V. V. Raman Phvsics Deoartment Rochester Institute of Technology Rochester, New York 14623
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William John Macquorn Rankine:
1820-1872
Son of a civil engineer, William Rankine was born on July 5, 1820 in Edinburgh, Scotland. When quite young he had to discontinue attending school because of ill health, and this began his private studies. A discerning uncle is said to have resented Rankine with Newton's "Principia" when the lad was only fourteen. At the age of 16, Rankine entered the University of Edinburgh, and during his very first year there he wrote a paper on the "Undulatory Theory of Light."l This essay won him a eold medal. Another essav which he wrote during his early years examined the foundations of the scientific method. From 1838 Rankine worked for four years on a variety of engineering projects which ranged from surveying and railroad constructions to river improvements and harbor developments. During these years he reflected much on the questions involved, and wrote on these problems. He developed a new method of curve setting which came to he known as Rankine's method. Until 1848 Rankine was orimarilv involved with practical problems, and was basically a civil e n g i n e e ~ . ~ Although his interest in engineering never faded during his lifetime, a new field of interest attracted Rankine from 1848 on: he began investigating the nature and properties of heat. In 1849 he published his first paper on a purely scientific theme, entitled, "On an Equation between Tem~eratureand the Maximum Elasticity of Steam and other Vapours."3 A question which engaged the attention of many investigators during the nineteenth century was the determination of the saturation pressure of various liquids. Many empirical formulas were being put forward for this.* Rankine gave the formula Inp
=
a - -ia - Y t
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Rankine deduced this relationship from theoretical considerations (31. In fact, he showed that the difference hetween the total heats of vapor a t any two temperatures T and T' is equal to the specific heat a t constant pressure, C,, times the temperature difference. Thus according to Rankine H - H' = Cp(T - T') This relation not only confirmed Regnault's result, but also showed that the coefficient of T in the latter's formula may be interpreted as the specific heat of steam. As early as 1842 Rankine had begun certain investigations on the theory of heat, but had laid them aside hecause, as he put it, "of want of experimental data." In 1849 he resumed the work once again, and completed an important paper on the mechanical action of heat.= Here he developed his hypothesis of molecular vortices. However crude and artificial this hypothesis may sound from the modern standpoint, it was certainly one of the first to consider a structure for the atom. For, according to Rankine
tz
where p is the "maximum pressure of a vapour in contact with its liquid; t, the temperature, measured on the air thermometer, from a point which may be called the ABSOLUTE ZERO . . . ." Rankine noted that his equation followed from theory and that the values of the constants a,6, r, for each fluid were to be determined from experiments. Rankine himself replaced this formula by a more comolicated one developed from theoretical considerations twenty years later.5 In this context a related problem may be mentioned. During the first half of the nineteenth century one spoke of Watt's law according to which the total heat of steam was a constant. Total heat was defined as the amount of heat required to raise unit mass of a given liquid from a certain temperature to another well defined temperature
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at which it is evaporated under constant saturated pressure. In the case of water, for example, if h is the amount of heat necessary to raise unit mass of water from ODCto T C , and L the latent heat of steam at that temperature, then the total heat would be given by, H = h L. I t was suggested by some that Watt's law was not exact, and that it was L rather than H which was constant. Precise experiments by Regnault in 1847 established an empirical relationship between H and T as
'The wave theory of light had not yet been universally accepted by this time. 2He assisted his father who was himself an engineer. Rankine also went to Ireland where he participated in the construction of the Dublin and Drogheda railway. 3This paper was published in the Edinburgh New Philosophical Journal, July, 1849; but from now on we shall give references to "Miscellaneous Scientific Papers," by W. J. Macquorn Rankine (1).
4J. Dalton, T. Young, J. B. Biot, and G. Kirehhoff were among those who had given empirical formulas for this. JA similar formula was derived by A. Duprb (2), hence it is sometimes known as DuprB's formula. Callender improved on Rankine's formula in 1900. 6The paper was read before the Royal Society of Edinburgh on February 4,1850.
