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© 1996-2006 HyperJeff Network Sketching the History of History | Philo | | Blog Statistical Mechanics [ Sources, Links, Notes ] and

(From about 1575 to 1980)

Ideas of atomism, that is a mode Anti- of within bodies and that quity is the result of such motion, are all floating around. Hero of Alexandria (see also here) writes Pneumatics, an investigation 1st on atmospheric air, summarizing a cent great deal of what was known at the AD time on syphons, pumps, the effects of heat on , and engine designs. Al-Baqilani (d 1013) said to have 9th introduced atomism to the Muslim cent Kalam (perhaps influencing Leibniz). The loss of permanent 11th when materials are subjected to high The aeolipile of cent known in China. Hero F Commandine translates Hero of Alexandria's Pneumatics into Latin 1575 (translated earlier in 1547 into Italian by Aleotti). Santorre Santorio (see here also) (1561-1636) is known to have been using an early thermoscope and also writes Commentariar in artem medicinalem Galeni. Santorre writes 1612 to Galilei (1564-1642) including sketches of his device, to which Galileo replies that it was an invention of his. The priority remains unclear.

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Thermoscopes of Santorio are 1615 sensitive enough to detect near-by body heat and candles. Johannes van Helmont defines "" 1620 (the Flemish word for chaos) for air-like substances. Galileo points out that simple pumps can only raise water about 32 feet, 1638 though this had been common knowledge to pump makers of the time. Ferdinand II, Grand Duke of Tuscany, invents a using in 1641 a glass tube with one end sealed, a slight improvement to Galileo's thermoscope. (1608-1647) 1643 invents the barometer, also producing the first partial vacuum. René Descartes' (1596-1650) treatise Principa Philosophiae published in Amsterdam. The extends effords to formulate a fully 1644 mathematico-mechanical model of the world, including concepts of nonlocality, the absence of any vacuum and his vortex model of atoms. Gilles Personne de Roberval (1602-1675) performed an oft-quoted experiment on air pressure whereby a carp's swim-bladder is partially 1647 removed, squeezed of almost all air and tied shut. The carp is then placed in a Torricellian vacuum and the bladder is observed to expand. Florin Perrier experimentally shows that the height achieved by mercury 1648 in a barometer decreased as one scaled a mountain, a theoretical

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prediction of his brother-in-law, Blaise , and also known as the Puy de DĂ´me experiment. ca (Coffee begins to be important to and 1650 catch on in Europe.) Jean Pecquet's (1622-1674) book on psychology popularizes the Roberval experiment (English translation in 1653). He also introduces the term 1651 "elater" as the tendency of air to expand, and theorizes that air on the earth's surface is compressed by the weight of the atmospheric air. Otto von Guericke's (1602-86) experiment with two iron hemispheres held together by a strong partial vacuum being strong 1654 enough to resist the pull of a train of horses on either side.

Ferdinand II invents the sealed thermometer. Robert Boyle (1627-91) publishes New Experiments Physio- Mechanicall, touching the Spring of the Air, and its Effects. One experiment clearly shows the dependency on Torricelli's vacuum on ambient air pressure. Also presented are discussions of both Pecquet's idea of air modelled by coiled-up wool-like 1660 or spring-like atoms (which was preferred by Boyle) and of Descartes' idea of whirling particles which repell one another at short Robert Boyle distances.

In response to Boyle's ideas, Franciscus Linus (1595-1675) proposes a theory whereby a vacuum is explained by the creation of an

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invisible collection of thread-like "funiculus," which strive to hold nearby objects together.

Richard Townley (1628-1707) and 's (1623-1668) experiments establishing the PV law for expansion (the so-called "Boyle's Law" or "Marriotte's Law"). Boyle adds an appendix to his 1660 work, responding to the criticisms of Linus and Thomas Hobbes, 1661 presenting improved experimental results and giving a version of what is now known as "Boyle's Law" for the case of compression. Boyle's "Defense of the Doctrine 1662 touching the Spring and Weight of the Air." (1623-1662) writes On the Equilibrium of Liquids (published posthumously) suggesting that pressure is transmitted equally in all directions in a fluid (later known as 1663 "Pascal's law"), probably discovered around 1648.

Power's book Experimental Philosophy, publishing early results on the PV law. Johann Joachim Becher's Subterranean Physics, a tract on alchemy and experimental results on 1669 minerals, introduces the idea that a "terra pingus" (oily earth) causes fire. (This idea is later picked up to form the phlogiston theory of heat.) Boyle discovers that when acid interacts with certain metals a 1670 flammable gas is produced, known now as Hydrogen.

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Christiaan Huygens (1629-95) 1673 builds a motor driven by the explosion of gunpowder. John Mayow suggests that air may consist of two different from 1674 experiments done on mice and candles, reported in his Five Medico- Physical Treatises. Edmé Mariotte (~1620-1684) independently finds relationship between pressure and , in his 1676 work On the Nature of Air. (Known as "Mariotte's law" in , and "Boyle's law" elsewhere.) Mariotte's The Motion of Water and 1685 Other Fluids published (posthumously). Denis Papin (1647-1712) uses 1690 pressure to move a piston for the first time. Georg Ernts Stahl introduces the idea 1697 of phlogiston as the agent of burning and rusting. Guillaume Amontons extrapolates the idea of from the observation that equal drops in produce equal drops in pressure, and since pressure cannot become negative, there must be a 1702 lower limit to temperature.

Ole Christensen Rømer devises a temperature scale based on the two phenomena of the boiling point of water and the temperature at which snow begins to form. Francis Hauksbee shows that sound 1705 needs air for propagation. 1712 Thomas Newcomen's .

