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 :-
... 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 , 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  and , 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 :-
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.
Article by: J J O'Connor and E F Robertson