约翰·普莱费尔John Playfair

约翰·普莱费尔是牧师James Playfair的长子，James Playfair是苏格兰邓迪附近小镇本维（当时在珀斯郡，现在在安格斯）的牧师。他在家里由父亲教育，直到十四岁，然后被送到圣安德鲁斯大学攻读普通学位，目的是进入教会。普莱费尔在1762年获得了大学的奖学金，在那里他的才能和对学习的热情赢得了教授们的尊重和友谊。他在数学科学方面的进步如此之快，以至于自然哲学教授（我[EFR]在1960年代在圣安德鲁斯学习时，物理学仍被称为自然哲学）威尔基教授在生病时，发现他是最有资格讲授自然哲学讲座的人。普莱费尔于1765年从圣安德鲁斯大学获得文学硕士学位。

1766年，当他还只有十八岁时，普莱费尔参加了阿伯丁马里沙尔学院数学讲席的竞争。在这场持续了十一日的竞争中，他脱颖而出，获得了极大的认可。在这样一场竞争中取得成功所需的数学知识是巨大的。然而，普莱费尔没有成功，在六名候选人中排名第三，落后于被任命为讲席的Trail牧师博士和继任讲席的汉密尔顿博士。然而，普莱费尔在非常年轻的时候，就证明了他非凡的才能和对数学的全面知识。

继续在圣安德鲁斯大学学习神学，普莱费尔在圣安德鲁斯的圣玛丽学院进行他的神学研究。1769年完成学业后，他离开了大学，从那时起直到1773年，他大部分时间都在爱丁堡度过。在那里，他与苏格兰启蒙运动的杰出人物交往（见[3]）；其中包括数学家杜格尔德·斯图尔特（马修·斯图尔特之子）、经济学家亚当·斯密、化学家约瑟夫·布莱克、地质学家詹姆斯·赫顿、建筑师和工程师罗伯特·亚当以及历史学家罗宾逊校长等伟大scholars。

在1769年至1773年期间，普莱费尔曾两次尝试获得学术职位。他的第一次尝试是在1769年，但没有成功。然而，他继续从事牧师职业，并于1770年获得邓迪长老会的讲道许可。1772年，普莱费尔申请圣安德鲁斯大学的自然哲学讲席，该职位在他的朋友威尔基去世后空缺，但再次任命了另一位候选人。由于未能获得学术职位，普莱费尔回到爱丁堡，在那里一直待到1772年他父亲去世。

普莱费尔被格雷勋爵提名接替他的父亲担任利夫和本维的教区牧师，他搬到利夫监督他的兄弟姐妹的教育。然而，在他的提名得到确认之前，几乎过了一年，因为格雷勋爵的推荐权被律师王室争议。案件提交到最高民事法院，1773年8月，普莱费尔通过教会大会的决议获得确认。然后他被任命为利夫和本维的牧师，接替他的父亲。

在此期间，普莱费尔没有忽视自己的学术研究，除了偶尔访问爱丁堡外，他还在1774年前往珀斯郡的Schiehallion，与皇家天文学家内维尔·马斯基林一起进行实验。他们成为终身朋友，内维尔·马斯基林将他介绍给了当时领先的科学人士。他说服普莱费尔将他第一篇成功的数学论文提交给伦敦皇家学会，该论文于1779年发表在Philosophical Transactions上。这篇由普莱费尔 On the Arithmetic of Impossible Quantities撰写的第一篇数学论文被描述为展示了[12]：-

……比那个时代任何英国数学家都表现出对纯分析研究的更大品味。

普莱费尔成为宗教会议的moderator，但此后不久，他在1782年收到了一份有利可图的提议，辞去教会职务，成为Raith的Ferguson两个儿子的导师。他从1782年到1787年辅导Ronald Ferguson和他的兄弟。这涉及搬到更靠近爱丁堡的地方，因此他能够参与该市的知识生活。普莱费尔参与了1783年爱丁堡皇家学会的建立，并且是该学会的原始Fellow之一。在一次假期中，他首次访问伦敦，在那里内维尔·马斯基林将他介绍给了科学界。

