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The Wave Theory of Heat: A Forgotten Stage in the Transition from the Caloric Theory to Thermodynamics

Published online by Cambridge University Press:  05 January 2009


Research on thermal “black-body” radiation played an essential role in the origin of the quantum theory at the beginning of the twentieth century. This is a well-known fact, but historians of science up to now have not generally recognized that studies of radiant heat were also important in an earlier episode in the development of modern physics: the transition from caloric theory to thermodynamics. During the period 1830–50, many physicists were led by these studies to accept a “wave theory of heat”, although this theory subsequently faded into obscurity.

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Copyright © British Society for the History of Science 1970

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1 More often called the “undulatory” theory in the nineteenth century; but the modern terminology, already well established even in historical writings on the “wave” theory of light, seems preferable. It should be noted that by some modern criteria the wave theory of heat is not a distinct “theory” since it did not lead to quantitative predictions different from those of the caloric or mechanical theories, but instead could be viewed as a combination of the two (see discussion in text, below). However, physicists at the time did not seem to be worried by this circumstance, and usually presented it as a distinct alternative to the caloric theory. Another version of the wave theory of heat, which was perhaps more popular before the nineteenth century, asserted that heat itself is the vibrations of material particles, but that these can be transmitted from one particle to another by ether vibrations. This version would appear to be excluded by the postulate that heat and light are qualitatively identical and are vibrations of the same medium.

2 T[raill], T. S., “Heat”, Encyclopaedia Britannica, 7th ed. (Edinburgh, 1842), xi, 180197.Google Scholar I am indebted to Mr. V. A. Stenberg, Director of Research at the Britannica, for providing me with a copy of this article. The 7th edition does not seem to be available in any major American library, which may partly account for the mistaken idea that this article first appeared in 1856. In the 8th edition the article is reprinted with an additional section at the end referring to the work of Joule, Rankine, and Thomson on the mechanical equivalent of heat; this work is said to support the “mechanical or dynamical theory of heat” of Rumford and Davy, thereby contradicting the remarks at the beginning of the article.

3 For our purposes the most important source is Newton, Isaac, Opticks, 4th ed. (London, 1730), Qu. 18Google Scholar, which suggests that heat is transmitted through a vacuum by ether vibrations; but this seems to be contradicted by remarks in Qu. 28.

4 Klein, Martin J., “Max Planck and the Beginnings of the Quantum Theory”, Archive for History of Exact Sciences, i (1962), 459479.Google Scholar Unfortunately, scientists writing on the development of quantum theory continue to state that Planck was attempting to resolve a paradox discovered by Rayleigh, that the total energy of the ether would be infinite if each mechanical degree of freedom had an equal share of energy (see below and note 60).

5 Lilley, S., “Attitudes to the nature of heat about the beginning of the nineteenth century”, Actes du 5e congrès international d'histoire des sciences, Lausanne, 1947, pp. 130139Google Scholar; Archives internationales d'histoire des sciences (1940), 630639.Google Scholar This is confirmed by the contemporary evidence I have seen; for example, E. S. Fischer, Professor of Mathematics and Natural Philosophy at Bonn, wrote that chemists were unanimous in adopting the caloric theory: see Elements of Natural Philosophy (Boston, 1827, translated from Biot's French translation), p. 57.Google Scholar

6 In reading the literature of the early nineteenth century, I have been impressed by the great caution and open-mindedness with which many scientists presented their views on heat, particularly some of the writers who are usually labelled as supporters of the caloric theory. It was very common to say that most of the phenomena can be explained equally well by considering heat as a substance or as a quality (or “mode of motion”); even if the former view was to be adopted for the sake of convenience, it was not to be regarded as firmly established beyond any doubt; furthermore, even if heat is really a fluid substance, it may have some association with molecular motion. This point has been emphasized by Mendoza, E. in his introduction to Reflections on the Motive Power of Fire by Sodi Carnot and other papers on the Second Law of Thermodynamics by É. Clapeyron and R. Clausius (New York, 1960), p. xvi.Google Scholar As examples he cites Lavoisier, and Laplace, , “Mémoire sur la Chaleur” (Paris, 1780)Google Scholar and Lamé, 's Cours de Physique (Paris, 1836)Google Scholar. I will discuss Lamé's opinions below—I do not think they can be put in the same category with those of Lavoisier and Laplace—but as additional evidence one can consult Olmsted, Denison, “On the present state of chemical science”, American Journal of Science, xi (1826), 349358; xii (1827), 114, esp. p. 355Google Scholar; “Remarks on Dr. Hare's essay on the question, whether heat can be ascribed to motion?” Ibid., xii (1827), 359–363, esp. p. 363; Black, Joseph, Lectures on the Elements of Chemistry (Philadelphia, 1807), i, 29, 33.Google Scholar Thenard, in what Maurice Crosland has called “the standard textbook of chemistry in France for nearly a quarter of a century” [The Society of Arcueil (London, 1967), p. 330]Google Scholar, accepted the caloric theory yet admitted that since caloric seems to be weightless its real existence is dubious: see Thenard, Louis Jacques, Traité de chimie élémentaire, théorique, et pratique, 4 vols., 5th ed. (Paris, 1827), i, 35.Google Scholar

7 Brown, Sanborn, “Count Rumford and the caloric theory of heat”, Proceedings of the American Philosophical Society, xciii (1949), 316325.Google Scholar

8 Cajori, Florian, “On the history of caloric”, Isis, iv (22), 483492.Google Scholar It was probably Cajori who first used the Britannica article of Traill as evidence for the survival of caloric theory into the 1850's: see A History of Physics (New York, 1929, reprinted 1962), p. 122.Google Scholar

