William John Macquorn Rankine

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W J M Rankine

William John Macquorn Rankine (July 2, 1820 - December 24, 1872) was a Scottish engineer and physicist. He was a founding contributor to the science of thermodynamics. Rankine developed a fully complete theory of the steam engine. His steam engine manuals were used for many decades.


Early life

Born in Edinburgh to British Army lieutenant David Rankine and Barbara Grahame, Rankine was initially educated at home owing to his poor health. In 1836 Rankine began to study a spectrum of scientific topics at the University of Edinburgh, including natural history under Robert Jameson and natural philosophy under James Forbes, winning several scholastic awards and prizes. During vacations, he assisted his father who had become superintendent of the Edinburgh and Dalkeith Railway. He left Edinburgh in 1838 without graduating, perhaps because of straitened family finances, and became apprenticed to Sir John Benjamin Macneill, surveyor to the Irish Railway Commission. Even at this early stage of his career, he developed a technique (Rankine's method) for laying out circular curves, fully exploiting the theodolite and making a substantial improvement in accuracy and productivity over existing methods.

Returning to Scotland in 1842 and hearing of the Versailles accident, Rankine started to investigate the fatigue of railroad axles, publishing his findings in 1843 on the importance of stress concentration. Over the next five years he worked on a variety of civil engineering projects.

The year 1842 also marked Rankine's first attempt to reduce the phenomena of heat to a mathematical form but he was frustrated by his lack of experimental data.



In 1848, his interests turned to molecular physics at a time when the atomic hypothesis was still controversial and immature. Rankine attempted to apply his hypothesis of molecular vortices to the phenomena of birefringence (possibly motivated by the earlier work of Forbes) and of elasticity but without success.

Undaunted, he returned to his youthful fascination with the mechanics of the heat engine. Though his theory of circulating streams of elastic vortices whose volumes spontaneously adapted to their environment sounds fanciful to scientists formed on a modern account, by 1849, he had succeeded in finding the relationship between saturated vapour pressure and temperature. The following year, he used his theory to establish relationships between the temperature, pressure and density of gases, and expressions for the latent heat of evaporation of a liquid. He accurately predicted the surprising fact that the apparent specific heat of saturated steam would be negative.

Enboldened by his success, he set out to calculate the efficiency of heat engines and used his theory as a basis to deduce the principle, enunciated by Sadi Carnot, that the maximum efficiency of a heat engine is a function only of the two temperatures between which it operates. Though a similar result had alredy been derived by Rudolf Clausius and William Thomson, 1st Baron Kelvin, the work marked the first step on Rankine's journey to develop a more complete theory of heat.

From 1853, Rankine recast the results of his molecular theories in terms of a macroscopic account of energy and its transformation. He distinguished between actual energy which was lost in dynamic processes and potential energy by which it was replaced. He assumed the sum of the two energies to be constant, an idea already familiar in the conservation of energy. From 1854, he made wide use of his thermodynamic function which he later realised was identical to entropy. By 1855, Rankine had formulated a science of energetics which gave an account of dynamics in terms of energy and transformation rather than force and motion. The theory was very influential in the 1890s.

Energetics offered Rankine an alternative, and rather more mainstream, approach, to his science and, from the mid 1850s, he made rather less use of his molecular vortices. However, as late as 1864, he contended that the microscopic theories of heat proposed by Clausius and James Clark Maxwell, based on linear atomic motion, were inadequate. It was only in 1869 that Rankine admitted the success of these rival theories. By that time, his own model of the atom had become almost identical with that of Thomson.

He used his own theories to develop a number of practical results and to elucidate their physical principles including:

He proposed the Rankine temperature scale in 1859.


to be done

Other work

He served as professor of engineering at the University of Glasgow from 1855, pursuing engineering research along a number of lines in civil and mechanical engineering.

Civil engineering

Rankine made contributions to:

Naval architecture

to be done

Personal life

Rankine held the rank of Senior Major in the reservist Scottish Rifle Volunteers. He was an enthusiastic singer who composed his own songs.

He died in Glasgow, a bachelor.


Important works


  • Manual of Applied Mechanics, (1858);
  • Manual of the Steam Engine and Other Prime Movers, (1859);
  • Manual of Civil Engineering, (1861);
  • Machinery and Millwork, (1869).


it:William John Macquorn Rankine


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