1785年，普莱费尔被任命为爱丁堡大学的联合数学教授，这一职位他将担任二十年。两年后，在完成对弗格森家族的辅导职责后，他搬到了爱丁堡，与他的母亲和姐妹们团聚，她们已在爱丁堡居住了几年。从1787年起，普莱费尔在Transactions of the Royal Society of Edinburgh上发表了各种主题的文章，并为Edinburgh Review做出了贡献。

1793年，普莱费尔的兄弟詹姆斯，在伦敦作为一名建筑师立足，突然去世。普莱费尔中断了他的研究来处理家庭事务。次年，他收养了詹姆斯的长子威廉Henry Playfair，当时只有六岁。威廉将追随父亲的脚步，也成为一名著名的建筑师。

在18世纪，大学里系统地学习几何是从欧几里得的Elements开始的，而学校通常满足于接受定理和构造而不加证明。然而，随着对分析研究兴趣的增长，数学家们开始要求更多的严谨性。1795年，普莱费尔出版了一版Elements，打算供他的学生使用。主要的创新是普莱费尔使用代数符号来缩写他在课堂上教授的证明。这是为了避免几何理论的“乏味和迂回”。

18世纪研究Elements的人遇到的困难集中在两个问题上。首先，是有争议的“平行”公设。第二个问题是欧几里得的比例理论，源自欧多克索斯。格拉斯哥大学的罗伯特·西姆松在其1756年版的Elements中，基于另一个假设给出了平行公理的证明。普莱费尔在1795年通过重新陈述欧几里得的欧几里得的平行公理解决了这一困难：-

过同一点不能作两条直线同时平行于同一条直线而不重合。

这种形式的公理当然并不新鲜，因为早在五世纪普罗克洛中就已经给出了。奇怪的是，普莱费尔的名字竟会与这条公理联系在一起，尤其是因为他明确指出他是从普罗克洛中推导出这条公理的。后来的作者将其重新表述为：-

给定一条直线和直线外一点，过该给定点可以作且仅可以作一条直线平行于该直线。

这就是通常所称的普莱费尔公理。[16]

普莱费尔在他所编欧几里得前六卷中统一了图形中点和边的记号。对于这些专门讨论平面几何的卷，普莱费尔又增加了三卷，意在补充前六卷；即关于求积 of the Circle and the Geometry of Solids、Elements of Plane and Spherical Trigonometry和The Arithmetic of Sines。他还以附录形式收入了一节注释，说明了他对各卷所作改动的理由，并对平行线这一困难主题作了富有启发性的讨论。它竟然出了六版，这一事实表明了普莱费尔所编欧几里得的受欢迎程度。[15]的作者声称：-

……普莱费尔的介入使欧几里得在其不可避免的命运面前多保存了一百年！

普莱费尔在1797年初患了严重的风湿病。然而这并没有阻止他写作，在此期间他写了An Analytical Treatise on the Conic Sections和一篇Essay on the Accidental Discoveries Which Have Been Made By Men of Science, Whilst In Pursuit of Something Else, Or When They Had No Determinate Object in View。

他的朋友詹姆斯·赫顿的去世促使普莱费尔撰写了一篇传记回忆录，这篇回忆录逐渐演变成对詹姆斯·赫顿地质学理论批评者的回应。这反过来又催生了普莱费尔的地质学著作Illustrations of the Huttonian Theory of the Earth。普莱费尔以不同于詹姆斯·赫顿原始表述的风格呈现了詹姆斯·赫顿的理论。詹姆斯·赫顿的表述风格相当奇特，使他的理论难以理解，因此他获得的赞誉少于他应得的。这种风格导致了许多错误的歪曲，并招致少数读过它的人的抨击。普莱费尔简洁而雄辩的风格由一系列章节组成，清晰地陈述了赫顿理论，给出了支持它的事实，以及反对它的论据。普莱费尔表述的成功可以从此后给予詹姆斯·赫顿的声誉和赞誉来判断，詹姆斯·赫顿现在被视为第一位伟大的英国地质学家。Illustrations[12]：-

……不仅使詹姆斯·赫顿的理论流行起来，而且有助于创建现代地质科学。

普莱费尔从1797年到1802年花了将近五年时间撰写Illustrations。他的大部分业余时间都在大不列颠旅行，以进行地质学研究。普莱费尔曾希望将研究扩展到欧洲大陆，但由于欧洲的战争而未能如愿。他把注意力转向爱尔兰，访问了都柏林和巨人堤道。

