In thermodynamics, molecular vortices was an atomic structure hypothesis, used to account for the interactions of heat and contractions and expansions of elastic atmospheres, in which each atom of matter consisted of a nuclei about which a revolving or oscillating atmosphere existed. [1] The theory was conceived between 1842 and 1849 by Scottish engineering physicist William Rankine. [2]

The origin of the vortex atom heat theory seems to trace to a combination of the 1830s publications of Scottish physicist James Forbes on the undulatory theory of heat and light the 1842 publication of Elements of Chemistry by Scottish chemistry Thomas Graham who discussed the ‘material theory of heat’ (an adaption of the caloric theory), in which heat was considered as indestructible particles, and the ‘undulatory theory of heat’ (an adaption of the undulatory of light), in which undulations in imponderable medium of space or ether are propagated that produce the impression of heat. [3]

Forbes was Scottish engineering physicist William Rankine’s natural philosophy professor at the Edinburgh University, during the years 1836 to 1837, and Graham was related to the mother of William Rankine. It is likely that Rankine was stimulated by these thoughts on the nature of heat. [2] At Edinburgh, under the guidance of Forbes, Rankine published two essays, “On the Undulatory Theory of Heat” and “Methods in Physical Investigation”, in which the seeds of his thoughts on a theory of molecular vortices took root. In early October of 1849, Rankine gave Forbes an entire paper on the hypothesis of molecular vortices which consisted of, first, the details of the hypothesis:

“[The hypothesis of molecular vortices] ascribes the elasticity connected with heat to the centrifugal force of small revolutions of the particles of bodies.”

This being considered the statical part. Second, the paper outlined the application of the model to the mechanical action of heat, the dynamical part. [2] On February 4th, 1850, Rankine read both parts of the paper, titled “On the Centrifugal Theory of Elasticity, as Applied to Gases and Vapours” and “On the Mechanical Action of Heat, especially in Gases and Vapours”, to the Royal Society of Edinburgh. In the first of these, Rankine states his molecular vortices hypothesis: [4]

“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 these atmospheres, revolving or oscillating about their nuclei or central points.”

Furthermore, according to Rankine:

“The vibration which, according to the undulatory hypothesis, constitutes radiant light and heart, is a motion of the atomic nuclei or centers, and is propagated by means of their mutual attractions and repulsions.”

Rankine acknowledged that his molecular model had many conceptual resemblances to the models of earlier philosophers, including German mathematical physicist Franz Aepinus and British chemist Humphry Davy. In his model, each atom of matter consisted of a nucleus surrounded by an elastic atmosphere, self-repulsive but retained by the attraction of the nucleus. In alignment with the views of English physicist James Joule, a quantity of heat was considered the vis viva of revolutions or oscillations among the particles of the atmospheres which Rankine supposed to constitute vortices about the nuclei. [2]

In afterthought, Rankine states explicitly that his “researches were commenced in 1842, and after having been laid aside for nearly seven years, from want of experimental data, were resumed in consequence of the appearance of the experiments of M. Regnault (1847) on gases and vapours”.

Soon after receiving Rankine’s papers, he dispatched a copy to his colleague William Thomson. Later that year, in 1850, Rankine told Thomson that his “first attempt to apply mathematical reasoning to the subject arose from my seeing the translation … of Clapeyron’s paper [1834] on the opposite [material] theory.” [5]

In thermodynamics, the theory of heat generation due to actions of atomic vortices resulted to discredit much of Rankine’s views on the equations of the first two laws of thermodynamics. The conception of a vortex atomic structure, however, got many scientists thinking. Scottish physicist James Maxwell, a friend of Rankine, for one, was significantly influenced by Rankine’s ideas on the physical interpretation of the vortex atom. Firstly, Rankine’s heat generation theory was in direct conflict with Maxwell’s kinetic theory of heat generation due to atomic collision. In any event, the kinetic theory eventually won out over the vortex theory, and one positive result of this intellectual exercise seems to have been the lasting image of rotating atom structures. [6]
Spinning cells (original)Spinning cells (Maxwell)
Scottish physicist James Maxwell's 1856 "spinning cells" (original: left; 2003 version: right), or what he called “mechanical illustrations to assist the imagination”, the precursor models to the his eventual formulation of electromagnetic theory; seeded, in some way, from Scottish engineering physicist William Rankine’s1842 molecular vortices model precursors. [8]

Maxwell, significantly, thought would later go on to found the equations of electromagnetic theory to explain the interactions of the electricity, magnetism, and induced movements of currents in wires. On May 1857, Maxwell remarked in a letter to his friend, mathematician Cecil James Monro (1833 – 1882), that: [7]

"I have been grinding at many things and lately during this letter at a vortical theory of magnetism & electricity which is very crude but has some merits."

This is the first indication of Maxwell’s version of a theory of molecular vortices, proposed as a physical representation of lines of force, which is developed in his four-part paper “On Physical Lines of Force” (1861-62). In this paper, Maxwell advances from his discussion of the physical geometry of lines of force, in “On Faraday’s Lines of Force” (1856), to a physical mechanics of the field.