The hypothesis of molecular vortices may be defined to be that which assumes that each atom of matter consists of a nucleus or central point enveloped by an elastic atmosphere, which is retained in its position by attractive forces . . . and that the elasticity due to heat arises from the centrifugal force of revolutions or oscillations among the particles of the atmosphere . . . It may he noted in passing that contrary to widespread belief, it was not Rutherford who first coined the term nucleus to refer to the central part of the atom. In this same paper Rankine also expressed the idea that "quantity of heat is the uk uiua (old term for kinetic energy) of those revolutions and oscillations." And he deduced a law according to which "temperature is a function of the velocity of revolution in the molecular vortices, divided by the coefficient of elasticity of the atmospheric atmospheres. . ." Todav even a freshman student in science knows that t h e temperature of a body is related to the kinetic energy of its constituents. hut he seldom realizes that this fundamental result is not even a hundred and fifty years old. Much less is he aware of the initial tentative struggles and suggestions in this direction. Surely Rankine was one of the pioneers in this field. In a paper read before the Philosophical Society of Glasgow in January 1853 (5) Rankine introduced the term potential energy into science.7 He said that potential or latent energy is to be measured "by the product of a change of state into the resistance against which that change is made."s In the same paper Rankine also introduced the expression actual or sensible energy as a "measurable, transmissible, and transformahle condition, whose presence causes a substance to tend to change its state in one or more respects." This term was replaced in course of time by the now current kinetic energy.9 Soon after this Rankine read another paper before the Royal Society of Edinburgh, in which he introduced the concept of heat potential in the following context 16) In order to investigate the laws according to which heat is converted into mechanical power, in a machine working by the expansion of an elastic hody, it will be convenient to use afunction
of such a nature that the difference between two of its values, corresponding to two different volumes of the hody at the same total heat, represents the ratio of the heat converted into power by expansion between those volumes, to the given constant total heat. I shall call this function a heatpotential. The following year (7) Rankine developed the idea of the thermodynamic function, which was basically the same quantity as his heat potential, but with an additional term depending on temperature change. It was in the same year, 1854, that Clausius introduced his Aequiualenzwerth (which was later changed into entropy). The fundamental equivalence between Rankine's thermodynamic function and Clausius' entropy was not recognized for a long time. Even Maxwell realized this only much later. In a letter written to Tait in 1873 Maxwell remarked10 It is only under the conduct of Professor Willard Gibbs that I have been led to recant an error that I had imbibed from your BAC*, namely that the entropy of Clausius is the unauailable energy while that of T' [Tait] is the available energy. . . . the entropy of Clausius is neither the one nor the other, it is only Rankine's thermodynamic function. Of course Rankine himself never used the term entmpy although it could well have been one of his own numerous verbal inventions. For Rankine was fond of introducing new and often strange sounding words into science. Some of these, like potential energy and strain, have sumived. Others have not. Consider, for example, the following:
thlipsimetric and tasimetric invariants, tasinomic and platythliptic coefficients, orthotatic and euthytatic axes, metatatic and pentatic isotropy. These are only some of the terms introduced by Rankine in a paper on the axes of elasticity and crystalline forms (9). During the nineteenth century, when the atomic hypothesis began to be taken a little more seriously than durine the aee of Democritus. nhvsicists and chemists wondered if tKey had sufficient jistkcation for accepting the existence of entities decidedlv"bevond . their direct perception. In the early stages there were two school^ of thought on this question. According to the one, atoms and molecules were mere fantasies and ought to he banned from scientific discourses altogether. According to the other, one should not overlook the need and udfulness of such assumptions. These investigators did grant that atoms and molecules were too speculative to be declared as having objective existence; but a t the same time they did not shy away from using concepts if they provided reasonable and quantitative explanations for observed effects. Rankine recognized these intrinsic difficulties, and he classified the methods by which physical theories are formulated into two large classes which he described as the ahstractive and the hypothetical methods (10). After definine., a . nhvsical . theorv as a "svstem of nrinciples, with its consequences methbdically deduced,"'he went o n to characterize the ahstractive method as one in which only what is directly perceivable and discernible to the senses is taken into account. In other words, in the ahstractive method one adopts Newton's famous motto of hypothesis non fingo. On the other hand, in the hypothetical method, said Rankine, one introduces entities "accordinn- to a conjectural conception of nature, in a manner not apparent to the senses, by a modification of some other class of objects or phenomena whose laws are already known." This analysis of physical theories appeared as a prelude to Rankine's paper~onthe science of energetics, yet another term which he coined. This discussion did not attract much attention because, as Morris Cohen observed, "it came in the heyday of mechanical models, when everyone was trying to derive the principle of energy from the principles of mechanics" (11). But in later years many philosophers of science made reference to Rankine's categorization of physical theories 112, 13). Pierre Duhem, writing