威廉·约翰·麦夸恩·兰金William John Macquorn Rankine

威廉·约翰·麦夸恩·兰金的母亲是芭芭拉·格雷厄姆，一位格拉斯哥银行家的女儿，他的父亲是David Rankine，一位土木工程师，也是步枪旅的中尉。尽管他是父母孩子中的第二个，但他的哥哥弗洛伦斯·南丁格尔·大卫年幼时便去世了，所以兰金是作为独生子被抚养长大的。那是一种严格的宗教教育，他的父亲不仅教他算术技能，还教他力学。兰金小时候身体不好，只能短期上学。他的大部分教育是在家里由私人教师完成的，但他确实在1828-29年间在艾尔学院上过大约一年学，1830年还在格拉斯哥高中短暂就读过。

兰金的兴趣在音乐和数学之间。起初他强烈地被数论吸引，但当他14岁时，他的一个叔叔给了他一本艾萨克·牛顿的Principia的拉丁文版本，他急切地阅读了它。从1836年到1838年的两年间，兰金在爱丁堡大学学习，参加了广泛的科学科目讲座，但选择不参加数学课。他在1836年因一篇关于The wave theory of light的论文获得了一枚金牌，两年后又因一篇关于Methods in physical investigation的论文获得了另一枚金牌。他没有取得学位，而是选择在1838年离开大学，成为工程师弗瑞兹·约翰本杰明·麦克尼尔的学徒。这不是兰金第一次接触工程，因为他在爱丁堡大学学习期间，曾参与他父亲监督的爱丁堡和达尔基斯铁路的工作。

从1839年到1841年，兰金参与了约翰本杰明·麦克尼尔涉及的众多项目，包括河流改善、供水工程、铁路和两个港口。一些工作将兰金带到了爱尔兰。回到爱丁堡后，他与父亲一起进行了一些调查工作，他们发表了An experimental inquiry into the advantages attending the use of cylindrical wheels on railways（1842年）。提交给土木工程师学会的更多论文受到了高度评价，其中几篇为兰金赢得了奖项。

兰金于1855年被任命为格拉斯哥大学土木工程与力学钦定讲席教授。他的[2]：-

……就职演说主张力学中理论与实践的统一，并概述了一种三分知识理论——理论、实践以及理论在实践中的应用——这为新一类工程科学家跨越理论与实践的领域留下了空间。

他决定创立一个苏格兰版本的土木工程师学会，因此于1857年辞去了总部位于伦敦的学会职务，并成为新成立的苏格兰工程师学会的首任会长。除了在1857-59年担任会长外，他还在1869-70年被选为第二任期。

兰金对数学应用的研究在他作为工程师的职业生涯早期就开始了。在当学徒工程师期间，他对地球冷却进行了数学分析（1840年）。他研究热学，阅读埃米尔·克拉佩龙的著作，并试图从他自己的假设推导出萨迪·卡诺定律。R H Atkin在评论[14]时，描述了兰金关于热力学的思想，并特别将其方法与鲁道夫·克劳修斯的方法进行了比较：-

兰金显然像我们今天一样，将能量分为两种，即动能和势能，他的热力学理论是通过考虑一种能量向另一种能量的转化而发展起来的。他从物质由分子涡旋构成的假设出发（未考虑循环过程），并由此考虑得出了“压力”、“比热”等量。他对能量的分类与鲁道夫·克劳修斯的分类相似，但并不完全相同。兰金和鲁道夫·克劳修斯都从一种能量向另一种能量转化的角度探讨热力学第二定律。但是，鲁道夫·克劳修斯考虑的是循环过程中热与功之间的转换以及热从高温向低温的流动，而兰金则专注于动能（分子）向势能的转变，并通过使用他的“热势”函数将这种变化与热流联系起来。

Hutchison在[9]和[10]中考察了兰金所定义的熵函数及其对他所发展的热力学理论的影响。兰金的工作由詹姆斯·克拉克·麦克斯韦加以扩展。兰金还撰写了关于铁路车轴金属疲劳、土力学中的土压力以及墙体稳定性的著作。他还发展了求解框架结构中力分布的方法，并从事流体力学和船舶设计的研究。他于1849年当选为爱丁堡皇家学会会士，1853年当选为伦敦皇家学会会士。他还于1856年当选为美国艺术与科学院院士，1868年当选为瑞典皇家科学院院士。他于1857年获得都柏林三一学院的名誉学位。

他最重要的著作包括Manual of Applied Mechanics（1858年）、Manual of the Steam Engine and Other Prime Movers（1859年）、Civil Engineering（1862年）、Machinery and Millwork（1869年）、Useful Rules and Tables（1866年）、Mechanical Textbook（1873年）和On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance。

至于他在专业研究之外的兴趣，他是[2]：-

他是一位热忱的大提琴手、钢琴家和声乐家，他唯一出版的作品是一首名为《铁马》的歌曲的钢琴伴奏；作为英国协会红狮，他在1871年被誉为狮王，写下了古怪而幽默的诗作，如《恋爱中的数学家》和《三英尺规则》（对公制体系的抗议）。这些《歌曲与寓言》（1874年）在他去世后出版，配有Jemima 休‧布来克本的插图，她是格拉斯哥学院数学教授的夫人。

兰金在生命的最后六个月里健康状况迅速恶化。最初的症状是他的视力受损，然后他的言语功能丧失，最后他变得部分瘫痪。

William Rankine's mother was Barbara Grahame, the daughter of a Glasgow banker, and his father was David Rankine, a civil engineer and lieutenant in the rifle brigade. Although he was the second of his parents children, his older brother David died when young so William was brought up as an only child. It was a strict religious upbringing with his father teaching him not only arithmetical skills but also mechanics. William did not enjoy good health as a child and could only attend school for short periods. Most of his education took place at home with private tutors but he did attend Ayr Academy for about a year in 1828-29 and also for a short while Glasgow High School in 1830.