The title of Maxwell’s paper is in reference to English physicist Michael Faraday’s 1852 paper “On the physical character of the lines of magnetic force”, in which Faraday affirms the physical reality of lines of force, and their causal action, as distinct from a purely geometrical treatment of their distribution in space. In his 1856 paper, Maxwell used what he called “mechanical illustrations to assist the imagination”, as those shown above. [8]

The visual picture of conductors, such as copper, containing rotating or spinning cells (atoms) interspersed with ‘idle wheel’ particles (conceived as particles of electricity), such that via cell rotation, induced by alternations or changes in the direction of magnetic field, particles moved through the metal. [8]

Others to have been influenced by the vortex model and in general Rankine's thermodynamics theories include German physicist Rudolf Clausius, to whom was sent a copy of Rankine's 1850 papers on the suggestion of William Thomson, German physicist Hermann Helmholtz, who in 1858 outlined a theory of “vortex rings” in fluids, Scottish physicist Peter Tait who in 1867 devised a floating smoke ring experiment to illustrate Helmholtz’s theory, and Thomson, who a month after seeing Tait's smoke ring experiment wrote an article titled "On Vortex Rings" arguing atoms are vortices in the ether of space. [9]

Electron discovery
In 1883, British physicist J. J. Thomson wrote a paper on vortex rings, using the Helmholtz ring model in which atoms of gas were considered to consist of approximately circular vortex rings; the logic of which served as a basic atom model helping him to later discover the electron in 1897 and devise his plum pudding model (1904) of atomic structure. [10]

In his autobiography of 1936, J. J. Thomson recalled that his early work on vortex atoms yielded “some interesting results and ideas which I afterwards found valuable in connection with the theory of the structure of the atom.” [11] In particular, Thomson thought of electric force in term of the vortex model. The vortex atom continued to be discussed by a few chemists and physicists even after 1900, but at that time it was realized that the theory was unable to produce real progress. [12]

1. Laider, Keith J. (1993). The World of Physical Chemistry, (pgs. 140-41). Oxford University Press.
2. Smith, Crosbie. (1998). The Science of Energy - a Cultural History of Energy Physics in Victorian Britain, (pgs. 102-07). Chicago: The University of Chicago Press.
3. Graham, Thomas. (1858). Elements of Inorganic Chemistry, (section: “Nature of Heat”, pgs. 96-97). Blanchard and Lea.
4. Rankine, William, J.M. (1881). Miscellaneous Scientific Papers, (III: “On the Centrifugal Theory of Elasticity, as applied to Gases and Vapours”, pgs. 16-48, IV: “On the Centrifugal Theory of Elasticity and its connection with the Theory of Heat”, pgs. 49-66). C. Griffin and Co.
5. Rankine to Thomson, 19 Aug. 1850, R18, Kelvin Collection, ULC; Rankine 1881: 234 [1853].
6. (a) Maxwell, James C. (1878). “Tait’s ‘Thermodynamics’ (I)”, (pgs. 257-59). Nature, Jan. 31.
(b) Maxwell, James C. (1878). “
Tait’s ‘Thermodynamics’ (II)”, (pgs. 278-81). Nature, Feb. 07.
7. (a) Harman, Peter M. (1998). The Natural Philosophy of James Clerk Maxwell, (pg. 98). Cambridge University Press.
(b) Maxwell, James. (1862). “On Physical Lines of Force” (Part III: “The Theory of Molecular Vortices applied to Statical Electricty”, pgs. 12-24), Philosophical Magazine, Taylor and Francis.
(c) Rankine, William. (1851). “On Elasticity”, Camb. and Dub. Math. Journ.
8. (a) Mahon, Basil. (2003). The Man who Changed Everything – the Life of James Clerk Maxwell, (pgs. 100-01). Wiley.
(b) Maxwell, James Clerk 1890. The Scientific Papers of J.C. Maxwell, ed. W.D. Niven. Cambridge: Cambridge University Press.
9. (a) Preston, Thomas and Cotter, Joseph R. (1904). The Theory of Heat, (section 60: “The Vortex Atom”, pgs. 78-81). MacMillan.
(b) Helmholtz, Hermann. (1858). “On the Integrals of the Hydrodynamic Equations which express Vortex Motion.” (Ueber Integrale der hydrodynamischen Gleichungen welche den Wirbelbewegungen entsprechen”, Journal fur die reine und angewandte mathematic, 55, pgs. 25-55; translated by P.G. Tait, Phil. Mag., [series 4], 33 (1867).
(c) Thomson, William. (1867). “On Vortex Atoms” [URL], Proceedings of the Royal Society of Edinburgh, Vol. VI, 1867, pp. 94-105. (reprinted in Phil. Mag. Vol. XXXIV, 1867, pp. 15-24).
10. Thomson, J.J. (1883). “On a Theory of the Electric Discharge in Gases”, The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, (pgs. 427-34).
11. Thomson, J.J. (1936). Recollections and Reflections (ref. 11), pg. 95.
12. Buchwald, Jed Z. and Warwick, Andrew. (2001). Histories of the Electron, (pg. 219). MIT Press.

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