椭圆轨道，但未能给出证明。在接下来的几周里，哈雷在这些问题上的工作因围绕父亲失踪和死亡的困难而中断，但到1682年8月，哈雷通过拜访剑桥的艾萨克·牛顿进一步研究这个问题。在那里他发现，艾萨克·牛顿已经证明了这一点以及其他极其重要的结果，但似乎并不打算发表它们。

西德尼·查普曼在[11]中写道：-

……哈雷……有天才认识到艾萨克·牛顿更伟大的数学天才，敦促他撰写《自然哲学的数学原理》，然后自掏腰包支付出版费用，因为皇家学会当时破产了……

詹姆斯·惠特布雷德·李·格莱舍在1888年于剑桥发表的一次演讲中，谈到了哈雷在促使艾萨克·牛顿的Principia出版方面所起的作用：-

……如果没有哈雷，《原理》就不会存在。……他支付了所有费用，校对了校样，搁置了自己的工作，以最大程度地推进印刷。他所有的信件都显示出对这项工作的极度投入。

此时哈雷肯定不是富人，尽管最终他允许Principia出版的财务支出从销售中得到了偿还，他现在寻求一个学术职位。1691年，他申请了牛津大学空缺的萨维尔天文学讲席。鉴于他在天文学方面的杰出研究，人们会期望他被任命到这个讲席，但约翰·佛兰斯蒂德强烈反对这一任命。

约翰·佛兰斯蒂德对艾萨克·牛顿并不友好，特别是因为他觉得艾萨克·牛顿在其月球理论中没有充分认可皇家天文台所做的观测。哈雷与艾萨克·牛顿的密切关系使他在约翰·佛兰斯蒂德眼中更加降低。然而，约翰·佛兰斯蒂德用来反对哈雷的论点是他无疑真诚相信的，他写信给牛津说哈雷会[7]：-

……败坏这所大学的青年。

约翰·佛兰斯蒂德 认为 哈雷 的基督教观点与当时要求字面信仰《圣经》的标准观点不一致，这是完全正确的。艾萨克·牛顿 还向 哈雷 抱怨说，哈雷 怀疑《圣经》创世故事在科学上的正确性。尽管 哈雷 竭力声称自己的信仰是正统的，大卫·格雷戈里 仍被任命为讲席。

缺乏学术职位并没有阻碍哈雷的科学工作。事实上，他为皇家学会担任过各种职务，从1685年到1693年任Philosophical Transactions的编辑。他通过学会的出版物频繁发表重要成果。1686年，哈雷发表了一幅显示海洋上空盛行风的世界地图。它有一个殊荣：是第一幅发表的气象图。另一项创新性工作是他在1693年发表的布雷斯劳城死亡率表。这是最早将人口死亡率和年龄联系起来的工作之一，对后来人寿保险中精算表的编制产生了很大影响。

大约从1695年起，哈雷开始仔细研究彗星的轨道。艾萨克·牛顿倾向于认为彗星具有抛物线轨道，但哈雷相信椭圆轨道可能存在。利用他的彗星轨道理论，他计算出1682年的彗星（现在称为哈雷彗星）是周期性的，并且与1531年和1607年的彗星是同一个天体。他后来还将这颗彗星与1305年、1380年和1456年出现的彗星认定为同一颗。1705年，他发表预测说它将在76年后回归，声称它会在1758年12月出现。这不是一个容易的计算，因为哈雷必须考虑木星对轨道产生的摄动。尽管到1758年哈雷已经去世十五年，但当彗星于1758年12月25日被观测到时（比哈雷预期的稍晚一点），他获得了持久的声誉。

艾萨克·牛顿 于 1696 年成为伦敦皇家铸币厂的厂长，他利用自己的影响力，使 哈雷 在同年被任命为切斯特铸币厂的副主管。这是一个他担任了两年的职位，之后该职位被撤销。离开切斯特铸币厂后，哈雷 被威廉三世授予一艘军舰“帕拉莫尔·平克”号的指挥权。这并不像听起来那么奇怪，因为 哈雷 一直在研究利用罗盘偏差确定经度，而这正是这次航行的主要目的，尽管威廉三世还要求他 [16]：-