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Gabriel 's mercury 1714 thermometer introducing his temperature scale. (see notes) Jakob Hermann (1678-1733) proposes the first definite measure of the heat of molecular motion in his work on rational mechanics, 1716 Phoronomia. He postulates that (in modern lingo) pressure is proportional to and to the square of the average velocity of the particles of motion. Stahl's Foundations of Dogmatic and Experimental popularizes Jakob Hermann 1723 phlogiston and the ideas of Johann Becher. Hermann Boerhaave proposes that 1724 heat is a fluid of some sort. Leonhard Euler (1707-1783), extending Johann Bernoulli's work on Descartes' vortex cosmology, models air with tightly-spaced, spinning spheres. He formulate an relating humidity, 1729 pressure, density and velocity, finding the Townley-Power-Boyle law as an approximation. He calculates air molecules to be about 477 m/s at mean conditions, and that this is about the speed of sound. Johann Juncker's Conspectus of 1730 Chemistry systematically expands phlogiston theory. (1700-1782), in a treatise on hydrodynamics worked out in the period from 1728 to 1733, 1733 gives a derivation of the from a billiard ball model, derives the Boyle-Mariotte relation and used conservation of mechanical to Daniel Bernoulli

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show that as temperature changes the pressure will change proportionally to the square of the particle velocities. This text marks the first truly statistical treatment of kinetic theory. A significantly updated edition of the text is published in 1738. The paper is all but forgotten until 1859. George Martine establishes that the volume of an object is not 1739 proportional to the amount of heat it has. Anders (1701-1744) publishes "Observations on two persistent degrees on a thermometer," basing his scale on the 1742 freezing point (100 degrees) and boiling points (0 degrees) of water. (The system is reoriented in 1745 by Carl Linnaeus, a.k.a. Carl von Linné.) Mikhail Vasilievich Lomonossov publishes a paper on the causes of 1744 heat and cold, stating that heat is a form of motion. (also, Carl von Linné, 1707-1778) 1744 reorients Celsius's scale. Lomonosov formulates laws of and . Through about 1760, he performs a number of theoretical investigations 1748 about molecular structures, speculating on the effects of translation, vibration, and rotations of such molecules. William Cullen's An Essay on the Cold Produced by Evaporating Fluids and 1756 some Other Means of Producing Cold.

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Rudjer Giuseppe Boskovic (1711-1787) mathematically models molecules via points subjected to intermolecular which are 1758 attractive nearby but repulsive at greater distances. His efforts, however, are too vaguely worked out to base a theory on. Joseph Black (1728-1799) finds that when melting ice, heat can be 1761 absorbed without changing temperature. James invents his steam engine, 1765 which is over six times more effective than Newcomen's. Johan Carl Wilcke calculates the 1772 of ice. Wilcke comes up with the concept of 1781 specific . Lavoisier establishes an early version of the conservation of matter through 1782 Phlogiston Theory his finding of constancy of weight (~1660's to ~1790's) before and after chemical reactions. Kinetic Heat Theory (~1716 to ~1760's) Lavoisier's work, Reflections on (then ~1816 to present) Phlogiston, on the weaknesses of Caloric Heat Theory 1783 (~1780's to ~1860's) phlogiston theory with respect to Wave Theory of Heat combustion. (~1830's to ~1860's) Lavoisier and Laplace's work Statistical Mechanics 1786 (~1850's to present) Memoir on Heat. (Bernoulli excepted) Quantum Statistics Jackues-Alexandre Charles (~1900's to present) determines that at a given 1787 temperature change, different gases expand the same amount (known as "Charles's law"). Lavoisier's book Elementary Treatise 1789 on Chemistry, containing the law of mass conservation.

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Richard Kirwan (~1733-1812), previously a staunch defender of phlogiston theory, concedes that the experimental evidence says otherwise.

Pierre Prévost's theory of heat and radiation exchange, stating that cold 1791 is the absence of heat, hot bodies radiate continually and that a lack of radiation indicates equilibrium with surroundings temperature.

Jeremias Richter (1762-1807) founds stoichiometry, the principle of fixed chemical reactions. Cannon-boring experiments of (Count Rumford) (1753-1814) demonstrating the conversion of work into heat in his work Enquiry 1798 Concerning the Source of Heat which is Excited by , showing also that additional weight of an object due to heating (a prediction of ) was not detected. Ice-rubbing experiments of Humphrey Davy (1778-1829) demonstrating the conversion of work into heat, and suggesting that an indefinite amount of heat could be generated from a body (whereas 1799 caloric theory severely limits its available amount).

Joseph-Louis Proust formulates that elements in a compound always combine in definite mass ratios ("Proust's Law"). William Herschel (1792-1871) 1800 publishes "An investigation of the powers of prismatic colours to heat

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and illuminate objects" investigating the effects of different wavelengths of on a thermometer, finding light just beyond the red to be the hottest. Johann Ritter discovers ultraviolet radiation while doing work with silver chloride.

1801 John (1766-1844) finds that two gases in the same region produce the same pressure as if they occupied the region alone, known as the law of partial . Joseph-Louis Gay-Lussac (1778-1850) finds that, at a given pressure, the 1802 change in volume is proportional to the change in temperature. Dalton formulates his atomic theory of matter, stating that chemicals are formed by integer numbers of atoms, by studying the weights of chemicals and reactants.

Claude-Louis Berthollet demonstrates that reaction rates depend on both 1803 the amount of substances present as well as their affinities in his work Essay on Static Chemistry.

William Henry finds that a gas's mass when dissolved in a liquid is proportional to the pressure (later known as "Henry's law"). (1766-1832) writes An Experimental Inquiry into the Nature 1804 and Propagation of Heat, showing that light and radiated heat have similar properties. Pierre-Simon Laplace (1749-1827) 1805 formulates his theory of capillary forces based on his studies of

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molecular forces in liquids. Thomas Young (1773-1829) formulates a precursor to the modern formulation of energy, mathematically associating it with Pierre-Simon mv2 (twice the modern "kinetic 1806 Laplace energy").