9 Brown, Sanborn, “The caloric theory of heat”, American Journal of Physics, xviii (1950), 367373.CrossRefGoogle Scholar

10 See Kuhn, Thomas S., “The caloric theory of adiabatic compression”, Isis, xlix (1958), 132140CrossRefGoogle Scholar; Finn, Bernard S., “Laplace and the speed of sound”, Isis, lv (1964), 719CrossRefGoogle Scholar; Crosland, Maurice, The Society of Arcueil (London, 1967), pp. 302307.CrossRefGoogle Scholar

11 A convenient edition which includes most of Fourier's work is The Analytical Theory of Heat by Joseph Fourier, translated, with notes, by Alexander Freeman (New York, 1955). Among recent historical studies may be mentioned Florent Bureau, “La theorie analytique de la chaleur de J. B. J. Fourier”, Bulletin de la Classe des Sciences, Académie Royale Belgique, xxxix (1953), 11161127Google Scholar; Bellone, Enrico, “Il significato metodologico dell'eliminazione dei modelli del calorico promossa da Joseph Fourier”, Physis, ix (1967), 301310.Google Scholar Fourier himself, as is well known, denied that he adopted any particular hypothesis about the nature of heat. However, he did accept the similarity of heat and light (see p. 32 in Freeman's translation).

12 Henry, William, “A review of some experiments, which have been supposed to disprove the materiality of heat”, Memoirs of the Manchester Philosophical Society, v (1802), 603621Google Scholar; Murray, John, Elements of Chemistry (Edinburgh, 1801), 163.Google Scholar The argument can be found in the literature as late as 1830, e. g. John Bostock's article “Heat” in Brewster's Ediburgh Encyclopaedia (Edinburgh, 1830), x, 690.Google Scholar

13 Cornell, E. S., “Early studies in radiant heat”, Annals of Science, i (1936), 217225CrossRefGoogle Scholar; Wolf, A., A History of Science, Technology & Philosophy in the 18th Century, 2nd ed. (London, 1952), i, 206212.Google Scholar

14 See Barr, E. Scott, “The Infrared pioneers—I. Sir William Herschel”, Infrared Physics, i (1961), 14CrossRefGoogle Scholar; Lovell, D. J., “Herschel's dilemma in the interpretation of thermal radiation”, Isis, lix (1968), 4660CrossRefGoogle Scholar; Powell, Baden, “Report on the present state of our knowledge of the science of radiant heat”, British Association Report, ii (1832), 259300Google Scholar: Langley, S. P., “The history of a doctrine”, Popular Science Monthly, xxxiv (1889), 212221, 385396.Google Scholar

15 See Barr, E. Scott, “The Infrared pioneers—II. Macedonio Melloni”, Infrared Physics, ii (1962), 6773CrossRefGoogle Scholar; Tedesco, G., “Opera e vita di Macedonio Melloni”, Nuovo Cimento Supplemento [10] ii (1955), 501509CrossRefGoogle Scholar; Dascola, G., “Mostra di documenti e cimeli melloniani”Google Scholar, ibid., 518–522.

16 As soon as Faraday reported his discovery of the rotation of polarization of light by a magnet, French physicists looked for and found the same effect with radiant heat; see de la Provostaye, F. and Desains, P., “Rotation du plan de polarisation de la chaleur produite par le magnetisme”, Annales de chimie et de physique [3], xxvii (1849), 232237.Google Scholar

17 In 1835, Melloni was reluctant to accept the complete identity of heat and light (as suggested by Ampère, see below), arguing that light and radiant heat “proceed from two distinct causes”. But in a footnote he added that “These two causes themselves are, perhaps, but different effects of a single cause”. He insisted that light and heat are “two essentially distinct modifications which the aethereal fluid suffers in its mode of existence”. See Melloni, M., “Observations et expériences relatives à la théorie de l'identité des agents qui produisent la lumière et la chaleur rayonnante”, Comptes Rendus … Académie des Sciences, Paris, i (1835), 503508Google Scholar; Annales de chimie et de physique [2], lx (1836), 418426Google Scholar; Taylor's Scientific Memoirs, i (1837), 388392Google Scholar; Annalen der Physik [2], xxxvi (1836), 486494.Google Scholar Melloni declared himself a definite supporter of the wave theory and affirmed the identity of heat and light in 1842: see “Sur l'identité des diverses radiations lumineuses, calorifiques et chimiques”, Comptes Rendus … Académie des Sciences, Paris, xv (1842), 454460.Google Scholar

18 Melloni, M., “Recherches sur les radiations des corps incandescents et sur les couleurs élémentaires du spectre”, Archive des Sciences Physiques, Geneva, v (1847), 238258Google Scholar; Phil. Mag. [3], xxxii (1848), 262276Google Scholar (quoted from pp. 274–275). For further discussion see his book La Thermo-chrôse (Naples, 1850), long footnote on pp. 272276.Google Scholar

19 Davy, H., Elements of Chemical Philosophy (Philadelphia, 1812), pp. 4653, 120.CrossRefGoogle Scholar [This and other books cited below were originally published in Britain, but I have cited the American edition when it was the only one easily available.]

20 Young, T., “On the theory of light and colours”, Phil. Trans., xcii (1802), 1248 (quoted from p. 32).CrossRefGoogle Scholar

21 Young, T., A course of lectures on Natural Philosophy and the Mechanical Arts (London, 1807), i, 654.Google Scholar

22 Fox, Robert, “The background to the discovery of Dulong and Petit's law”, British Journal for the History of Science, iv (19681969), 122.CrossRefGoogle Scholar

23 Ibid., quoted from Jac. Berzelius Bref, ed. Söderbaum, H. G. (Uppsala, 19121932), iiGoogle Scholar, Part 1, 13–14 (translation by S.G.B.).