1803年，普莱费尔在Transactions of the Royal Society of Edinburgh中发表了他的赫顿传记概述。一个多世纪后，这部作品被描述为[12]：-

……一部以其明晰的处理和优雅的引导，在英语地质学文献中至今无与伦比的作品。

普莱费尔在爱丁堡大学数学教授职位上是一位成功的教师，讲课时对这门学科充满热情，竭尽全力激发学生对数学研究的热情，并当众表扬那些取得成就的学生以资奖励。他被描述为一位“有魅力的教师”，他[3]：-

……在1800年后以相当的自信延续了一种既定的辉煌阐述和有效教学法的传统，这一传统至少自十七世纪以来就与苏格兰扎实的长老会学校教育及其雄辩的大学设施联系在一起。

普莱费尔是英国最早教授现代分析的人之一。他的这一主题课程有许多早已完成学业的人参加。为表达感激之情，班级成员向普莱费尔赠送了一个珍贵的天文环，它被安置在天文学会天文台。然而，尽管作为数学家取得了成功，普莱费尔还是在1805年将数学讲席换成了自然哲学讲席。两年后，他当选为伦敦皇家学会会士。

爱丁堡天文机构成立于1811年，比英格兰的皇家天文学会早九年，是英国第一个专门致力于天文学的学会。普莱费尔是其首任会长。卡尔顿山上的新天文台主要是在普莱费尔的努力推动下建成的。

1812年，普莱费尔出版了他的Outlines of Natural Philosophy的第一卷，同样主要是为他的学生使用而编写的。第一卷涵盖动力学、力学、流体静力学、水力学、气体静力学和气体动力学。第二卷完全致力于天文学，而原本打算完成整个系列并涵盖光学、电学和磁学主题的第三卷，从未完成。

1815年，普莱费尔接替其朋友兼同事罗比森教授，担任爱丁堡皇家学会的秘书。普莱费尔在该学会的Transactions上发表了多篇论文，其中包括一套根据他自己观测构建的气象表。

1815年晚些时候，随着拿破仑战败，欧洲恢复了和平，普莱费尔开始了一次为期17个月、行程4000英里的欧洲大陆地质考察，为Illustrations of the Huttonian Theory of the Earth第二版收集材料。尽管已68岁，普莱费尔仍踏上了穿越法国和瑞士的艰苦而漫长的旅程，继续前往意大利南端，考察他所到之处的世界部分地区的地质构造。他的大侄子James George Playfair在部分时间里陪同他，协助他记录旅途的细节。

Illustrations的第二版被设计为比第一版重要得多的著作。它意在更像今天的科学文本，从充分证实的事实开始，随后是从这些事实中推导出的一般推论，并考察各种曾被假设的地质模型。普莱费尔的目标是将地质学原理建立在无可置疑的假设和论证之上。它将以普莱费尔的地质学模型及其应用作为结论。

然而，当普莱费尔收到请求，要他撰写一篇题为Dissertation on the Progress of the Mathematical and Physical Science since the Revival of Letters in Europe的文章，供Dissertation on the Progress of the Mathematical and Physical Science since the Revival of Letters in Europe补编使用时，这一计划被打断了。1818年，在看到爱丁堡天文机构的新天文台开始动工后，他搬到法夫的伯恩蒂斯兰，以完成这篇文章。在伯恩蒂斯兰期间，他还写了他的Memoir on Naval Tactics，该书于Transactions of the Royal Society of Edinburgh中在他去世后出版。

完成Dissertation后不久，普莱费尔患了严重的膀胱疾病，这使他无法继续计划中的Illustrations第二版，并打断了他的讲座。他恢复得足以完成在爱丁堡的课程，但遗憾的是，Illustrations第二版从未完成。1819年6月，膀胱疾病以更严重的程度复发，普莱费尔回到伯恩蒂斯兰。尽管遭受着极其剧烈的疼痛，他在生命的最后日子里仍口述对Dissertation校样的修改。

在持续一个月的疾病之后，普莱费尔去世了。他的葬礼在老卡尔顿墓地举行，有500多名哀悼者参加，墓地俯瞰着他帮助创建的天文台。他的坟墓毗邻著名哲学家弗洛伦斯·南丁格尔·大卫休谟的坟墓，然而坟墓上没有任何表明安葬者是谁的标记，而且遗憾的是，多年来它一直被忽视。