……尝试发现西大洋以南存在什么陆地。

他于 1698 年 11 月从朴茨茅斯启航，但因船员问题被迫返回，当时已到达巴巴多斯。1699 年 9 月，他再次启航，对大西洋沿岸进行了彻底探索。1700 年 9 月返回后，哈雷 发表了罗盘偏差图，给出了第一批标有等 declination 线的图表。

1701年，哈雷回到“帕拉莫尔·平克”号上，考察了英格兰南部的潮汐和海岸。随后又有更多旅程，因为安妮女王派他视察亚得里亚海周围的港口，另一次旅程则让他前往的里雅斯特为防御工事提供建议。

哈雷 于 1704 年在 约翰·沃利斯 去世后被任命为牛津大学萨维尔几何学教授。这当然令 约翰·佛兰斯蒂德 不快，他曾写道（例如见 [13]）：-

约翰·沃利斯博士去世了——哈雷先生指望接替他的位置——此人现在说话、骂人、喝白兰地都像个船长。

哈雷的就职演讲大获成功。Thomas Hearne（见[5]）这样描述它：-

哈雷于5月24日星期三发表就职演讲，令大学里大多数人非常满意。在向大学致意之后，他接着谈论几何学的起源与进展，并介绍了古代和现代最著名的几何学家。在我国英格兰的几何学家中，他特别提到了Henry 亨利·萨维尔爵士；但他最高的赞誉给了约翰·沃利斯博士和艾萨克·牛顿先生……

这次演讲在[24]中被描述为：-

……从数学角度看具有持久的吸引力。

1710年，哈雷利用克劳狄乌斯·托勒密的星表推断恒星必定有自身的微小运动，并且他相信自己能够在三颗恒星中探测到这种自行。事实上，正如雅克·卡西尼后来所证明的[25]，他数据中的误差太大，使他无法做到这一点。

哈雷在他那个时代的事件和争论中发挥了积极作用。在艾萨克·牛顿与哥特弗里德·威廉·莱布尼茨关于谁发明了微积分的争论中，他支持艾萨克·牛顿，担任皇家学会为解决争端而设立的委员会的秘书。哈雷为平息争端做了很多工作，但似乎也特意加剧了他与约翰·佛兰斯蒂德的争端。1712年，他与艾萨克·牛顿安排，在约翰·佛兰斯蒂德的观测完成之前很久就将其发表。更糟糕的是，哈雷在约翰·佛兰斯蒂德不知情的情况下写了一篇序言，其中[11]：-

……他攻击约翰·佛兰斯蒂德迟钝、隐秘、缺乏公共精神。

1720年，他接替约翰·佛兰斯蒂德成为皇家天文学家，尽管被任命时已64岁，他仍担任该职位21年。约翰·佛兰斯蒂德的遗孀非常愤怒，将丈夫在皇家天文台的所有仪器卖掉，使哈雷无法使用它们。

在格林尼治皇家天文台，哈雷使用了第一台中星仪，并设计了一种通过月球观测确定海上经度的方法。他通过一个完整的18年沙罗周期观测月球。早期的月球观测仅在合或对当关系对太阳进行，而艾萨克·牛顿的月球理论正是基于这些早期观测。然而，哈雷作为皇家天文学家的工作受到了批评。一些人声称他进行了毫无价值的观测，其精度并不比约翰·佛兰斯蒂德的观测更高。还有人声称哈雷的观测执行得很草率。例如在[16]中：-

哈雷不考虑时间的秒的小数部分，并认为10角秒是“可达到的精度极限”。此外，他的时钟调节不良，他的记录系统没有条理。

然而，在[22]中，Ronan认为这些批评是不公平的。他在那篇文章中列出了哈雷作为皇家天文学家的成就。

哈雷的其他活动包括研究考古学、地球物理学、天文学史以及多项式方程的求解。在他创造力鼎盛时期，他是英国科学界不可或缺的一部分。

Edmond (or Edmund) Halley's father was also called Edmond (or Edmund) Halley. He came from a Derbyshire family and was a wealthy soap-maker in London at a time when the use of soap was spreading throughout Europe. There is some confusion over both the date and year of Halley's birth. The confusion over the date is simply due to the change in calendar (29 October by the calendar of his time). The confusion over the year is less easy to decide, but we give 1656 which Halley himself claimed as the year of his birth.