24 Biot, J. B., Précis élémentaire de physique experimentale, 2nd ed. (Paris, 1821), ii, 627Google Scholar, reprinted with little or no change in the 3rd ed. (Paris, 1824), ii, 625. Biot discusses the similarity of light and heat, and concludes that whether caloric has a material existence “like light”, or consists in vibrations propagated through a medium, the results would be the same. But still he leans toward the former view. Johann Carl Fischer concluded a long article on heat, with much emphasis on radiant heat experiments, with the statement that whether heat is a substance or motion still remains to be decided: see Physikalisches Wörterbuch (Göttingen, 1827), x, 633699.Google ScholarThomson, Thomas, in An Outline of the sciences of heat and electricity (London, 1830)Google Scholar, claimed that the wave theory of heat was held by “the greater number of the French and German chemists of the last century” but concluded (p. 335) that the problem of heat is still insoluble, though he leaned slightly toward the vibrational theories.

25 Gay-Lussac, J. L., “Sur la calorique du vide”, Annales de chimie et de physique [2], xiii (1820), 304308.Google Scholar I am indebted to Mr. Stuart Pierson of the Smithsonian Institution for bringing this reference to my attention. A detailed discussion of the historical background of this paper of Gay-Lussac may be found in the recent article by Costabel, Pierre, “Le ‘Calorique du vide’ de Clément et Desormes (1812–1819)”, Archives internationales d'histoire des sciences, xxi (1968), 314.Google Scholar

26 Translated in Mendoza, 's edition, op. cit. (6), p. 63.Google Scholar According to Mendoza, most of these notes were written around the time of the original composition of the Reflexions: see “Contributions to the study of Sadi Carnot and his work”, Archives internationales d'histoire des sciences, xii (1959), 377396.Google Scholar

27 “Idées de Mr Ampère sur la chaleur et sur la lumière”, Bibliothèque Universelle, Geneva, xlix (1832), 225235.Google ScholarAmpère, A. M., “Note sur la chaleur et sur la lumière considérées comme resultant de mouvement vibratories”, Annales de chimie et de physique, lviii (1835), 432444Google Scholar; Bibliothèque Universelle, Geneva, lix (1835), 2637Google Scholar; Phil. Mag. [3], vii (1835), 342349.Google Scholar The quotations from Ampère's paper are taken from the English translation in Phil. Mag.

28 “… the summation of the products of the masses of all its molecules by the squares of their velocities at a given moment, adding double the integral of the sum of the products of the forces multiplied by the differentials of the spaces described, in the direction of those forces, by each molecule.” This is clearly just twice the sum of the kinetic and potential energies of the system; Ampère refers to the two terms as explicit and implicit vis viva, respectively.

29 “Lettre de M. C. Matteucci à M. Arago sur quelques phénomènes relatifs au calorique (Annali delle Science, Marzo e Aprile 1832)”, Bibliothèque Universelle, Geneva, l (1832), 16.Google Scholar

30 [A. de la Rive], editorial remarks on Pierre Prevost's Exposition élémentaire des principes qui servent de base à la theorie de la chaleur rayonnante (Geneva & Paris), in Bibliothèque Universelle, Geneva, li (1832), 243258Google Scholar; and on Poisson, S. D.'s Théorie Mathématique de la Chaleur (Paris, 1835)Google Scholar, in ibid., lix (1835), 144–166 (esp. p. 154); lx (1835), 279–309.

31 Lardner, Dionysius, Treatise on Heat [The Cabinet Cyclopedia] (London, 1833), pp. 394398.Google Scholar

32 MrsSomerville, , On the connection of the physical sciences (Philadelphia, 1834), p. 195.Google Scholar

33 See editorial note in Phil. Mag. [3], vii (1835), 157Google Scholar (the editors at that time were Brewster, Richard Taylor and Richard Phillips).

34 Forbes, James D., “On the refraction and polarization of heat”, Transactions of the Royal Society of Edinburgh, xiii (1835), 131168 (esp. p. 147)CrossRefGoogle Scholar; “Note respecting the undulatory theory of heat, and on the circular polarization of heat by total reflection”, Phil. Mag. [3], vii (1836), 246249.Google Scholar

35 Lamé, G., “Mémoire sur les lois de l'équilibre de l'ether dans les corps diaphanes”, Annales de chimie et de physique, lv (1833), 322335Google Scholar; “Mémoire sur les vibrations lumineuses des milieux diaphanes”, ibid., lvii (1834), 211–219. In the textbook cited by Mendoza, , op. cit. (6)Google Scholar, Lamé clearly prefers the wave theory to the emission theory, though he states (perhaps to avoid offending Poisson) that it is not necessary to decide between them. [Cours de Physique de l'École Polytechnique (Paris, 1836), pp. 297–298]. We may infer something about how much weight Lame's opinion might carry from the assessment in a recent article by Herivel, J. W., “Aspects of French theoretical physics in the nineteenth century”, British Journal for the History of Science, iii (19661967), 109132.CrossRefGoogle Scholar In addition to providing much useful information about the situation in Paris which is relevant to the background of the wave theory of heat, Herivel points out that in the period 1850–1870, “and for that matter in the decade immediately preceding 1850, [there was] no creative French theoretical physicist remotely of the calibre of Thomson or Clausius, let alone Maxwell”. In a footnote he specifies that “creative” is to be taken “as opposed to a competent, and even original, theoretical physicist such as G. Lamé (1795–1870)” (ibid., p. 115). Stretching this just a bit, we could say that the best physicist in France was a supporter of the wave theory of heat, even if some of the others opposed it.