普莱费尔在至少三个纯科学分支中为自己赢得了很高的声誉，主要不是作为发现者，而是作为理论的阐述者。在数学领域，他通过科学期刊和百科全书上的文章以及他的讲座课程，将大陆方法引入英国。他的侄子James George Playfair于1822年编辑了The Works of John Playfair，写道[11]：-

……我们相信，说他是他那个时代最博学的数学家之一，并无冒险之处，而且他是最早——如果不是第一个——将后来大陆几何学家的美妙发现介绍给同胞的人之一，并在欧洲知识体系中赋予那些重要改进以应有的价值和真正地位，自我们杰出的艾萨克·牛顿时代以来，这些改进使整个抽象科学的面貌焕然一新……的确，他最高度地拥有精细而强大理解力的所有特征——既敏锐又警觉——但也许更以其进程的谨慎和稳健而非其运动的辉煌或迅速而著称——并且在其整个进程中，由对一切宏伟事物的最真诚热情和对真理或智力能量中一切美好事物的最公正品味所引导和装饰，他惯常与之打交道。

普莱费尔的性格使他成为一个受欢迎的人物。他拥有一种12：-

……贵族与文人这两种贵族身份的亲切结合。

亨利·科伯恩勋爵写道，普莱费尔是6：-

受所有男人钦佩，被所有女人爱戴，他始终是她们美德与才智的捍卫者，社会因他的存在而感到更加幸福、更加体面。

他的侄子在11中写道：-

……尽管他是最善于社交的人，也最乐于鼓励和同情他人的欢快与愉悦，但他自己的情绪总体上与其说是欢快，不如说是愉快，或者至少从未升至任何喧闹或狂欢……他自己的满足感通常可以从那缓慢而温和的微笑中看出，这微笑逐渐浮现在他仁慈而睿智的面容上，以最温和、最真诚的博爱表情照亮这位智者的面庞。

在16中，普莱费尔的贡献被总结如下：-

在他所有著作中都显而易见的那种广博学识、冷静理智和清晰思想，也体现在他的讲课中。据他众多杰出学生中的一位所说，他是一位‘迷人的教师，举止如此朴素、自然和真诚，风格如此纯净，论证如此清晰’。通过整合前几代人的学识并整理他那个时代的发现和理论，他对自己所讲授的科目给出了全面而统一的阐述，从而为数学和自然哲学领域未来的建设性研究奠定了基础。

John Playfair was the eldest son of the Reverend James Playfair, minister of Benvie, a small town near Dundee (then in Perthshire, now in Angus), Scotland. He was educated by his father at home until the age of fourteen, when he was sent to the University of St Andrews to study for a general degree with the aim of entering the Church. Playfair was awarded a scholarship to the University in 1762, and there his aptitude and keenness to study gained him both the respect and friendship of his professors. His progress in the mathematical sciences was so rapid that the professor of natural philosophy (physics was still called natural philosophy in St Andrews when I [EFR] studied it in the 1960s), Professor Wilkie, when suffering from an illness, found him to be the person best qualified to deliver his lectures on natural philosophy. Playfair graduated from the University of St Andrews with an M.A. in 1765.

In 1766, while still only eighteen, Playfair entered a contest for the Chair of Mathematics at Marischal College in Aberdeen. In this contest, which lasted eleven days, he distinguished himself and gained great recognition. The extent of mathematical knowledge required to be successful in such a contest was immense. Playfair was unsuccessful, however, finishing third out of the six candidates, behind the Reverend Dr Trail, who was appointed to the Chair, and Dr Hamilton, who succeeded him in the Chair. However Playfair, at a very young age, had proved his extraordinary talent combined with his comprehensive knowledge of mathematics.

Going on to study divinity at the University of St Andrews, Playfair undertook his theological studies at St Mary's College, St Andrews. On completion of his studies in 1769, he left the University, and from then on spent much of his time until 1773 in Edinburgh. There he mixed with the luminaries of the Scottish Enlightenment (see [3]); which included such great scholars as Dugald Stewart the mathematician (son of Matthew Stewart), Adam Smith the economist, Joseph Black the chemist, James Hutton the geologist, Robert Adam the architect and engineer, and Principal Robinson the historian.

