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John James Waterston a Pioneer of the Kinetic Theory of Gases Jaime Wisniak*

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PARA QUITARLE EL POLVO La química en la historia, para la enseñanza. John James Waterston A pioneer of the kinetic theory of gases Jaime Wisniak* Resumen mostly in straight lines, except when deflected with John James Waterston (1811-1883) puede ser consid- occasional collisions with the walls of the containing erado el último de los pioneros de la teoría cinética. vessel and with each other. The colliding particles El mejoró en forma notable la teoría desarrollada por are supposed to act upon each other only within very Herapath y demostró que la velocidad cuadrática small distances and for very short times before and media de las moléculas de un gas, puro o mezclado, after collision, their motion being free in the intervals está conectada directamente con su temperatura ab- between such distances and times (free path). The soluta. Fue el primero en publicar el teorema de duration of free paths are assumed to be indefinitely equipartición de la energía y demostró cómo su large as compared to the durations of the encounters teoría podía ser utilizada para calcular la velocidad and of the mutual actions. The motion as a whole is del sonido así como el diámetro de una molécula. conserved by reason of the absolute elasticity of the Lamentablemente su publicación fundamental su- moving particles, while the directions of the move- frió el mismo destino que la de Herapath: su rechazo ments of the individual particles are persistently por la Sociedad Real y, por tanto, desconocida por changed by their mutual collisions. Molecules of el mundo científico. Afortunadamente, Lord different gases differ in mass, but all molecules of the Rayleigh la encontró y publicó años después de la same gas have the same mass. The everlasting mo - muerte de Waterston. tion of the particles can be explained assuming that the rebound by collision occurs without loss of ki- Abstract netic energy or momentum. The kinetic theory in- John James Waterston (1811-1883) may be consid- terprets the pressure, or elasticity of a gas, as the ered the last of the pioneers of the kinetic theory. He aggregate of the pressures exerted by the various improved substantially the theory developed by Her - molecules when they collide with the boundary; only path and demonstrated that the mean square velocity at relatively high pressures does the effect of inter- of the molecules of a gas, in the pure state or mixed, molecular forces become important. The ideal gas is directly connected to the absolute temperature of laws are easily deduced from this model by Newto - the same. He was the first to establish the theorem nian mechanics, and the temperature is identified of equipartition of energy. He showed how his theory with the mean-square velocity could be used to calculate the velocity of sound, as One of the original assumptions of the kinetic well as the diameter of a molecule. Regrettably his theory is the perfect elasticity of the molecules, a fact basic publication suffered the same fate as that of that was not clearly understood and gave place to Herapath: rejection by the Royal Society and thus much discussion. Inasmuch as no perfectly elastic unknown to the scientific world. Fortunately Lord solid is known, there is no basis in experience for this Rayleigh found it and had it published, years after assumption. In actual solids part of the kinetic energy Waterston’s death. of colliding spheres is transformed into heat due to The kinetic theory regards a mass of gas as a friction in the deformation of the bodies. Neverthe- collection of a great number of independently mov- less, the kinetic theory develops the notion that heat ing minute solid particles, molecules, or atoms, sepa- is the energy of molecules in motion. rated by spaces relatively large in comparison with The ideas current at Waterston’s time, and al- the diameter of the particles, These entities move most universally accepted, were that the particles of gases were stationary, being held in position by repulsive forces that were thought to exist between them. These repulsive forces were themselves attrib- * Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel 84105. uted to the presence, either round or between the gas E-mail: [email protected] particles, of the subtle, weightless and highly elastic Recibido: 17 de julio de 2006; aceptado: 5 de octubre de fluid of heat that was known to most scientists as 2006. caloric, as Antoine-Laurent Lavoisier (1743-1794) 146 Educación Química 18[2] PARA QUITARLE EL POLVO named it in 1787. The theory negated that atomic John James Waterston was born in Edinburgh, vibrations alone could account for the phenomena Scotland on 1811, the sixth of a family of nine, who of heat; the role of the æther was essential. In addi - remained deeply attached to one another throughout tion, atoms in a gas could not move freely through their lives. His father