Young's System of Chemistry contains the first published account of Dalton's ideas on atomic theory. Jean Baptiste Joseph Fourier (1768-1830) completes his On the Propagation of Heat in Bodies, 1807 introducing many mathematical novelties, including his series expansion techniques. (Dec 31st) Gay-Lussac states that 1808 gases chemically combine in exact proportions of volume. Siméon-Denis Poisson (1781-1840) develops his mathematical theory of heat, based on the work of Fourier.

Amedev Avogadro (1776-1856) hypothesizes that the "number of integral molecules in any gases is [...] always proportional to the volumes", Jean Fourier and that the ratio of the of 1811 molecules is proportional to the ratio of gas at equal temperature and pressure (later becoming "Avogadro's law").

Jöns Jakob Berzelius states that electrical and chemical forces are one and the same and that atoms are electrically charged, in his work Theory of Chemical Proportions and the Chemical Action of Electricity.

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Davy writes Elements of Chemical Philosophy, including a hypothesis that in addition to the vibrational and undulatory motion of , gasses as well exhibit rotational motion about an axis. 1812 Delaroche and BĂ©rard's measurements of specific heats at atmospheric pressure of a large number of gasses. Their measurements agreed with Laplace's predictions and remained a cornerstone for caloric theory. John Herapath (1790-1868) writes, "On the physical properties of gases," 1816 essentially proposing the same theory, but developed independently, as that of Daniel Bernoulli. Pierre-Louis Dulong and AlĂ©xis ThĂ©rèse Petit (1791-1820) find constant specific heat at constant pressure for metals over wide range 1819 of temperatures, finding that the product of the specific heat and the atomic mass remains constant (known as the "Law of Dulong and Petit"). Herapath publishes, "A mathematical investigation into the causes, laws, and principal phaenomena of heat, gases, gravitation, etc," in the Annals of Philos. He explained in outline how kinetic theory could give accounts of sound propagation, changes 1821 and diffusion. The paper is all but ignored due to rejection by the Royal Society of London, and Humphry Davy in particular.

Thomas Johann Seebeck discovers a process by which heat is converted

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into electricity in the junction of some metals, known as theormoelectricity. Fourier's essay Analytic Theory of Heat is published, furthering his techniques of analysis.

Charles Cagniard de la Tour, in 1822 liquification experiments, finds that both temperature and pressure must be appropriately controlled, and discovers what is now know as the critical point of a substance. Sadi Carnot (1796-1832) publishes "Reflections on the Motive Power of Fire," introducing the cycle analysis, showing that when heat passes between two bodies theormodynamic work (which he defines) is done, and proposes an 1824 idea for an internal combustion engine.

Pierre-Simon Laplace (1749-1827) publishes several papers refining an idea of 's that gasses are formed through repulsive interactions. Robert Brown (1773-1858), investigating the well-known irregular seen of particles Sadi Carnot suspended in liquid under a 1827 microscope, shows that such motions cannot be attributed to any vitality of the particles themselves, through studies of many organic and inorganic substances. Gustave-Gaspard Coriolis defines the term "" in his studies 1829 published as On the Calculation of Mechanical Action.

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Thomas Graham (1805-1869) experimentally uncovers the law of gas diffusion, by which the rate of a gas's diffusion, squared, is proportional to its density. Heinrich Friedrich Emil Lenz 1833 determines that resistence in metals increases with temperature. Clapeyron formulates the first version of the second law of thermodynimcs, based on studies of steam engines.

Jean-Charles-Athanase Peltier shows 1834 that heat can be absorbed or given William Thomson off when current is passed one way or the other across a junction between two different metals (knows as the Peltier effect). von Suerman's experiments on air at reduced pressures verifying 1837 Clappeyron's version of Carnot's formulas. Julius Robert Mayer (1814-1878) clearly formulates the conservation of energy, and that heat is a form of (mechanical) energy. 1842 The 1840's were marked by the nearly William Thomson, Lord 's simultaneous and (1824-1907) On the Uniform Motion independent of Heat in Homogeneous Solid conceptualization of the conservation of energy by Bodies. Mayer, , Helmholtz and Ludvig (through 1848) Through a series of August Colding experiments, (1815-88). (1818-1889) establishes the exact relationship between heat and mechanical work. (Joule's work is 1843 little read.)

John James Waterston (1811-1883) anonymously publishes Thoughts on the Mental Functions containing in a

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note at the end a full and accurate account of the and the introduction of the idea of a mean free path. The work goes all but completely unread. Waterston submits a papers on the kinetic theory of gases to the Royal Society, who rejects it. The paper precisely lays out the ideas of energy 1845 equipartition and gives the first modern kinetic definition of temperature. A short abstract appears a year later, and again in 1851, but the work is ignored. Joule publishes "On Matter, Living , and Heat" in the Manchester Courier, stating the principle of the conservation of energy and giving the conversion from heat to kinetic energy.

Hermann Ludwig Ferdinand von Helmholtz (1821-94) publishes his On the Conservation of Energy, extending Carnot's princple of the 1847 'impossibility of unlimited moving force' (kinetic energy) to a mathematical formulation of the 'principle of conservation of living force' (vis viva / kinetic energy). (Independent of Joule's publications.) James Joule John William Draper finds that all substances begin to glow around 525°C, starting in the red and eventually becoming white. Joule reads a paper using Herapath's kinetic theory. The paper contains the first numerical results from the 1848 kinetic theory. (Not published until 1851, and not well known until Clausius's reference to it in 1857.)

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William John 's (1820-1872) researches into mechanics and heat (mainly through 1855).

Kelvin develop's a scale of absolute temperature (now known as the "Kelvin" scale) based on the theory of Carnot. (1822-1892), using Carnot's theories, predicts the lower of the freezing point of water under high pressures. 1849 Kelvin, in speaking of Carnot's theory, coins the term "thermodynamics." (1792-1871) publishes (anonymously, though generally known) an article on Quetelet's work in statistics, introducing much of the continental work on statistics to British 1850 scientists.