During the period between 1769 and 1773, Playfair had twice attempted to obtain an academic post. His first attempt was in 1769 but it was unsuccessful. He continued, however, in his vocation as a minister and was licensed to preach by Dundee Presbytery in 1770. In 1772 Playfair applied for the Chair of Natural Philosophy in the University of St Andrews, which was left vacant after the death of his friend Wilkie but again another candidate was appointed. Having failed to obtain an academic post Playfair returned to Edinburgh where he remained until his father's death in 1772.

Playfair was nominated by Lord Gray to succeed his father as the Parish Minister of Liff and Benvie and he moved to Liff to supervise the education of his brothers and sisters. Almost a year had elapsed, however, before his nomination was confirmed, as Lord Gray's rights of presentation were disputed by the Crown of Lawyers. The case went before the Court of Session and, in August 1773, Playfair received confirmation by a resolution of the General Assembly of the Church. He was then ordained the Minister of Liff and Benvie in succession to his father.

During this period Playfair did not neglect his own academic studies, and beside making occasional visits to Edinburgh, he made an excursion in 1774 to Schiehallion, Perthshire, to conduct experiments with Neville Maskelyne, the Astronomer Royal. They became lifelong friends and Maskelyne introduced him to the leading scientific men of the day. He persuaded Playfair to submit his first successful paper on mathematics to the Royal Society of London and this was published in the Philosophical Transactions in 1779. This first mathematical paper by Playfair On the Arithmetic of Impossible Quantities, has been described as exhibiting [12]:-

... a greater taste for purely analytical investigation than shown by any of the British mathematicians of that age.

Playfair became Moderator of the Synod but soon after this he received, in 1782, a lucrative offer to resign his church position and to become the tutor to the two sons of Ferguson of Raith. He tutored Ronald Ferguson and his brother from 1782 until 1787. This involved moving closer to Edinburgh, and he was thus able to participate in the city's intellectual life. Playfair became involved in the establishment of the Royal Society of Edinburgh in 1783 and was one of the original Fellows of that Society. During a vacation he made his first visit to London, where Maskelyne introduced him to the scientific world.

In 1785 Playfair was appointed Joint Professor of Mathematics in the University of Edinburgh, a position which he was to hold for twenty years. Two years later, after completing his tutoring duties for the Ferguson's, he moved to Edinburgh, joining his mother and sisters, who had for some years been resident in Edinburgh. From 1787 Playfair published on various topics in the Transactions of the Royal Society of Edinburgh and also contributed to the Edinburgh Review.

In 1793 Playfair's brother James, who was established in London as an architect, died suddenly. Playfair interrupted his studies to make the family's arrangements. In the following year, he adopted James's eldest son, William Henry Playfair, then only six years of age. William would follow in his father's footsteps and also become an renowned architect.

In the eighteenth century geometry was systematically studied from Euclid's Elements in the universities, while the schools were generally content to accept the theorems and constructions without proof. However, mathematicians began to demand more rigour with the growing interest in analytic investigation. In 1795 Playfair published an edition of the Elements which he intended for use by his students. The main innovation was Playfair's use of algebraic notation to abbreviate the proofs which he taught in his class. This was intended to avoid the "tediousness and circumlocution" of geometric theory.

The difficulties encountered by those who studied the Elements in the eighteenth century centred around two problems. Firstly, there was the contentious "parallel" postulate. The second problem was Euclid's theory of proportion, derived from Eudoxus. Robert Simson of Glasgow University had, in his 1756 edition of the Elements, given a proof of the parallel axiom based on another assumption. Playfair solved this difficulty in 1795 with a retatement of Euclid's Euclid's parallel axiom:-

Two straight lines cannot be drawn through the same point, parallel to the same straight line, without coinciding with one another.