36 Whewell, William, History of the Inductive Sciences (London, 1837), ii, 180184.Google Scholar Aside from its value as contemporary evidence for the acceptance of the wave theory of heat, Whewell's work is almost the only publication on the history of science which discusses this theory. Rosenberger mentions Ampère's theory but states incorrectly that Ampère was the only scientist who attributed both heat and light to vibrations of the same ether; see Rosenberger, Ferd, Die Geschichte der Physik (Braunschweig, 18871890), iii, 230–223Google Scholar; see also note 76, below.

37 [J. C. Poggendorff] editorial note added to the German translation of a paper by Melloni, in Annalen der Physik und Chemie [2], xxxviii (1836), 2Google Scholar; anonymous article on “Recent researches on heat” in Magazine of Popular Science, i (1836), 145160Google Scholar; Pinault, l'Abbé, Traité élémentaire de physique, 2nd ed. (Paris, 1836), p. 292Google Scholar; Baumgartner, Andreas, Anfangsgründe der Naturlehre (Wien, 1837), pp. 131132Google Scholar [this book contains one of the first uses of the word Thermodynamik, defined here as the study of the motion of heat]; Webster, Thomas, The elements of Physics (London, 1837), p. 280Google Scholar; Person, C. C., Éléments de physique (Paris, 1837), ii, 224225.Google Scholar

38 Poisson, S. D., Théorie Mathématique de la Chaleur (Paris, 1835)Google Scholar; Mémoire et notes formant un supplément … (Paris, 1837), p. 27 f.Google Scholar

39 West, William, “On a remarkable analogy between ponderable bodies, and caloric and electricity”, Phil. Mag. [3], v (1834), 110112.Google Scholar

40 Poisson, , op. cit. (38)Google Scholar; Barton, John, “On the physical causes of the principal phenomena of heat”, Phil. Mag. [3], x (1837), 342Google Scholar; Hare, Robert, A compendium of the course of chemical instruction in the Medical Department of the University of Pennsylvania, new section added to the fourth edition (Philadelphia, 1840), 7576Google Scholar; Johnston, John, A Manual of Chemistry (Philadelphia, 1842), 59Google Scholar; Brandes, H. W., Vorlesungen über die Naturlehre (Leipzig, 1844), pp. 471, 558Google Scholar; Gmelin, Leopold, Handbook of Chemistry, trans. from German ed. of 1843 (London, 1848), pp. 163, 167, 212.Google Scholar

41 Mossotti, O. F., Sur les forces qui régissent la constitution intérieure des corps, aperçu pour servir à la determination de la cause et des lois de l'action moléculaire (Turin, 1836)Google Scholar; Taylor's Scientífic Memoirs, i (1837) 448469Google Scholar; other works on this subject reprinted in his Scritti (Pisa, 1951). The editors of Philosophical Magazine said that his “mutual identification of the attractive forces of electricity, aggregation, and gravitation” constituted “one of the most remarkable discoveries of the present area in science” (see vol. x (1837), 320–321).

42 Challis, James, “On capillary attraction and the molecular forces of fluids”, Phil. Mag. [3], vii (1836), 8996Google Scholar; Kelland, Philip, “On the motion of a system of particles, considered with reference to the phenomena of sound and heat”, Trans. Cambridge Phil. Soc. vi (1837), 235288Google Scholar; “On molecular equilibrium, Part I”, ibid., vii (1839), 25–59; “Reply to some objections against the theory of molecular action according to Newton's law”, Phil. Mag. [3], xxi (1842), 124130, 202208, 263270Google Scholar; “On Mossotti's theory of molecular action”, ibid., xx (1842), 8–10; Earnshaw, S., “On the nature of the molecular forces which regulate the constitution of the luminiferous ether”, Trans. Cambridge Phil. Soc., vii (1839), 97112.Google Scholar This last paper by Earnshaw contains the famous “Earnshaw theorem” in electrostatics which was used as an argument against all static atomic models based on the equilibrium of some arrangement of charged particles, around 1900; see American Journal of Physics, xxvii (1959), 418.Google Scholar See also Babbage, Charles, The Ninth Bridgewater Treatise, a fragment (London, 1837), pp. 180185Google Scholar; Exley, Thomas, “Remarks on M. Mossotti's theory of physics, suggested by Mr. Babbage's notice of the same”, Phil. Mag. [3], xi (1837), 496504Google Scholar; Cooper, Paul, “Notice of a theory of molecular action”, Phil. Mag. [3], x (1837), 355Google Scholar; R.L.E., “Remarks on M. Mossotti's theory of molecular action”, ibid., xix (1841), 384–387. Various theories of this kind are summarized by Todhunter, Isaac, A History of the theory of elasticity and of the strength of materials from Galilei to the present time (Cambridge, 1886).Google Scholar

43 Kelland, Philip, Theory of Heat (Cambridge, 1837), pp. iii, 104, 145, 181182.Google Scholar Kelland published a further explanation of his views in a note added to a new edition of Thomas Young's Course of Lectures on Natural Philosophy (London, 1845), p. 506.Google Scholar He states that although recent experiments on polarization and conduction do show the wave nature of heat, most other phenomena such as latent heat cannot be explained by a purely wave theory as yet. The facts “appear to demand a corpuscular theory, wholly or partly accompanied by transverse vibrations. The hypothesis which I have advanced [in Theory of Heat] is, that heat is due to the existence of repulsive atoms which penetrate all material substances; so that expansion arises from the accumulation of such atoms; but that the transmission of heat is partly effected by transverse pulses … Solar heat is transmitted altogether by such transverse pulses, so that its intensity is measured by the intensity of the pulses, whilst the heat of a fire is perhaps due in part to normal ones, or, which is the same thing, to a flow of atoms impelling by their repulsion those which are in advance of them.” (I am indebted to Dr. Charles Weiner for this reference.)

