Building on the work of Clausius, between the years 1873-76 the American mathematical physicist Willard Gibbs published a series of three papers, the most famous one being the paper On the Equilibrium of Heterogeneous Substances.

Based on Gibbs ' work, Nernst extended the theory to include the contribution from electric potential on charged species.

In 1875, in the work of Josiah Willard Gibbs, the basic thermodynamic quantities were energy potentials, such as internal energy, as dependent variables, and entropy, considered as a fundamental independent variable.

That work appeared in the Transactions of the Connecticut Academy, which had few readers capable of understanding Gibbs's work, but he shared reprints with his correspondents in Europe and received a particularly favorable response from James Clerk Maxwell, at the University of Cambridge, who made three plaster casts illustrating Gibbs's construct with his own hands and mailed one to Gibbs ( see Maxwell's thermodynamic surface ).

In that work Gibbs rigorously and ingeniously applied the concepts of thermodynamics to the interpretation of physico-chemical phenomena, successfully explaining and interrelating what had previously been a mass of isolated facts.

Gibbs continued to work without pay until 1880, when the new Johns Hopkins University in Baltimore, Maryland offered him a position paying $ 3, 000 per year.

In other mathematical work, he re-discovered the " Gibbs phenomenon " in the theory of Fourier series ( which, unbeknownst to him and to later scholars, had been described fifty years before by an obscure English mathematician, Henry Wilbraham ).

In his work on optics just as much as in his work on thermodynamics, Gibbs deliberately avoided speculating about the microscopic structure of matter, which proved a wise course in view of the revolutionary developments in quantum mechanics that began around the time of his death.

Gibbs had few students and his retiring personality and intense focus on his scientific work were such that he was generally unavailable personally.

When Gibbs submitted his long paper on the equilibrium of heterogeneous substances to the Academy, both Elias Loomis and Hubert Anson Newton protested that they did not understand Gibbs's work at all, but they helped to raise the money needed to pay for the typesetting of the many equations and mathematical symbols in the paper.

Gibbs succeeded in interesting his European correspondents in that work, which was translated into German ( then the leading language for chemistry ) by Wilhelm Ostwald in 1892 and into French by Henri Louis Le Châtelier in 1899.

Gibbs did receive the major honors then possible for an academic scientist in the US: he was elected to the National Academy of Sciences in 1879 and was awarded the 1880 Rumford Prize from the American Academy of Arts and Sciences for his work on chemical thermodynamics.

That work was based largely on the thermodynamics of Kirchhoff, Boltzmann, and Gibbs.

The first half of the 20th century saw the publication of two influential textbooks that soon came to be regarded as founding documents of chemical thermodynamics, both of which used and extended Gibbs's work in that field: these were Thermodynamics and the Free Energy of Chemical Processes ( 1923 ), by Gilbert N. Lewis and Merle Randall, and Modern Thermodynamics by the Methods of Willard Gibbs ( 1933 ), by Edward A. Guggenheim.

) Yale's J. W. Gibbs Laboratory and its J. Willard Gibbs Assistant Professorship in Mathematics are also named in his honor, and the university has hosted two symposia dedicated to Gibbs's life and work, one in 1989 and another on the centenary of his death, in 2003.

For processes involving a system at constant pressure p and temperature T, the Gibbs free energy is the most useful because, in addition to subsuming any entropy change due merely to heat, it does the same for the pdV work needed to " make space for additional molecules " produced by various processes.

Thus, in traditional use, the term “ free ” was attached to Gibbs free energy, i. e., for systems at constant pressure and temperature, or to Helmholtz free energy, i. e., for systems at constant volume and temperature, to mean ‘ available in the form of useful work .’ With reference to the Gibbs free energy, we add the qualification that it is the energy free for non-volume work.

Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and / or its surrounding.

As Helion's work showed more and more nostalgia for the world of man and nature, the pure abstractionists expressed some disapproval ; ;

Furthering Ørsted ’ s experimental work, Ampère showed that two parallel wires carrying electric currents attract or repel each other, depending on whether the currents flow in the same or opposite directions, respectively-this laid the foundation of electrodynamics.

Unlike his translation of the Pastoral Care, Alfred here deals very freely with his original and though the late Dr. G. Schepss showed that many of the additions to the text are to be traced not to Alfred himself, but to the glosses and commentaries which he used, still there is much in the work which is solely Alfred's and highly characteristic of his style.

