Francois Massieu

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In existographies, Francois Massieu (123-59 BE) (1832-1896 ACM) (EPD:F0) (CR:26) (LH:11) (TL:38) was a French engineer, physicist, mineralogist, geologist, and philosopher, noted for his 1869 "On the Characteristic Functions of Various Fluids", which was the first systematic discourse on “thermodynamic potentials” (Ѻ) applied to bodies, specifically fluid bodies; some characterize his "Massieu function" as the Legendre transform of entropy; influential to Willard Gibbs, who adopted his Greek letter nomenclature for defining the various thermodynamic functions, as show in the pictured characteristic function notation table.[1]


Characteristic function

See main: Characteristic function

In 1869, Massieu, in his "On the Characteristic Functions of Various Fluids", gave, supposedly, the first systematic discourse on “thermodynamic potentials” (Ѻ) applied to bodies, specifically fluid bodies, which is shown below, between Clausius and Gibbs:[2][3]

Characteristic function notation table 2.jpg

In 1876, Massieu published Thermodynamics: Memoir on the Characteristic Functions of Various Fluids and on the Theory of Vapors.[4]

In 1876, Willard Gibbs, in his On the Equilibrium of Heterogeneous Substances, adopted Massieu's Greek letter nomenclature for defining the various thermodynamic functions, as show in the above characteristic function notation table.[5]

Some characterize the so-called "Massieu function" as the Legendre transform of entropy.


In 1897, Edmund Nivoit, a French engineer, in his “Notice of the Life and Work of Massieu”, summarized Massieu as follows:[6]

“It is especially in the field of thermodynamics that Massieu left a luminous trace of his passage. It is probable that he was encouraged to follow this path, where were also his personal tastes and habits of mind, by his colleague from the Faculty of Rennes, Athanase Dupre, who published a series of papers on the mechanical theory of heat, in the Annals of Chemistry and Physics. More than once it had recourse to the penetrating mind and keen Massieu to increase the rigor of the demonstrations or to shed light on some obscure point, he was sometimes even brought on his advice, abandon proposals hazardous. It also fully inserted in his memoirs of his collaborator two notes: one on the molecular attraction, the other on the work of complete disintegration, or total work required to separate molecules from each other, despite the forces they opposed.

In 1870, Massieu presented, to the Academy of Sciences, a brief on the characteristic functions of the various fluids and value theory, which I will try to give a brief idea. Everyone agrees that the state of a body is completely defined when we know two of the three quantities that represent the volume of this body, its temperature and pressure on its surface. Any one of these quantities must be regarded, for each body, as a function of two others taken to the independent variables.

Based on the fundamental principles of thermodynamics and choosing as variables, the volume and temperature or pressure and temperature, Massieu established by a simple calculation, an equation where both are exact differentials and from which he derived a function, independent of any hypothesis, he called the characteristic function of the body considered, because it implicitly contains all the thermodynamic properties of the body. It may indeed serve to express, either by itself or through partial derivatives, the pressure on the body or volume (as the independent variables that have been taken), the entropy of Clausius or function, internal energy, then by a little less simple calculations, the two specific heats, a constant pressure, the other at constant volume, the two coefficients of expansion at constant pressure and volume, the coefficient of compressibility .

Massieu then applied his theory to the ideal gas, which follow the laws of Mariotte and Gay-Lussac, the saturated vapor and superheated vapor. For ideal gases, it naturally finds no new property, since the properties of these bodies are used to precisely determine the complete expressions of the fundamental principles of thermodynamics. For saturated vapor, it also reflected by an elegant analysis, formulas already known, including one that calculates the density of dry saturated steam under various pressures using the experimental data of Regnault. His aim in this analysis is to show the simplicity and generality of his method.

Regarding the superheated steam, the elements of uncertainty abound, since the only experimental data that one has to determine the characteristic function, which is the value of the specific heat of water vapor varies with temperature and with the pressure. The author first establishes its formulas without any hypothesis, but to translate them into numbers, it is obliged to make various assumptions. He admits that the first specific heat of water vapor is constant and its value is equal to the figure obtained by Regnault in specific conditions, which amounts to assimilate in this report to a perfect gas vapors. This is a perfectly acceptable assumption for the practice, if we do not take a very rigorous.