44 Williams, L. Pearce, “The physical sciences in the first half of the nineteenth century; Problems and sources”, History of Science, i (1962), 115CrossRefGoogle Scholar; Kargon, Robert, “The decline of the caloric theory of heat: a case study”, Centauras, x (1964), 253257Google Scholar; Oersted, H. C., Recherches sur l'identité des forces chimiques et électriques (Paris, 1813), pp. 159200.Google Scholar

45 See Grove's lecture of 1843, cited below in note 52, p. 53; William, and Chambers, Robert, Elements of Natural Philosophy (New York, 1849), p. 31Google Scholar; Petrie, William, “On the relation between the changes of temperature and volume of gases”, Edinburgh New Philosophical Journal, li (1851), 120125Google Scholar; Coues, S. E., Outlines of a System of Mechanical Philosophy (Boston, 1851), p. 26Google Scholar; Colburn, Zerah, An inquiry into the nature of heat (London, 1863)Google Scholar; Cazin, A., “Recent progress in relation to the theory of heat”, Smithsonian Institution Report, 1868, pp. 231244.Google Scholar

46 Fresnel, A., “Note sur la répulsion que des corps échauffés exercent les uns sur les autres à des distances sensibles”, Annales de chimie et de physique [2], xxix (1825), 5762Google Scholar: “Observation à ajouter à la note sur les repulsions des corps échauffes”, ibid., 107–108; Powell, Baden, “On the repulsive power of heat”, Phil. Trans., cxxiv (1834), 485589CrossRefGoogle Scholar; “Notes on repulsion by heat, etc.”, Phil. Mag. [3], xii (1838), 317321Google Scholar; Addams, R., “Notice of some experiments which show a repulsive action between heated surfaces and certain pulverulent bodies”, Phil. Mag. [3], vi (1835), 415417Google Scholar; Crookes, William, “On repulsion resulting from radiation”, Phil. Trans., clxiv (1874), 501527.CrossRefGoogle Scholar The Crookes paper shows the connection between this earlier research on the repulsion of heat, possibly associated with an emission theory, and the radiometer fad of the 1870's. Maxwell showed in 1873 that the wave theory does predict radiation pressure (for both light and radiant heat), but the magnitude of this is so small in ordinary circumstances that it is completely masked by gas-surface interactions even at fairly low pressures. See Woodruff, A. E., “William Crookes and the Radiometer”, Isis, lvii (1966), 188198CrossRefGoogle Scholar; Brush, S. G. and Everitt, C. W. F., “Maxwell, Osborne Reynolds, and the Radiometer”, Historical Studies in the Physical Sciences, i (1969), 105125.CrossRefGoogle Scholar

47 [Claude] Pouillet, , Élémens de physique expesrimentale et de meteorologie, 2nd ed. (Paris, 1832), pp. 237238Google Scholar; “Mémoire sur la théorie des fluides élastiques et sur la chaleur latente des vapeurs”, Comptes RendusAcadémie des Sciences, Paris, xxiv (1847), 915943.Google Scholar Pouillet was Professor of Physics at the École Polytechnique. He did not change his statements about heat in the 1847 and 1856 editions of his textbook, but later German editions (1847, 1852, etc.) edited by Job. Müller dropped the support for caloric theory. Soubeiran, E., Précis élémentaire de physique, 2nd ed. (Paris, 1846)Google Scholar; Pinaud, Aug, Programme d'un cours élémentaire de physique, 5th ed. (Paris, 1848), p. 113.Google Scholar

48 Comstock, J. L., Elements of Chemistry, 10th ed. (New York, 1834), p. 11 and 29th ed. (New York, 1839), p. 11Google Scholar; also in the 1852 edition; Grund, Francis J., Elements of Natural Philosophy, 2nd ed. (Boston, 1835), p. 186.Google Scholar

49 Arnott, Neil, Elements of Physics (Philadelphia, 1841), p. 281Google Scholar [Arnott was at the Royal College of Physicians in London]; Clemens, F. A., Grundriss der Naturlehre (Königsberg, 1839), ii, 7576Google Scholar; Cooke, Josiah P., Elements of Chemical Physics (Boston, 1860), p. 430.Google Scholar

50 Babinet, , “Sur la chaleur dans l'hypothèse des vibrations”, Comptes Rendus … Académie des Sciences, Paris, vii (1838), 781Google Scholar [cf. ibid., lxiii (1866), 581–588, 662–666]; Couche, “… présente, à l'occasion d'une note récente de M. Melloni, des considerations théoriques sur les phénomènes de chaleur et de lumière”, ibid., xviii (1844), 312; Paget, “… une Note sur une nouvelle théorie de la chaleur”, ibid., xix (1844), 1406; Briot, “Essai sur la théorie mécanique de la chaleur”, ibid., xxiv (1847), 877.

51 See “Considerations sur la production de la lumière et de la chaleur du soleil (Commissaires, MM. Pouillet, Babinet)”, ibid., xxiii (1846), 220; “Mémoire sur la production de la lumière et de la chaleur de soleil (Commissaires, MM. Arago, Cauchy)”, ibid., xxiii (1846), 544; “Sur la transformation de la force vive en chaleur, et reciproquement”, ibid., xxvii (1848), 385–387.