This form of axiom was certainly not new as it had already been given in the fifth century by Proclus. It is curious that Playfair's name should be associated with this axiom, particularly since he clearly points out that he derived the axiom from Proclus. Later writers rephrased this as:-

Given a line and a point not on the line, it is possible to draw exactly one line through the given point parallel to the line.

and this is what is usually known as Playfair's Axiom. [16]

Playfair standardised the notation for points and sides of figures in the first six books of his edition of Euclid. To these books, which specifically deal with plane geometry, Playfair added three more books intended to supplement the preceding six; On the Quadrature of the Circle and the Geometry of Solids, Elements of Plane and Spherical Trigonometry and The Arithmetic of Sines. He also included a section of notes in the form of an appendix, which gave his reasons for the alterations made throughout the volumes, and an illuminating discussion on the difficult topic of parallel lines. The fact that it ran to six editions shows the popularity of Playfair's edition of Euclid. The author of [15] claims that:-

... Playfair's intervention saved Euclid for a hundred years from its inevitable fate!

Playfair suffered a severe attack of rheumatism, during the early part of 1797. This did not prevent him writing however, and during this time he wrote An Analytical Treatise on the Conic Sections, and an Essay on the Accidental Discoveries Which Have Been Made By Men of Science, Whilst In Pursuit of Something Else, Or When They Had No Determinate Object in View.

The death of his friend, James Hutton, moved Playfair to compose a biographical memoir, which gradually became a reply to the critics of Hutton's theories of geology. This in turn gave rise to Playfair's geological work Illustrations of the Huttonian Theory of the Earth. Playfair presented Hutton's theories in a different style from Hutton's original presentation. Hutton had a rather peculiar style of presentation which made his theory less intelligible and, as a result, he had received less acclaim than he deserved. It was a style which led to many erroneous misrepresentations and to attacks from the few who had read it. Playfair's simple and eloquent style consisted of a series of chapters clearly stating the Huttonian theory, giving the facts to support it, and the arguments given against it. The success of Playfair's presentation can be judged by the fame and credit which have since been given to Hutton, who is now regarded as the first great British geologist. The Illustrations [12]:-

... not only gave popularity to Hutton's theory, but help to create the modern science of geology.

Playfair spent almost five years, from 1797 to 1802, writing the Illustrations. The majority of his spare time he spent travelling through Great Britain, in pursuit of his geological studies. Playfair had hoped to extend his researches to the Continent, but he was prevented in doing so by the war in Europe. He turned his attention to Ireland, making visits to Dublin and to the Giant's Causeway.

In 1803 Playfair published his biographical sketch of Hutton in the Transactions of the Royal Society of Edinburgh. This work was described over a century later as [12]:-

... a work for which luminous treatment and graceful direction, stands still without a rival in English Geological literature.

Playfair was a successful teacher in his position as Professor of Mathematics at the University of Edinburgh, lecturing with a verve for the subject, doing his utmost to inspire his students with an enthusiasm for mathematical investigation, and rewarding those who succeeded by praising them in front of the class. He was described as a 'magnetic teacher' who [3]:-

... carried on with considerable aplomb after 1800 an established tradition of brilliant exposition and effective pedagogy associated since at least the seventeenth century with Scotland's solid Presbyterian schooling and its eloquent university facilities.

Playfair was among the first in Britain to teach modern analysis. His course on this topic was attended by many who had long before completed their academic studies. To express their gratitude, class members presented Playfair with a precious astronomical circle, which was placed in the Observatory of the Astronomical Institution. However, despite his success as a mathematician, Playfair exchanged the Chair of Mathematics for the Chair of Natural Philosophy in 1805. Two years later he was elected a Fellow of the Royal Society of London.

The Astronomical Institution of Edinburgh was founded in 1811, preceding the Royal Astronomical Society in England by nine years, making it the first British society devoted to astronomy. Playfair was its first president. The New Observatory on Calton Hill was built largely through Playfair's efforts in support of the project.

In 1812 Playfair published the first of the volumes of his Outlines of Natural Philosophy, again intended primarily for the use of his students. The first volume covered dynamics, mechanics, hydrostatics, hydraulics, aerostatics, and pneumatics. The second volume was entirely devoted to astronomy, while a third volume, which was intended to complete the series and cover the subjects of optics, electricity, and magnetism, was never completed.

In 1815 Playfair succeeded his friend and colleague, Professor Robison, as the Secretary of the Royal Society of Edinburgh. Playfair published many papers in the Transactions of the Society including a set of meteorological tables constructed from his own observations.