Rudolf Clausius (1822-88) gives a verbal formulation of the second law, for which there is no mechanism whose only function is the transfer of heat. Hermann von Kelvin independently rediscovers the Helmholtz idea of absolute zero (149 years after Amontons), extrapolating from Charles' law that it must be about 1851 -273°C, and suggesting that the energy of the molecules would tend to zero. He also derives the second law of thermodynamics using Carnot's ideas.

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Henri-Victor Regnault (1810-1878) shows that gas behavior doesn't quite follow Boyle's law at low temperatures and extrapolates a value of -273°C for absolute zero. 1852 Joule and Kelvin show that expanding gases become cooler in the process, the latter giving the first general statement of the principle of the "universal tendency toward dissipation of energy." Hendrik Roozeboom experimentally determines the phase law, later derived mathematically by Gibbs. 1854 Clausius proposes the function dQ/T as a way to compare heat flows with heat conversions. Rankine's Outlines of the Science of 1855 Energetics. Karl Krönig (1822-79) writes a paper suggesting that gas molecules in equilibrium travel in straight lines until they collide with something, published in Poggendorfs Annalen 1856 der Physik. Whereas the efforts of Bernoulli, Euler, Herapath, Hermann and Joule were largely ignored, Karl Krönig's efforts were widely read, though not constituting an advance in kinetic theory. Clausius publishes a paper on a mathematical kinetic theory, explaining and 1857 establishing heat as energy distributed statistically among particles. Clausius introduces the idea of the 1858 mean free path of a particle in working out a kinetic theory of

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diffusion. James Clerk (1831-79) reads a paper on kinetic theory, printed in 1860 as "Illustrations of the Dynamical Theory of Gases," using random velocity distributions for gases, and showing to be independent of temperature. The paper is originally intended to show internal inconsistencies in the kinetic theory, but through its rigor it greatly refined the theory and provided new insights. 1859 Gustav Robert Kirchhoff (1824-1887) derives from the second law of thermodynamics that objects cannot be distinguished by their thermal radiation at a given uniform temperature, one must also use reflected light.

Bernoulli's paper republished due to renewed interest in kinetic theory. James Clerk (Herapath henceforth goes into Maxwell obscurity.) 's paper "Pressure Melting Effect" describing the lowering of the freezing point of water using pressure.

Maxwell shows a discrepancy between the prediction by kinetic 1860 theory of the specific heat of diatomic gases and experiment. (Not to be resolved satisfactorally until the early stages of quantum theory.) This paper is the first of four works on kinetic theory by Maxwell, bringing a new level of rigour and sophistication to the theory.

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Thomas Andrews (1813-1885), in a series of experiments with CO 2 through 1869, finds that at low temperatures Boyle's law breaks down, and there are regions on a PV chart where, for a given isotherm, changes in volume produce no 1861 change in pressure. This region is recognized to be the liquid-vapour equilibrial state. He rigorously finds the critical point and triple point.

Kirchhoff formulates the notion of a blackbody. John Tyndall's (1820-1893) Heat as a mode of Motion, popularizing Maxwell's ideas on heat.

Andrews shows that, contrary to 1863 expectations, above a substance's critical point it may be continuous changed from gas to liquid and vice versa through variations of temperature and pressure. Clausius uses Carnot's techniques to derive "" (and shows the two expressible in the same ways as the older caloric theory), a term coined for the quantity defined early by him, dQ/T. In a public speech entitled "The entropy of the universe tends to a maximum," he shows how 1865 thermodynamics seem to imply an eventual heat death for the universe.

Josef Loschmidt's (1821-95) points out that Maxwell's conclusion that the proportionality of the mean free path to V/Nd2 could be used to estimate the size of an atom. With further considerations, he estimates

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the size of an air molecule to be about 10-7 cm, about 4 times too large, but the best estimate to date. Maxwell models interatomic forces 1866 by a inverse fifth-power law, though only as an interim solution. Maxwell publishes his major work on kinetic theory, On the Dynamical Theory of Gases.

Kelvin's On Vortex-Atoms. 1867 (Spurred on by Maxwell's work, serious debates on the statistical interpretation of irreversibility begin.) 's (1844-1906) extends Maxwell's distribution law to include external forces. In the case of 1868 , he worked through the distribution of densities and pressures and that thermal equilibrium was maintained. Maxwell, helping out P G Tait, who was drafting an textbook on thermodynamics, comes up with his parabol of the daemon to conceptually explain heat statistics.

Boltzmann suggests that one may derive the probabilistic picture from Ludwig the kinetic one by heuristically Boltzmann 1871 assuming that all microstates must be realized in a system before returning to a specific microstate, and thus measured values should average the effects of such states. (Known as the "ergodic theorem," and so named by Ehrenfest in 1911.)

James Thomson suggests that even

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below the critical point, a substance may smoothly transition between gas and liquid from considerations of experimental data on pressure and volume. In a 100-page paper entitled, "Further Studies of the Thermal Equilibrium of Gas Molecules," Boltzmann's derives his transport equation (Η-Theorem), showing explicitly that isolated systems must always evolve in such a way that 1872 entropy increases. He introduces a number of mathematical innovations, including a technique of discretizing the allowed energy levels for a molecule, and allowing this energy bin to go to zero. Little read at first, the paper later meets with wide-spread opposition. (1839-1903) publishes Graphical Methods in the Thermodynimcs of Fluids and A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces, introducing many new graphical techniques. From 1873 to 1878 he publishes a series of important articles in the Transactions of the 1873 Connecticut Academy of Arts and Sciences, widely influencing scientists in the US and in Europe. Josiah Gibbs Johannes Diderik van der Waals (1837-1923), in doctoral dissertation, gives the first correct approximation for the effects of a non-vanishing ratio of molecule diameter to average distance by assuming long-range attractive and short-range repulsive

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forces, applying this to the case of gases at high densities. Using his "equation of state," he gives the first successful attempt to explain a (gas-liquid) . The theory both accounted for Andrews's critical point phenomena and confirmed James Thomson's hypothesis. Kelvin points out that the irreversibility of Boltzmann's kinetic theory seems to contradict the 1874 underlying classical laws of physics remaining time-invariant (the so-called "reversibility paradox," sometimes attributed to Loschmidt). Gibbs publishes the first part of On the Equilibrium of Heterogeneous Substances (the 2nd part in 1878). The works deal with chemical reactions, phase equilibrium and the 1876 use of free energy.