52 Grove, William Robert, A lecture on the progress of physical science since the opening of the London Institution (London, 1842), p. 27Google Scholar; see also “On the correlation of physical forces” (1843) in Youmans, E. L. (ed.), The correlation and conservation ef forces (New York, 1865), p. 55.Google Scholar

53 Mohr, F., “Views of the nature of heat”, Phil. Mag. [5], ii (1876), 110113CrossRefGoogle Scholar, trans, from Liebig, 's Annalen der Chemie, xxiv (1837), 141147.Google Scholar In his note at the end of this translation, P. G. Tait asserts that this paper “contains, in a considerably superior form, almost all that is correct in Mayer's paper”. See also [Karl] Mohr, Friedrich, Allgemeine Theorie der Bewegung und Kraft, als Grundlage der Physik und Chemie (Braunschweig, 1869)Google Scholar, which includes a reprint of the original 1837 paper in German; Oesper, Ralph E., “Karl Friedrich Mohr”, Journal of Chemical Education, iv (1927), 13571363.CrossRefGoogle Scholar In his textbook on heat (London, 1884, reprinted with corrections 1904, p. 247) Tait discussed the experiments showing the identity of light and radiant heat, and remarked: “It is curious to notice that the original speculations of Mohr, of date 1837, as to the true nature of heat were mainly based on these discoveries.”

54 Henry, Joseph, “Remarks on the corpuscular hypothesis of the constitution of matter”, Proceedings of the American Philosophical Society, iv (1846), 287290Google Scholar; “On the theory of the so-called imponderables”, ibid., vi (1851), 84–91; see also his report on the interference of heat-rays, ibid., iv (1846), 285, and “On heat, and on a thermal telescope”, American Journal of Science, v (1848), 113114.Google Scholar In the last paper cited he says, “The facts with regard to heat as well as light therefore show that the theory of undulation is not an imagination, but the expression of a law”. Henry met Melloni in Paris in 1837 and this encounter may have stimulated his interest in radiant heat: see Edinburgh New Philosophical Journal, xxvi (1839), 300Google Scholar, and Coulson, Thomas, Joseph Henry (Princeton, 1950), p. 122.Google Scholar

54a See note 18.

55 Berzelius, J. J., Traité de Chimie, nouvelle édition entièrement refondue d'après la 4me édition allemande, publiée in 1838 (Bruxelles, 1839), i, 35Google Scholar; Traité de chimie minérale, végetale et animale, seconde édition française (Paris, 1845), i, 35.Google Scholar

56 Brücke, Ernst, “Ueber das Verhalten der optischen Medien des Auges gegen Licht—und Wärmestrahlen”, Annalen der Physik [2], lxv (1845), 593607.CrossRefGoogle Scholar The identity of heat and light was rejected by Moser, L., “Ueber die Verschiedenheit der Licht—und Wärmestrahlen”Google Scholar, ibid., lviii (1843), 105–111.

57 Peclet, E., Traité élémentaire de physique, 4th ed. (Bruxelles, 1838), pp. 234235Google Scholar; Peyré, J.-M.-M., Cours de Physique, 2nd ed. (Paris, 1840), p. 256Google Scholar; Persoz, J., Introduction à l'étude de la chimie moléculaire (Paris and Strasbourg, 1839), p. 218Google Scholar; Despretz, C., Traité élémentaire de physique, 3rd ed. (Paris, 1832), p. 77Google Scholar; Johnston, John, A Manual of Chemistry (Middletown, 1840), pp. 13, 57Google Scholar; Daniell, J. Frederic, An introduction to the study of chemical phenomena (London, 1843), pp. 208209.Google Scholar

58 Bailly, C., Nouveau manuel complèt de physique (Paris, 1841), pp. 204207.Google Scholar

59 [Antoine] Becquerel, , Traité de Physique (Paris, 1842), i, 163Google Scholar; MrsSomerville, , On the connection of the physical sciences, 7th ed. (London, 1846), p. 258Google Scholar; Draper, John W., Textbook on Natural Philosophy (New York, 1847), p. 253Google Scholar; Peclet, E., Traité élémentaire de physique (Bruxelles, 1847), p. 361Google Scholar; Müller, Johann, Principles of Physics and Meteorology, trans. from German (London, 1847), p. 497Google Scholar [Müller argues that because radiant heat consists in ether vibrations, therefore sensible heat must consist in vibrations of the material parts of bodies; many others followed this line of argument at least implicitly]; Bird, Golding, Elements of Natural Philosophy (London, 1848), p. 487Google Scholar; Buys-Ballot, C. H. D., Scheets eener physiologie van het onbewerktuigte ryk de natuur (Utrecht, 1849)Google Scholar, as summarized by Rosenberger, , op. cit. (36), pp. 538540Google Scholar; Graham, Thomas, Elements of Chemistry, 2nd American ed. based on the 2nd English ed. of 1850 (Philadelphia, 1852), p. 96.Google Scholar The authors of many of the textbooks cited in note 74 below probably held similar views in the 1840's. I have not attempted to track down all the first editions, since the evidence already obtained seems to be sufficient to establish the point. An elaborate critical review of opinions about the nature of heat, with references to a number of works published in the early nineteenth century, may be found in Muncke's article “Wärme” in Gehler's Physikalisches Wörterbuch, Bd. 10, 1st Abt. (Leipzig, 1841).