was George Waterston, origi- space, they were constrained to vibrate about fixed nally a schoolmaster and later an Edinburgh manu - equilibrium positions. Caloric was characterized by facturer of sealing wax and other stationery requisi- the following attributes: (a) it was an elastic fluid, the tes. George Waterston was greatly interested in particles of which repelled one another strongly, (b) literature, science, and music. His family thus grew the particles of caloric were attracted by particles of up in an atmosphere of culture and often came into ordinary matter, the magnitude of the attraction contact with young literary men, such as John Hill being different for different substances and for differ- Burton (1809-1881), the future historian of political ent states of aggregation, (c) caloric was indestructi - and social economy, Thomas De Quincey (1785- ble and uncreatable, (d) caloric could be either 1859), an essayist and critic, and George Combe sensible or latent, and in the latter state was com- (1788-1858), the apostle of phrenology (Haldane, bined chemically with the particles of matter to form 1928). the liquid or vapour. Sensible caloric was supposed The Waterston firm was founded in 1752 by to form an atmosphere around the particles of the William Waterston, grandfather of John James. body, and (e) caloric did not have appreciable weight Originally a schoolmaster in East Lothian, William (Roller, 1950). Manifest caloric was assumed to pos- established a business in Edinburgh as a wax chan- sess the peculiar property of being attracted by ordi- dler and for the manufacture and supply of sealing nary matter, but repelled by itself in inverse propor- wax and the flambeaus or links used in those days tion to distance. Hence the molecules of a gas or before public lighting of the streets. William Water- other substance containing manifest caloric repelled ston married Catherine Sandeman, daughter of a one another in direct proportion to their concentra- Perth merchant, and a woman of great character and tion, while they also repelled one another in propor- ability, who after her husband’s death, carried on the tion to the amount of manifest caloric they con- business vigorously. Catherine was the niece of tained. Absolute zero on this theory would represent Robert Sandeman (1718-1771), a well-known relig- a state in which there is no manifest caloric in the ious leader, and with her there came into the family, molecules. It was further assumed that when the rise not only an additional tradition of culture, but also of temperature is produced by friction or compres- the religious teaching of his uncle Robert and his sion, this was due to the liberation of latent caloric, father-in-law John Glas (1695-1773). Sandeman and while the cooling which accompanied expansion Glas were the originators of the religious body and other processes was due to caloric becoming known as Glasites or Sandemanians, active in Eng- latent. The caloric theory also lent itself admirably land and America. Glas was a Forfarshire Prebyste- to mathematical treatment. rian minister who objected to State interference with Leonhard Euler (1707-1783), Daniel Bernouilli Church, and was therefore deposed, but continued (1700-1782), John Herapath (1790-1868), and John to act on his convictions, together with members of James Waterston (1811-1883) may be considered the his congregation and others who held similar opin- principal scientists who prior to 1850 attempted a ions (Haldane, 1928). more or less complete mathematical treatment of One of the English Sandemanians was Michael gases based on a set of molecular postulates. He we Faraday’s (1791-1867) father. Michael Faraday him - describe the contribution of Waterston, which would self remained throughout his life an active member lead to the seminal contribution of James Clerk of the Sandemanian Church in London. The princi- Maxwell (1831-1879). ples of Glas and Sandeman were closely akin to those requisite in a real leader in pure science, and it is Life and career significant that two such men such as Faraday and Most of the details available about the personal life John James Waterston were connected in their up- of John Jaime Waterston (1811-1883) appear in the bringing with this very small religious body book by Haldane, which also carries most of Water- (Haldane, 1928). ston’s publications (published and unpublished) All the Waterston children were educated at the (Haldane, 1928). Edinburgh High School, then the leading school in Abril de 2007 147 PARA QU ITARLE EL POLVO Scotland. On leaving the High School, Waterston department of the Admiralty. The head of the De - became an apprentice with Messrs Grainger and partment was Captain (afterwards Admiral) Francis Miller, civil engineers, and at the same time attended Beaufort (1744-1857), who subsequently communi - lectures at the University and took a very active part cated Waterston’s paper on kinetic theory to the in the student’s Literary Society.
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