But the industry does not seek to obtain strong overheating, and rightly so, because, as Massieu shows the theory, they would be of little use in steam engines arranged like those we use. The almost unique advantage they bring is to reduce heat losses due to condensation in the cylinder. Just a small amount of heat used to superheat steam admitted, for a relatively large reduction in the expenditure of the steam. In a second case, the author represents the specific heat by a formula with three factors, it can be calculated using the known law of maximum tension. Just as this law has not quite a general character, since the integral contained in the formula that translates is caught between two specific limits, which are the saturation temperature and infinite temperature, we understand that can give the form of a function, but only the numerical value of some coefficients. This second hypothesis, however, provide much better results that approached those obtained with the previous, where specific heat is regarded as constant, and it should be preferred when the overheating becomes an inconsiderable.

The characteristic function of a body is so good, as we see, the condensation of all its thermodynamic properties. It suffices to express a limited number of numerical coefficients, and when, or could obtain these data, one must choose among those that experience provides the easiest, the thermodynamic theory of this body is complete.

She still has a valuable property which greatly increases its scientific value and gives a great philosophical interest. It is a kind of touchstone, with which to test any statement relating to the mechanical theory of heat and recognize if it is pure alloy. Thus Massieu has demonstrated the inaccuracy of some theorems formulated hastily by way of analogy and he did see that other, instead of corresponding to general truths, applicable only to body of a certain category.

An eminent judge, Joseph Bertrand (Thermodynamique, 1887), did not hesitate to declare, in a report read to the Academy of Sciences July 25, 1870, that "the introduction of this function in formulas that summarize all the possible consequences of the two fundamental theorems for the theory seems a similar service and has almost equivalent to that given Clausius' theorem in relating the Carnot entropy.

Shortly after the release of this remarkable memoir, which discontinued its author among the masters of thermodynamics, Massieu released a memo written to please a few people who were interested in his work, in which he gives a full statement of two fundamental principles, he had accepted without question and without the show: one, known as the principle of equivalence between heat and work, stated by Meyer and the other due to Carnot, which defines the influence of temperature on the thermal phenomena whose machines are registered.

He thought, the great mathematician Lagrange, that if these formulas are very useful in the development of a science, they often interfere with the clarity of the exposition of its principles. There are about thirty years, when Massieu was engaged in his search for rational mechanics, the mechanical theory of heat was again applied only within narrow limits to the study of steam engines. In education we continued to rely mostly on two assumptions which are incorrect, however, was well demonstrated. They assumed that because the saturated vapor follow the laws of Mariotte and Gay-Lussac, who are already not absolutely rigorous for gas in perfect condition, and more than vapor, when they relax in a cylinder engine to remain without saturation or overheating occur or partial condensation.

In fact many scholars, such as Clausius, Zeuner, Rankine, Combes, and Resal, have shown how practical implications could be drawn from the new theory and gave some numerical examples. But it had not yet established formulas that can be applied widely in construction workshops and permitting, is to discuss the pros and cons of various measures adopted in the machinery, or to sense the value changes that might be tempted to introduce.

Massieu had planned to fill this gap and to publish a text of a rational theory of steam engines, based on the fundamental principles of thermodynamics. He possessed all the elements of this work he could do was to coordinate and establish numerical tables that would have been the translation of its most important formulas. This might have been such a work, developed by a man so admirably prepared, it is easily understood. The introduction and first two chapters, including the statement of principles, as well as studying the properties of gases and vapors are only completed. Clarity is dominant, too abstract calculations have been avoided with the utmost care, which makes reading easier for those people who have only the rudiments of calculus. The third chapter, on superheated steam, which was to be the original part of the book, is sketched.”

In c.2016, the School of Space Science in Rennes, posted the following online general overview of Massieu, which seems to focus on his work a civil engineer, related to city drainage and hygiene:[7]

Francois Massieu: father of the mains drainage. He does not have a street in Rennes yet the Rennes people owe him a lot. Running water and sewers, that's him! Born in 1832, in Vatteville (Seine-Inférieure), François Massieu received his secondary education in Rouen, before entering Polytechnique in 1851, then in 1853 at the Ecole des mines. Appointed mining engineer in Caen in 1859, he devoted his spare time to pure science studies and defended two mathematics theses in 1861 at the Sorbonne. The same year, he succeeded Durocher, the first holder of the chair of geology at the Faculty of Sciences of Rennes. He taught there for 26 years as a professor in charge of geology and mineralogy. We know of few geological publications, except the geological map of the department of Ille-et-Vilaine published in 1866. He is best known for his work on locomotive brakes which served as a reference for engineers. Having joined the City Council, he deals in particular with hygiene and sanitation issues, writes reports on important issues: water supply, creation of a sewer network, reconstruction high school. Water collection in the Loisance and Minette basins is also the case. Called in 1886 to Paris as chief engineer of the western railways, he gave up his teaching. Having become inspector general of mines and director of control of the railways of the East, he died in Paris in 1896.”