(Karl Paul Gottfried von Linde builds the first practical refrigerator using liquid ammonia.) Boltzmann formulates a statistical mechanical version of the second law of thermodynamics in the paper, "On the Relation Between the Second Law of the Mechanical Theory of Heat and the Probability Calculus with Respect to the Theorems on Thermal Equilibrium". There he formulates 1877 that the entropy of a system is proportional to the log of the phase space volume occupied by the macrostate of the system, S = k ln Ω, making use of his mathematical innovation of using finite areas of phase space.

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Liquification of oxygen achieved, after nearly one hundred years of trying, by Louis Paul Cailletet (1832-1913) (on Dec 2nd) and Raoul Pierre Pictet (1846-1929) (on Dec 22nd). Josef Stephan (1835-1893) determines that the amount of radiation given off by a body through 1879 heating is proportional to the fourth power of its temperature (known as the "Stephan-Boltzmann law"), RĎ„ = ĎT4. Boltzmann (1844-1906) succeeds in theoretically deriving the radiation law found by Stephan, showing that a mechanical pressure and must be associated with the 1884 radiation in order to satistfy the second law.

Gibbs coins the term "statistical mechanics" for the kinetic theory's treatment of thermodynamic issues. Lodge promotes the idea that mechanical energy can be localized and flow, as inspired by the work a year earlier by Poynting in electromagnetic theory. 1885 (1825-1898) finds a formula for describing the four spectral wavelengths then known for hydrogren as found by Ångstrom. Jules Henri Poincaré (1854-1912) derives his recurrence theorem, whereby a system with fixed 1889 total and volume will eventually return arbitrarily closely to any given state.

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Gibbs' last work, Elementary Principles in Statistical Mechanics. Edward Parnell Culverwell (1855-1931) points out the apparent contradiction between Boltzmann's H-theorem and the irreversibility of 1890 the micromechanical processes on which it is based, suggesting that some kind of takes place at this micro level, perhaps in connection with the ether. Wilhelm Carl Werner Otto Fritz Franz Wien (1864-1928) experimentally finds that the wavelength of maximum radiation of 1893 thermal body is proportional to the inverse of its temperature (known as "Wien's law") using an oven with a small hole as an approximation to a theoretical black-body. S H Burbury points out that the H-theorem relies on the uncorrelated nature of molecular interactions, but that this may not be valid after an individual collision, and hence not in general valid without some external randomizing element. Boltzmann 1894 calls this the hypothesis of molecular disorder, specifically referring to the low probabilitiy of two molecules colliding twice within any significant time frame, but mentioning that this would become an issue for gases at high densities. Pierre (1859-1906), in his doctoral dissertation, defined both ferro-, dia-, and , 1895 showing that ferromagnets lose their magnetic properties as their temperature is increased, eventually

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losing it completely above a certain temperature specific to that material (the "Curie point"). He suggests that is an atomic property, while the other two are properties of bulk matter.

Wilhelm Röntgen (1845-1923) discovers a new penetrating kind of radiation, dubbed X-rays. Ernst Zermelo (1871-1953), starting with the postulate that the second law is true, tries to show the inherent contradictions of the purely mechanical basis of statistical mechanics, making use of PoincarĂ©'s result on recurrence (his "recurrence paradox"). 1896 Wien proposes an explicit form for the black body distribution law, Ď = αν3exp{-βν/T}, which fit the existing data.

Antoine Henri (1852-1908) discovers radioactivity in fluorescent materials. Joseph John Thomson (1856-1940) demonstrates that cathode rays were 1897 electrically charged particle streams, know shortly thereafter as electrons. Boltzmann publishes his Lectures 1898 on Gas Theory. Otto Lummer (1860-1925) and Ernst Pringsheim complete the first accurate measurements of the spectral radiancy of blackbodies, 1899 showing the breakdown of Wien's law at high temperatures and low frequencies.

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Emile Hilaire Amagat publishes The Laws of Gases of extensive experiments with gases under very high pressures.

JJ Thomson and Philipp Lenard (1862-1947) begin experimental investigations of photoelectric radiation. Kelvin proposes a modification to Wein's law of the form Ď ~ ν2exp{-βν/T}.

Max Karl Ernst Ludwig Planck (1858-1947), studying blackbody radiation and following Boltzmann's techniques of dividing the energy 1900 continuum into cells, proposes fixing cell sizes to be proportional to oscillator frequency, and in so doing derives the correct radiation spectrum for blackbodies. Planck proposes the constant, h (Planck's Planck's 1900 analysis constant), as a quantum of action in did not, at the time, imply any new law about the phase space. microstructure of matter, nor was there any reason Gibbs publishes Elementary to believe that Principles in Statistical Mechanics, extrapolation of the his treatise on the subject, deriving Rayleigh-Jeans law signalled any failure of common thermodynamic properties classical methods. from particle statistics, giving his full 1902 account of ensemble theory and their relationships (including the so-called "Gibbs paradox," though there was nothing paradoxical about it at the time). Marian von Smoluchowski and (1879-1955) independently investigate Brownian 1905 motion, the motion of very small particles suspended in liquid. This is shown to be an observable effect of the fluctuations of statistical

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mechanical movement, despite producing no net effect on average.

Einstein publishes a paper on the photoelectric effect, basing his analysis on an analog of the statistical mechanical approach for classical electromagnetic fields modelled as quanta of light.