Halley's father lost much in the great fire of London, which was in the year in which Halley was ten years old. His father still could afford a good education for his son and Halley was tutored privately at home before being sent to St Paul's School. It was at St Paul's School that Halley showed his talents to the full, being [16]:-

... equally distinguished in classics and mathematics, [he] rose to be captain of the school at fifteen, constructed dials, observed the change in the variation of the compass, and studied the heavens so closely that it was remarked by Moxon the globe maker 'that if a star were displaced in the globe he would presently find it out'.

So Halley entered Queen's College Oxford in 1673, when he was seventeen years old, already an expert astronomer with a fine collection of instruments purchased for him by his father. He began working with Flamsteed in 1675, the Astronomer Royal, assisting him with observations both at Oxford and at Greenwich. Flamsteed, in a paper of 1675 published in the Philosophical Transactions of the Royal Society, remarked:-

Edmond Halley, a talented young man of Oxford, was present at these observations and assisted carefully with many of them.

Halley made important observations at Oxford, including an occultation of Mars by the Moon on 11 June 1676, which he published in the Philosophical Transactions of the Royal Society. It is a little unclear what happened to Halley's undergraduate career, but what is certain is that he gave up his studies in 1676 and sailed to St Helena in the southern hemisphere in November of that year. The most likely explanation is that with the opening of the Royal Observatory at Greenwich in 1675, Flamsteed undertook the task of mapping the northern hemisphere stars and Halley decided to complement this programme with undertaking a similar task for the southern hemisphere.

Such a task could not be undertaken without financial support, and indeed Halley obtained such support from his father and from no less person than King Charles II who provided a letter asking the East India Company to take Halley and a colleague to St Helena (the southern-most territory under British rule). Other important men also supported the venture, including Brouncker who was president of the Royal Society and Jonas Moore who had been a major influence in the founding of the Royal Observatory.

The weather in St Helena proved less good for astronomical observations than Halley had hoped, but despite this his eighteen month spell on the island resulted in his cataloguing 341 southern hemisphere stars and discovered a star cluster in Centaurus. During the voyage [16]:-

... he improved the sextant, collected a number of valuable facts relative to the ocean and atmosphere, noted the equatorial retardation of the pendulum, and made on St Helena, on 7 November 1677, the first complete observation of a transit of Mercury.

He proposed using transits of Mercury (and even better of Venus) to determine the distance of the Sun and therefore the scale of the solar system using Kepler's third law. Halley returned to England in 1678 and published his catalogue of southern hemisphere stars. Despite not having graduated from Oxford he found himself with the reputation of one of the leading astronomers. Honours quickly came his way. He became a graduate of the University of Oxford on 3 December 1678 without taking the degree examinations, the degree being conferred on the command of King Charles II. He was also elected a member of the Royal Society on 30 November 1678 becoming, at the age of 22, one of its youngest ever Fellows.

In 1679 the Royal Society sent Halley to Danzig to arbitrate in a dispute between Hooke and Hevelius. Hooke claimed that Hevelius's observations, made without telescopic sights, could not be accurate. Hevelius at this time was 68 years old and must have been somewhat dismayed to find that a 23 year old man had been sent to judge him. However, Halley was [1]:-

... a man of great natural diplomacy...

and after two months checking the observations Hevelius was making, he declared them to be accurate.

The fame and recognition which Halley achieved so quickly did nothing to endear him to Flamsteed who, despite his praise for Halley in his student days, soon turned against him. Having the Astronomer Royal as an enemy is not the best recommendation for a young astronomer, even one as famous as Halley, who would soon pay the price.