Later in 1815 peace in Europe followed the defeat of Napoleon and Playfair began a 17 month, 4000 mile geological study of the Continent to gather material for the second edition of the Illustrations of the Huttonian Theory of the Earth. Although 68 years of age, Playfair set out on an arduous and extensive journey through France and Switzerland, continuing to the southern tip of Italy, examining the geological structure of the parts of the world he visited. He was accompanied for part of the time by his eldest nephew, James George Playfair, who assisted him by recording the details of their journeys.

The second edition of the Illustrations was designed to be a much more major work than the first. It was intended to be more like scientific texts of today, beginning with the well authenticated facts, followed by general inferences that were deduced from these facts, with an examination of the various geological models that had been hypothesised. It was Playfair's aim to base the principles of geology on unquestionable assumptions and arguments. It would conclude with Playfair's model of geology and its applications.

However, this plan was interrupted when Playfair received a request he write an essay entitled Dissertation on the Progress of the Mathematical and Physical Science since the Revival of Letters in Europe for the supplement to Encyclopaedia Britannica. He moved to Burntisland in Fife in 1818 after seeing work begin on the New Observatory for the Astronomical Institution of Edinburgh, in order to complete this essay. While in Burntisland, he also wrote his Memoir on Naval Tactics, published posthumously in the Transactions of the Royal Society of Edinburgh.

Soon after completing the Dissertation Playfair suffered a severe attack of a disease of the bladder which prevented him from continuing his planned second edition of the Illustrations and interrupted his lectures. He regained his health sufficiently to finish the course of lectures in Edinburgh but, sadly, the second edition of the Illustrations was never completed. In June 1819 the bladder disease recurred with increased severity and Playfair returned to Burntisland. Although suffering very severe pain, he spent the last days of his life dictating corrections to the proof sheets of the Dissertation.

After an illness lasting a month Playfair died. There were over 500 mourners at his burial in the Old Calton Burial Ground, overlooked by the Observatory which he helped to create. His grave is adjacent to that of David Hume, the famous philosopher, however it does not bear any indication whatever of who is interred there and, sadly, over the years has been neglected.

Playfair earned for himself a high reputation in at least three branches of pure science, not primarily as a discoverer but rather as an expounder of theories. In the field of mathematics he introduced continental methods to Britain through his articles in scientific journals and encyclopaedias, and by his lecture courses. His nephew, James George Playfair, who edited The Works of John Playfair in 1822 wrote [11]:-

... we believe we hazard nothing in saying that he was one of the most learned mathematicians of his age, and among the first, if not the very first, who introduced the beautiful discoveries of the later continental geometers to the knowledge of his countrymen, and gave their just value and true place, in the scheme of European knowledge, to those important improvements by which the whole aspect of the abstract sciences has been renovated since the days of our illustrious Newton.... He possessed, indeed, in the highest degree, all characteristics both of a fine and powerful understanding, - at once penetrating and vigilant, - but more distinguished, perhaps, for the caution on sureness of its march, than for the brilliancy or rapidity of its movements, -and guided and adorned through all its progress by the most genuine enthusiasm for all that is grand, and the justest taste for all that is beautiful in the Truth or the Intellectual Energy with which he was habitually conversant.

Playfair's character made him a popular personality. He possessed a [12]:-

... cordial combination of the two aristocracies of rank and of letters.

Lord Henry Coburn wrote that Playfair was [6]:-

Admired by all men, and beloved by all women, of whose virtues and intellect he was always champion, society felt itself the happier and the more respectable from his presence.

His nephew writes in [11]:-

... though the most social of human beings, and the most disposed to encourage and sympathise with the gaiety and joviality of others, his own spirits were in general rather cheerful than gay, or at least never rose to any turbulence or tumult of merriment... His own satisfaction might generally be traced in the slow and temperate smile, gradually mantling over his benevolent and intelligent features, and lighting up the countenance of the Sage with the expression of the mildest and most genuine philanthropy.

In [16] Playfair's contributions are summed up as follows:-

The wide learning, the calm intellect and the clear thought, so apparent in all his writings, also marked his lectures. He was, according to one of his many illustrious pupils, 'a charming teacher, so simple, unaffected and sincere in manner, so chaste in style, so clear in demonstration'. By consolidating the learning of past generations and collating the discoveries and theories of his own time, he gave a comprehensive and unified presentation of the subjects he professed and thus laid the basis for future constructive researches in the fields of mathematics and natural philosophy.