Paul Langevin (1872-1946) developes a more satisfactory theory of para- and diamagnetism, applying statistical mechanics to gases of molecules with permanent dipole moments, also explaining the inverse temperature dependence of paramagnetic susceptibility, though later shown by Bohr to be inconsistent with statistical mechanics obeying . Walther Nernst (1864-1941) formulates his "heat theorem," stating that in the limit of absolute zero temperature, both the entropy change and the go to 1906 zero (subsequently recognized as the Third law of thermodynamics).

Pierre Weiss (1865-1940) creates general theory of paramagnetic to ferromagnetic transitions. Andrei Andreyevich Markov (1856-1922) develops his theory of Albert Einstein linked probabilities.

1907 Einstein publishes a paper on the specific heats of solids, deriving the law of Dulong-Petit from atomic oscillators confined to quantized , working out well with the

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recent theorem of Nernst.

Pierre Weiss explains by way of small domains of magnetic polarization within a material. Jean-Baptiste Perrin calculates the approximate size of a water molecule in experimental tests of Einstein's work on Brownian motion, further convincing many of the atomic hypothesis. 1908 Planck begins formulating derivations of the black-body law starting with an assumption of energy quantization.

JJ Thomson solidifies his "plum- pudding" model of the atom. Constantin CarathĂ©odory publishes a purely mathematical and axiomatic account of thermodynamics. 1909 Einstein corrects the blackbody derivation of Planck, which was technically only valid for hν<

1911 Planck's first paper explicitly quantizing the allowed radiation of oscillators in a blackbody.

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Arnold Sommerfeld (1868-1951) notes that elementary regions of phase space should be related to Planck's constant.

Otto Sackur (1880-1914) suggests the need for an absolute definition of entropy, in order that quantum systems be taken into account (suggesting that phase space be divided into cells of volume h3).

Ladislaw Natanson proposes that Planck's law is the result of the indistinguishability of states of light quanta.

Niels Henrik David Bohr (1885-1962) defends his dissertation and begins constructing atomic models which try to forge a connection with Planck's constant as a fundamental constant of quantization.

Heike Kamerlingh Onnes (1853-1926) experimentally finds that mercury will become superconductive when cooled very close to absolute zero and also discovers superfluidity.

Paul (1880-1933) and Tatiana Afanassjewa Ehrenfest (1876-1964) publish a work giving a detailed criticism of the ensemble theories in statistical mechanics.

Nernst's experiments with many substances, shows specific heats going to zero at absolute zero in general, providing strong support for the new quantum theories.

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Poincaré proves that one can invert the Planck distribution via a Fourier transform and deduce that black-body radiation implies a quantization of energy states.

1912 Sackur and H Tetrode independently solve Boltzmann's Law to obtain S = Nk ln[(2ĎmkT)(3/2)V/Nh3] + (5/2)Nk showing a need for quantization in classical gas laws. Artur Rosenthal (1887-1959) and Michel Plancherel (1885-1967) prove that the ergodic hypothesis is not viable for any dynamical system (opening the way to the quasi-ergodic hypothesis and certain theorems in ergodic theory).

Paul Ehrenfest shows how to estimate 1913 rotational effects of a diatomic gas on specific heat by replacing integrals with sums over discrete contributions from quantized states. The work is later refined by E Holm (1913) and by Planck (1915).

Bohr's article, "On the Constitution of Atoms and Molecules." (1868-1953), in experiments with the photoelectric effect, both confirms the theoretical work of Einstein and confirms the value of Planck's constant independent of work done 1916 with blackbodies.

Einstein produces a derivation of the black-body radiation distribution with the assumption of both spontaneous as well as stimulated

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emission of radiation by matter.

Nernst predicts a state of degeneration can be reached for any gas at a low enough temperature, through extensions of his thermodynamic theory.

Sydney Chapman (1888-1970) and David Enskog (1884-1947) develop ways to solve the Maxwell-Boltzmann tronsport equations for a general class of inter-molecular force laws.

Gilbert Newton Lewis (1875-1946) devises a theory of molecular bonding based on atoms consisting of a series of concentric cubes, the edges of which may share electrons with other atoms. (The idea is popularized, starting in 1919, by (1881-1957).) Arthur Stanley Eddington (1882-1944) publishes a paper on 1917 radiative equilibrium, suggesting that the ionization of atoms in stars. Meghnad Saha (1893-1956) writes, "Ionization in the solar chromosphere," analyzing spectral lines of stars as atomic dissociation in the chromosphere, where lower pressures override the lower temperatures of a star, also (in a second paper) predicting that lower- 1920 temperature sun-spots will show lines of rubidium and cesium (an effect detected in 1922 by H N Russell).

Wilhelm Lenz (1888-1957) models crystals by a lattice of dipolar atoms which feel nearest-neighbor interactions, obtaining the Curie law

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for magnetization and suggestions its applications to ferromagnetism. Louis Victor Pierre Raymond duc de Broglie (1892-1987) applies Sackur's technique of quantizing phase space to derive the Wien distribution law for energy density: du = (8Ďh/c3) exp(-hν/kT) ν3 dν 1922 (1887-1962) and Ralph Howard Fowler (1889-1944) publish "On the partition of energy," developing a new approach to evaluating statistical probabilities using complex analysis and the method of steepest descent. Lewis's Thermodynamics and the Free Energy of Chemical Substances, 1923 bringing thermodynamics in closer contact with chemistry. (June) Satyendranath Bose (1894-1974) sends Einstein a copy of his paper, containing a new derivation of Planck's radiation law based purely on photon statistics, after it was rejected by Philosophical Magazine. Einstein translates it into German and submits it to the Zeitschrift fĂĽr Physik for him with a recommendation. 1924 Einstein presents a paper showing Satyendranath that in the limit of high temperatures, Bose a gas of indistinguishable Bose particles approaches the characteristics of a Boltzmann gas.

de Broglie writes two papers in the Comptes rendus of the Academy elaborating on a fundamental principle of wave-particle duality. The

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works mature into his 1925 doctoral thesis. (1882-1970), Werner Karl Heisenberg (1901-1976), and Pascual Jordan formulate quantum mechanics based on the of matrix algebra.