Rankine's interests were divided between music and mathematics. At first he was strongly attracted to number theory but when he was 14 years old one of his uncles gave him a Latin edition of Newton's Principia which he read eagerly. For two years from 1836 to 1838 Rankine studied at the University of Edinburgh, attending a wide range of lectures in science subjects, but choosing not to attend mathematics classes. He won a Gold Medal for an essay on The wave theory of light in 1836 and another Gold Medal for an essay on Methods in physical investigation two years later. He did not take a degree but chose to leave university in 1838 and become an apprentice to the engineer John Benjamin MacNeill. This was not Rankine's first experience of engineering for while he studied at Edinburgh University he had worked on the Edinburgh and Dalkeith Railway which his father was overseeing.

From 1839 to 1841 Rankine worked on numerous projects that John Benjamin MacNeill was involved with, including river improvements, waterworks, railways and both harbours. Some of the work took Rankine to Ireland. After his return to Edinburgh he undertook some investigative work with his father and they published An experimental inquiry into the advantages attending the use of cylindrical wheels on railways (1842). Further papers read to the Institution of Civil Engineers were highly thought of and several won Rankine prizes.

Rankine was appointed to the regius chair of civil engineering and mechanics at Glasgow in 1855. His [2]:-

... inaugural address espoused the harmony of theory with practice in mechanics, and outlined a tripartite theory of knowledge - theory, practice, and the application of theory to practice - which left room for a new breed of engineering scientists to bridge theoretical and practical domains.

He decided to found a Scottish version of the Institution of Civil Engineers and so he resigned from the London based Institution in 1857 and became the first president of the new Institution of Engineers in Scotland. As well as holding the presidency in 1857-59, he was elected for a second term in 1869-70.

Rankine's study of the applications of mathematics began quite early in his career as an engineer. While an apprentice engineer he made a mathematical analysis of the cooling of the earth (1840). He worked on heat, reading Clapeyron's works, and attempted to derive Sadi Carnot's law from his own hypothesis. R H Atkin, reviewing [14], describes Rankine's ideas on thermodynamics, and in particular compares his approach with that of Clausius:-

Rankine apparently regarded energy, as we do today, as being classified into two kinds, viz., kinetic and potential, and his thermodynamic theory was developed by considering the transformation of one into the other. He began with the hypothesis that matter was constituted by molecular vortices (without considering the cyclic process) and obtained the quantities "pressure", "specific heat", etc., from that consideration. His classification of energy was similar to, but not exactly the same as, that of Clausius. Both Rankine and Clausius approached the second law of thermodynamics from the point of view of the transformation from one kind of energy to the other. But whereas Clausius considered the conversion between heat and work and the flow of heat from high to low temperature in a cyclic process, Rankine concentrated on the change from kinetic (molecular) to potential energies, and related this change to heat flow by use of his "heat-potential" function.

Hutchison, in [9] and [10], looks at the entropy function which Rankine defined and its implications for the theory of thermodynamics which he developed. Rankine's work was extended by Maxwell. Rankine also wrote on fatigue in the metal of railway axles, on earth pressures in soil mechanics, and the stability of walls. He also developed methods to solve the force distribution in frame structures and worked on hydrodynamics and the design of ships. He was elected a fellow of the Royal Society of Edinburgh in 1849 and a fellow of the Royal Society of London in 1853. He was also elected to the American Academy of Arts and Sciences in 1856 and to the Royal Swedish Academy of Sciences in 1868. He was awarded an honorary degree from Trinity College, Dublin, in 1857.

Among his most important works are Manual of Applied Mechanics (1858), Manual of the Steam Engine and Other Prime Movers (1859), Civil Engineering (1862), Machinery and Millwork (1869), Useful Rules and Tables (1866), Mechanical Textbook (1873), and On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance.

As to his interests outside his professional studies, he was [2]:-

A keen cellist, pianist, and vocalist, his one published composition was a piano accompaniment to a song entitled the 'Iron Horse'; as a British Association red lion, hailed as lion-king in 1871, he penned quirky and humorous poems like 'The Mathematician in Love' and 'The Three-Foot Rule' (a protest against the metric system). These Songs and Fables (1874) appeared posthumously with illustrations by Jemima Blackburn, wife of Glasgow College's mathematics professor.

Rankine's health deteriorated rapidly during the final six months of his life. The first symptoms saw his vision become impaired, then his speech failed and finally he became partially paralysed.