60 Rayleigh, , “Remarks upon the law of complete radiation”, Phil. Mag. [5], xlix (1900), 539540CrossRefGoogle Scholar; reprinted with a note, dated 1902, on Planck's formula, in Rayleigh, 's Scientific Papers (Cambridge), iv (1903), 483485.Google Scholar Rayleigh's intention in this paper was not to deduce a distribution function for black-body radiation as a rigorous consequence of classical physics, but to improve Wien's distribution by using the assumption that equipartition applies only to low frequencies. In this way he obtained the formula θk2dk (θ = absolute temperature, k = wave number), which if integrated over all k would of course diverge; but Rayleigh explicitly stated that for large k one must introduce an exponential factor e-ck/θ. Thus he recognized that equipartition could not apply to high frequencies, but did not by any means imply that this was to be regarded as a failure of classical physics.

61 Kuhn, Thomas S., “Energy conservation as an example of simultaneous discovery”, in Clagett, Marshall (ed.), Critical Problems in the History of Science (Madison, 1959), pp. 321356Google Scholar; reprinted in Barber, Bernard & Hirsch, Walter (eds.), The Sociology of Science (New York, 1962), pp. 486515.Google Scholar

61a Mohr, , op. cit. (53).Google Scholar

61b See note 52.

62 von Helmholtz, Hermann, Ueber die Erhaltung der Kraft (Berlin, 1847)Google Scholar; the passage referred to may be found on pages 108–109 of my anthology, Kinetic Theory, vol. i (Oxford, 1965).Google Scholar

63 von Helmholtz, Hermann, “Wärme, physiologisch”, Encyklopädisch Handwörterbuch der medicinischen Wissenschaften (1845), reprinted in his Wissenschaftliche Abhandlungen (Leipzig, 18821895), ii, 680725Google Scholar; quotation from pp. 699–700.

64 Joule, J. P., “On the changes of temperature produced by the rarefaction and condensation of air”, Phil. Mag. [3], xxvi (1845). 369383.Google Scholar

65 Joule, J. P., “On the mechanical equivalent of heat and on the constitution of elastic fluids”, British Association Report, xviii (1848), 2122Google Scholar [transition to Herapath theory, no mention of radiant heat]; “On the mechanical equivalent of heat”, Phil. Trans., cxl (1850), 6182Google Scholar [radiant heat and similar subjects “do not exactly come within the scope of the present memoir”]. Further indication of Joule's ambivalent attitude toward the wave theory of heat is found in an undated draft manuscript at Manchester University: “Fresh arguments were, however, constantly adduced in favour of the vibratory hypothesis and the labours of Forbes and others added new proofs of the real nature [the word “character” is deleted] of heat [phrase “when in the year 1843” deleted]. To these I need not advert at any length [phrase “but will proceed to the researches made by” deleted] as the subject of radiation of heat is [phrase “not necessarily connected with our subject” deleted] an exceedingly complicated one and would occupy too much time nor is the proof derived from the phenomena of radiation a decisive one …” (from papers held at the Department of History of Science and Technology, The University of Manchester Institute of Science and Technology; a microfilm copy was kindly provided by Dr. Arnold J. Pacey).

66 Faraday, Michael, “On Heat”, Magazine of Science, vi (1845), 126, 131132, 139140, 151152, 215216.Google Scholar

67 Faraday, Michael, “Thoughts on ray-vibrations”, Phil. Mag. [3], xxviii (1845), 447452.Google Scholar

68 Mayer, J. R., Bemerkungen über das mechanische Aequivalent der Wärme (Heilbronn and Leipzig, 1851)Google Scholar; Phil. Mag. [4], xxv (1863), 493521 (quoted from p. 498).Google Scholar

69 Rankine, W. J. M., “On the mechanical action of heat, especially in gases and vapours”, Transactions of the Royal Society of Edinburgh, xx (1850), 147190.Google Scholar

70 Waterston, J. J., “On the physics of media that are composed of free and perfectly elastic molecules in a state of motion”, Phil. Trans., clxxxiii (1893), 579Google Scholar [received 11 December 1845, read 5 March 1846]; reprinted in The Collected Scientific Papers of John James Waterston, ed. Haldane, J. S. (Edinburgh, 1928).Google Scholar

71 See Strutt, R. J., Life of John William Strutt, Third Baron Rayleigh (London, 1924; augmented edn., Madison, 1968, pp. 169171, 417)Google Scholar; Brush, S. G., Kinetic Theory, vol. i (Oxford, 1965), pp. 1718Google Scholar; Waterston, 's Papers, op. cit. (70).Google Scholar

72 Waterston, , Papers, pp. 278279.Google Scholar

73 Soret, Louis, “Sur l'equivalence du travail mécanique et de la chaleur. Revue des recherches experimentales”, Archive des Sciences Physiques, xxvi (1854), 3354.Google Scholar Soret quotes Joule's remark [op. cit. (64)] about heat waves excited by rotating molecules, not realizing that Joule has since dropped his interest in radiant heat (see text above). See also Icilius, G. von Quintus, Experimental-Physik (Hannover, 1855)Google Scholar who accepts the wave theory of heat and implies that it is compatible with the mechanical theory; Jamin, J., Cours de Physique de l'École Polytechnique (Paris, 1859), ii, 248, 436.Google Scholar