Einstein, citing works by Bose and de Broglie, suggests that the analogy between quantum gases and molecular gases are complete, and that both photons and molecules have both particle and wave characteristics. He also points out that molecules at low temperatures cannot be considered independent entities, even in the absence of intermolecular forces, and will form a quantum condensate.

Samuel A Goudsmit's (1902-1979) 1925 hypothesis an extra degree of freedom to electrons termed "spin" due to the mathematical similarity to classical spin. Later, with George Eugene Uhlenbeck (1900-1988), half-integer quantum numbers are introduced in the theory of the hydrogen atom.

Wolfgang Pauli (1900-1958) formulates the exclusion principle for the electron, accounting for a number of chemical properties in atoms and molecules.

Planck devises a new derivation of thermodynamic formulas for Boltzmann gases using the formulations, z = exp(-Îľ/kT), Z = zN / N!

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Ernst Ising (1900-), following the investigations of Lenz, publishes a paper dealing with magnetic models via dipolar atomic interactions. Born introduces into quantum mechanics his probability interpretation of interactions.

Enrico Fermi (1901-1954) derives the statistical properties of gases which obey the Pauli exclusion principle.

Erwin Rudolf Josef Alexander Schrödinger (1887-1961) developes a second formulation of quantum theory in terms of wave mechanics independently.

Paul Adrien Maurice Dirac (1902-1984) relates the symmetry of quantum mechanical wave functions to the statistics of Bose, Einstein and Fermi. He also derives the Planck 1926 distribution from first principles.

Eddington's The Internal Paul Dirac Constitution of the Stars, relating the radiation pressure of stars to their luminosity.

Fowler shows that some of the properties of white dwarf stars could be accounted for by treating them as (Fermi) quantum degenerate gases, being an early example of quantum statistics explaining the properties of large macroscopic objects.

Robert Hutchings Goddard launches the first rocket, using liquid fuel and reaching a height of 184 feet and 60 miles per hour.

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John von Neumann (1903-1957) formulates a fully quantum mechanical generalization of statistical mechanics.

Bohr pronounces his notion of complimentarity in quantum theory.

Heisenberg formulates the uncertainty principle of quantum mechanics.

Dirac and Pauli independently propose to model metals with molecules obeying Fermi-Dirac statistics.

Pauli explains the paramagnetic 1927 susceptibility of metals using electron spin and the exclusion principle.

Willem Hendrik Keesom (1876-1956) and M Wolfke find discontinuities in several properties of helium at very low temperatures and suggest that it may be due to a phase change, calling them helium I and II.

Walter Heitler (1904-) and Fritz London (1900-1954) apply Heisenberg's resonance theory to the covalent molecular bond between two hydrogen atoms, showing stability to a function of electron spins, and arguing against the stability of such helium bonds. Sommerfeld treats electrons in metals as a degenerate using the new techniques of quantum 1928 theory.

Dirac comes up with a relativistic quantum mechanical wave equation

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for the electron.

Felix Bloch (1905-) suggests a theory of metals based on electrons layered periodic positive potentials which can sustain small displacements which lead to resistance via scattering of electrons by the lattice vibrations.

John Clarke Slater (1900-1976) is the first to study the quantum mechanical treatment of the molecular formation of rare gases (helium).

Linus Pauling (1901-) applies the Heitler-London treatment to chemical bonds. Edmund Clifton Stoner (1899-1968), using (special) relativistic formulas for electron energies, suggests that beyond a certain density in stars the outward degenerate gas pressure would no longer sustain itself against 1929 the inward gravitational attraction (though he did not speculate about what would then happen).

Slater formulates a multi-electron wave function which can generally satisfy the Pauli exclusion principle.

Discovery of the lambda point of John von helium at which it becomes a 1930 Neumann superfluid (so-named in 1941) at 2.2°K. George David Birkhoff (1884-1944) proves the general ergodic theoreom. 1931 Pauling publishes his work on chemical bonds, proving the stability of such bonds.

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Aleksandr Yakovlevich Khinchin (1894-1959), in work through 1934, 1932 founds the modern study of stationary random processes. Walther Meissner (1882-1974) and R Ochsenfeld report that metals cooled below their superconducting 1933 temperatures in a magnetic field completely expell all lines of magnetic induction, becoming a perfect diamagnet. William Lawrence Bragg (1890-1971) and Williams formulates an for paramagnetic to ferromagnetic transitions.

1934 Cornelius Jacobus Gorter (1907-1980) and Hendrik Bruygt Gerhard Casimir (1909-) form an analysis of the expulsion of magnetic fields in superconducting metals in a magnetic field. William Francis Giauque achieves a temperature of only 0.1°K for helium using a magnetic trap to slow the motion of the molecules.

Lev Davidovich Landau (1908-1968) publishes his phenomenological mean-field treatment for phase transitions. 1935 Subrahmanyan Chandrasekhar (1910-1995) derives the maximum mass formula for a degenerate Fermi Lev Landau gas.

Fritz Wolfgang London (1900-1954) and brother Heinz London work on a theory of macroscopic objects using classical electrodynamical theory and some

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additional assumptions.

Hans Bethe (1906-) improves on Bragg-Williams theory by adding short-range atomic interactions.