in the early years of this century (141, expressed the view that hypothetical theories had no place in science, for all that science can hope to accomplish is to give "a simplified and orderly representation grouping laws according to a classification which grows more and more complete, more and more natural." And he disagreed (15) with Rankine's contention that "a hypothetical theory is liecessary, as a first step, in order to put simplicity and order into the expression of phenomena before it is possible to make progress in the construction of an ahstractive theory." However, it would seem from the evolution of microphysics that Rankine was quite right. In vet another uhilosouhical reflection on the evolution of science ~ a n k i i espoke" on the "Concord in the Mechanical Sciences between Theory and Practice." Here he analyzed the classical thesis of Aristotelian physics that there are two systems of natural laws: one purely ideal and rational, applicable to the heavenly bodies; and the other, practical and sublunar, applicable to the corrupt'G. Green was the first to introduce the notion of the potential function in 1828. 8Thisis essentially equivalent to F.d or the work done. 91t was Thamsan and Tait who brought in the term kinetic energy in 1868. l0Quotedby E. E. Daub (81. "This was also published as an introduction to Rankine's "Manual of Applied Mechanics." Volume 50, Number 4, April 1973
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ible world here below. Rankine suggested that although such a distinction had long since been abandoned by the rise of modem science, vestiges of such thinking still persisted even in the nineteenth century. Rankine's exposition of the science of energetics, though presented in twenty short sections (16). was the "generalized expression of a method of reasoning, which has already been applied with success to special branches of physics." Its long range impact was considerable. Thomson and Taitlz wiote their "Treatise on Natural Philosophy"-a work that is said (17) to have marked "an epoch in the teaching of the foundations of physical science scarcely less important than that in which Newton produced his immortal Principian-from the point of view of energetics. And Wilhelm Ostwald took inspiration from Rankine to found his all embracing philosophy of energetics. An implication of the second law was the utter irreversibility of all natural processes leading to the ultimate heat death. Some philosophers and scientists were upset by such a possihility, and attempted to consider possible escapes from such a doom (18). Rankine's highly speculative-attempt in this direction was presented in an interesting paper entitled "On the Reconstruction of the Mechanical Energy of the Universe" (191 where he considered the possibility of reflecting walls in the universe, thanks to which radiation may not escape into limitless infinity. He argued It is conceivable that, at some indefinitely distant period, an opposite condition of the world may take place, in whieh the energy which is now being diffused may be reconstructed into foci, and stores of chemical power may again he produced from inert compounds which are now being continually formed. We have referred thus far only to some of Rankiie's contributions to the theory of heat and thermodynamics. But he worked and published on other subjects also. In addition to more than a hundred and fiftv scientific napers Rankine also authored a number of textbooks wGch were widely use. His "Apnlied Mechanics" was described as "the best work on the application of the doctrines of pure mechanics to general engineering problems." In his text on "Civil Engineering'' he extended the principles developed in the previous work to problems of particular interest to the civil engineer. This book is replete with much statistical information. His "Manual of the Steam Engine and other Prime Movers" discussed thermodynamics in relation to its application to steam engines. The chapter on thermodynamics in this book is one of the first nuhlished treatises on the suhiect. This is not the place to dfscuss the many controversies that raeed over auestions of orioritv and credit in thermodynaml'cs during that period, and in which Rankine's name was involved.13 Suffice it to sav that Rankine's own contrihtions were significant and ronsiderable. One reason whv his name is nor so often hrouaht into discussions of thermodynamics is t h a t Rankine's papers were largely in terms of his vortex theory which has long since gone out of date. Also, as Professor Truesdell has pointed out,14 although "a complete history of thermodynamics would lZThework was published in 1867. Thomson and Tait were referred to as T and T' because of their close collaboration. 13This is a suhiect of much historical interest. For a clear discussion of c an kine's versus Celsius's role in the early, development of thermodynamics, see Daub (20). "In a lecture entitled "The Tragicomedy of Thermodynamics in the Nineteenth Century" delivered at the University of Rochester an October 14, 1970. 15The so-called energy, intensity, and capacity factors were intraduced by Rankine (231.
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have to take account of the work of Kelvin and Rankine . . . their writings are verbose, complex, obscure, tortured and smothered by details of experiments and tables of numbers." Indeed Maxwell himself, after paying due hommage to Rankine's abilities and to the powers of his imagination, noted in reference to Rankine's statement of the second law (21), ". . although, as a literary form, it seems cast in the same mould (of very good style), its actual meaning is inscrutable . . . .:' Rankine was a patriotic Briton. He joined the volunteer movement in which he became first a captain, then a senior major. He' was fond of music and poetry, and composed some himself. His most famous composition was a sonz in defense of the British svstem of units and measures against a possible introduction of the metric system into Britain. A stanza in that song ran as follows Some talk of millimeters, and same of kilograms, And same of decditws. t u mearurr beer and drams: HUI I'm a Hrirish Workman. to