Sirodot | Photo confusion

Of note, in 2015 someone added a photo of Simon Sirodot to the French Wikipedia article on Massieu. The issue wasn't noticed until Dec 2020, when Libb Thims noticed the confusion; hence, there exists a certain amount of ongoing photo-misatribution spread on the Internet, and in some books[8], in respect to this issue.



Massieu was influenced by: Athanase Dupre (1808-1869).


Massieu influenced: Willard Gibbs.


Quotes | On

The following are quotes on Massieu:

Massieu has shown how all the properties of a fluid ‘which are considered in thermodynamics’ may be deduced from a single function, which he calls a characteristic function of the fluid considered; he introduces two different functions of this kind, vis, a function of the temperature and volume, which he denotes by Ψ, and a function of the temperature and pressure, which he denotes by Ψ’; in both cases he considers a constant quantity (one kilogram) of the fluid, which is regarded as invariable in composition.”
Willard Gibbs (1876), On the Equilibrium of Heterogeneous Substances [9]

Quotes | By

The following are quotes by Massieu:

“They cut the man into two parts, soul and body, the philosopher took one, the naturalist took the other; they both have worked, studied on their behalf, but have lost sight and we find ourselves today in the presence of a ‘duality’, convenient perhaps, but unwise, in that it overlooked the man to deal with only two elements that constitute it. But in doing so we run the risk of being wrong. If one wanted to know the chemical properties of water [], seek it in those of oxygen [] and hydrogen []? No, because he knows that there is little relationship between the characteristics of a substance and those of simple bodies which enter into its composition. To study humans, it is perhaps even more reserve, his corpse is certainly different from his living, his soul is a being whose morality tells us in existence, but whose philosophy can boast of acquire specific knowledge, since it can be studied in a free state, the revelation can only speak in this regard. But what science and philosophy can and should perhaps only study, is a man indivisible and tangible for us, where the angel and the beast are inseparable, which has a body and ailments, but also passions and faculties, such as intelligence, memory and reason.”
— Francois Massieu (c.1869), “Speech deliver at the start of the Faculties of Rennes”[6]

End matter


  1. Characteristic function notation table – Hmolpedia 2020.
  2. Massieu, Francois. (1869). “On the Various Functions Characteristic of Fluids and on the Theory of Vapors” (Sur les Functions Caracteristiques des Divers Fluides et Sur la Theorie des Vapeurs), Comptes Rendus, 69: 858-62, 1057-61.
  3. Thims, Libb. (2020). Human Chemical Thermodynamics — Chemical Thermodynamics Applied to the Humanities: Meaning, Morality, Purpose; Sociology, Economics, Ecology; History, Philosophy, Government, Anthropology, Politics, Business, Jurisprudence; Religion, Relationships, Warfare, and Love (§2: Alphabet) (pdf). Publisher.
  4. Massieu, Francois. (1876). Thermodynamics: Memoir on the Characteristic Functions of Various Fluids and on the Theory of Vapors (Thermodynamique: Mêmoire sur les fonctions catactéristiques des divers fluides et sur la théorie des vapeurs ) (92-pgs) (WC)(GB). Académie des Sciences de L'Institut National de France.
  5. Characteristic function notation table – Hmolpedia 2020.
  6. 6.0 6.1 Nivoit, Edmond. (1897). “Notice of the Life and Work of Mr. Massieu, Inspector General of Mines” (French → English), Annales des Mines, 9th Series, Volume. 11.
  7. Francois Massieu (French → English) – School of Space Sciences in Rennes.
  8. Splinter, Robert. (2017). Illustrated Encyclopedia of Applied Engineering Physics (Massieu [photo of Simon Sirodot shown], pg. 336). CRC.
  9. Gibbs, Willard. (1876). On the Equilibrium of Heterogeneous Substances (Massieu, pgs. 86, 358). Publisher.

Further reading

  • Duhem, Pierre. (1886). Thermodynamic Potential and its Applications to Chemical Mechanics and the Study of Electrical Phenomena (Le potentiel thermodynamique et ses applications à la mécanique chimique et à l'étude des phénomènes électriques) (Massieu, 8+ pgs). Publisher.
  • Joubin, Louis. (1900). History of the Faculty of Sciences at Rennes (Histoire de la Faculté des sciences de Rennes) (Massieu, 11-pgs). F. Simon

External links

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