74 Allen, Zachariah, Philosophy of the mechanics of nature (New York, 1852), pp. 41, 344Google Scholar; Solar Light and Heat (New York, 1879), pp. 28, 68Google Scholar; Greisz, C. B., Lehrbuch der Physik (Wiesbaden, 1853), p. 390Google Scholar; Müller, Johann, Grundriss der Physik und Meteorologie, 4th ed. (Braunschweig, 1853), p. 460Google Scholar; Soret, L., op. cit. (73)Google Scholar; Brown, Andrew, The Philosophy of Physics (Redfield, N.Y., 1859), pp. 215225, 273277Google Scholar; Icilius, Quintus, op. cit. (73)Google Scholar; Daguin, P. A., Traité élémentaire de Physique (Toulouse and Paris, 1855, 1861), i, 626, ii, 910Google Scholar, and similar remarks in the 4th ed. (Paris, 1878); Ganot, A., Traité élémentaire de Physique, 6th ed. (Paris, 1856), p. 210Google Scholar; English translation of Ganot's book, Elementary Treatise on Physics, 12th ed. (New York, 1886), p. 260Google Scholar; Redtenbacher, F., Das Dynamiden-System (Mannheim, 1857)Google Scholar; Hickok, Laurens P., Rational Cosmology (New York, 1858), pp. 175 f.Google Scholar; Wenck, Julius, Die Physik (Leipzig, 1858), p. 342Google Scholar; Silliman, Benjamin, First Principles of Physics (Philadelphia, 1859), p. 303Google Scholar; Jamin, J., op. cit. (73)Google Scholar; Mousson, Alb, Die Physik (Zürich, 1860), ii, 4Google Scholar; Hogg, Jabez, Elements of experimental and natural philosophy (London, 1861), p. 236Google Scholar; Marié-Davy, art. “Chaleur” in the Privat-Deschanel and Focillon Dictionnaire General des Sciences (Paris, 1864), pp. 430436Google Scholar; Norton, W. A., “On molecular physics”, American Journal of Science, xxxviii (1864), 6178, 207233CrossRefGoogle Scholar, and several subsequent papers; Tyndall, John, “The constitution of the universe”, Fortnightly Review, iii (1865), 129144Google Scholar; Puschl, Carl, Das Strahlungsvermögen der Atome (Wien, 1869)Google Scholar; Challis, James, Notes on the Principles of Pure and Applied Calculation (Cambridge, 1869)Google Scholar; Olmsted, Denison, An Introduction to Natural Philosophy, 4th ed. (New York, 1870), p. 310Google Scholar; Hudson, Henry, “Electrical repulson”, English Mechanic, xix (1874), 121Google Scholar; Favé, , “Consequences vraisemblables de la théorie mécanique de la chaleur”, Les Mondes, xli (1876), 336Google Scholar; Cazin, Achille, “Effets mécaniques de la chaleur”, Revue Scientifique, ii (1865), 431Google Scholar; Guillemin, Amédée, Le Monde Physique (Paris, 1884), iv, 6Google Scholar; Miller-Hauenfels, Albert R. V., Richtigstellung der in bisheriger Fassung unrichtigen mechanischen Wärmetheorie und Grundzüge einer allgemeinen Theorie der Aetherbewegungen (Wien, 1889)Google Scholar; Joannis, , “Chaleur. I. Généralités”, La Grande Encyclopédie (Paris, 18861902), x, 239243Google Scholar; Mewes, Rudolf, “Zusammenhang zwischen der kinetischen und der Vibrations Theorie der Gase”, Dinglers Polytechnisches Journal (Stuttgart), cccxvii (1902), 758760, 800804, cccxviii (1903), 4245, 7578.Google Scholar The above is not to be regarded as merely a list of cranks or third-rate scientists; many of these men may have had considerable influence through their teaching positions and the use of their textbooks.

75 Whewell, , op. cit. (36)Google Scholar; Rosenberger, , op. cit. (36).Google Scholar

76 To my knowledge the only modern writer who gives a reasonably accurate (though greatly abbreviated) statement on this subject is Chalmers, T. W., in his book Historic Researches (New York, 1952), pp. 2829.Google Scholar

77 Thomson, William, “An account of Carnot's theory of the motive power of heat; with numerical results deduced from Regnault's experiments on steam”, Transactions of the Royal Society of Edinburgh, xvi (1849), 541574.CrossRefGoogle Scholar J. P. Joule, in a paper read to the Royal Society of London on 21 June 1849, stated that “the scientific world [was] preoccupied with the hypothesis that heat is a substance” but it was not clear that he thought this was still true in 1849; see Joule, 's Scientific Papers (London, 1884), i, 302.Google Scholar

78 Merton, Robert K., “Singletons and multiples in scientific discovery: A chapter in the sociology of science”, Proceedings of the American Philosophical Society, cv (1961), 470486.Google Scholar

79 Thomson, William, “On the dynamical theory of heat, with numerical results deduced from Mr. Joule's equivalent of a thermal unit, and M. Regnault's observations on steam”, Transactions of the Royal Society of Edinburgh, xx (1851), 261288.Google Scholar

80 Kuhn, , op. cit. (61)Google Scholar, note 98, has called attention to this curious statement, and asks: “But if Davy established the dynamical theory in 1799 and if the rest of conservation follows from it, as Kelvin implies, what had Kelvin himself been doing before 1852?” In Thomson's article on “Heat” for the 9th edition of the Encyclopaedia Britannica (Edinburgh and New York, 1880), xi, 495–526 (replacing Traill's article quoted at the beginning of this paper), he gave a classic statement of the “combined myth” mentioned in the text above: “It is remarkable that, while Davy's experiment alone sufficed to overthrow the hypothesis that heat is matter, and Rumford's, with the addition of just a little consideration of its relations to possibilities or probabilities of inevitable alternatives, did the same, fifty years passed before the scientific world became converted to their conclusion—a remarkable instance of the tremendous efficiency of bad logic in confounding public opinion and obstructing true philosophic thought.” The article does not mention the wave theory of heat.

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