Halley did not seek a teaching post at this stage, preferring the freedom to travel and undertake research without commitments. In 1680 he set out on a European tour with a school friend, Robert Nelson. Halley observed a comet while near Calais and travelled to Paris where, together with Cassini, he made further observations in an attempt to determine its orbit. Much of 1681 Halley spent in Italy. Back in England in the following year Halley married Mary Tooke, while his father remarried (Halley's mother having died ten years earlier).

Not only did marriage bring financial responsibilities to Halley, but his father's marriage seems to have been a total disaster and as a consequence of this support from his father soon dried up. Further personal problems followed, for in March 1684 his father vanished and was found dead five weeks later. Halley had to administer his father's personal estate and he became involved in family, property and legal matters which are described fully in [12].

Just before his father disappeared, Halley had been involved in an exciting piece of research. He had shown that Kepler's third law implied the inverse square law of attraction and presented the results at a meeting of the Royal Society on 24 January 1684 . Wren, Hooke and Halley then discussed whether it could be shown that the inverse square law implies elliptical orbits for the planets, but failed to come up with a proof. Halley's work on these problems was disrupted during the following weeks by the difficulties surrounding his father's disappearance and death, but by August 1682 Halley was pursuing the problem further by visiting Newton in Cambridge. There he discovered that Newton had already achieved a proof of this and of other highly significant results but did not seem to be going to publish them.

Chapman writes in [11]:-

... Halley ... had the genius to recognise the even greater mathematical genius of Newton, to urge him to write the Principia Mathematica, and then pay for the costs of publication out of his own pocket because the Royal Society was currently broke ...

Glaisher, in an address delivered in Cambridge in 1888, spoke of the role which Halley played in getting Newton's Principia published:-

... but for Halley the Principia would not have existed. ... He paid all the expenses, he corrected the proofs, he laid aside his own work in order to press forward to the utmost the printing. All his letters show the most intense devotion to the work.

By now Halley was certainly not a rich man and although in the end his financial outlay which allowed the Principia to be published was reimbursed from the sales, he now sought an academic post. In 1691 he applied for the vacant Savilian Chair of Astronomy at Oxford. Given his outstanding research in astronomy, one would have expected him to be appointed to this chair but Flamsteed was strongly against the appointment.

Flamsteed was not well disposed towards Newton particularly since he felt that Newton had not given sufficient credit to observations made by the Royal Observatory in his theory of the moon. Halley's close association with Newton lowered him still further in Flamsteed's eyes. However, the argument that Flamsteed used against Halley was one which he undoubtedly believed in sincerely, writing to Oxford that Halley would [7]:-

... corrupt the youth of the university.

Flamsteed was quite right in believing that Halley's view of Christianity was at odds with the standard view of that time which required a literal belief in the Bible. Newton also complained to Halley about the fact that Halley doubted the scientific correctness of the biblical story of the creation. Despite Halley vigorously claiming that his beliefs were conventional, David Gregory was appointed to the chair.

The lack of an academic post did not hold Halley back in his scientific work. Indeed he worked for the Royal Society in various roles, being editor of the Philosophical Transactions from 1685 to 1693. He published frequently important results through the Society's publications. In 1686 Halley published a map of the world showing the prevailing winds over the oceans. It has the distinction of being the first meteorological chart to be published. Another innovative piece of work was the mortality tables for the city of Breslau which he published in 1693. It was one of the earliest works to relate mortality and age in a population and was highly influential in the future production of actuarial tables in life insurance.

From around 1695 Halley made a careful study of the orbits of comets. Newton favoured comets having parabolic orbits, but Halley believed that elliptical orbits might exist. Using his theory of cometary orbits he calculated that the comet of 1682 (now called Halley's comet) was periodic and was the same object as the comet of 1531, and 1607. He later also identified this comet with one which appeared in 1305, 1380, and 1456. In 1705 he published his prediction that it would return in 76 years, claiming that it would appear in December 1758. It was not an easy calculation for Halley had to take into account the perturbations to the orbit produced by Jupiter. Although Halley had been dead for fifteen years by 1758, he achieved lasting fame when the comet was observed on 25 December 1758 (very slightly later than Halley expected).