Further investigation and theoretical work showed that the effect was a radiationless effect more than an internal conversion effect by use of elementary quantum mechanics and transition rate and transition probability calculations.

Henry Moseley's work showed experimentally in 1913 ( see Moseley's law ) that the effective nuclear charge was very close to the atomic number ( Moseley found only one unit difference ), and Moseley referenced only the papers of Van den Broek and Rutherford.

Long considered a mathematical curiosity, it was during the 1960s that theoretical work showed black holes were a generic prediction of general relativity.

Shannon's work on information theory showed that to achieve so called perfect secrecy, it is necessary for the key length to be at least as large as the message to be transmitted and only used once ( this algorithm is called the One-time pad ).

This work showed that the quantum approach to chemical bonds could be fundamentally and quantitatively correct, but the mathematical methods used could not be extended to molecules containing more than one electron.

However, the work of Friedrich Hund, Robert Mulliken, and Gerhard Herzberg showed that molecular orbital theory provided a more appropriate description of the spectroscopic, ionization and magnetic properties of molecules.

Tin Machine resumed work the same month, but their audience and critics, ultimately left disappointed by the first album, showed little interest in a second.

In his work, Planck showed that hot objects emit electromagnetic radiation in discrete packets, which leads to a finite total energy emitted as black body radiation.

Faraday's disc was inefficient and of no use as a practical generator, but it showed the possibility of generating electric power using magnetism, a possibility that would be taken up by those that followed on from his work.

Faraday's and Ampère's work showed that a time-varying magnetic field acted as a source of an electric field, and a time-varying electric field was a source of a magnetic field.

Spencer Jones ' work of 1939 showed that the positions of the Sun actually observed, when compared with those obtained from Newcomb's formula, show the need for the following correction to the formula to represent the observations:

Abbot's studies were chiefly in Oriental languages and textual criticism of the New Testament, though his work as a bibliographer showed such results as the exhaustive list of writings ( 5300 in all ) on the doctrine of the future life, appended to W. R. Alger's History of the Doctrine of a Future Life, as it has prevailed in all Nations and Ages ( 1862 ), and published separately in 1864.

Later work by Eberhard showed that the key properties of local hidden variable theories which lead to Bell's inequalities are locality and counter-factual definiteness.

Fine's work showed that, taking locality as a given, there exist scenarios in which two statistical variables are correlated in a manner inconsistent with counter-factual definiteness, and that such scenarios are no more mysterious than any other, despite the inconsistency with counter-factual definiteness seeming ' counter-intuitive '.

The BBC reported that in 2002 work done by Edward Castronova showed that Everquest was the 77th richest country in the world, sandwiched between Russia and Bulgaria and its GDP per capita was higher than that of the People's Republic of China and India.

In 1909, tests showed cellulose diacetate to be a viable replacement base, and Kodak began selling acetate-base films the following year in 22 mm widths for Edison's work on the Home Kinetoscope, which was commercially released in 1912.

Stimulated by their discussions with Wilkins and what Watson learned by attending a talk given by Franklin about her work on DNA, Crick and Watson produced and showed off an erroneous first model of DNA.

This work showed that the black hole information paradox is resolved when quantum gravity is described in an unusual string-theoretic way.

Contrary to such views, Abraham Robinson showed in 1960 that infinitesimals are precise, clear, and meaningful, building upon work by Edwin Hewitt and Jerzy Łoś.

Originally his work focused on technique-some argue that it had that focus at the cost of relevance, especially in Rain ( Regen, 1929 ), a 10-minute short filmed over 2 years which features impressive cinematography and a number of ' characters ' but no information about them aside from what was visible, and in The Bridge ( De Brug, 1928 ), which showed a frank admiration of engineering and also featured a number of " characters " but again did not give any information about them.

" Though Jahangir believed it to be the work of the slave who presented it to him, Sayyid Ahmad and Henry Beveridge suggest that it was of European origin, and possibly showed the Transfiguration.

In his earliest work, Neusner had argued that the most credible evidence showed that the Second Commonwealth Pharisees were a sectarian group centered on " table fellowship " and ritual food purity practices, and less interested in wider Jewish values or social issues.