Edward Armand Guggenhaim (1901-) develops a theory of liquid solutions using nearest-neighbor rules, into what is now callod the "quasi- chemical" (QC) method. (1904-) (see links) and Sally F Harrison (1913-), along with Maria Goeppert-Mayer (1906-1972), initiate the modern theory of gas condensation, in work 1936 through 1938, by use of "cluster integrals" representing the interactions of many molecules to find the virial coefficients of intermolecular forces. Peter Leonidovich Kapitza (1894-?) determines that helium II has a viscosity of about 1500 times smaller than helium I and terms the phenomena "superfluidity." At almost the same time, John Frank Allen (1908-) and A D Miscner discover the 1937 same effect independently (publishing 19 days later).

John Edward Leonard-Jones (1894-1954) and A F Devonshire formulate (through '39) the "6-12 potential" for intermolecular forces. Claude Elwood Shannon (1916-) publishes A Symbolic Analysis of Relay and Switching Circuits, 1938 instigating the study of information theory and giving a systematic way of mathematically treating noise.

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London's theoretical work on liquid helium and Bose-Einstein condensation. W Conyer Herring calculates bulk properties of materials from quantum 1939 principles, specifically explaining how beryllium acts as a metal. Fowler and Guggenheim extend the QC method, applying it to models 1940 which take into account longer-range interactions. (1903-1976) (also see links) gives his solution to the two-dimensional Lenz-Ising model, showing that a phase transition will 1942 occur. "[I]t is the first exact solution of a nontrivial problem in statistical mechanics, in which interparticle forces are taken into account without approximation" (SG Brush). Evgenni Mikhailovich Lifshitz (1915-1985) shows that "second- sound" waves in superfluids can be 1944 detected as temperature deviations. The effect is experimentally confirmed shortly there after by V Peshkov. Nikolai Nikolaevich Bogolyubov (1909-) writes his Problems of Dynamical Theory in . He works on a generalization of the Boltzmann equation, using the time-reversal invariant Liouville equation, further clarifying the 1946 internal structure of statistical mechanics.

Khinchin refines Boltzmann's theorem to read that, as a function of the size of an ensembles, the time average of a system becomes

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arbitrary close to the canonical average.

Richard A Ogg, Jr suggests that pairs of electrons behave as bosons, and that superconductivity may be thought of as a Bose-Einstein condensate. (The idea is ignored until about 1954.) Shannon's major publication on information theory and symbolic 1948 logic, A Mathematical Theory of Communication. Herbert Frölich (1905-) suggests that interactions between electrons may be the basis of an 1950 explanation of superconductivity, giving one of the first uses of quantum field theory to statistical mechanics. Richard Phillips Feynman (1918-1988) begins his work on the theory of superconducting helium 1953 using his path-integral approach, further clarifying how previous theoretical attempts have worked and/or failed. Erwin Wilhelm Mueller's (1911-1977) field ion microscope is the first instrument to allow imaging of individual atoms.

W Noll proves that by taking the 1955 appropriate phase averages, any molecular system modelled by statistical mechanics can be shown to satisfy exactly the equivalent field equations for a continuous material, thus theoretically showing the equivalence of the two approaches.

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Leon Cooper (1930-), (1908-) and John Robert Schrieffer (1931-) form a many-electron theory 1956 of superconduction which gives good agreement with experiment and produces the Meissner effect. Khinchin's book, Mathematical Foundations of Information Theory.

1957 Berni Julian Alder (1925-) and Thomas Everett Wainwright (1927-) computationally discover the hard-sphere phase transition. George Allen Baker, Jr (1932-) found a method of determining the 1961 singularities at the critical point via series expansions of Lenz-Ising models. Benjamin Widom's (1927-) work on 1965 theory using a modified van der Waals theory. Alder and Wainwright discover vortex 1968 diffusion in liquids. Kenneth Wilson (1936-), extending earlier work by Leo Kadanoff (in 1966), applies the technique of the 1971 group to study of scaling laws for phase transition theory. Michel Ellis Fisher (1931-) and Widom show that the Lenz-Ising model generalized to arbitrary dimensions display a continuous 1972 transition between classical and non-classical laws, where correlation lengths tend toward infinity at critical points. Heinrich Rohrer and Gerd Binnig 1980 develop the scanning tunnelling microscope, allowing for imaging of

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atoms embedded on surfaces.

Sources: Brush, Stephen G, Statistical Physics and the Atomic Theory of Matter From Boyle and Newton to Landau and Onsager (out of print) Bunch, Bryan & Hellemans, Alexander, The Timetables of Science Eisberg, R and Resnick, R, Quantum Physics, 2nd ed, 1985 Flamm, Dieter, "History and outlook of statistical physics," physics/9803005, 4 March, 1998 Flamm, Dieter, "Ludwig Boltzmann - A Pioneer of Modern Physics," physics/9710007, 7 October, 1997 Kuhn, Thomas S, Black-Body Theory and the Quantum Discontinuity, 1894-1912 Mendoza, E, "A Sketch for a History of Early thermodynamics," Physics Today, February 1961, p 32 Mendoza, E, "A Sketch for a History of the Kinetic Theory of Gases," Physics Today, March 1961 Mendelssohn, K, The Quest for Absolute Zero (out of print) Moore, Walter, Schrödinger: Life and Thought Truesdell, C, Essays in the History of Mechanics (out of print)

And the great MacTutor History of Mathematics Archive

Links: The Pneumatics of Hero of Alexandria Paul Charlesworth's History of Science pages Chris Hillman's Entropy in the Physical Sciences Biographies of and some available at the History of Chemistry page About Temperature by Project Skymath Fahrenheit's Paper of 1724 The Origin of the Celsius Temperature Scale Wave Mechanics: Louis de Broglie

The Lars Onsager Archive Register of Joseph Mayer's Papers

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Notes: Would like to get into more history of probability theory as it applied to these histories. Need to read more works by Mr Truesdell (the above book is great). Filling out more pre-17th century material would really enhance the perspective of the timeline. Certain mathematico-conceptual issues eventually have to be dealt with.

If there's anything that you feel should be address, or addressed more fully, or if there are references which you'd like to suggest I look into, please feel free to email the author at hyperjeff@mac.com.

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