Newton became Warden of the Royal Mint in London in 1696 and he used his influence to have Halley appointed as deputy controller of the mint at Chester in the same year. It was a post he held for two years before it was abolished. After leaving the mint at Chester, Halley was given the command of a warship, the Paramore Pink, by William III. This was not as strange as it sounds, for Halley had been working on determining the longitude using variation of the compass and this was the main purpose of the voyage, although he was also required by William III to [16]:-

... attempt the discovery of what land lies to the south of the western ocean.

He sailed from Portsmouth in November 1698 but problems with his crew forced him to return, having reached Barbados. In September 1699 he sailed again making a thorough exploration of the Atlantic shores. After his return in September 1700, Halley published charts of the variation of the compass, giving the first charts with lines of equal declination plotted.

Back on the Paramore Pink in 1701, Halley investigated the tides and coasts of southern England. Further journeys followed, for Queen Anne sent him to inspect the harbours around the Adriatic, and another journey saw him travel to Trieste to advise on fortifications.

Halley was appointed Savilian professor of geometry at Oxford in 1704 following the death of Wallis. This certainly did not please Flamsteed who had written (see for example [13]):-

Dr Wallis is dead - Mr Halley expects his place - who now talks, swears and drinks brandy like a sea captain.

Halley's inaugural lecture proved a great success. It was described by Thomas Hearne (see [5]):-

Mr Halley made his inaugural speech on Wednesday May 24, which very much pleased the generality of the University. After some compliments to the university, he proceeded to the original and progress of geometry, and gave an account of the most celebrated of the ancient and modern geometricians. Of those of our English nation he spoke in particular of Sir Henry Savile; but his greatest encomiums were upon Dr Wallis and Mr Newton ...

This lecture is described in [24] as:-

... of abiding interest from the mathematics standpoint.

In 1710, using Ptolemy's catalogue, Halley deduced that the stars must have small motions of their own and he believed that he was able to detect this proper motion in three stars. In fact the errors in his data were too large to enable him to do this as Jacques Cassini later demonstrated [25].

Halley played an active role in the events and controversies of his time. He supported Newton in his controversy with Leibniz over who invented the calculus, serving as secretary of a committee set up by the Royal Society to resolve the dispute. Halley did much to calm disputes, but also seemed to go out of his way to make his dispute with Flamsteed worse. In 1712 he arranged with Newton to publish Flamsteed's observations long before they were complete. To make matters worse, Halley wrote a preface, without Flamsteed's knowledge, in which [11]:-

... he attacked Flamsteed for sluggishness, secretiveness, and lack of public spirit.

In 1720 he succeeded Flamsteed as Astronomer Royal, a position he was to hold for 21 years despite being 64 years old when appointed. Flamsteed's widow was so angry that she had all her husband's instruments from the Royal Observatory sold so that Halley would not have the use of them.

At the Greenwich Royal Observatory Halley used the first transit instrument and devised a method for determining longitude at sea by means of lunar observations. He observed the Moon through one complete 18-year saros. Earlier observations of the Moon were made only at conjunction or at opposition to the Sun and it was these earlier observations on which Newton's lunar theory had been based. However, Halley has been criticised for his work as Astronomer Royal. Some claim that he made valueless observations which were no more accurate than those of Flamsteed. It has also been claimed that Halley's observations were carelessly carried out. For example in [16]:-

Halley took no account of fractional parts of seconds of time, and considered 10" of arc 'as the utmost attainable limit of accuracy'. His clocks were besides ill-regulated, and his system of registration unmethodical.

In [22], however, Ronan argues that the criticisms are unfair. He lists in that article Halley's achievements as Astronomer Royal.

Halley's other activities included studying archaeology, geophysics, the history of astronomy, and the solution of polynomial equations. He was an integral part of the English scientific community at the height of its creativity.